11.56/4.67	YES
14.38/5.45	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
14.38/5.45	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.38/5.45	
14.38/5.45	
14.38/5.45	H-Termination with start terms of the given HASKELL could be proven:
14.38/5.45	
14.38/5.45	(0) HASKELL
14.38/5.45	(1) LR [EQUIVALENT, 0 ms]
14.38/5.45	(2) HASKELL
14.38/5.45	(3) CR [EQUIVALENT, 0 ms]
14.38/5.45	(4) HASKELL
14.38/5.45	(5) IFR [EQUIVALENT, 0 ms]
14.38/5.45	(6) HASKELL
14.38/5.45	(7) BR [EQUIVALENT, 0 ms]
14.38/5.45	(8) HASKELL
14.38/5.45	(9) COR [EQUIVALENT, 14 ms]
14.38/5.45	(10) HASKELL
14.38/5.45	(11) NumRed [SOUND, 0 ms]
14.38/5.45	(12) HASKELL
14.38/5.45	(13) Narrow [SOUND, 0 ms]
14.38/5.45	(14) AND
14.38/5.45	    (15) QDP
14.38/5.45	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.38/5.45	        (17) YES
14.38/5.45	    (18) QDP
14.38/5.45	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.38/5.45	        (20) YES
14.38/5.45	    (21) QDP
14.38/5.45	        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.38/5.45	        (23) YES
14.38/5.45	
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(0)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (\vv1 ->case vv1 of { 
14.38/5.45	(x,i)->  if p x then i : [] else []; 
14.38/5.45	_-> []; 
14.38/5.45	 } ) (zip xs (enumFrom 0));
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(1) LR (EQUIVALENT)
14.38/5.45	Lambda Reductions:
14.38/5.45	The following Lambda expression
14.38/5.45	"\ab->(a,b)"
14.38/5.45	is transformed to
14.38/5.45	"zip0 a b = (a,b);
14.38/5.45	"
14.38/5.45	The following Lambda expression
14.38/5.45	"\vv1->case vv1 of {
14.38/5.45	(x,i)  -> if p x then i : [] else [];
14.38/5.45	_  -> []}
14.38/5.45	"
14.38/5.45	is transformed to
14.38/5.45	"findIndices0 p vv1 = case vv1 of {
14.38/5.45	(x,i)  -> if p x then i : [] else [];
14.38/5.45	_  -> []}
14.38/5.45	;
14.38/5.45	"
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(2)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));
14.38/5.45	
14.38/5.45	findIndices0 p vv1 = case vv1 of { 
14.38/5.45	(x,i)->  if p x then i : [] else []; 
14.38/5.45	_-> []; 
14.38/5.45	 } ;
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(3) CR (EQUIVALENT)
14.38/5.45	Case Reductions:
14.38/5.45	The following Case expression
14.38/5.45	"case vv1 of {
14.38/5.45	(x,i)  -> if p x then i : [] else [];
14.38/5.45	_  -> []}
14.38/5.45	"
14.38/5.45	is transformed to
14.38/5.45	"findIndices00 p (x,i) = if p x then i : [] else [];
14.38/5.45	findIndices00 p _ = [];
14.38/5.45	"
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(4)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));
14.38/5.45	
14.38/5.45	findIndices0 p vv1 = findIndices00 p vv1;
14.38/5.45	
14.38/5.45	findIndices00 p (x,i) =  if p x then i : [] else [];
14.38/5.45	findIndices00 p _ = [];
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(5) IFR (EQUIVALENT)
14.38/5.45	If Reductions:
14.38/5.45	The following If expression
14.38/5.45	"if p x then i : [] else []"
14.38/5.45	is transformed to
14.38/5.45	"findIndices000 i True = i : [];
14.38/5.45	findIndices000 i False = [];
14.38/5.45	"
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(6)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));
14.38/5.45	
14.38/5.45	findIndices0 p vv1 = findIndices00 p vv1;
14.38/5.45	
14.38/5.45	findIndices00 p (x,i) = findIndices000 i (p x);
14.38/5.45	findIndices00 p _ = [];
14.38/5.45	
14.38/5.45	findIndices000 i True = i : [];
14.38/5.45	findIndices000 i False = [];
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(7) BR (EQUIVALENT)
14.38/5.45	Replaced joker patterns by fresh variables and removed binding patterns.
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(8)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));
14.38/5.45	
14.38/5.45	findIndices0 p vv1 = findIndices00 p vv1;
14.38/5.45	
14.38/5.45	findIndices00 p (x,i) = findIndices000 i (p x);
14.38/5.45	findIndices00 p wv = [];
14.38/5.45	
14.38/5.45	findIndices000 i True = i : [];
14.38/5.45	findIndices000 i False = [];
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(9) COR (EQUIVALENT)
14.38/5.45	Cond Reductions:
14.38/5.45	The following Function with conditions
14.38/5.45	"undefined |Falseundefined;
14.38/5.45	"
14.38/5.45	is transformed to
14.38/5.45	"undefined  = undefined1;
14.38/5.45	"
14.38/5.45	"undefined0 True = undefined;
14.38/5.45	"
14.38/5.45	"undefined1  = undefined0 False;
14.38/5.45	"
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(10)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));
14.38/5.45	
14.38/5.45	findIndices0 p vv1 = findIndices00 p vv1;
14.38/5.45	
14.38/5.45	findIndices00 p (x,i) = findIndices000 i (p x);
14.38/5.45	findIndices00 p wv = [];
14.38/5.45	
14.38/5.45	findIndices000 i True = i : [];
14.38/5.45	findIndices000 i False = [];
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(11) NumRed (SOUND)
14.38/5.45	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(12)
14.38/5.45	Obligation:
14.38/5.45	mainModule Main 
14.38/5.45	module Maybe where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	module List where {
14.38/5.45	import qualified Main;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	elemIndices :: Eq a => a  ->  [a]  ->  [Int];
14.38/5.45	elemIndices x = findIndices (== x);
14.38/5.45	
14.38/5.45	findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
14.38/5.45	findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom (Pos Zero)));
14.38/5.45	
14.38/5.45	findIndices0 p vv1 = findIndices00 p vv1;
14.38/5.45	
14.38/5.45	findIndices00 p (x,i) = findIndices000 i (p x);
14.38/5.45	findIndices00 p wv = [];
14.38/5.45	
14.38/5.45	findIndices000 i True = i : [];
14.38/5.45	findIndices000 i False = [];
14.38/5.45	
14.38/5.45	}
14.38/5.45	module Main where {
14.38/5.45	import qualified List;
14.38/5.45	import qualified Maybe;
14.38/5.45	import qualified Prelude;
14.38/5.45	}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(13) Narrow (SOUND)
14.38/5.45	Haskell To QDPs
14.38/5.45	
14.38/5.45	digraph dp_graph {
14.38/5.45	node [outthreshold=100, inthreshold=100];1[label="List.elemIndices",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
14.38/5.45	3[label="List.elemIndices ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
14.38/5.45	4[label="List.elemIndices ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
14.38/5.45	5[label="List.findIndices (ww3 ==) ww4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
14.38/5.45	6[label="concatMap (List.findIndices0 (ww3 ==)) (zip ww4 (enumFrom (Pos Zero)))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
14.38/5.45	7[label="concat . map (List.findIndices0 (ww3 ==))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
14.38/5.45	8[label="concat (map (List.findIndices0 (ww3 ==)) (zip ww4 (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
14.38/5.45	9[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zip ww4 (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
14.38/5.45	10[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww4 (enumFrom (Pos Zero))))",fontsize=16,color="burlywood",shape="box"];322[label="ww4/ww40 : ww41",fontsize=10,color="white",style="solid",shape="box"];10 -> 322[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	322 -> 11[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	323[label="ww4/[]",fontsize=10,color="white",style="solid",shape="box"];10 -> 323[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	323 -> 12[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	11[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 (ww40 : ww41) (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
14.38/5.45	12[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 [] (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
14.38/5.45	13[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 (ww40 : ww41) (numericEnumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14.38/5.45	14[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) [])",fontsize=16,color="black",shape="triangle"];14 -> 16[label="",style="solid", color="black", weight=3];
14.38/5.45	15[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 (ww40 : ww41) (Pos Zero : (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
14.38/5.45	16[label="foldr (++) [] []",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
14.38/5.45	17[label="foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zip0 ww40 (Pos Zero) : zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
14.38/5.45	18[label="[]",fontsize=16,color="green",shape="box"];19[label="foldr (++) [] (List.findIndices0 (ww3 ==) (zip0 ww40 (Pos Zero)) : map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
14.38/5.45	20[label="(++) List.findIndices0 (ww3 ==) (zip0 ww40 (Pos Zero)) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
14.38/5.45	21[label="(++) List.findIndices00 (ww3 ==) (zip0 ww40 (Pos Zero)) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
14.38/5.45	22[label="(++) List.findIndices00 (ww3 ==) (ww40,Pos Zero) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
14.38/5.45	23[label="(++) List.findIndices000 (Pos Zero) (ww3 == ww40) foldr (++) [] (map (List.findIndices0 (ww3 ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];324[label="ww3/LT",fontsize=10,color="white",style="solid",shape="box"];23 -> 324[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	324 -> 24[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	325[label="ww3/EQ",fontsize=10,color="white",style="solid",shape="box"];23 -> 325[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	325 -> 25[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	326[label="ww3/GT",fontsize=10,color="white",style="solid",shape="box"];23 -> 326[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	326 -> 26[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	24[label="(++) List.findIndices000 (Pos Zero) (LT == ww40) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];327[label="ww40/LT",fontsize=10,color="white",style="solid",shape="box"];24 -> 327[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	327 -> 27[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	328[label="ww40/EQ",fontsize=10,color="white",style="solid",shape="box"];24 -> 328[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	328 -> 28[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	329[label="ww40/GT",fontsize=10,color="white",style="solid",shape="box"];24 -> 329[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	329 -> 29[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	25[label="(++) List.findIndices000 (Pos Zero) (EQ == ww40) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];330[label="ww40/LT",fontsize=10,color="white",style="solid",shape="box"];25 -> 330[label="",style="solid", color="burlywood", weight=9];
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14.38/5.45	332 -> 32[label="",style="solid", color="burlywood", weight=3];
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14.38/5.45	28[label="(++) List.findIndices000 (Pos Zero) (LT == EQ) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
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14.38/5.45	30[label="(++) List.findIndices000 (Pos Zero) (EQ == LT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
14.38/5.45	31[label="(++) List.findIndices000 (Pos Zero) (EQ == EQ) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
14.38/5.45	32[label="(++) List.findIndices000 (Pos Zero) (EQ == GT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
14.38/5.45	33[label="(++) List.findIndices000 (Pos Zero) (GT == LT) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
14.38/5.45	34[label="(++) List.findIndices000 (Pos Zero) (GT == EQ) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
14.38/5.45	35[label="(++) List.findIndices000 (Pos Zero) (GT == GT) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
14.38/5.45	36[label="(++) List.findIndices000 (Pos Zero) True foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
14.38/5.45	37[label="(++) List.findIndices000 (Pos Zero) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];37 -> 46[label="",style="solid", color="black", weight=3];
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14.38/5.45	45[label="(++) (Pos Zero : []) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3];
14.38/5.45	46[label="(++) [] foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];46 -> 52[label="",style="solid", color="black", weight=3];
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14.38/5.45	48[label="(++) (Pos Zero : []) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];48 -> 54[label="",style="solid", color="black", weight=3];
14.38/5.45	49[label="(++) [] foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];49 -> 55[label="",style="solid", color="black", weight=3];
14.38/5.45	50[label="(++) (Pos Zero : []) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];50 -> 56[label="",style="solid", color="black", weight=3];
14.38/5.45	51[label="Pos Zero : [] ++ foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];51 -> 57[label="",style="dashed", color="green", weight=3];
14.38/5.45	52[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];336[label="ww41/ww410 : ww411",fontsize=10,color="white",style="solid",shape="box"];52 -> 336[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	336 -> 58[label="",style="solid", color="burlywood", weight=3];
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14.38/5.45	337 -> 59[label="",style="solid", color="burlywood", weight=3];
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14.38/5.45	338 -> 60[label="",style="solid", color="burlywood", weight=3];
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14.38/5.45	55 -> 259[label="",style="dashed", color="red", weight=0];
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14.38/5.45	55 -> 261[label="",style="dashed", color="magenta", weight=3];
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14.38/5.45	59[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 [] (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];59 -> 67[label="",style="solid", color="black", weight=3];
14.38/5.45	60[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (ww410 : ww411) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];60 -> 68[label="",style="solid", color="black", weight=3];
14.38/5.45	61[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 [] (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];61 -> 69[label="",style="solid", color="black", weight=3];
14.38/5.45	62 -> 47[label="",style="dashed", color="red", weight=0];
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14.38/5.45	263[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (ww41110 : ww41111) (numericEnumFrom $! Pos ww11 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];263 -> 275[label="",style="solid", color="black", weight=3];
14.38/5.45	264[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 [] (numericEnumFrom $! Pos ww11 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];264 -> 276[label="",style="solid", color="black", weight=3];
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14.38/5.45	293 -> 294[label="",style="dashed", color="red", weight=0];
14.38/5.45	293[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (ww41110 : ww41111) (enforceWHNF (WHNF (Pos (primPlusNat ww11 (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat ww11 (Succ Zero)))))))",fontsize=16,color="magenta"];293 -> 295[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	293 -> 296[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	192[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 (ww4110 : ww4111) (numericEnumFrom (Pos (primPlusNat ww5 (Succ Zero))))))",fontsize=16,color="black",shape="box"];192 -> 195[label="",style="solid", color="black", weight=3];
14.38/5.45	194[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (ww4110 : ww4111) (numericEnumFrom (Pos (primPlusNat ww7 (Succ Zero))))))",fontsize=16,color="black",shape="box"];194 -> 197[label="",style="solid", color="black", weight=3];
14.38/5.45	295 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	295[label="primPlusNat ww11 (Succ Zero)",fontsize=16,color="magenta"];295 -> 297[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	296 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	296[label="primPlusNat ww11 (Succ Zero)",fontsize=16,color="magenta"];296 -> 298[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	294[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (ww41110 : ww41111) (enforceWHNF (WHNF (Pos ww13)) (numericEnumFrom (Pos ww12)))))",fontsize=16,color="black",shape="triangle"];294 -> 299[label="",style="solid", color="black", weight=3];
14.38/5.45	195[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 (ww4110 : ww4111) (Pos (primPlusNat ww5 (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];195 -> 198[label="",style="solid", color="black", weight=3];
14.38/5.45	197[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (ww4110 : ww4111) (Pos (primPlusNat ww7 (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];197 -> 200[label="",style="solid", color="black", weight=3];
14.38/5.45	297[label="ww11",fontsize=16,color="green",shape="box"];245[label="primPlusNat ww5 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];342[label="ww5/Succ ww50",fontsize=10,color="white",style="solid",shape="box"];245 -> 342[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	342 -> 255[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	343[label="ww5/Zero",fontsize=10,color="white",style="solid",shape="box"];245 -> 343[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	343 -> 256[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	298[label="ww11",fontsize=16,color="green",shape="box"];299[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (ww41110 : ww41111) (numericEnumFrom (Pos ww12))))",fontsize=16,color="black",shape="box"];299 -> 300[label="",style="solid", color="black", weight=3];
14.38/5.45	198[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zip0 ww4110 (Pos (primPlusNat ww5 (Succ Zero))) : zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];198 -> 201[label="",style="solid", color="black", weight=3];
14.38/5.45	200[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero))) : zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];200 -> 203[label="",style="solid", color="black", weight=3];
14.38/5.45	255[label="primPlusNat (Succ ww50) (Succ Zero)",fontsize=16,color="black",shape="box"];255 -> 268[label="",style="solid", color="black", weight=3];
14.38/5.45	256[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];256 -> 269[label="",style="solid", color="black", weight=3];
14.38/5.45	300[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (ww41110 : ww41111) (Pos ww12 : (numericEnumFrom $! Pos ww12 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];300 -> 301[label="",style="solid", color="black", weight=3];
14.38/5.45	201[label="foldr (++) [] (List.findIndices0 (LT ==) (zip0 ww4110 (Pos (primPlusNat ww5 (Succ Zero)))) : map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];201 -> 204[label="",style="solid", color="black", weight=3];
14.38/5.45	203[label="foldr (++) [] (List.findIndices0 (EQ ==) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero)))) : map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];203 -> 206[label="",style="solid", color="black", weight=3];
14.38/5.45	268[label="Succ (Succ (primPlusNat ww50 Zero))",fontsize=16,color="green",shape="box"];268 -> 282[label="",style="dashed", color="green", weight=3];
14.38/5.45	269[label="Succ Zero",fontsize=16,color="green",shape="box"];301[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zip0 ww41110 (Pos ww12) : zipWith zip0 ww41111 (numericEnumFrom $! Pos ww12 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];301 -> 302[label="",style="solid", color="black", weight=3];
14.38/5.45	204[label="(++) List.findIndices0 (LT ==) (zip0 ww4110 (Pos (primPlusNat ww5 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];204 -> 207[label="",style="solid", color="black", weight=3];
14.38/5.45	206[label="(++) List.findIndices0 (EQ ==) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];206 -> 209[label="",style="solid", color="black", weight=3];
14.38/5.45	282[label="primPlusNat ww50 Zero",fontsize=16,color="burlywood",shape="box"];344[label="ww50/Succ ww500",fontsize=10,color="white",style="solid",shape="box"];282 -> 344[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	344 -> 287[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	345[label="ww50/Zero",fontsize=10,color="white",style="solid",shape="box"];282 -> 345[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	345 -> 288[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	302[label="foldr (++) [] (List.findIndices0 (GT ==) (zip0 ww41110 (Pos ww12)) : map (List.findIndices0 (GT ==)) (zipWith zip0 ww41111 (numericEnumFrom $! Pos ww12 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];302 -> 303[label="",style="solid", color="black", weight=3];
14.38/5.45	207[label="(++) List.findIndices00 (LT ==) (zip0 ww4110 (Pos (primPlusNat ww5 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];207 -> 210[label="",style="solid", color="black", weight=3];
14.38/5.45	209[label="(++) List.findIndices00 (EQ ==) (zip0 ww4110 (Pos (primPlusNat ww7 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];209 -> 212[label="",style="solid", color="black", weight=3];
14.38/5.45	287[label="primPlusNat (Succ ww500) Zero",fontsize=16,color="black",shape="box"];287 -> 290[label="",style="solid", color="black", weight=3];
14.38/5.45	288[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];288 -> 291[label="",style="solid", color="black", weight=3];
14.38/5.45	303 -> 304[label="",style="dashed", color="red", weight=0];
14.38/5.45	303[label="(++) List.findIndices0 (GT ==) (zip0 ww41110 (Pos ww12)) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41111 (numericEnumFrom $! Pos ww12 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];303 -> 305[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	210[label="(++) List.findIndices00 (LT ==) (ww4110,Pos (primPlusNat ww5 (Succ Zero))) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];210 -> 213[label="",style="solid", color="black", weight=3];
14.38/5.45	212[label="(++) List.findIndices00 (EQ ==) (ww4110,Pos (primPlusNat ww7 (Succ Zero))) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];212 -> 215[label="",style="solid", color="black", weight=3];
14.38/5.45	290[label="Succ ww500",fontsize=16,color="green",shape="box"];291[label="Zero",fontsize=16,color="green",shape="box"];305 -> 259[label="",style="dashed", color="red", weight=0];
14.38/5.45	305[label="foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 ww41111 (numericEnumFrom $! Pos ww12 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];305 -> 306[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	305 -> 307[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	304[label="(++) List.findIndices0 (GT ==) (zip0 ww41110 (Pos ww12)) ww14",fontsize=16,color="black",shape="triangle"];304 -> 308[label="",style="solid", color="black", weight=3];
14.38/5.45	213[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) (LT == ww4110) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];346[label="ww4110/LT",fontsize=10,color="white",style="solid",shape="box"];213 -> 346[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	346 -> 216[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	347[label="ww4110/EQ",fontsize=10,color="white",style="solid",shape="box"];213 -> 347[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	347 -> 217[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	348[label="ww4110/GT",fontsize=10,color="white",style="solid",shape="box"];213 -> 348[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	348 -> 218[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	215[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (EQ == ww4110) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];349[label="ww4110/LT",fontsize=10,color="white",style="solid",shape="box"];215 -> 349[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	349 -> 220[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	350[label="ww4110/EQ",fontsize=10,color="white",style="solid",shape="box"];215 -> 350[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	350 -> 221[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	351[label="ww4110/GT",fontsize=10,color="white",style="solid",shape="box"];215 -> 351[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	351 -> 222[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	306[label="ww41111",fontsize=16,color="green",shape="box"];307[label="ww12",fontsize=16,color="green",shape="box"];308[label="(++) List.findIndices00 (GT ==) (zip0 ww41110 (Pos ww12)) ww14",fontsize=16,color="black",shape="box"];308 -> 309[label="",style="solid", color="black", weight=3];
14.38/5.45	216[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) (LT == LT) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];216 -> 223[label="",style="solid", color="black", weight=3];
14.38/5.45	217[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) (LT == EQ) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];217 -> 224[label="",style="solid", color="black", weight=3];
14.38/5.45	218[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) (LT == GT) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];218 -> 225[label="",style="solid", color="black", weight=3];
14.38/5.45	220[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (EQ == LT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];220 -> 229[label="",style="solid", color="black", weight=3];
14.38/5.45	221[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (EQ == EQ) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];221 -> 230[label="",style="solid", color="black", weight=3];
14.38/5.45	222[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) (EQ == GT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];222 -> 231[label="",style="solid", color="black", weight=3];
14.38/5.45	309[label="(++) List.findIndices00 (GT ==) (ww41110,Pos ww12) ww14",fontsize=16,color="black",shape="box"];309 -> 310[label="",style="solid", color="black", weight=3];
14.38/5.45	223[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) True foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];223 -> 232[label="",style="solid", color="black", weight=3];
14.38/5.45	224[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];224 -> 233[label="",style="solid", color="black", weight=3];
14.38/5.45	225 -> 224[label="",style="dashed", color="red", weight=0];
14.38/5.45	225[label="(++) List.findIndices000 (Pos (primPlusNat ww5 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];229[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];229 -> 237[label="",style="solid", color="black", weight=3];
14.38/5.45	230[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) True foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];230 -> 238[label="",style="solid", color="black", weight=3];
14.38/5.45	231 -> 229[label="",style="dashed", color="red", weight=0];
14.38/5.45	231[label="(++) List.findIndices000 (Pos (primPlusNat ww7 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];310[label="(++) List.findIndices000 (Pos ww12) (GT == ww41110) ww14",fontsize=16,color="burlywood",shape="box"];352[label="ww41110/LT",fontsize=10,color="white",style="solid",shape="box"];310 -> 352[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	352 -> 311[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	353[label="ww41110/EQ",fontsize=10,color="white",style="solid",shape="box"];310 -> 353[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	353 -> 312[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	354[label="ww41110/GT",fontsize=10,color="white",style="solid",shape="box"];310 -> 354[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	354 -> 313[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	232[label="(++) (Pos (primPlusNat ww5 (Succ Zero)) : []) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];232 -> 239[label="",style="solid", color="black", weight=3];
14.38/5.45	233[label="(++) [] foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];233 -> 240[label="",style="solid", color="black", weight=3];
14.38/5.45	237[label="(++) [] foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="triangle"];237 -> 243[label="",style="solid", color="black", weight=3];
14.38/5.45	238[label="(++) (Pos (primPlusNat ww7 (Succ Zero)) : []) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];238 -> 244[label="",style="solid", color="black", weight=3];
14.38/5.45	311[label="(++) List.findIndices000 (Pos ww12) (GT == LT) ww14",fontsize=16,color="black",shape="box"];311 -> 314[label="",style="solid", color="black", weight=3];
14.38/5.45	312[label="(++) List.findIndices000 (Pos ww12) (GT == EQ) ww14",fontsize=16,color="black",shape="box"];312 -> 315[label="",style="solid", color="black", weight=3];
14.38/5.45	313[label="(++) List.findIndices000 (Pos ww12) (GT == GT) ww14",fontsize=16,color="black",shape="box"];313 -> 316[label="",style="solid", color="black", weight=3];
14.38/5.45	239[label="Pos (primPlusNat ww5 (Succ Zero)) : [] ++ foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];239 -> 245[label="",style="dashed", color="green", weight=3];
14.38/5.45	239 -> 246[label="",style="dashed", color="green", weight=3];
14.38/5.45	240[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];355[label="ww4111/ww41110 : ww41111",fontsize=10,color="white",style="solid",shape="box"];240 -> 355[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	355 -> 247[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	356[label="ww4111/[]",fontsize=10,color="white",style="solid",shape="box"];240 -> 356[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	356 -> 248[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	243[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="burlywood",shape="box"];357[label="ww4111/ww41110 : ww41111",fontsize=10,color="white",style="solid",shape="box"];243 -> 357[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	357 -> 251[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	358[label="ww4111/[]",fontsize=10,color="white",style="solid",shape="box"];243 -> 358[label="",style="solid", color="burlywood", weight=9];
14.38/5.45	358 -> 252[label="",style="solid", color="burlywood", weight=3];
14.38/5.45	244[label="Pos (primPlusNat ww7 (Succ Zero)) : [] ++ foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];244 -> 253[label="",style="dashed", color="green", weight=3];
14.38/5.45	244 -> 254[label="",style="dashed", color="green", weight=3];
14.38/5.45	314[label="(++) List.findIndices000 (Pos ww12) False ww14",fontsize=16,color="black",shape="triangle"];314 -> 317[label="",style="solid", color="black", weight=3];
14.38/5.45	315 -> 314[label="",style="dashed", color="red", weight=0];
14.38/5.45	315[label="(++) List.findIndices000 (Pos ww12) False ww14",fontsize=16,color="magenta"];316[label="(++) List.findIndices000 (Pos ww12) True ww14",fontsize=16,color="black",shape="box"];316 -> 318[label="",style="solid", color="black", weight=3];
14.38/5.45	246 -> 233[label="",style="dashed", color="red", weight=0];
14.38/5.45	246[label="[] ++ foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];247[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 (ww41110 : ww41111) (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];247 -> 257[label="",style="solid", color="black", weight=3];
14.38/5.45	248[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 [] (numericEnumFrom $! Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];248 -> 258[label="",style="solid", color="black", weight=3];
14.38/5.45	251[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (ww41110 : ww41111) (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];251 -> 265[label="",style="solid", color="black", weight=3];
14.38/5.45	252[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 [] (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];252 -> 266[label="",style="solid", color="black", weight=3];
14.38/5.45	253 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	253[label="primPlusNat ww7 (Succ Zero)",fontsize=16,color="magenta"];253 -> 267[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	254 -> 237[label="",style="dashed", color="red", weight=0];
14.38/5.45	254[label="[] ++ foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 ww4111 (numericEnumFrom $! Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];317[label="(++) [] ww14",fontsize=16,color="black",shape="triangle"];317 -> 319[label="",style="solid", color="black", weight=3];
14.38/5.45	318[label="(++) (Pos ww12 : []) ww14",fontsize=16,color="black",shape="box"];318 -> 320[label="",style="solid", color="black", weight=3];
14.38/5.45	257 -> 160[label="",style="dashed", color="red", weight=0];
14.38/5.45	257[label="foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 (ww41110 : ww41111) (Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (primPlusNat ww5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="magenta"];257 -> 270[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	257 -> 271[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	257 -> 272[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	257 -> 273[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	258 -> 14[label="",style="dashed", color="red", weight=0];
14.38/5.45	258[label="foldr (++) [] (map (List.findIndices0 (LT ==)) [])",fontsize=16,color="magenta"];258 -> 274[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	265 -> 168[label="",style="dashed", color="red", weight=0];
14.38/5.45	265[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (ww41110 : ww41111) (Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (primPlusNat ww7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="magenta"];265 -> 277[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	265 -> 278[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	265 -> 279[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	265 -> 280[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	266 -> 14[label="",style="dashed", color="red", weight=0];
14.38/5.45	266[label="foldr (++) [] (map (List.findIndices0 (EQ ==)) [])",fontsize=16,color="magenta"];266 -> 281[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	267[label="ww7",fontsize=16,color="green",shape="box"];319[label="ww14",fontsize=16,color="green",shape="box"];320[label="Pos ww12 : [] ++ ww14",fontsize=16,color="green",shape="box"];320 -> 321[label="",style="dashed", color="green", weight=3];
14.38/5.45	270 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	270[label="primPlusNat ww5 (Succ Zero)",fontsize=16,color="magenta"];271[label="ww41110",fontsize=16,color="green",shape="box"];272[label="ww41111",fontsize=16,color="green",shape="box"];273 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	273[label="primPlusNat ww5 (Succ Zero)",fontsize=16,color="magenta"];274[label="LT",fontsize=16,color="green",shape="box"];277[label="ww41110",fontsize=16,color="green",shape="box"];278[label="ww41111",fontsize=16,color="green",shape="box"];279 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	279[label="primPlusNat ww7 (Succ Zero)",fontsize=16,color="magenta"];279 -> 285[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	280 -> 245[label="",style="dashed", color="red", weight=0];
14.38/5.45	280[label="primPlusNat ww7 (Succ Zero)",fontsize=16,color="magenta"];280 -> 286[label="",style="dashed", color="magenta", weight=3];
14.38/5.45	281[label="EQ",fontsize=16,color="green",shape="box"];321 -> 317[label="",style="dashed", color="red", weight=0];
14.38/5.45	321[label="[] ++ ww14",fontsize=16,color="magenta"];285[label="ww7",fontsize=16,color="green",shape="box"];286[label="ww7",fontsize=16,color="green",shape="box"];}
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(14)
14.38/5.45	Complex Obligation (AND)
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(15)
14.38/5.45	Obligation:
14.38/5.45	Q DP problem:
14.38/5.45	The TRS P consists of the following rules:
14.38/5.45	
14.38/5.45	   new_foldr1(EQ, ww4111, ww7, ww8) -> new_psPs(ww4111, ww7)
14.38/5.45	   new_foldr1(GT, ww4111, ww7, ww8) -> new_psPs0(ww7, ww4111)
14.38/5.45	   new_psPs(:(ww41110, ww41111), ww7) -> new_foldr1(ww41110, ww41111, new_primPlusNat(ww7), new_primPlusNat(ww7))
14.38/5.45	   new_foldr1(LT, :(ww41110, ww41111), ww7, ww8) -> new_foldr1(ww41110, ww41111, new_primPlusNat(ww7), new_primPlusNat(ww7))
14.38/5.45	   new_psPs0(ww7, :(ww41110, ww41111)) -> new_foldr1(ww41110, ww41111, new_primPlusNat(ww7), new_primPlusNat(ww7))
14.38/5.45	
14.38/5.45	The TRS R consists of the following rules:
14.38/5.45	
14.38/5.45	   new_primPlusNat(Succ(ww50)) -> Succ(Succ(new_primPlusNat0(ww50)))
14.38/5.45	   new_primPlusNat(Zero) -> Succ(Zero)
14.38/5.45	   new_primPlusNat0(Succ(ww500)) -> Succ(ww500)
14.38/5.45	   new_primPlusNat0(Zero) -> Zero
14.38/5.45	
14.38/5.45	The set Q consists of the following terms:
14.38/5.45	
14.38/5.45	   new_primPlusNat0(Succ(x0))
14.38/5.45	   new_primPlusNat0(Zero)
14.38/5.45	   new_primPlusNat(Succ(x0))
14.38/5.45	   new_primPlusNat(Zero)
14.38/5.45	
14.38/5.45	We have to consider all minimal (P,Q,R)-chains.
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(16) QDPSizeChangeProof (EQUIVALENT)
14.38/5.45	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. 
14.38/5.45	
14.38/5.45	From the DPs we obtained the following set of size-change graphs:
14.38/5.45	*new_psPs(:(ww41110, ww41111), ww7) -> new_foldr1(ww41110, ww41111, new_primPlusNat(ww7), new_primPlusNat(ww7))
14.38/5.45	The graph contains the following edges 1 > 1, 1 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_psPs0(ww7, :(ww41110, ww41111)) -> new_foldr1(ww41110, ww41111, new_primPlusNat(ww7), new_primPlusNat(ww7))
14.38/5.45	The graph contains the following edges 2 > 1, 2 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_foldr1(LT, :(ww41110, ww41111), ww7, ww8) -> new_foldr1(ww41110, ww41111, new_primPlusNat(ww7), new_primPlusNat(ww7))
14.38/5.45	The graph contains the following edges 2 > 1, 2 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_foldr1(EQ, ww4111, ww7, ww8) -> new_psPs(ww4111, ww7)
14.38/5.45	The graph contains the following edges 2 >= 1, 3 >= 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_foldr1(GT, ww4111, ww7, ww8) -> new_psPs0(ww7, ww4111)
14.38/5.45	The graph contains the following edges 3 >= 1, 2 >= 2
14.38/5.45	
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(17)
14.38/5.45	YES
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(18)
14.38/5.45	Obligation:
14.38/5.45	Q DP problem:
14.38/5.45	The TRS P consists of the following rules:
14.38/5.45	
14.38/5.45	   new_foldr(ww41110, ww41111, ww13, ww12) -> new_foldr0(ww41111, ww12)
14.38/5.45	   new_foldr0(:(ww41110, ww41111), ww11) -> new_foldr(ww41110, ww41111, new_primPlusNat(ww11), new_primPlusNat(ww11))
14.38/5.45	
14.38/5.45	The TRS R consists of the following rules:
14.38/5.45	
14.38/5.45	   new_primPlusNat(Succ(ww50)) -> Succ(Succ(new_primPlusNat0(ww50)))
14.38/5.45	   new_primPlusNat(Zero) -> Succ(Zero)
14.38/5.45	   new_primPlusNat0(Succ(ww500)) -> Succ(ww500)
14.38/5.45	   new_primPlusNat0(Zero) -> Zero
14.38/5.45	
14.38/5.45	The set Q consists of the following terms:
14.38/5.45	
14.38/5.45	   new_primPlusNat0(Succ(x0))
14.38/5.45	   new_primPlusNat0(Zero)
14.38/5.45	   new_primPlusNat(Succ(x0))
14.38/5.45	   new_primPlusNat(Zero)
14.38/5.45	
14.38/5.45	We have to consider all minimal (P,Q,R)-chains.
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(19) QDPSizeChangeProof (EQUIVALENT)
14.38/5.45	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. 
14.38/5.45	
14.38/5.45	From the DPs we obtained the following set of size-change graphs:
14.38/5.45	*new_foldr0(:(ww41110, ww41111), ww11) -> new_foldr(ww41110, ww41111, new_primPlusNat(ww11), new_primPlusNat(ww11))
14.38/5.45	The graph contains the following edges 1 > 1, 1 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_foldr(ww41110, ww41111, ww13, ww12) -> new_foldr0(ww41111, ww12)
14.38/5.45	The graph contains the following edges 2 >= 1, 4 >= 2
14.38/5.45	
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(20)
14.38/5.45	YES
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(21)
14.38/5.45	Obligation:
14.38/5.45	Q DP problem:
14.38/5.45	The TRS P consists of the following rules:
14.38/5.45	
14.38/5.45	   new_foldr2(EQ, :(ww41110, ww41111), ww5, ww6) -> new_foldr2(ww41110, ww41111, new_primPlusNat(ww5), new_primPlusNat(ww5))
14.38/5.45	   new_psPs1(:(ww41110, ww41111), ww5) -> new_foldr2(ww41110, ww41111, new_primPlusNat(ww5), new_primPlusNat(ww5))
14.38/5.45	   new_psPs2(ww5, :(ww41110, ww41111)) -> new_foldr2(ww41110, ww41111, new_primPlusNat(ww5), new_primPlusNat(ww5))
14.38/5.45	   new_foldr2(GT, ww4111, ww5, ww6) -> new_psPs2(ww5, ww4111)
14.38/5.45	   new_foldr2(LT, ww4111, ww5, ww6) -> new_psPs1(ww4111, ww5)
14.38/5.45	
14.38/5.45	The TRS R consists of the following rules:
14.38/5.45	
14.38/5.45	   new_primPlusNat(Succ(ww50)) -> Succ(Succ(new_primPlusNat0(ww50)))
14.38/5.45	   new_primPlusNat(Zero) -> Succ(Zero)
14.38/5.45	   new_primPlusNat0(Succ(ww500)) -> Succ(ww500)
14.38/5.45	   new_primPlusNat0(Zero) -> Zero
14.38/5.45	
14.38/5.45	The set Q consists of the following terms:
14.38/5.45	
14.38/5.45	   new_primPlusNat0(Succ(x0))
14.38/5.45	   new_primPlusNat0(Zero)
14.38/5.45	   new_primPlusNat(Succ(x0))
14.38/5.45	   new_primPlusNat(Zero)
14.38/5.45	
14.38/5.45	We have to consider all minimal (P,Q,R)-chains.
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(22) QDPSizeChangeProof (EQUIVALENT)
14.38/5.45	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. 
14.38/5.45	
14.38/5.45	From the DPs we obtained the following set of size-change graphs:
14.38/5.45	*new_foldr2(EQ, :(ww41110, ww41111), ww5, ww6) -> new_foldr2(ww41110, ww41111, new_primPlusNat(ww5), new_primPlusNat(ww5))
14.38/5.45	The graph contains the following edges 2 > 1, 2 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_foldr2(LT, ww4111, ww5, ww6) -> new_psPs1(ww4111, ww5)
14.38/5.45	The graph contains the following edges 2 >= 1, 3 >= 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_foldr2(GT, ww4111, ww5, ww6) -> new_psPs2(ww5, ww4111)
14.38/5.45	The graph contains the following edges 3 >= 1, 2 >= 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_psPs2(ww5, :(ww41110, ww41111)) -> new_foldr2(ww41110, ww41111, new_primPlusNat(ww5), new_primPlusNat(ww5))
14.38/5.45	The graph contains the following edges 2 > 1, 2 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	*new_psPs1(:(ww41110, ww41111), ww5) -> new_foldr2(ww41110, ww41111, new_primPlusNat(ww5), new_primPlusNat(ww5))
14.38/5.45	The graph contains the following edges 1 > 1, 1 > 2
14.38/5.45	
14.38/5.45	
14.38/5.45	----------------------------------------
14.38/5.45	
14.38/5.45	(23)
14.38/5.45	YES
14.57/5.50	EOF