12.83/5.03	YES
14.80/5.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
14.80/5.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.80/5.61	
14.80/5.61	
14.80/5.61	H-Termination with start terms of the given HASKELL could be proven:
14.80/5.61	
14.80/5.61	(0) HASKELL
14.80/5.61	(1) CR [EQUIVALENT, 0 ms]
14.80/5.61	(2) HASKELL
14.80/5.61	(3) BR [EQUIVALENT, 0 ms]
14.80/5.61	(4) HASKELL
14.80/5.61	(5) COR [EQUIVALENT, 22 ms]
14.80/5.61	(6) HASKELL
14.80/5.61	(7) Narrow [SOUND, 0 ms]
14.80/5.61	(8) AND
14.80/5.61	    (9) QDP
14.80/5.61	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.80/5.61	        (11) YES
14.80/5.61	    (12) QDP
14.80/5.61	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.80/5.61	        (14) YES
14.80/5.61	    (15) QDP
14.80/5.61	        (16) QDPOrderProof [EQUIVALENT, 68 ms]
14.80/5.61	        (17) QDP
14.80/5.61	        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
14.80/5.61	        (19) TRUE
14.80/5.61	    (20) QDP
14.80/5.61	        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.80/5.61	        (22) YES
14.80/5.61	    (23) QDP
14.80/5.61	        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
14.80/5.61	        (25) QDP
14.80/5.61	        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.80/5.61	        (27) YES
14.80/5.61	
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(0)
14.80/5.61	Obligation:
14.80/5.61	mainModule Main 
14.80/5.61	module Maybe where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	module List where {
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.80/5.61	merge cmp xs [] = xs;
14.80/5.61	merge cmp [] ys = ys;
14.80/5.61	merge cmp (x : xs) (y : ys) = case x `cmp` y of { 
14.80/5.61	GT-> y : merge cmp (x : xs) ys; 
14.80/5.61	_-> x : merge cmp xs (y : ys); 
14.80/5.61	 } ;
14.80/5.61	
14.80/5.61	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.80/5.61	merge_pairs cmp [] = [];
14.80/5.61	merge_pairs cmp (xs : []) = xs : [];
14.80/5.61	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.80/5.61	
14.80/5.61	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.80/5.61	mergesort cmp = mergesort' cmp . map wrap;
14.80/5.61	
14.80/5.61	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.80/5.61	mergesort' cmp [] = [];
14.80/5.61	mergesort' cmp (xs : []) = xs;
14.80/5.61	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.80/5.61	
14.80/5.61	sort :: Ord a => [a]  ->  [a];
14.80/5.61	sort l = mergesort compare l;
14.80/5.61	
14.80/5.61	wrap :: a  ->  [a];
14.80/5.61	wrap x = x : [];
14.80/5.61	
14.80/5.61	}
14.80/5.61	module Main where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(1) CR (EQUIVALENT)
14.80/5.61	Case Reductions:
14.80/5.61	The following Case expression
14.80/5.61	"case cmp x y of {
14.80/5.61	GT  -> y : merge cmp (x : xs) ys;
14.80/5.61	_  -> x : merge cmp xs (y : ys)}
14.80/5.61	"
14.80/5.61	is transformed to
14.80/5.61	"merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.80/5.61	merge0 y cmp x xs ys _ = x : merge cmp xs (y : ys);
14.80/5.61	"
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(2)
14.80/5.61	Obligation:
14.80/5.61	mainModule Main 
14.80/5.61	module Maybe where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	module List where {
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.80/5.61	merge cmp xs [] = xs;
14.80/5.61	merge cmp [] ys = ys;
14.80/5.61	merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);
14.80/5.61	
14.80/5.61	merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.80/5.61	merge0 y cmp x xs ys _ = x : merge cmp xs (y : ys);
14.80/5.61	
14.80/5.61	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.80/5.61	merge_pairs cmp [] = [];
14.80/5.61	merge_pairs cmp (xs : []) = xs : [];
14.80/5.61	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.80/5.61	
14.80/5.61	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.80/5.61	mergesort cmp = mergesort' cmp . map wrap;
14.80/5.61	
14.80/5.61	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.80/5.61	mergesort' cmp [] = [];
14.80/5.61	mergesort' cmp (xs : []) = xs;
14.80/5.61	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.80/5.61	
14.80/5.61	sort :: Ord a => [a]  ->  [a];
14.80/5.61	sort l = mergesort compare l;
14.80/5.61	
14.80/5.61	wrap :: a  ->  [a];
14.80/5.61	wrap x = x : [];
14.80/5.61	
14.80/5.61	}
14.80/5.61	module Main where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(3) BR (EQUIVALENT)
14.80/5.61	Replaced joker patterns by fresh variables and removed binding patterns.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(4)
14.80/5.61	Obligation:
14.80/5.61	mainModule Main 
14.80/5.61	module Maybe where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	module List where {
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.80/5.61	merge cmp xs [] = xs;
14.80/5.61	merge cmp [] ys = ys;
14.80/5.61	merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);
14.80/5.61	
14.80/5.61	merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.80/5.61	merge0 y cmp x xs ys vy = x : merge cmp xs (y : ys);
14.80/5.61	
14.80/5.61	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.80/5.61	merge_pairs cmp [] = [];
14.80/5.61	merge_pairs cmp (xs : []) = xs : [];
14.80/5.61	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.80/5.61	
14.80/5.61	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.80/5.61	mergesort cmp = mergesort' cmp . map wrap;
14.80/5.61	
14.80/5.61	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.80/5.61	mergesort' cmp [] = [];
14.80/5.61	mergesort' cmp (xs : []) = xs;
14.80/5.61	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.80/5.61	
14.80/5.61	sort :: Ord a => [a]  ->  [a];
14.80/5.61	sort l = mergesort compare l;
14.80/5.61	
14.80/5.61	wrap :: a  ->  [a];
14.80/5.61	wrap x = x : [];
14.80/5.61	
14.80/5.61	}
14.80/5.61	module Main where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(5) COR (EQUIVALENT)
14.80/5.61	Cond Reductions:
14.80/5.61	The following Function with conditions
14.80/5.61	"undefined |Falseundefined;
14.80/5.61	"
14.80/5.61	is transformed to
14.80/5.61	"undefined  = undefined1;
14.80/5.61	"
14.80/5.61	"undefined0 True = undefined;
14.80/5.61	"
14.80/5.61	"undefined1  = undefined0 False;
14.80/5.61	"
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(6)
14.80/5.61	Obligation:
14.80/5.61	mainModule Main 
14.80/5.61	module Maybe where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	module List where {
14.80/5.61	import qualified Main;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.80/5.61	merge cmp xs [] = xs;
14.80/5.61	merge cmp [] ys = ys;
14.80/5.61	merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);
14.80/5.61	
14.80/5.61	merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.80/5.61	merge0 y cmp x xs ys vy = x : merge cmp xs (y : ys);
14.80/5.61	
14.80/5.61	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.80/5.61	merge_pairs cmp [] = [];
14.80/5.61	merge_pairs cmp (xs : []) = xs : [];
14.80/5.61	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.80/5.61	
14.80/5.61	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.80/5.61	mergesort cmp = mergesort' cmp . map wrap;
14.80/5.61	
14.80/5.61	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.80/5.61	mergesort' cmp [] = [];
14.80/5.61	mergesort' cmp (xs : []) = xs;
14.80/5.61	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.80/5.61	
14.80/5.61	sort :: Ord a => [a]  ->  [a];
14.80/5.61	sort l = mergesort compare l;
14.80/5.61	
14.80/5.61	wrap :: a  ->  [a];
14.80/5.61	wrap x = x : [];
14.80/5.61	
14.80/5.61	}
14.80/5.61	module Main where {
14.80/5.61	import qualified List;
14.80/5.61	import qualified Maybe;
14.80/5.61	import qualified Prelude;
14.80/5.61	}
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(7) Narrow (SOUND)
14.80/5.61	Haskell To QDPs
14.80/5.61	
14.80/5.61	digraph dp_graph {
14.80/5.61	node [outthreshold=100, inthreshold=100];1[label="List.sort",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
14.80/5.61	3[label="List.sort vz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
14.80/5.61	4[label="List.mergesort compare vz3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
14.80/5.61	5[label="(List.mergesort' compare) . map List.wrap",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
14.80/5.61	6[label="List.mergesort' compare (map List.wrap vz3)",fontsize=16,color="burlywood",shape="box"];935[label="vz3/vz30 : vz31",fontsize=10,color="white",style="solid",shape="box"];6 -> 935[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	935 -> 7[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	936[label="vz3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 936[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	936 -> 8[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	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];
14.80/5.61	8[label="List.mergesort' compare (map List.wrap [])",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
14.80/5.61	9[label="List.mergesort' compare (List.wrap vz30 : map List.wrap vz31)",fontsize=16,color="burlywood",shape="box"];937[label="vz31/vz310 : vz311",fontsize=10,color="white",style="solid",shape="box"];9 -> 937[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	937 -> 11[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	938[label="vz31/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 938[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	938 -> 12[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	10[label="List.mergesort' compare []",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
14.80/5.61	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];
14.80/5.61	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];
14.80/5.61	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];
14.80/5.61	15[label="List.mergesort' compare (List.wrap vz30 : [])",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
14.80/5.61	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];
14.80/5.61	17[label="List.wrap vz30",fontsize=16,color="black",shape="triangle"];17 -> 19[label="",style="solid", color="black", weight=3];
14.80/5.61	18 -> 589[label="",style="dashed", color="red", weight=0];
14.80/5.61	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 -> 590[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	18 -> 591[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	19[label="vz30 : []",fontsize=16,color="green",shape="box"];590 -> 744[label="",style="dashed", color="red", weight=0];
14.80/5.61	590[label="List.merge compare (List.wrap vz30) (List.wrap vz310)",fontsize=16,color="magenta"];590 -> 745[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	590 -> 746[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	591[label="map List.wrap vz311",fontsize=16,color="burlywood",shape="triangle"];939[label="vz311/vz3110 : vz3111",fontsize=10,color="white",style="solid",shape="box"];591 -> 939[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	939 -> 747[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	940[label="vz311/[]",fontsize=10,color="white",style="solid",shape="box"];591 -> 940[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	940 -> 748[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	589[label="List.mergesort' compare (vz78 : List.merge_pairs compare vz79)",fontsize=16,color="burlywood",shape="triangle"];941[label="vz79/vz790 : vz791",fontsize=10,color="white",style="solid",shape="box"];589 -> 941[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	941 -> 749[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	942[label="vz79/[]",fontsize=10,color="white",style="solid",shape="box"];589 -> 942[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	942 -> 750[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	745 -> 17[label="",style="dashed", color="red", weight=0];
14.80/5.61	745[label="List.wrap vz30",fontsize=16,color="magenta"];746 -> 17[label="",style="dashed", color="red", weight=0];
14.80/5.61	746[label="List.wrap vz310",fontsize=16,color="magenta"];746 -> 751[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	744[label="List.merge compare vz81 vz80",fontsize=16,color="burlywood",shape="triangle"];943[label="vz80/vz800 : vz801",fontsize=10,color="white",style="solid",shape="box"];744 -> 943[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	943 -> 752[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	944[label="vz80/[]",fontsize=10,color="white",style="solid",shape="box"];744 -> 944[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	944 -> 753[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	747[label="map List.wrap (vz3110 : vz3111)",fontsize=16,color="black",shape="box"];747 -> 754[label="",style="solid", color="black", weight=3];
14.80/5.61	748[label="map List.wrap []",fontsize=16,color="black",shape="box"];748 -> 755[label="",style="solid", color="black", weight=3];
14.80/5.61	749[label="List.mergesort' compare (vz78 : List.merge_pairs compare (vz790 : vz791))",fontsize=16,color="burlywood",shape="box"];945[label="vz791/vz7910 : vz7911",fontsize=10,color="white",style="solid",shape="box"];749 -> 945[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	945 -> 756[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	946[label="vz791/[]",fontsize=10,color="white",style="solid",shape="box"];749 -> 946[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	946 -> 757[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	750[label="List.mergesort' compare (vz78 : List.merge_pairs compare [])",fontsize=16,color="black",shape="box"];750 -> 758[label="",style="solid", color="black", weight=3];
14.80/5.61	751[label="vz310",fontsize=16,color="green",shape="box"];752[label="List.merge compare vz81 (vz800 : vz801)",fontsize=16,color="burlywood",shape="box"];947[label="vz81/vz810 : vz811",fontsize=10,color="white",style="solid",shape="box"];752 -> 947[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	947 -> 759[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	948[label="vz81/[]",fontsize=10,color="white",style="solid",shape="box"];752 -> 948[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	948 -> 760[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	753[label="List.merge compare vz81 []",fontsize=16,color="black",shape="box"];753 -> 761[label="",style="solid", color="black", weight=3];
14.80/5.61	754[label="List.wrap vz3110 : map List.wrap vz3111",fontsize=16,color="green",shape="box"];754 -> 762[label="",style="dashed", color="green", weight=3];
14.80/5.61	754 -> 763[label="",style="dashed", color="green", weight=3];
14.80/5.61	755[label="[]",fontsize=16,color="green",shape="box"];756[label="List.mergesort' compare (vz78 : List.merge_pairs compare (vz790 : vz7910 : vz7911))",fontsize=16,color="black",shape="box"];756 -> 764[label="",style="solid", color="black", weight=3];
14.80/5.61	757[label="List.mergesort' compare (vz78 : List.merge_pairs compare (vz790 : []))",fontsize=16,color="black",shape="box"];757 -> 765[label="",style="solid", color="black", weight=3];
14.80/5.61	758[label="List.mergesort' compare (vz78 : [])",fontsize=16,color="black",shape="box"];758 -> 766[label="",style="solid", color="black", weight=3];
14.80/5.61	759[label="List.merge compare (vz810 : vz811) (vz800 : vz801)",fontsize=16,color="black",shape="box"];759 -> 767[label="",style="solid", color="black", weight=3];
14.80/5.61	760[label="List.merge compare [] (vz800 : vz801)",fontsize=16,color="black",shape="box"];760 -> 768[label="",style="solid", color="black", weight=3];
14.80/5.61	761[label="vz81",fontsize=16,color="green",shape="box"];762 -> 17[label="",style="dashed", color="red", weight=0];
14.80/5.61	762[label="List.wrap vz3110",fontsize=16,color="magenta"];762 -> 769[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	763 -> 591[label="",style="dashed", color="red", weight=0];
14.80/5.61	763[label="map List.wrap vz3111",fontsize=16,color="magenta"];763 -> 770[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	764[label="List.mergesort' compare (vz78 : List.merge compare vz790 vz7910 : List.merge_pairs compare vz7911)",fontsize=16,color="black",shape="box"];764 -> 771[label="",style="solid", color="black", weight=3];
14.80/5.61	765[label="List.mergesort' compare (vz78 : vz790 : [])",fontsize=16,color="black",shape="box"];765 -> 772[label="",style="solid", color="black", weight=3];
14.80/5.61	766[label="vz78",fontsize=16,color="green",shape="box"];767 -> 814[label="",style="dashed", color="red", weight=0];
14.80/5.61	767[label="List.merge0 vz800 compare vz810 vz811 vz801 (compare vz810 vz800)",fontsize=16,color="magenta"];767 -> 815[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	767 -> 816[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	767 -> 817[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	767 -> 818[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	767 -> 819[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	768[label="vz800 : vz801",fontsize=16,color="green",shape="box"];769[label="vz3110",fontsize=16,color="green",shape="box"];770[label="vz3111",fontsize=16,color="green",shape="box"];771[label="List.mergesort' compare (List.merge_pairs compare (vz78 : List.merge compare vz790 vz7910 : List.merge_pairs compare vz7911))",fontsize=16,color="black",shape="box"];771 -> 774[label="",style="solid", color="black", weight=3];
14.80/5.61	772[label="List.mergesort' compare (List.merge_pairs compare (vz78 : vz790 : []))",fontsize=16,color="black",shape="box"];772 -> 775[label="",style="solid", color="black", weight=3];
14.80/5.61	815[label="vz801",fontsize=16,color="green",shape="box"];816[label="vz810",fontsize=16,color="green",shape="box"];817[label="vz811",fontsize=16,color="green",shape="box"];818[label="compare vz810 vz800",fontsize=16,color="black",shape="triangle"];818 -> 830[label="",style="solid", color="black", weight=3];
14.80/5.61	819[label="vz800",fontsize=16,color="green",shape="box"];814[label="List.merge0 vz88 compare vz89 vz90 vz91 vz92",fontsize=16,color="burlywood",shape="triangle"];949[label="vz92/LT",fontsize=10,color="white",style="solid",shape="box"];814 -> 949[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	949 -> 831[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	950[label="vz92/EQ",fontsize=10,color="white",style="solid",shape="box"];814 -> 950[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	950 -> 832[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	951[label="vz92/GT",fontsize=10,color="white",style="solid",shape="box"];814 -> 951[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	951 -> 833[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	774 -> 589[label="",style="dashed", color="red", weight=0];
14.80/5.61	774[label="List.mergesort' compare (List.merge compare vz78 (List.merge compare vz790 vz7910) : List.merge_pairs compare (List.merge_pairs compare vz7911))",fontsize=16,color="magenta"];774 -> 777[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	774 -> 778[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	775 -> 589[label="",style="dashed", color="red", weight=0];
14.80/5.61	775[label="List.mergesort' compare (List.merge compare vz78 vz790 : List.merge_pairs compare [])",fontsize=16,color="magenta"];775 -> 779[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	775 -> 780[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	830[label="primCmpChar vz810 vz800",fontsize=16,color="burlywood",shape="box"];952[label="vz810/Char vz8100",fontsize=10,color="white",style="solid",shape="box"];830 -> 952[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	952 -> 865[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	831[label="List.merge0 vz88 compare vz89 vz90 vz91 LT",fontsize=16,color="black",shape="box"];831 -> 866[label="",style="solid", color="black", weight=3];
14.80/5.61	832[label="List.merge0 vz88 compare vz89 vz90 vz91 EQ",fontsize=16,color="black",shape="box"];832 -> 867[label="",style="solid", color="black", weight=3];
14.80/5.61	833[label="List.merge0 vz88 compare vz89 vz90 vz91 GT",fontsize=16,color="black",shape="box"];833 -> 868[label="",style="solid", color="black", weight=3];
14.80/5.61	777[label="List.merge compare vz78 (List.merge compare vz790 vz7910)",fontsize=16,color="burlywood",shape="box"];953[label="vz7910/vz79100 : vz79101",fontsize=10,color="white",style="solid",shape="box"];777 -> 953[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	953 -> 782[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	954[label="vz7910/[]",fontsize=10,color="white",style="solid",shape="box"];777 -> 954[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	954 -> 783[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	778[label="List.merge_pairs compare vz7911",fontsize=16,color="burlywood",shape="triangle"];955[label="vz7911/vz79110 : vz79111",fontsize=10,color="white",style="solid",shape="box"];778 -> 955[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	955 -> 784[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	956[label="vz7911/[]",fontsize=10,color="white",style="solid",shape="box"];778 -> 956[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	956 -> 785[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	779[label="List.merge compare vz78 vz790",fontsize=16,color="burlywood",shape="triangle"];957[label="vz790/vz7900 : vz7901",fontsize=10,color="white",style="solid",shape="box"];779 -> 957[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	957 -> 786[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	958[label="vz790/[]",fontsize=10,color="white",style="solid",shape="box"];779 -> 958[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	958 -> 787[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	780[label="[]",fontsize=16,color="green",shape="box"];865[label="primCmpChar (Char vz8100) vz800",fontsize=16,color="burlywood",shape="box"];959[label="vz800/Char vz8000",fontsize=10,color="white",style="solid",shape="box"];865 -> 959[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	959 -> 912[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	866[label="vz89 : List.merge compare vz90 (vz88 : vz91)",fontsize=16,color="green",shape="box"];866 -> 913[label="",style="dashed", color="green", weight=3];
14.80/5.61	867[label="vz89 : List.merge compare vz90 (vz88 : vz91)",fontsize=16,color="green",shape="box"];867 -> 914[label="",style="dashed", color="green", weight=3];
14.80/5.61	868[label="vz88 : List.merge compare (vz89 : vz90) vz91",fontsize=16,color="green",shape="box"];868 -> 915[label="",style="dashed", color="green", weight=3];
14.80/5.61	782[label="List.merge compare vz78 (List.merge compare vz790 (vz79100 : vz79101))",fontsize=16,color="burlywood",shape="box"];960[label="vz790/vz7900 : vz7901",fontsize=10,color="white",style="solid",shape="box"];782 -> 960[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	960 -> 789[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	961[label="vz790/[]",fontsize=10,color="white",style="solid",shape="box"];782 -> 961[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	961 -> 790[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	783[label="List.merge compare vz78 (List.merge compare vz790 [])",fontsize=16,color="black",shape="box"];783 -> 791[label="",style="solid", color="black", weight=3];
14.80/5.61	784[label="List.merge_pairs compare (vz79110 : vz79111)",fontsize=16,color="burlywood",shape="box"];962[label="vz79111/vz791110 : vz791111",fontsize=10,color="white",style="solid",shape="box"];784 -> 962[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	962 -> 792[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	963[label="vz79111/[]",fontsize=10,color="white",style="solid",shape="box"];784 -> 963[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	963 -> 793[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	785[label="List.merge_pairs compare []",fontsize=16,color="black",shape="box"];785 -> 794[label="",style="solid", color="black", weight=3];
14.80/5.61	786[label="List.merge compare vz78 (vz7900 : vz7901)",fontsize=16,color="burlywood",shape="box"];964[label="vz78/vz780 : vz781",fontsize=10,color="white",style="solid",shape="box"];786 -> 964[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	964 -> 795[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	965[label="vz78/[]",fontsize=10,color="white",style="solid",shape="box"];786 -> 965[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	965 -> 796[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	787[label="List.merge compare vz78 []",fontsize=16,color="black",shape="box"];787 -> 797[label="",style="solid", color="black", weight=3];
14.80/5.61	912[label="primCmpChar (Char vz8100) (Char vz8000)",fontsize=16,color="black",shape="box"];912 -> 916[label="",style="solid", color="black", weight=3];
14.80/5.61	913 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	913[label="List.merge compare vz90 (vz88 : vz91)",fontsize=16,color="magenta"];913 -> 917[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	913 -> 918[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	914 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	914[label="List.merge compare vz90 (vz88 : vz91)",fontsize=16,color="magenta"];914 -> 919[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	914 -> 920[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	915 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	915[label="List.merge compare (vz89 : vz90) vz91",fontsize=16,color="magenta"];915 -> 921[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	915 -> 922[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	789[label="List.merge compare vz78 (List.merge compare (vz7900 : vz7901) (vz79100 : vz79101))",fontsize=16,color="black",shape="box"];789 -> 800[label="",style="solid", color="black", weight=3];
14.80/5.61	790[label="List.merge compare vz78 (List.merge compare [] (vz79100 : vz79101))",fontsize=16,color="black",shape="box"];790 -> 801[label="",style="solid", color="black", weight=3];
14.80/5.61	791 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	791[label="List.merge compare vz78 vz790",fontsize=16,color="magenta"];792[label="List.merge_pairs compare (vz79110 : vz791110 : vz791111)",fontsize=16,color="black",shape="box"];792 -> 802[label="",style="solid", color="black", weight=3];
14.80/5.61	793[label="List.merge_pairs compare (vz79110 : [])",fontsize=16,color="black",shape="box"];793 -> 803[label="",style="solid", color="black", weight=3];
14.80/5.61	794[label="[]",fontsize=16,color="green",shape="box"];795[label="List.merge compare (vz780 : vz781) (vz7900 : vz7901)",fontsize=16,color="black",shape="box"];795 -> 804[label="",style="solid", color="black", weight=3];
14.80/5.61	796[label="List.merge compare [] (vz7900 : vz7901)",fontsize=16,color="black",shape="box"];796 -> 805[label="",style="solid", color="black", weight=3];
14.80/5.61	797[label="vz78",fontsize=16,color="green",shape="box"];916[label="primCmpNat vz8100 vz8000",fontsize=16,color="burlywood",shape="triangle"];966[label="vz8100/Succ vz81000",fontsize=10,color="white",style="solid",shape="box"];916 -> 966[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	966 -> 923[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	967[label="vz8100/Zero",fontsize=10,color="white",style="solid",shape="box"];916 -> 967[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	967 -> 924[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	917[label="vz88 : vz91",fontsize=16,color="green",shape="box"];918[label="vz90",fontsize=16,color="green",shape="box"];919[label="vz88 : vz91",fontsize=16,color="green",shape="box"];920[label="vz90",fontsize=16,color="green",shape="box"];921[label="vz91",fontsize=16,color="green",shape="box"];922[label="vz89 : vz90",fontsize=16,color="green",shape="box"];800 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	800[label="List.merge compare vz78 (List.merge0 vz79100 compare vz7900 vz7901 vz79101 (compare vz7900 vz79100))",fontsize=16,color="magenta"];800 -> 810[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	801 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	801[label="List.merge compare vz78 (vz79100 : vz79101)",fontsize=16,color="magenta"];801 -> 811[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	802[label="List.merge compare vz79110 vz791110 : List.merge_pairs compare vz791111",fontsize=16,color="green",shape="box"];802 -> 812[label="",style="dashed", color="green", weight=3];
14.80/5.61	802 -> 813[label="",style="dashed", color="green", weight=3];
14.80/5.61	803[label="vz79110 : []",fontsize=16,color="green",shape="box"];804 -> 814[label="",style="dashed", color="red", weight=0];
14.80/5.61	804[label="List.merge0 vz7900 compare vz780 vz781 vz7901 (compare vz780 vz7900)",fontsize=16,color="magenta"];804 -> 820[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	804 -> 821[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	804 -> 822[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	804 -> 823[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	804 -> 824[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	805[label="vz7900 : vz7901",fontsize=16,color="green",shape="box"];923[label="primCmpNat (Succ vz81000) vz8000",fontsize=16,color="burlywood",shape="box"];968[label="vz8000/Succ vz80000",fontsize=10,color="white",style="solid",shape="box"];923 -> 968[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	968 -> 925[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	969[label="vz8000/Zero",fontsize=10,color="white",style="solid",shape="box"];923 -> 969[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	969 -> 926[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	924[label="primCmpNat Zero vz8000",fontsize=16,color="burlywood",shape="box"];970[label="vz8000/Succ vz80000",fontsize=10,color="white",style="solid",shape="box"];924 -> 970[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	970 -> 927[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	971[label="vz8000/Zero",fontsize=10,color="white",style="solid",shape="box"];924 -> 971[label="",style="solid", color="burlywood", weight=9];
14.80/5.61	971 -> 928[label="",style="solid", color="burlywood", weight=3];
14.80/5.61	810 -> 814[label="",style="dashed", color="red", weight=0];
14.80/5.61	810[label="List.merge0 vz79100 compare vz7900 vz7901 vz79101 (compare vz7900 vz79100)",fontsize=16,color="magenta"];810 -> 825[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	810 -> 826[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	810 -> 827[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	810 -> 828[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	810 -> 829[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	811[label="vz79100 : vz79101",fontsize=16,color="green",shape="box"];812 -> 779[label="",style="dashed", color="red", weight=0];
14.80/5.61	812[label="List.merge compare vz79110 vz791110",fontsize=16,color="magenta"];812 -> 834[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	812 -> 835[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	813 -> 778[label="",style="dashed", color="red", weight=0];
14.80/5.61	813[label="List.merge_pairs compare vz791111",fontsize=16,color="magenta"];813 -> 836[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	820[label="vz7901",fontsize=16,color="green",shape="box"];821[label="vz780",fontsize=16,color="green",shape="box"];822[label="vz781",fontsize=16,color="green",shape="box"];823[label="compare vz780 vz7900",fontsize=16,color="blue",shape="box"];972[label="compare :: Char -> Char -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 972[label="",style="solid", color="blue", weight=9];
14.80/5.61	972 -> 837[label="",style="solid", color="blue", weight=3];
14.80/5.61	973[label="compare :: ([] a) -> ([] a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 973[label="",style="solid", color="blue", weight=9];
14.80/5.61	973 -> 838[label="",style="solid", color="blue", weight=3];
14.80/5.61	974[label="compare :: ((@3) a b c) -> ((@3) a b c) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 974[label="",style="solid", color="blue", weight=9];
14.80/5.61	974 -> 839[label="",style="solid", color="blue", weight=3];
14.80/5.61	975[label="compare :: Ordering -> Ordering -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 975[label="",style="solid", color="blue", weight=9];
14.80/5.61	975 -> 840[label="",style="solid", color="blue", weight=3];
14.80/5.61	976[label="compare :: Float -> Float -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 976[label="",style="solid", color="blue", weight=9];
14.80/5.61	976 -> 841[label="",style="solid", color="blue", weight=3];
14.80/5.61	977[label="compare :: (Ratio a) -> (Ratio a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 977[label="",style="solid", color="blue", weight=9];
14.80/5.61	977 -> 842[label="",style="solid", color="blue", weight=3];
14.80/5.61	978[label="compare :: Double -> Double -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 978[label="",style="solid", color="blue", weight=9];
14.80/5.61	978 -> 843[label="",style="solid", color="blue", weight=3];
14.80/5.61	979[label="compare :: (Either a b) -> (Either a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 979[label="",style="solid", color="blue", weight=9];
14.80/5.61	979 -> 844[label="",style="solid", color="blue", weight=3];
14.80/5.61	980[label="compare :: Bool -> Bool -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 980[label="",style="solid", color="blue", weight=9];
14.80/5.61	980 -> 845[label="",style="solid", color="blue", weight=3];
14.80/5.61	981[label="compare :: Integer -> Integer -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 981[label="",style="solid", color="blue", weight=9];
14.80/5.61	981 -> 846[label="",style="solid", color="blue", weight=3];
14.80/5.61	982[label="compare :: Int -> Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 982[label="",style="solid", color="blue", weight=9];
14.80/5.61	982 -> 847[label="",style="solid", color="blue", weight=3];
14.80/5.61	983[label="compare :: ((@2) a b) -> ((@2) a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 983[label="",style="solid", color="blue", weight=9];
14.80/5.61	983 -> 848[label="",style="solid", color="blue", weight=3];
14.80/5.61	984[label="compare :: () -> () -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 984[label="",style="solid", color="blue", weight=9];
14.80/5.61	984 -> 849[label="",style="solid", color="blue", weight=3];
14.80/5.61	985[label="compare :: (Maybe a) -> (Maybe a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];823 -> 985[label="",style="solid", color="blue", weight=9];
14.80/5.61	985 -> 850[label="",style="solid", color="blue", weight=3];
14.80/5.61	824[label="vz7900",fontsize=16,color="green",shape="box"];925[label="primCmpNat (Succ vz81000) (Succ vz80000)",fontsize=16,color="black",shape="box"];925 -> 929[label="",style="solid", color="black", weight=3];
14.80/5.61	926[label="primCmpNat (Succ vz81000) Zero",fontsize=16,color="black",shape="box"];926 -> 930[label="",style="solid", color="black", weight=3];
14.80/5.61	927[label="primCmpNat Zero (Succ vz80000)",fontsize=16,color="black",shape="box"];927 -> 931[label="",style="solid", color="black", weight=3];
14.80/5.61	928[label="primCmpNat Zero Zero",fontsize=16,color="black",shape="box"];928 -> 932[label="",style="solid", color="black", weight=3];
14.80/5.61	825[label="vz79101",fontsize=16,color="green",shape="box"];826[label="vz7900",fontsize=16,color="green",shape="box"];827[label="vz7901",fontsize=16,color="green",shape="box"];828[label="compare vz7900 vz79100",fontsize=16,color="blue",shape="box"];986[label="compare :: Char -> Char -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 986[label="",style="solid", color="blue", weight=9];
14.80/5.61	986 -> 851[label="",style="solid", color="blue", weight=3];
14.80/5.61	987[label="compare :: ([] a) -> ([] a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 987[label="",style="solid", color="blue", weight=9];
14.80/5.61	987 -> 852[label="",style="solid", color="blue", weight=3];
14.80/5.61	988[label="compare :: ((@3) a b c) -> ((@3) a b c) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 988[label="",style="solid", color="blue", weight=9];
14.80/5.61	988 -> 853[label="",style="solid", color="blue", weight=3];
14.80/5.61	989[label="compare :: Ordering -> Ordering -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 989[label="",style="solid", color="blue", weight=9];
14.80/5.61	989 -> 854[label="",style="solid", color="blue", weight=3];
14.80/5.61	990[label="compare :: Float -> Float -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 990[label="",style="solid", color="blue", weight=9];
14.80/5.61	990 -> 855[label="",style="solid", color="blue", weight=3];
14.80/5.61	991[label="compare :: (Ratio a) -> (Ratio a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 991[label="",style="solid", color="blue", weight=9];
14.80/5.61	991 -> 856[label="",style="solid", color="blue", weight=3];
14.80/5.61	992[label="compare :: Double -> Double -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 992[label="",style="solid", color="blue", weight=9];
14.80/5.61	992 -> 857[label="",style="solid", color="blue", weight=3];
14.80/5.61	993[label="compare :: (Either a b) -> (Either a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 993[label="",style="solid", color="blue", weight=9];
14.80/5.61	993 -> 858[label="",style="solid", color="blue", weight=3];
14.80/5.61	994[label="compare :: Bool -> Bool -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 994[label="",style="solid", color="blue", weight=9];
14.80/5.61	994 -> 859[label="",style="solid", color="blue", weight=3];
14.80/5.61	995[label="compare :: Integer -> Integer -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 995[label="",style="solid", color="blue", weight=9];
14.80/5.61	995 -> 860[label="",style="solid", color="blue", weight=3];
14.80/5.61	996[label="compare :: Int -> Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 996[label="",style="solid", color="blue", weight=9];
14.80/5.61	996 -> 861[label="",style="solid", color="blue", weight=3];
14.80/5.61	997[label="compare :: ((@2) a b) -> ((@2) a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 997[label="",style="solid", color="blue", weight=9];
14.80/5.61	997 -> 862[label="",style="solid", color="blue", weight=3];
14.80/5.61	998[label="compare :: () -> () -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 998[label="",style="solid", color="blue", weight=9];
14.80/5.61	998 -> 863[label="",style="solid", color="blue", weight=3];
14.80/5.61	999[label="compare :: (Maybe a) -> (Maybe a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];828 -> 999[label="",style="solid", color="blue", weight=9];
14.80/5.61	999 -> 864[label="",style="solid", color="blue", weight=3];
14.80/5.61	829[label="vz79100",fontsize=16,color="green",shape="box"];834[label="vz791110",fontsize=16,color="green",shape="box"];835[label="vz79110",fontsize=16,color="green",shape="box"];836[label="vz791111",fontsize=16,color="green",shape="box"];837 -> 818[label="",style="dashed", color="red", weight=0];
14.80/5.61	837[label="compare vz780 vz7900",fontsize=16,color="magenta"];837 -> 869[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	837 -> 870[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	838[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];838 -> 871[label="",style="solid", color="black", weight=3];
14.80/5.61	839[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];839 -> 872[label="",style="solid", color="black", weight=3];
14.80/5.61	840[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];840 -> 873[label="",style="solid", color="black", weight=3];
14.80/5.61	841[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];841 -> 874[label="",style="solid", color="black", weight=3];
14.80/5.61	842[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];842 -> 875[label="",style="solid", color="black", weight=3];
14.80/5.61	843[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];843 -> 876[label="",style="solid", color="black", weight=3];
14.80/5.61	844[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];844 -> 877[label="",style="solid", color="black", weight=3];
14.80/5.61	845[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];845 -> 878[label="",style="solid", color="black", weight=3];
14.80/5.61	846[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];846 -> 879[label="",style="solid", color="black", weight=3];
14.80/5.61	847[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];847 -> 880[label="",style="solid", color="black", weight=3];
14.80/5.61	848[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];848 -> 881[label="",style="solid", color="black", weight=3];
14.80/5.61	849[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];849 -> 882[label="",style="solid", color="black", weight=3];
14.80/5.61	850[label="compare vz780 vz7900",fontsize=16,color="black",shape="triangle"];850 -> 883[label="",style="solid", color="black", weight=3];
14.80/5.61	929 -> 916[label="",style="dashed", color="red", weight=0];
14.80/5.61	929[label="primCmpNat vz81000 vz80000",fontsize=16,color="magenta"];929 -> 933[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	929 -> 934[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	930[label="GT",fontsize=16,color="green",shape="box"];931[label="LT",fontsize=16,color="green",shape="box"];932[label="EQ",fontsize=16,color="green",shape="box"];851 -> 818[label="",style="dashed", color="red", weight=0];
14.80/5.61	851[label="compare vz7900 vz79100",fontsize=16,color="magenta"];851 -> 884[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	851 -> 885[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	852 -> 838[label="",style="dashed", color="red", weight=0];
14.80/5.61	852[label="compare vz7900 vz79100",fontsize=16,color="magenta"];852 -> 886[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	852 -> 887[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	853 -> 839[label="",style="dashed", color="red", weight=0];
14.80/5.61	853[label="compare vz7900 vz79100",fontsize=16,color="magenta"];853 -> 888[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	853 -> 889[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	854 -> 840[label="",style="dashed", color="red", weight=0];
14.80/5.61	854[label="compare vz7900 vz79100",fontsize=16,color="magenta"];854 -> 890[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	854 -> 891[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	855 -> 841[label="",style="dashed", color="red", weight=0];
14.80/5.61	855[label="compare vz7900 vz79100",fontsize=16,color="magenta"];855 -> 892[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	855 -> 893[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	856 -> 842[label="",style="dashed", color="red", weight=0];
14.80/5.61	856[label="compare vz7900 vz79100",fontsize=16,color="magenta"];856 -> 894[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	856 -> 895[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	857 -> 843[label="",style="dashed", color="red", weight=0];
14.80/5.61	857[label="compare vz7900 vz79100",fontsize=16,color="magenta"];857 -> 896[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	857 -> 897[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	858 -> 844[label="",style="dashed", color="red", weight=0];
14.80/5.61	858[label="compare vz7900 vz79100",fontsize=16,color="magenta"];858 -> 898[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	858 -> 899[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	859 -> 845[label="",style="dashed", color="red", weight=0];
14.80/5.61	859[label="compare vz7900 vz79100",fontsize=16,color="magenta"];859 -> 900[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	859 -> 901[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	860 -> 846[label="",style="dashed", color="red", weight=0];
14.80/5.61	860[label="compare vz7900 vz79100",fontsize=16,color="magenta"];860 -> 902[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	860 -> 903[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	861 -> 847[label="",style="dashed", color="red", weight=0];
14.80/5.61	861[label="compare vz7900 vz79100",fontsize=16,color="magenta"];861 -> 904[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	861 -> 905[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	862 -> 848[label="",style="dashed", color="red", weight=0];
14.80/5.61	862[label="compare vz7900 vz79100",fontsize=16,color="magenta"];862 -> 906[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	862 -> 907[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	863 -> 849[label="",style="dashed", color="red", weight=0];
14.80/5.61	863[label="compare vz7900 vz79100",fontsize=16,color="magenta"];863 -> 908[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	863 -> 909[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	864 -> 850[label="",style="dashed", color="red", weight=0];
14.80/5.61	864[label="compare vz7900 vz79100",fontsize=16,color="magenta"];864 -> 910[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	864 -> 911[label="",style="dashed", color="magenta", weight=3];
14.80/5.61	869[label="vz7900",fontsize=16,color="green",shape="box"];870[label="vz780",fontsize=16,color="green",shape="box"];871[label="error []",fontsize=16,color="red",shape="box"];872[label="error []",fontsize=16,color="red",shape="box"];873[label="error []",fontsize=16,color="red",shape="box"];874[label="error []",fontsize=16,color="red",shape="box"];875[label="error []",fontsize=16,color="red",shape="box"];876[label="error []",fontsize=16,color="red",shape="box"];877[label="error []",fontsize=16,color="red",shape="box"];878[label="error []",fontsize=16,color="red",shape="box"];879[label="error []",fontsize=16,color="red",shape="box"];880[label="error []",fontsize=16,color="red",shape="box"];881[label="error []",fontsize=16,color="red",shape="box"];882[label="error []",fontsize=16,color="red",shape="box"];883[label="error []",fontsize=16,color="red",shape="box"];933[label="vz80000",fontsize=16,color="green",shape="box"];934[label="vz81000",fontsize=16,color="green",shape="box"];884[label="vz79100",fontsize=16,color="green",shape="box"];885[label="vz7900",fontsize=16,color="green",shape="box"];886[label="vz7900",fontsize=16,color="green",shape="box"];887[label="vz79100",fontsize=16,color="green",shape="box"];888[label="vz7900",fontsize=16,color="green",shape="box"];889[label="vz79100",fontsize=16,color="green",shape="box"];890[label="vz7900",fontsize=16,color="green",shape="box"];891[label="vz79100",fontsize=16,color="green",shape="box"];892[label="vz7900",fontsize=16,color="green",shape="box"];893[label="vz79100",fontsize=16,color="green",shape="box"];894[label="vz7900",fontsize=16,color="green",shape="box"];895[label="vz79100",fontsize=16,color="green",shape="box"];896[label="vz7900",fontsize=16,color="green",shape="box"];897[label="vz79100",fontsize=16,color="green",shape="box"];898[label="vz7900",fontsize=16,color="green",shape="box"];899[label="vz79100",fontsize=16,color="green",shape="box"];900[label="vz7900",fontsize=16,color="green",shape="box"];901[label="vz79100",fontsize=16,color="green",shape="box"];902[label="vz7900",fontsize=16,color="green",shape="box"];903[label="vz79100",fontsize=16,color="green",shape="box"];904[label="vz7900",fontsize=16,color="green",shape="box"];905[label="vz79100",fontsize=16,color="green",shape="box"];906[label="vz7900",fontsize=16,color="green",shape="box"];907[label="vz79100",fontsize=16,color="green",shape="box"];908[label="vz7900",fontsize=16,color="green",shape="box"];909[label="vz79100",fontsize=16,color="green",shape="box"];910[label="vz7900",fontsize=16,color="green",shape="box"];911[label="vz79100",fontsize=16,color="green",shape="box"];}
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(8)
14.80/5.61	Complex Obligation (AND)
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(9)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_primCmpNat(Succ(vz81000), Succ(vz80000)) -> new_primCmpNat(vz81000, vz80000)
14.80/5.61	
14.80/5.61	R is empty.
14.80/5.61	Q is empty.
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(10) QDPSizeChangeProof (EQUIVALENT)
14.80/5.61	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. 
14.80/5.61	
14.80/5.61	From the DPs we obtained the following set of size-change graphs:
14.80/5.61	*new_primCmpNat(Succ(vz81000), Succ(vz80000)) -> new_primCmpNat(vz81000, vz80000)
14.80/5.61	The graph contains the following edges 1 > 1, 2 > 2
14.80/5.61	
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(11)
14.80/5.61	YES
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(12)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_merge_pairs(:(vz79110, :(vz791110, vz791111)), ba) -> new_merge_pairs(vz791111, ba)
14.80/5.61	
14.80/5.61	R is empty.
14.80/5.61	Q is empty.
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(13) QDPSizeChangeProof (EQUIVALENT)
14.80/5.61	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. 
14.80/5.61	
14.80/5.61	From the DPs we obtained the following set of size-change graphs:
14.80/5.61	*new_merge_pairs(:(vz79110, :(vz791110, vz791111)), ba) -> new_merge_pairs(vz791111, ba)
14.80/5.61	The graph contains the following edges 1 > 1, 2 >= 2
14.80/5.61	
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(14)
14.80/5.61	YES
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(15)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_merge0(vz88, vz89, vz90, vz91, EQ, ba) -> new_merge(vz90, :(vz88, vz91), ba)
14.80/5.61	   new_merge0(vz88, vz89, vz90, vz91, GT, ba) -> new_merge(:(vz89, vz90), vz91, ba)
14.80/5.61	   new_merge0(vz88, vz89, vz90, vz91, LT, ba) -> new_merge(vz90, :(vz88, vz91), ba)
14.80/5.61	   new_merge(:(vz780, vz781), :(vz7900, vz7901), bb) -> new_merge0(vz7900, vz780, vz781, vz7901, new_compare(vz780, vz7900, bb), bb)
14.80/5.61	
14.80/5.61	The TRS R consists of the following rules:
14.80/5.61	
14.80/5.61	   new_compare1(vz780, vz7900, bc, bd) -> error([])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Zero) -> GT
14.80/5.61	   new_compare4(vz780, vz7900) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_Either, cb), cc)) -> new_compare9(vz780, vz7900, cb, cc)
14.80/5.61	   new_compare11(vz780, vz7900) -> error([])
14.80/5.61	   new_primCmpNat0(Zero, Zero) -> EQ
14.80/5.61	   new_compare(vz780, vz7900, ty_Float) -> new_compare0(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(app(app(ty_@3, bf), bg), bh)) -> new_compare6(vz780, vz7900, bf, bg, bh)
14.80/5.61	   new_compare(vz780, vz7900, ty_Int) -> new_compare11(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Maybe, cd)) -> new_compare13(vz780, vz7900, cd)
14.80/5.61	   new_compare(vz780, vz7900, ty_@0) -> new_compare12(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_[], be)) -> new_compare5(vz780, vz7900, be)
14.80/5.61	   new_compare(vz780, vz7900, ty_Integer) -> new_compare2(vz780, vz7900)
14.80/5.61	   new_compare13(vz780, vz7900, cd) -> error([])
14.80/5.61	   new_compare2(vz780, vz7900) -> error([])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Succ(vz80000)) -> new_primCmpNat0(vz81000, vz80000)
14.80/5.61	   new_compare3(Char(vz8100), Char(vz8000)) -> new_primCmpNat0(vz8100, vz8000)
14.80/5.61	   new_compare(vz780, vz7900, ty_Ordering) -> new_compare7(vz780, vz7900)
14.80/5.61	   new_compare5(vz780, vz7900, be) -> error([])
14.80/5.61	   new_compare9(vz780, vz7900, cb, cc) -> error([])
14.80/5.61	   new_compare12(vz780, vz7900) -> error([])
14.80/5.61	   new_compare10(vz780, vz7900) -> error([])
14.80/5.61	   new_compare0(vz780, vz7900) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, ty_Double) -> new_compare4(vz780, vz7900)
14.80/5.61	   new_primCmpNat0(Zero, Succ(vz80000)) -> LT
14.80/5.61	   new_compare6(vz780, vz7900, bf, bg, bh) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, ty_Char) -> new_compare3(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, ty_Bool) -> new_compare10(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_@2, bc), bd)) -> new_compare1(vz780, vz7900, bc, bd)
14.80/5.61	   new_compare8(vz780, vz7900, ca) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Ratio, ca)) -> new_compare8(vz780, vz7900, ca)
14.80/5.61	   new_compare7(vz780, vz7900) -> error([])
14.80/5.61	
14.80/5.61	The set Q consists of the following terms:
14.80/5.61	
14.80/5.61	   new_compare10(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(ty_Maybe, x2))
14.80/5.61	   new_compare9(x0, x1, x2, x3)
14.80/5.61	   new_primCmpNat0(Succ(x0), Succ(x1))
14.80/5.61	   new_compare0(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.80/5.61	   new_compare8(x0, x1, x2)
14.80/5.61	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.80/5.61	   new_compare(x0, x1, ty_Integer)
14.80/5.61	   new_compare5(x0, x1, x2)
14.80/5.61	   new_primCmpNat0(Zero, Succ(x0))
14.80/5.61	   new_compare11(x0, x1)
14.80/5.61	   new_compare(x0, x1, ty_Float)
14.80/5.61	   new_compare6(x0, x1, x2, x3, x4)
14.80/5.61	   new_primCmpNat0(Succ(x0), Zero)
14.80/5.61	   new_compare(x0, x1, ty_Bool)
14.80/5.61	   new_compare2(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(ty_[], x2))
14.80/5.61	   new_compare(x0, x1, ty_Int)
14.80/5.61	   new_compare(x0, x1, app(ty_Ratio, x2))
14.80/5.61	   new_compare12(x0, x1)
14.80/5.61	   new_compare7(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.80/5.61	   new_compare3(Char(x0), Char(x1))
14.80/5.61	   new_compare(x0, x1, ty_Ordering)
14.80/5.61	   new_compare(x0, x1, ty_Char)
14.80/5.61	   new_compare1(x0, x1, x2, x3)
14.80/5.61	   new_primCmpNat0(Zero, Zero)
14.80/5.61	   new_compare(x0, x1, ty_@0)
14.80/5.61	   new_compare4(x0, x1)
14.80/5.61	   new_compare13(x0, x1, x2)
14.80/5.61	   new_compare(x0, x1, ty_Double)
14.80/5.61	
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(16) QDPOrderProof (EQUIVALENT)
14.80/5.61	We use the reduction pair processor [LPAR04,JAR06].
14.80/5.61	
14.80/5.61	
14.80/5.61	The following pairs can be oriented strictly and are deleted.
14.80/5.61	
14.80/5.61	   new_merge(:(vz780, vz781), :(vz7900, vz7901), bb) -> new_merge0(vz7900, vz780, vz781, vz7901, new_compare(vz780, vz7900, bb), bb)
14.80/5.61	The remaining pairs can at least be oriented weakly.
14.80/5.61	Used ordering:  Polynomial interpretation [POLO]:
14.80/5.61	
14.80/5.61	   POL(:(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(Char(x_1)) = x_1
14.80/5.61	   POL(EQ) = 0
14.80/5.61	   POL(GT) = 0
14.80/5.61	   POL(LT) = 0
14.80/5.61	   POL(Succ(x_1)) = 1 + x_1
14.80/5.61	   POL(Zero) = 1
14.80/5.61	   POL([]) = 1
14.80/5.61	   POL(app(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(error(x_1)) = 1
14.80/5.61	   POL(new_compare(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
14.80/5.61	   POL(new_compare0(x_1, x_2)) = 1 + x_1
14.80/5.61	   POL(new_compare1(x_1, x_2, x_3, x_4)) = 1
14.80/5.61	   POL(new_compare10(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare11(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare12(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare13(x_1, x_2, x_3)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare2(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare3(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare4(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare5(x_1, x_2, x_3)) = 1
14.80/5.61	   POL(new_compare6(x_1, x_2, x_3, x_4, x_5)) = 1
14.80/5.61	   POL(new_compare7(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	   POL(new_compare8(x_1, x_2, x_3)) = 1 + x_1
14.80/5.61	   POL(new_compare9(x_1, x_2, x_3, x_4)) = 1 + x_1
14.80/5.61	   POL(new_merge(x_1, x_2, x_3)) = x_1 + x_2 + x_3
14.80/5.61	   POL(new_merge0(x_1, x_2, x_3, x_4, x_5, x_6)) = 1 + x_1 + x_2 + x_3 + x_4 + x_6
14.80/5.61	   POL(new_primCmpNat0(x_1, x_2)) = x_1 + x_2
14.80/5.61	   POL(ty_@0) = 1
14.80/5.61	   POL(ty_@2) = 1
14.80/5.61	   POL(ty_@3) = 1
14.80/5.61	   POL(ty_Bool) = 1
14.80/5.61	   POL(ty_Char) = 1
14.80/5.61	   POL(ty_Double) = 1
14.80/5.61	   POL(ty_Either) = 1
14.80/5.61	   POL(ty_Float) = 1
14.80/5.61	   POL(ty_Int) = 1
14.80/5.61	   POL(ty_Integer) = 1
14.80/5.61	   POL(ty_Maybe) = 1
14.80/5.61	   POL(ty_Ordering) = 1
14.80/5.61	   POL(ty_Ratio) = 1
14.80/5.61	   POL(ty_[]) = 1
14.80/5.61	
14.80/5.61	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
14.80/5.61	none
14.80/5.61	
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(17)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_merge0(vz88, vz89, vz90, vz91, EQ, ba) -> new_merge(vz90, :(vz88, vz91), ba)
14.80/5.61	   new_merge0(vz88, vz89, vz90, vz91, GT, ba) -> new_merge(:(vz89, vz90), vz91, ba)
14.80/5.61	   new_merge0(vz88, vz89, vz90, vz91, LT, ba) -> new_merge(vz90, :(vz88, vz91), ba)
14.80/5.61	
14.80/5.61	The TRS R consists of the following rules:
14.80/5.61	
14.80/5.61	   new_compare1(vz780, vz7900, bc, bd) -> error([])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Zero) -> GT
14.80/5.61	   new_compare4(vz780, vz7900) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_Either, cb), cc)) -> new_compare9(vz780, vz7900, cb, cc)
14.80/5.61	   new_compare11(vz780, vz7900) -> error([])
14.80/5.61	   new_primCmpNat0(Zero, Zero) -> EQ
14.80/5.61	   new_compare(vz780, vz7900, ty_Float) -> new_compare0(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(app(app(ty_@3, bf), bg), bh)) -> new_compare6(vz780, vz7900, bf, bg, bh)
14.80/5.61	   new_compare(vz780, vz7900, ty_Int) -> new_compare11(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Maybe, cd)) -> new_compare13(vz780, vz7900, cd)
14.80/5.61	   new_compare(vz780, vz7900, ty_@0) -> new_compare12(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_[], be)) -> new_compare5(vz780, vz7900, be)
14.80/5.61	   new_compare(vz780, vz7900, ty_Integer) -> new_compare2(vz780, vz7900)
14.80/5.61	   new_compare13(vz780, vz7900, cd) -> error([])
14.80/5.61	   new_compare2(vz780, vz7900) -> error([])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Succ(vz80000)) -> new_primCmpNat0(vz81000, vz80000)
14.80/5.61	   new_compare3(Char(vz8100), Char(vz8000)) -> new_primCmpNat0(vz8100, vz8000)
14.80/5.61	   new_compare(vz780, vz7900, ty_Ordering) -> new_compare7(vz780, vz7900)
14.80/5.61	   new_compare5(vz780, vz7900, be) -> error([])
14.80/5.61	   new_compare9(vz780, vz7900, cb, cc) -> error([])
14.80/5.61	   new_compare12(vz780, vz7900) -> error([])
14.80/5.61	   new_compare10(vz780, vz7900) -> error([])
14.80/5.61	   new_compare0(vz780, vz7900) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, ty_Double) -> new_compare4(vz780, vz7900)
14.80/5.61	   new_primCmpNat0(Zero, Succ(vz80000)) -> LT
14.80/5.61	   new_compare6(vz780, vz7900, bf, bg, bh) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, ty_Char) -> new_compare3(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, ty_Bool) -> new_compare10(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_@2, bc), bd)) -> new_compare1(vz780, vz7900, bc, bd)
14.80/5.61	   new_compare8(vz780, vz7900, ca) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Ratio, ca)) -> new_compare8(vz780, vz7900, ca)
14.80/5.61	   new_compare7(vz780, vz7900) -> error([])
14.80/5.61	
14.80/5.61	The set Q consists of the following terms:
14.80/5.61	
14.80/5.61	   new_compare10(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(ty_Maybe, x2))
14.80/5.61	   new_compare9(x0, x1, x2, x3)
14.80/5.61	   new_primCmpNat0(Succ(x0), Succ(x1))
14.80/5.61	   new_compare0(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.80/5.61	   new_compare8(x0, x1, x2)
14.80/5.61	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.80/5.61	   new_compare(x0, x1, ty_Integer)
14.80/5.61	   new_compare5(x0, x1, x2)
14.80/5.61	   new_primCmpNat0(Zero, Succ(x0))
14.80/5.61	   new_compare11(x0, x1)
14.80/5.61	   new_compare(x0, x1, ty_Float)
14.80/5.61	   new_compare6(x0, x1, x2, x3, x4)
14.80/5.61	   new_primCmpNat0(Succ(x0), Zero)
14.80/5.61	   new_compare(x0, x1, ty_Bool)
14.80/5.61	   new_compare2(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(ty_[], x2))
14.80/5.61	   new_compare(x0, x1, ty_Int)
14.80/5.61	   new_compare(x0, x1, app(ty_Ratio, x2))
14.80/5.61	   new_compare12(x0, x1)
14.80/5.61	   new_compare7(x0, x1)
14.80/5.61	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.80/5.61	   new_compare3(Char(x0), Char(x1))
14.80/5.61	   new_compare(x0, x1, ty_Ordering)
14.80/5.61	   new_compare(x0, x1, ty_Char)
14.80/5.61	   new_compare1(x0, x1, x2, x3)
14.80/5.61	   new_primCmpNat0(Zero, Zero)
14.80/5.61	   new_compare(x0, x1, ty_@0)
14.80/5.61	   new_compare4(x0, x1)
14.80/5.61	   new_compare13(x0, x1, x2)
14.80/5.61	   new_compare(x0, x1, ty_Double)
14.80/5.61	
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(18) DependencyGraphProof (EQUIVALENT)
14.80/5.61	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(19)
14.80/5.61	TRUE
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(20)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_map(:(vz3110, vz3111)) -> new_map(vz3111)
14.80/5.61	
14.80/5.61	R is empty.
14.80/5.61	Q is empty.
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(21) QDPSizeChangeProof (EQUIVALENT)
14.80/5.61	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. 
14.80/5.61	
14.80/5.61	From the DPs we obtained the following set of size-change graphs:
14.80/5.61	*new_map(:(vz3110, vz3111)) -> new_map(vz3111)
14.80/5.61	The graph contains the following edges 1 > 1
14.80/5.61	
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(22)
14.80/5.61	YES
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(23)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_mergesort'(vz78, :(vz790, []), ba) -> new_mergesort'(new_merge2(vz78, vz790, ba), [], ba)
14.80/5.61	   new_mergesort'(vz78, :(vz790, :(vz7910, vz7911)), ba) -> new_mergesort'(new_merge1(vz78, vz790, vz7910, ba), new_merge_pairs0(vz7911, ba), ba)
14.80/5.61	
14.80/5.61	The TRS R consists of the following rules:
14.80/5.61	
14.80/5.61	   new_compare1(vz780, vz7900, bb, bc) -> error([])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Zero) -> GT
14.80/5.61	   new_compare4(vz780, vz7900) -> error([])
14.80/5.61	   new_compare11(vz780, vz7900) -> error([])
14.80/5.61	   new_primCmpNat0(Zero, Zero) -> EQ
14.80/5.61	   new_compare(vz780, vz7900, ty_Float) -> new_compare0(vz780, vz7900)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Double) -> new_compare4(vz7900, vz79100)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Bool) -> new_compare10(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, ty_Int) -> new_compare11(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Maybe, cc)) -> new_compare13(vz780, vz7900, cc)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_@0) -> new_compare12(vz7900, vz79100)
14.80/5.61	   new_compare14(vz7900, vz79100, app(app(app(ty_@3, be), bf), bg)) -> new_compare6(vz7900, vz79100, be, bf, bg)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_[], bd)) -> new_compare5(vz780, vz7900, bd)
14.80/5.61	   new_compare14(vz7900, vz79100, app(app(ty_Either, ca), cb)) -> new_compare9(vz7900, vz79100, ca, cb)
14.80/5.61	   new_merge_pairs0(:(vz79110, []), ba) -> :(vz79110, [])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Succ(vz80000)) -> new_primCmpNat0(vz81000, vz80000)
14.80/5.61	   new_merge1(vz78, :(vz7900, vz7901), :(vz79100, vz79101), ba) -> new_merge2(vz78, new_merge00(vz79100, vz7900, vz7901, vz79101, new_compare14(vz7900, vz79100, ba), ba), ba)
14.80/5.61	   new_compare3(Char(vz8100), Char(vz8000)) -> new_primCmpNat0(vz8100, vz8000)
14.80/5.61	   new_compare14(vz7900, vz79100, app(ty_Ratio, bh)) -> new_compare8(vz7900, vz79100, bh)
14.80/5.61	   new_compare(vz780, vz7900, ty_Ordering) -> new_compare7(vz780, vz7900)
14.80/5.61	   new_compare5(vz780, vz7900, bd) -> error([])
14.80/5.61	   new_compare12(vz780, vz7900) -> error([])
14.80/5.61	   new_merge2([], :(vz7900, vz7901), ba) -> :(vz7900, vz7901)
14.80/5.61	   new_compare0(vz780, vz7900) -> error([])
14.80/5.61	   new_compare6(vz780, vz7900, be, bf, bg) -> error([])
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Float) -> new_compare0(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_@2, bb), bc)) -> new_compare1(vz780, vz7900, bb, bc)
14.80/5.61	   new_merge_pairs0(:(vz79110, :(vz791110, vz791111)), ba) -> :(new_merge2(vz79110, vz791110, ba), new_merge_pairs0(vz791111, ba))
14.80/5.61	   new_merge00(vz88, vz89, vz90, vz91, LT, cd) -> :(vz89, new_merge2(vz90, :(vz88, vz91), cd))
14.80/5.61	   new_compare7(vz780, vz7900) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_Either, ca), cb)) -> new_compare9(vz780, vz7900, ca, cb)
14.80/5.61	   new_merge2(:(vz780, vz781), :(vz7900, vz7901), ba) -> new_merge00(vz7900, vz780, vz781, vz7901, new_compare(vz780, vz7900, ba), ba)
14.80/5.61	   new_compare14(vz7900, vz79100, app(app(ty_@2, bb), bc)) -> new_compare1(vz7900, vz79100, bb, bc)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Int) -> new_compare11(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, app(app(app(ty_@3, be), bf), bg)) -> new_compare6(vz780, vz7900, be, bf, bg)
14.80/5.61	   new_compare(vz780, vz7900, ty_@0) -> new_compare12(vz780, vz7900)
14.80/5.61	   new_merge2(vz78, [], ba) -> vz78
14.80/5.61	   new_compare(vz780, vz7900, ty_Integer) -> new_compare2(vz780, vz7900)
14.80/5.61	   new_compare13(vz780, vz7900, cc) -> error([])
14.80/5.61	   new_merge_pairs0([], ba) -> []
14.80/5.61	   new_compare14(vz7900, vz79100, app(ty_Maybe, cc)) -> new_compare13(vz7900, vz79100, cc)
14.80/5.61	   new_merge1(vz78, [], :(vz79100, vz79101), ba) -> new_merge2(vz78, :(vz79100, vz79101), ba)
14.80/5.61	   new_compare2(vz780, vz7900) -> error([])
14.80/5.61	   new_merge00(vz88, vz89, vz90, vz91, GT, cd) -> :(vz88, new_merge2(:(vz89, vz90), vz91, cd))
14.80/5.61	   new_compare9(vz780, vz7900, ca, cb) -> error([])
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Char) -> new_compare3(vz7900, vz79100)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Integer) -> new_compare2(vz7900, vz79100)
14.80/5.61	   new_compare10(vz780, vz7900) -> error([])
14.80/5.61	   new_merge00(vz88, vz89, vz90, vz91, EQ, cd) -> :(vz89, new_merge2(vz90, :(vz88, vz91), cd))
14.80/5.61	   new_compare(vz780, vz7900, ty_Double) -> new_compare4(vz780, vz7900)
14.80/5.61	   new_compare14(vz7900, vz79100, app(ty_[], bd)) -> new_compare5(vz7900, vz79100, bd)
14.80/5.61	   new_primCmpNat0(Zero, Succ(vz80000)) -> LT
14.80/5.61	   new_compare(vz780, vz7900, ty_Char) -> new_compare3(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, ty_Bool) -> new_compare10(vz780, vz7900)
14.80/5.61	   new_compare8(vz780, vz7900, bh) -> error([])
14.80/5.61	   new_merge1(vz78, vz790, [], ba) -> new_merge2(vz78, vz790, ba)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Ordering) -> new_compare7(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Ratio, bh)) -> new_compare8(vz780, vz7900, bh)
14.80/5.61	
14.80/5.61	The set Q consists of the following terms:
14.80/5.61	
14.80/5.61	   new_compare14(x0, x1, ty_Int)
14.80/5.61	   new_merge00(x0, x1, x2, x3, EQ, x4)
14.80/5.61	   new_merge1(x0, :(x1, x2), :(x3, x4), x5)
14.80/5.61	   new_compare(x0, x1, ty_Integer)
14.80/5.61	   new_merge00(x0, x1, x2, x3, GT, x4)
14.80/5.61	   new_primCmpNat0(Zero, Succ(x0))
14.80/5.61	   new_merge2([], :(x0, x1), x2)
14.80/5.61	   new_compare(x0, x1, app(ty_[], x2))
14.80/5.61	   new_compare14(x0, x1, app(ty_Ratio, x2))
14.80/5.61	   new_compare(x0, x1, ty_Float)
14.80/5.61	   new_compare13(x0, x1, x2)
14.80/5.61	   new_compare12(x0, x1)
14.80/5.61	   new_merge2(x0, [], x1)
14.80/5.61	   new_compare6(x0, x1, x2, x3, x4)
14.80/5.61	   new_merge_pairs0(:(x0, []), x1)
14.80/5.61	   new_compare14(x0, x1, ty_Integer)
14.80/5.61	   new_compare(x0, x1, app(ty_Maybe, x2))
14.80/5.61	   new_compare(x0, x1, ty_Char)
14.80/5.61	   new_merge00(x0, x1, x2, x3, LT, x4)
14.80/5.61	   new_compare14(x0, x1, app(ty_Maybe, x2))
14.80/5.61	   new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.80/5.61	   new_merge2(:(x0, x1), :(x2, x3), x4)
14.80/5.61	   new_compare9(x0, x1, x2, x3)
14.80/5.61	   new_compare(x0, x1, ty_Double)
14.80/5.61	   new_merge1(x0, x1, [], x2)
14.80/5.61	   new_compare10(x0, x1)
14.80/5.61	   new_compare14(x0, x1, ty_Float)
14.80/5.61	   new_primCmpNat0(Succ(x0), Succ(x1))
14.80/5.61	   new_compare5(x0, x1, x2)
14.80/5.61	   new_compare0(x0, x1)
14.80/5.61	   new_compare14(x0, x1, ty_Bool)
14.80/5.61	   new_compare(x0, x1, app(ty_Ratio, x2))
14.80/5.61	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.80/5.61	   new_compare14(x0, x1, ty_Double)
14.80/5.61	   new_compare1(x0, x1, x2, x3)
14.80/5.61	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.80/5.61	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.80/5.61	   new_merge1(x0, [], :(x1, x2), x3)
14.80/5.61	   new_compare11(x0, x1)
14.80/5.61	   new_compare8(x0, x1, x2)
14.80/5.61	   new_compare14(x0, x1, ty_Char)
14.80/5.61	   new_primCmpNat0(Succ(x0), Zero)
14.80/5.61	   new_compare(x0, x1, ty_Bool)
14.80/5.61	   new_compare2(x0, x1)
14.80/5.61	   new_compare(x0, x1, ty_Int)
14.80/5.61	   new_compare7(x0, x1)
14.80/5.61	   new_merge_pairs0(:(x0, :(x1, x2)), x3)
14.80/5.61	   new_compare14(x0, x1, app(app(ty_Either, x2), x3))
14.80/5.61	   new_compare3(Char(x0), Char(x1))
14.80/5.61	   new_compare14(x0, x1, ty_@0)
14.80/5.61	   new_compare14(x0, x1, ty_Ordering)
14.80/5.61	   new_compare14(x0, x1, app(ty_[], x2))
14.80/5.61	   new_compare(x0, x1, ty_Ordering)
14.80/5.61	   new_primCmpNat0(Zero, Zero)
14.80/5.61	   new_compare14(x0, x1, app(app(ty_@2, x2), x3))
14.80/5.61	   new_compare(x0, x1, ty_@0)
14.80/5.61	   new_merge_pairs0([], x0)
14.80/5.61	   new_compare4(x0, x1)
14.80/5.61	
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(24) DependencyGraphProof (EQUIVALENT)
14.80/5.61	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(25)
14.80/5.61	Obligation:
14.80/5.61	Q DP problem:
14.80/5.61	The TRS P consists of the following rules:
14.80/5.61	
14.80/5.61	   new_mergesort'(vz78, :(vz790, :(vz7910, vz7911)), ba) -> new_mergesort'(new_merge1(vz78, vz790, vz7910, ba), new_merge_pairs0(vz7911, ba), ba)
14.80/5.61	
14.80/5.61	The TRS R consists of the following rules:
14.80/5.61	
14.80/5.61	   new_compare1(vz780, vz7900, bb, bc) -> error([])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Zero) -> GT
14.80/5.61	   new_compare4(vz780, vz7900) -> error([])
14.80/5.61	   new_compare11(vz780, vz7900) -> error([])
14.80/5.61	   new_primCmpNat0(Zero, Zero) -> EQ
14.80/5.61	   new_compare(vz780, vz7900, ty_Float) -> new_compare0(vz780, vz7900)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Double) -> new_compare4(vz7900, vz79100)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Bool) -> new_compare10(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, ty_Int) -> new_compare11(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Maybe, cc)) -> new_compare13(vz780, vz7900, cc)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_@0) -> new_compare12(vz7900, vz79100)
14.80/5.61	   new_compare14(vz7900, vz79100, app(app(app(ty_@3, be), bf), bg)) -> new_compare6(vz7900, vz79100, be, bf, bg)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_[], bd)) -> new_compare5(vz780, vz7900, bd)
14.80/5.61	   new_compare14(vz7900, vz79100, app(app(ty_Either, ca), cb)) -> new_compare9(vz7900, vz79100, ca, cb)
14.80/5.61	   new_merge_pairs0(:(vz79110, []), ba) -> :(vz79110, [])
14.80/5.61	   new_primCmpNat0(Succ(vz81000), Succ(vz80000)) -> new_primCmpNat0(vz81000, vz80000)
14.80/5.61	   new_merge1(vz78, :(vz7900, vz7901), :(vz79100, vz79101), ba) -> new_merge2(vz78, new_merge00(vz79100, vz7900, vz7901, vz79101, new_compare14(vz7900, vz79100, ba), ba), ba)
14.80/5.61	   new_compare3(Char(vz8100), Char(vz8000)) -> new_primCmpNat0(vz8100, vz8000)
14.80/5.61	   new_compare14(vz7900, vz79100, app(ty_Ratio, bh)) -> new_compare8(vz7900, vz79100, bh)
14.80/5.61	   new_compare(vz780, vz7900, ty_Ordering) -> new_compare7(vz780, vz7900)
14.80/5.61	   new_compare5(vz780, vz7900, bd) -> error([])
14.80/5.61	   new_compare12(vz780, vz7900) -> error([])
14.80/5.61	   new_merge2([], :(vz7900, vz7901), ba) -> :(vz7900, vz7901)
14.80/5.61	   new_compare0(vz780, vz7900) -> error([])
14.80/5.61	   new_compare6(vz780, vz7900, be, bf, bg) -> error([])
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Float) -> new_compare0(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_@2, bb), bc)) -> new_compare1(vz780, vz7900, bb, bc)
14.80/5.61	   new_merge_pairs0(:(vz79110, :(vz791110, vz791111)), ba) -> :(new_merge2(vz79110, vz791110, ba), new_merge_pairs0(vz791111, ba))
14.80/5.61	   new_merge00(vz88, vz89, vz90, vz91, LT, cd) -> :(vz89, new_merge2(vz90, :(vz88, vz91), cd))
14.80/5.61	   new_compare7(vz780, vz7900) -> error([])
14.80/5.61	   new_compare(vz780, vz7900, app(app(ty_Either, ca), cb)) -> new_compare9(vz780, vz7900, ca, cb)
14.80/5.61	   new_merge2(:(vz780, vz781), :(vz7900, vz7901), ba) -> new_merge00(vz7900, vz780, vz781, vz7901, new_compare(vz780, vz7900, ba), ba)
14.80/5.61	   new_compare14(vz7900, vz79100, app(app(ty_@2, bb), bc)) -> new_compare1(vz7900, vz79100, bb, bc)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Int) -> new_compare11(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, app(app(app(ty_@3, be), bf), bg)) -> new_compare6(vz780, vz7900, be, bf, bg)
14.80/5.61	   new_compare(vz780, vz7900, ty_@0) -> new_compare12(vz780, vz7900)
14.80/5.61	   new_merge2(vz78, [], ba) -> vz78
14.80/5.61	   new_compare(vz780, vz7900, ty_Integer) -> new_compare2(vz780, vz7900)
14.80/5.61	   new_compare13(vz780, vz7900, cc) -> error([])
14.80/5.61	   new_merge_pairs0([], ba) -> []
14.80/5.61	   new_compare14(vz7900, vz79100, app(ty_Maybe, cc)) -> new_compare13(vz7900, vz79100, cc)
14.80/5.61	   new_merge1(vz78, [], :(vz79100, vz79101), ba) -> new_merge2(vz78, :(vz79100, vz79101), ba)
14.80/5.61	   new_compare2(vz780, vz7900) -> error([])
14.80/5.61	   new_merge00(vz88, vz89, vz90, vz91, GT, cd) -> :(vz88, new_merge2(:(vz89, vz90), vz91, cd))
14.80/5.61	   new_compare9(vz780, vz7900, ca, cb) -> error([])
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Char) -> new_compare3(vz7900, vz79100)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Integer) -> new_compare2(vz7900, vz79100)
14.80/5.61	   new_compare10(vz780, vz7900) -> error([])
14.80/5.61	   new_merge00(vz88, vz89, vz90, vz91, EQ, cd) -> :(vz89, new_merge2(vz90, :(vz88, vz91), cd))
14.80/5.61	   new_compare(vz780, vz7900, ty_Double) -> new_compare4(vz780, vz7900)
14.80/5.61	   new_compare14(vz7900, vz79100, app(ty_[], bd)) -> new_compare5(vz7900, vz79100, bd)
14.80/5.61	   new_primCmpNat0(Zero, Succ(vz80000)) -> LT
14.80/5.61	   new_compare(vz780, vz7900, ty_Char) -> new_compare3(vz780, vz7900)
14.80/5.61	   new_compare(vz780, vz7900, ty_Bool) -> new_compare10(vz780, vz7900)
14.80/5.61	   new_compare8(vz780, vz7900, bh) -> error([])
14.80/5.61	   new_merge1(vz78, vz790, [], ba) -> new_merge2(vz78, vz790, ba)
14.80/5.61	   new_compare14(vz7900, vz79100, ty_Ordering) -> new_compare7(vz7900, vz79100)
14.80/5.61	   new_compare(vz780, vz7900, app(ty_Ratio, bh)) -> new_compare8(vz780, vz7900, bh)
14.80/5.61	
14.80/5.61	The set Q consists of the following terms:
14.80/5.61	
14.80/5.61	   new_compare14(x0, x1, ty_Int)
14.80/5.61	   new_merge00(x0, x1, x2, x3, EQ, x4)
14.80/5.61	   new_merge1(x0, :(x1, x2), :(x3, x4), x5)
14.80/5.61	   new_compare(x0, x1, ty_Integer)
14.80/5.61	   new_merge00(x0, x1, x2, x3, GT, x4)
14.80/5.61	   new_primCmpNat0(Zero, Succ(x0))
14.80/5.61	   new_merge2([], :(x0, x1), x2)
14.80/5.61	   new_compare(x0, x1, app(ty_[], x2))
14.80/5.61	   new_compare14(x0, x1, app(ty_Ratio, x2))
14.80/5.61	   new_compare(x0, x1, ty_Float)
14.80/5.61	   new_compare13(x0, x1, x2)
14.80/5.61	   new_compare12(x0, x1)
14.80/5.61	   new_merge2(x0, [], x1)
14.80/5.61	   new_compare6(x0, x1, x2, x3, x4)
14.80/5.61	   new_merge_pairs0(:(x0, []), x1)
14.80/5.61	   new_compare14(x0, x1, ty_Integer)
14.80/5.61	   new_compare(x0, x1, app(ty_Maybe, x2))
14.80/5.61	   new_compare(x0, x1, ty_Char)
14.80/5.61	   new_merge00(x0, x1, x2, x3, LT, x4)
14.80/5.61	   new_compare14(x0, x1, app(ty_Maybe, x2))
14.80/5.61	   new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.80/5.61	   new_merge2(:(x0, x1), :(x2, x3), x4)
14.80/5.61	   new_compare9(x0, x1, x2, x3)
14.80/5.61	   new_compare(x0, x1, ty_Double)
14.80/5.61	   new_merge1(x0, x1, [], x2)
14.80/5.61	   new_compare10(x0, x1)
14.80/5.61	   new_compare14(x0, x1, ty_Float)
14.80/5.61	   new_primCmpNat0(Succ(x0), Succ(x1))
14.80/5.61	   new_compare5(x0, x1, x2)
14.80/5.61	   new_compare0(x0, x1)
14.80/5.61	   new_compare14(x0, x1, ty_Bool)
14.80/5.61	   new_compare(x0, x1, app(ty_Ratio, x2))
14.80/5.61	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.80/5.61	   new_compare14(x0, x1, ty_Double)
14.80/5.61	   new_compare1(x0, x1, x2, x3)
14.80/5.61	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.80/5.61	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.80/5.61	   new_merge1(x0, [], :(x1, x2), x3)
14.80/5.61	   new_compare11(x0, x1)
14.80/5.61	   new_compare8(x0, x1, x2)
14.80/5.61	   new_compare14(x0, x1, ty_Char)
14.80/5.61	   new_primCmpNat0(Succ(x0), Zero)
14.80/5.61	   new_compare(x0, x1, ty_Bool)
14.80/5.61	   new_compare2(x0, x1)
14.80/5.61	   new_compare(x0, x1, ty_Int)
14.80/5.61	   new_compare7(x0, x1)
14.80/5.61	   new_merge_pairs0(:(x0, :(x1, x2)), x3)
14.80/5.61	   new_compare14(x0, x1, app(app(ty_Either, x2), x3))
14.80/5.61	   new_compare3(Char(x0), Char(x1))
14.80/5.61	   new_compare14(x0, x1, ty_@0)
14.80/5.61	   new_compare14(x0, x1, ty_Ordering)
14.80/5.61	   new_compare14(x0, x1, app(ty_[], x2))
14.80/5.61	   new_compare(x0, x1, ty_Ordering)
14.80/5.61	   new_primCmpNat0(Zero, Zero)
14.80/5.61	   new_compare14(x0, x1, app(app(ty_@2, x2), x3))
14.80/5.61	   new_compare(x0, x1, ty_@0)
14.80/5.61	   new_merge_pairs0([], x0)
14.80/5.61	   new_compare4(x0, x1)
14.80/5.61	
14.80/5.61	We have to consider all minimal (P,Q,R)-chains.
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(26) QDPSizeChangeProof (EQUIVALENT)
14.80/5.61	We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 
14.80/5.61	
14.80/5.61	Order:Polynomial interpretation [POLO]:
14.80/5.61	
14.80/5.61	   POL(:(x_1, x_2)) = 1 + x_2
14.80/5.61	   POL(EQ) = 0
14.80/5.61	   POL(GT) = 1
14.80/5.61	   POL(LT) = 1
14.80/5.61	   POL(Succ(x_1)) = 1 + x_1
14.80/5.61	   POL(Zero) = 0
14.80/5.61	   POL([]) = 0
14.80/5.61	   POL(new_merge2(x_1, x_2, x_3)) = x_1
14.80/5.61	   POL(new_merge_pairs0(x_1, x_2)) = x_1
14.80/5.61	   POL(new_primCmpNat0(x_1, x_2)) = 1 + x_1 + x_2
14.80/5.61	
14.80/5.61	
14.80/5.61	
14.80/5.61	
14.80/5.61	From the DPs we obtained the following set of size-change graphs:
14.80/5.61	*new_mergesort'(vz78, :(vz790, :(vz7910, vz7911)), ba) -> new_mergesort'(new_merge1(vz78, vz790, vz7910, ba), new_merge_pairs0(vz7911, ba), ba) (allowed arguments on rhs = {2, 3})
14.80/5.61	The graph contains the following edges 2 > 2, 3 >= 3
14.80/5.61	
14.80/5.61	
14.80/5.61	
14.80/5.61	We oriented the following set of usable rules [AAECC05,FROCOS05].
14.80/5.61	
14.80/5.61	   new_merge_pairs0([], ba) -> []
14.80/5.61	   new_merge_pairs0(:(vz79110, []), ba) -> :(vz79110, [])
14.80/5.61	   new_merge_pairs0(:(vz79110, :(vz791110, vz791111)), ba) -> :(new_merge2(vz79110, vz791110, ba), new_merge_pairs0(vz791111, ba))
14.80/5.61	
14.80/5.61	----------------------------------------
14.80/5.61	
14.80/5.61	(27)
14.80/5.61	YES
14.80/5.64	EOF