10.09/4.20	YES
12.69/4.87	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.69/4.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.69/4.87	
12.69/4.87	
12.69/4.87	H-Termination with start terms of the given HASKELL could be proven:
12.69/4.87	
12.69/4.87	(0) HASKELL
12.69/4.87	(1) LR [EQUIVALENT, 0 ms]
12.69/4.87	(2) HASKELL
12.69/4.87	(3) BR [EQUIVALENT, 0 ms]
12.69/4.87	(4) HASKELL
12.69/4.87	(5) COR [EQUIVALENT, 0 ms]
12.69/4.87	(6) HASKELL
12.69/4.87	(7) LetRed [EQUIVALENT, 0 ms]
12.69/4.87	(8) HASKELL
12.69/4.87	(9) NumRed [SOUND, 0 ms]
12.69/4.87	(10) HASKELL
12.69/4.87	(11) Narrow [SOUND, 0 ms]
12.69/4.87	(12) AND
12.69/4.87	    (13) QDP
12.69/4.87	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.69/4.87	        (15) YES
12.69/4.87	    (16) QDP
12.69/4.87	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.69/4.87	        (18) YES
12.69/4.87	    (19) QDP
12.69/4.87	        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.69/4.87	        (21) YES
12.69/4.87	    (22) QDP
12.69/4.87	        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.69/4.87	        (24) YES
12.69/4.87	    (25) QDP
12.69/4.87	        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.69/4.87	        (27) YES
12.69/4.87	
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(0)
12.69/4.87	Obligation:
12.69/4.87	mainModule Main 
12.69/4.87	module Maybe where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Main where {
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Monad where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Prelude;
12.69/4.87	replicateM_ :: Monad b => Int  ->  b a  ->  b ();
12.69/4.87	replicateM_ n x = sequence_ (replicate n x);
12.69/4.87	
12.69/4.87	}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(1) LR (EQUIVALENT)
12.69/4.87	Lambda Reductions:
12.69/4.87	The following Lambda expression
12.69/4.87	"\_->q"
12.69/4.87	is transformed to
12.69/4.87	"gtGt0 q _ = q;
12.69/4.87	"
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(2)
12.69/4.87	Obligation:
12.69/4.87	mainModule Main 
12.69/4.87	module Maybe where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Main where {
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Monad where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Prelude;
12.69/4.87	replicateM_ :: Monad a => Int  ->  a b  ->  a ();
12.69/4.87	replicateM_ n x = sequence_ (replicate n x);
12.69/4.87	
12.69/4.87	}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(3) BR (EQUIVALENT)
12.69/4.87	Replaced joker patterns by fresh variables and removed binding patterns.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(4)
12.69/4.87	Obligation:
12.69/4.87	mainModule Main 
12.69/4.87	module Maybe where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Main where {
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Monad where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Prelude;
12.69/4.87	replicateM_ :: Monad a => Int  ->  a b  ->  a ();
12.69/4.87	replicateM_ n x = sequence_ (replicate n x);
12.69/4.87	
12.69/4.87	}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(5) COR (EQUIVALENT)
12.69/4.87	Cond Reductions:
12.69/4.87	The following Function with conditions
12.69/4.87	"undefined |Falseundefined;
12.69/4.87	"
12.69/4.87	is transformed to
12.69/4.87	"undefined  = undefined1;
12.69/4.87	"
12.69/4.87	"undefined0 True = undefined;
12.69/4.87	"
12.69/4.87	"undefined1  = undefined0 False;
12.69/4.87	"
12.69/4.87	The following Function with conditions
12.69/4.87	"take n vy|n <= 0[];
12.69/4.87	take vz [] = [];
12.69/4.87	take n (x : xs) = x : take (n - 1) xs;
12.69/4.87	"
12.69/4.87	is transformed to
12.69/4.87	"take n vy = take3 n vy;
12.69/4.87	take vz [] = take1 vz [];
12.69/4.87	take n (x : xs) = take0 n (x : xs);
12.69/4.87	"
12.69/4.87	"take0 n (x : xs) = x : take (n - 1) xs;
12.69/4.87	"
12.69/4.87	"take1 vz [] = [];
12.69/4.87	take1 wx wy = take0 wx wy;
12.69/4.87	"
12.69/4.87	"take2 n vy True = [];
12.69/4.87	take2 n vy False = take1 n vy;
12.69/4.87	"
12.69/4.87	"take3 n vy = take2 n vy (n <= 0);
12.69/4.87	take3 wz xu = take1 wz xu;
12.69/4.87	"
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(6)
12.69/4.87	Obligation:
12.69/4.87	mainModule Main 
12.69/4.87	module Maybe where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Main where {
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Monad where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Prelude;
12.69/4.87	replicateM_ :: Monad a => Int  ->  a b  ->  a ();
12.69/4.87	replicateM_ n x = sequence_ (replicate n x);
12.69/4.87	
12.69/4.87	}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(7) LetRed (EQUIVALENT)
12.69/4.87	Let/Where Reductions:
12.69/4.87	The bindings of the following Let/Where expression
12.69/4.87	"xs where {
12.69/4.87	xs  = x : xs;
12.69/4.87	} 
12.69/4.87	"
12.69/4.87	are unpacked to the following functions on top level
12.69/4.87	"repeatXs xv = xv : repeatXs xv;
12.69/4.87	"
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(8)
12.69/4.87	Obligation:
12.69/4.87	mainModule Main 
12.69/4.87	module Maybe where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Main where {
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Monad where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Prelude;
12.69/4.87	replicateM_ :: Monad a => Int  ->  a b  ->  a ();
12.69/4.87	replicateM_ n x = sequence_ (replicate n x);
12.69/4.87	
12.69/4.87	}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(9) NumRed (SOUND)
12.69/4.87	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(10)
12.69/4.87	Obligation:
12.69/4.87	mainModule Main 
12.69/4.87	module Maybe where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Main where {
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Monad;
12.69/4.87	import qualified Prelude;
12.69/4.87	}
12.69/4.87	module Monad where {
12.69/4.87	import qualified Main;
12.69/4.87	import qualified Maybe;
12.69/4.87	import qualified Prelude;
12.69/4.87	replicateM_ :: Monad a => Int  ->  a b  ->  a ();
12.69/4.87	replicateM_ n x = sequence_ (replicate n x);
12.69/4.87	
12.69/4.87	}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(11) Narrow (SOUND)
12.69/4.87	Haskell To QDPs
12.69/4.87	
12.69/4.87	digraph dp_graph {
12.69/4.87	node [outthreshold=100, inthreshold=100];1[label="Monad.replicateM_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.69/4.87	3[label="Monad.replicateM_ xw3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.69/4.87	4[label="Monad.replicateM_ xw3 xw4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.69/4.87	5[label="sequence_ (replicate xw3 xw4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
12.69/4.87	6[label="foldr (>>) (return ()) (replicate xw3 xw4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
12.69/4.87	7[label="foldr (>>) (return ()) (take xw3 (repeat xw4))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
12.69/4.87	8[label="foldr (>>) (return ()) (take3 xw3 (repeat xw4))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
12.69/4.87	9[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (xw3 <= Pos Zero))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
12.69/4.87	10[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (compare xw3 (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
12.69/4.87	11[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (not (compare xw3 (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12.69/4.87	12[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (not (primCmpInt xw3 (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];398[label="xw3/Pos xw30",fontsize=10,color="white",style="solid",shape="box"];12 -> 398[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	398 -> 13[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	399[label="xw3/Neg xw30",fontsize=10,color="white",style="solid",shape="box"];12 -> 399[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	399 -> 14[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	13[label="foldr (>>) (return ()) (take2 (Pos xw30) (repeat xw4) (not (primCmpInt (Pos xw30) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];400[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];13 -> 400[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	400 -> 15[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	401[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 401[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	401 -> 16[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	14[label="foldr (>>) (return ()) (take2 (Neg xw30) (repeat xw4) (not (primCmpInt (Neg xw30) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];402[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];14 -> 402[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	402 -> 17[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	403[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 403[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	403 -> 18[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	15[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not (primCmpInt (Pos (Succ xw300)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
12.69/4.87	16[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
12.69/4.87	17[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) (not (primCmpInt (Neg (Succ xw300)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
12.69/4.87	18[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
12.69/4.87	19[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not (primCmpNat (Succ xw300) Zero == GT)))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
12.69/4.87	20[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
12.69/4.87	21[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) (not (LT == GT)))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
12.69/4.87	22[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
12.69/4.87	23[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not (GT == GT)))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
12.69/4.87	24[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) (not False))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
12.69/4.87	25[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) (not False))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
12.69/4.87	26[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) (not False))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
12.69/4.87	27[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not True))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
12.69/4.87	28[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) True)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
12.69/4.87	29[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) True)",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
12.69/4.87	30[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) True)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
12.69/4.87	31[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) False)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
12.69/4.87	32[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="triangle"];32 -> 36[label="",style="solid", color="black", weight=3];
12.69/4.87	33 -> 32[label="",style="dashed", color="red", weight=0];
12.69/4.87	33[label="foldr (>>) (return ()) []",fontsize=16,color="magenta"];34 -> 32[label="",style="dashed", color="red", weight=0];
12.69/4.87	34[label="foldr (>>) (return ()) []",fontsize=16,color="magenta"];35[label="foldr (>>) (return ()) (take1 (Pos (Succ xw300)) (repeat xw4))",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
12.69/4.87	36[label="return ()",fontsize=16,color="blue",shape="box"];404[label="return :: () -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];36 -> 404[label="",style="solid", color="blue", weight=9];
12.69/4.87	404 -> 38[label="",style="solid", color="blue", weight=3];
12.69/4.87	405[label="return :: () -> IO ()",fontsize=10,color="white",style="solid",shape="box"];36 -> 405[label="",style="solid", color="blue", weight=9];
12.69/4.87	405 -> 39[label="",style="solid", color="blue", weight=3];
12.69/4.87	406[label="return :: () -> [] ()",fontsize=10,color="white",style="solid",shape="box"];36 -> 406[label="",style="solid", color="blue", weight=9];
12.69/4.87	406 -> 40[label="",style="solid", color="blue", weight=3];
12.69/4.87	37[label="foldr (>>) (return ()) (take1 (Pos (Succ xw300)) (repeatXs xw4))",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3];
12.69/4.87	38[label="return ()",fontsize=16,color="black",shape="triangle"];38 -> 42[label="",style="solid", color="black", weight=3];
12.69/4.87	39[label="return ()",fontsize=16,color="black",shape="triangle"];39 -> 43[label="",style="solid", color="black", weight=3];
12.69/4.87	40[label="return ()",fontsize=16,color="black",shape="triangle"];40 -> 44[label="",style="solid", color="black", weight=3];
12.69/4.87	41[label="foldr (>>) (return ()) (take1 (Pos (Succ xw300)) (xw4 : repeatXs xw4))",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3];
12.69/4.87	42[label="Just ()",fontsize=16,color="green",shape="box"];43[label="primretIO ()",fontsize=16,color="black",shape="box"];43 -> 46[label="",style="solid", color="black", weight=3];
12.69/4.87	44[label="() : []",fontsize=16,color="green",shape="box"];45[label="foldr (>>) (return ()) (take0 (Pos (Succ xw300)) (xw4 : repeatXs xw4))",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
12.69/4.87	46[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];47[label="foldr (>>) (return ()) (xw4 : take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
12.69/4.87	48[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="blue",shape="box"];407[label=">> :: (Maybe a) -> (Maybe ()) -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];48 -> 407[label="",style="solid", color="blue", weight=9];
12.69/4.87	407 -> 49[label="",style="solid", color="blue", weight=3];
12.69/4.87	408[label=">> :: (IO a) -> (IO ()) -> IO ()",fontsize=10,color="white",style="solid",shape="box"];48 -> 408[label="",style="solid", color="blue", weight=9];
12.69/4.87	408 -> 50[label="",style="solid", color="blue", weight=3];
12.69/4.87	409[label=">> :: ([] a) -> ([] ()) -> [] ()",fontsize=10,color="white",style="solid",shape="box"];48 -> 409[label="",style="solid", color="blue", weight=9];
12.69/4.87	409 -> 51[label="",style="solid", color="blue", weight=3];
12.69/4.87	49 -> 52[label="",style="dashed", color="red", weight=0];
12.69/4.87	49[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="magenta"];49 -> 53[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	50 -> 54[label="",style="dashed", color="red", weight=0];
12.69/4.87	50[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="magenta"];50 -> 55[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	51 -> 56[label="",style="dashed", color="red", weight=0];
12.69/4.87	51[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="magenta"];51 -> 57[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	53 -> 38[label="",style="dashed", color="red", weight=0];
12.69/4.87	53[label="return ()",fontsize=16,color="magenta"];52[label="(>>) xw4 foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="triangle"];52 -> 58[label="",style="solid", color="black", weight=3];
12.69/4.87	55 -> 39[label="",style="dashed", color="red", weight=0];
12.69/4.87	55[label="return ()",fontsize=16,color="magenta"];54[label="(>>) xw4 foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="triangle"];54 -> 59[label="",style="solid", color="black", weight=3];
12.69/4.87	57 -> 40[label="",style="dashed", color="red", weight=0];
12.69/4.87	57[label="return ()",fontsize=16,color="magenta"];56[label="(>>) xw4 foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="triangle"];56 -> 60[label="",style="solid", color="black", weight=3];
12.69/4.87	58[label="xw4 >>= gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4)))",fontsize=16,color="burlywood",shape="box"];410[label="xw4/Nothing",fontsize=10,color="white",style="solid",shape="box"];58 -> 410[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	410 -> 61[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	411[label="xw4/Just xw40",fontsize=10,color="white",style="solid",shape="box"];58 -> 411[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	411 -> 62[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	59[label="xw4 >>= gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4)))",fontsize=16,color="black",shape="box"];59 -> 63[label="",style="solid", color="black", weight=3];
12.69/4.87	60[label="xw4 >>= gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4)))",fontsize=16,color="burlywood",shape="box"];412[label="xw4/xw40 : xw41",fontsize=10,color="white",style="solid",shape="box"];60 -> 412[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	412 -> 64[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	413[label="xw4/[]",fontsize=10,color="white",style="solid",shape="box"];60 -> 413[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	413 -> 65[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	61[label="Nothing >>= gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs Nothing)))",fontsize=16,color="black",shape="box"];61 -> 66[label="",style="solid", color="black", weight=3];
12.69/4.87	62[label="Just xw40 >>= gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40))))",fontsize=16,color="black",shape="box"];62 -> 67[label="",style="solid", color="black", weight=3];
12.69/4.87	63[label="primbindIO xw4 (gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))))",fontsize=16,color="burlywood",shape="box"];414[label="xw4/IO xw40",fontsize=10,color="white",style="solid",shape="box"];63 -> 414[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	414 -> 68[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	415[label="xw4/AProVE_IO xw40",fontsize=10,color="white",style="solid",shape="box"];63 -> 415[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	415 -> 69[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	416[label="xw4/AProVE_Exception xw40",fontsize=10,color="white",style="solid",shape="box"];63 -> 416[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	416 -> 70[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	417[label="xw4/AProVE_Error xw40",fontsize=10,color="white",style="solid",shape="box"];63 -> 417[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	417 -> 71[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	64[label="xw40 : xw41 >>= gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41))))",fontsize=16,color="black",shape="box"];64 -> 72[label="",style="solid", color="black", weight=3];
12.69/4.87	65[label="[] >>= gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs [])))",fontsize=16,color="black",shape="box"];65 -> 73[label="",style="solid", color="black", weight=3];
12.69/4.87	66[label="Nothing",fontsize=16,color="green",shape="box"];67[label="gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)))) xw40",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
12.69/4.87	68[label="primbindIO (IO xw40) (gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (IO xw40)))))",fontsize=16,color="black",shape="box"];68 -> 75[label="",style="solid", color="black", weight=3];
12.69/4.87	69[label="primbindIO (AProVE_IO xw40) (gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))))",fontsize=16,color="black",shape="box"];69 -> 76[label="",style="solid", color="black", weight=3];
12.69/4.87	70[label="primbindIO (AProVE_Exception xw40) (gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_Exception xw40)))))",fontsize=16,color="black",shape="box"];70 -> 77[label="",style="solid", color="black", weight=3];
12.69/4.87	71[label="primbindIO (AProVE_Error xw40) (gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_Error xw40)))))",fontsize=16,color="black",shape="box"];71 -> 78[label="",style="solid", color="black", weight=3];
12.69/4.87	72[label="gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))) xw40 ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];72 -> 79[label="",style="solid", color="black", weight=3];
12.69/4.87	73[label="[]",fontsize=16,color="green",shape="box"];74[label="foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];74 -> 80[label="",style="solid", color="black", weight=3];
12.69/4.87	75[label="error []",fontsize=16,color="red",shape="box"];76[label="gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))) xw40",fontsize=16,color="black",shape="box"];76 -> 81[label="",style="solid", color="black", weight=3];
12.69/4.87	77[label="AProVE_Exception xw40",fontsize=16,color="green",shape="box"];78[label="AProVE_Error xw40",fontsize=16,color="green",shape="box"];79[label="foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];79 -> 82[label="",style="solid", color="black", weight=3];
12.69/4.87	80[label="foldr (>>) xw5 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];80 -> 83[label="",style="solid", color="black", weight=3];
12.69/4.87	81[label="foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];81 -> 84[label="",style="solid", color="black", weight=3];
12.69/4.87	82[label="foldr (>>) xw7 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];82 -> 85[label="",style="solid", color="black", weight=3];
12.69/4.87	83[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero))",fontsize=16,color="black",shape="box"];83 -> 86[label="",style="solid", color="black", weight=3];
12.69/4.87	84[label="foldr (>>) xw6 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];84 -> 87[label="",style="solid", color="black", weight=3];
12.69/4.87	85[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero)) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero))))",fontsize=16,color="black",shape="box"];85 -> 88[label="",style="solid", color="black", weight=3];
12.69/4.87	86[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];86 -> 89[label="",style="solid", color="black", weight=3];
12.69/4.87	87[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero))",fontsize=16,color="black",shape="box"];87 -> 90[label="",style="solid", color="black", weight=3];
12.69/4.87	88[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT)) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT))))",fontsize=16,color="black",shape="box"];88 -> 91[label="",style="solid", color="black", weight=3];
12.69/4.87	89[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];89 -> 92[label="",style="solid", color="black", weight=3];
12.69/4.87	90[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];90 -> 93[label="",style="solid", color="black", weight=3];
12.69/4.87	91[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];91 -> 94[label="",style="solid", color="black", weight=3];
12.69/4.87	92[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];92 -> 95[label="",style="solid", color="black", weight=3];
12.69/4.87	93[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];93 -> 96[label="",style="solid", color="black", weight=3];
12.69/4.87	94[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];94 -> 97[label="",style="solid", color="black", weight=3];
12.69/4.87	95[label="foldr (>>) xw5 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (Just xw40)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];95 -> 98[label="",style="solid", color="black", weight=3];
12.69/4.87	96[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];96 -> 99[label="",style="solid", color="black", weight=3];
12.69/4.87	97[label="foldr (>>) xw7 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];97 -> 100[label="",style="solid", color="black", weight=3];
12.69/4.87	98[label="foldr (>>) xw5 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];98 -> 101[label="",style="solid", color="black", weight=3];
12.69/4.87	99[label="foldr (>>) xw6 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];99 -> 102[label="",style="solid", color="black", weight=3];
12.69/4.87	100[label="foldr (>>) xw7 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];100 -> 103[label="",style="solid", color="black", weight=3];
12.69/4.87	101[label="foldr (>>) xw5 (take2 (primMinusNat xw300 Zero) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];418[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];101 -> 418[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	418 -> 104[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	419[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];101 -> 419[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	419 -> 105[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	102[label="foldr (>>) xw6 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];102 -> 106[label="",style="solid", color="black", weight=3];
12.69/4.87	103[label="foldr (>>) xw7 (take2 (primMinusNat xw300 Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (primMinusNat xw300 Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT)))))",fontsize=16,color="burlywood",shape="box"];420[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];103 -> 420[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	420 -> 107[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	421[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];103 -> 421[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	421 -> 108[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	104[label="foldr (>>) xw5 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];104 -> 109[label="",style="solid", color="black", weight=3];
12.69/4.87	105[label="foldr (>>) xw5 (take2 (primMinusNat Zero Zero) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];105 -> 110[label="",style="solid", color="black", weight=3];
12.69/4.87	106[label="foldr (>>) xw6 (take2 (primMinusNat xw300 Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];422[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];106 -> 422[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	422 -> 111[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	423[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];106 -> 423[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	423 -> 112[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	107[label="foldr (>>) xw7 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];107 -> 113[label="",style="solid", color="black", weight=3];
12.69/4.87	108[label="foldr (>>) xw7 (take2 (primMinusNat Zero Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (primMinusNat Zero Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];108 -> 114[label="",style="solid", color="black", weight=3];
12.69/4.87	109[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];109 -> 115[label="",style="solid", color="black", weight=3];
12.69/4.87	110[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];110 -> 116[label="",style="solid", color="black", weight=3];
12.69/4.87	111[label="foldr (>>) xw6 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];111 -> 117[label="",style="solid", color="black", weight=3];
12.69/4.87	112[label="foldr (>>) xw6 (take2 (primMinusNat Zero Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];112 -> 118[label="",style="solid", color="black", weight=3];
12.69/4.87	113[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];113 -> 119[label="",style="solid", color="black", weight=3];
12.69/4.87	114[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];114 -> 120[label="",style="solid", color="black", weight=3];
12.69/4.87	115[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not (primCmpNat (Succ xw3000) Zero == GT)))",fontsize=16,color="black",shape="box"];115 -> 121[label="",style="solid", color="black", weight=3];
12.69/4.87	116[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];116 -> 122[label="",style="solid", color="black", weight=3];
12.69/4.87	117[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];117 -> 123[label="",style="solid", color="black", weight=3];
12.69/4.87	118[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];118 -> 124[label="",style="solid", color="black", weight=3];
12.69/4.87	119[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpNat (Succ xw3000) Zero == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpNat (Succ xw3000) Zero == GT)))))",fontsize=16,color="black",shape="box"];119 -> 125[label="",style="solid", color="black", weight=3];
12.69/4.87	120[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (EQ == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (EQ == GT)))))",fontsize=16,color="black",shape="box"];120 -> 126[label="",style="solid", color="black", weight=3];
12.69/4.87	121[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not (GT == GT)))",fontsize=16,color="black",shape="box"];121 -> 127[label="",style="solid", color="black", weight=3];
12.69/4.87	122[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) (not False))",fontsize=16,color="black",shape="box"];122 -> 128[label="",style="solid", color="black", weight=3];
12.69/4.87	123[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not (primCmpNat (Succ xw3000) Zero == GT)))",fontsize=16,color="black",shape="box"];123 -> 129[label="",style="solid", color="black", weight=3];
12.69/4.87	124[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];124 -> 130[label="",style="solid", color="black", weight=3];
12.69/4.87	125[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (GT == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (GT == GT)))))",fontsize=16,color="black",shape="box"];125 -> 131[label="",style="solid", color="black", weight=3];
12.69/4.87	126[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not False)) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not False))))",fontsize=16,color="black",shape="box"];126 -> 132[label="",style="solid", color="black", weight=3];
12.69/4.87	127[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not True))",fontsize=16,color="black",shape="box"];127 -> 133[label="",style="solid", color="black", weight=3];
12.69/4.87	128[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) True)",fontsize=16,color="black",shape="box"];128 -> 134[label="",style="solid", color="black", weight=3];
12.69/4.87	129[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not (GT == GT)))",fontsize=16,color="black",shape="box"];129 -> 135[label="",style="solid", color="black", weight=3];
12.69/4.87	130[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) (not False))",fontsize=16,color="black",shape="box"];130 -> 136[label="",style="solid", color="black", weight=3];
12.69/4.87	131[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not True)) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not True))))",fontsize=16,color="black",shape="box"];131 -> 137[label="",style="solid", color="black", weight=3];
12.69/4.87	132[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) True) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) True)))",fontsize=16,color="black",shape="box"];132 -> 138[label="",style="solid", color="black", weight=3];
12.69/4.87	133[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) False)",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3];
12.69/4.87	134[label="foldr (>>) xw5 []",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3];
12.69/4.87	135[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not True))",fontsize=16,color="black",shape="box"];135 -> 141[label="",style="solid", color="black", weight=3];
12.69/4.87	136[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) True)",fontsize=16,color="black",shape="box"];136 -> 142[label="",style="solid", color="black", weight=3];
12.69/4.87	137[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) False) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) False)))",fontsize=16,color="black",shape="box"];137 -> 143[label="",style="solid", color="black", weight=3];
12.69/4.87	138[label="foldr (>>) xw7 [] ++ (xw41 >>= gtGt0 (foldr (>>) xw7 []))",fontsize=16,color="black",shape="box"];138 -> 144[label="",style="solid", color="black", weight=3];
12.69/4.87	139[label="foldr (>>) xw5 (take1 (Pos (Succ xw3000)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];139 -> 145[label="",style="solid", color="black", weight=3];
12.69/4.87	140[label="xw5",fontsize=16,color="green",shape="box"];141[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) False)",fontsize=16,color="black",shape="box"];141 -> 146[label="",style="solid", color="black", weight=3];
12.69/4.87	142[label="foldr (>>) xw6 []",fontsize=16,color="black",shape="box"];142 -> 147[label="",style="solid", color="black", weight=3];
12.69/4.87	143[label="foldr (>>) xw7 (take1 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take1 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];143 -> 148[label="",style="solid", color="black", weight=3];
12.69/4.87	144[label="xw7 ++ (xw41 >>= gtGt0 xw7)",fontsize=16,color="burlywood",shape="triangle"];424[label="xw7/xw70 : xw71",fontsize=10,color="white",style="solid",shape="box"];144 -> 424[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	424 -> 149[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	425[label="xw7/[]",fontsize=10,color="white",style="solid",shape="box"];144 -> 425[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	425 -> 150[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	145[label="foldr (>>) xw5 (take1 (Pos (Succ xw3000)) (Just xw40 : repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];145 -> 151[label="",style="solid", color="black", weight=3];
12.69/4.87	146[label="foldr (>>) xw6 (take1 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];146 -> 152[label="",style="solid", color="black", weight=3];
12.69/4.87	147[label="xw6",fontsize=16,color="green",shape="box"];148 -> 144[label="",style="dashed", color="red", weight=0];
12.69/4.87	148[label="foldr (>>) xw7 (take1 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw7 (take1 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41)))))",fontsize=16,color="magenta"];148 -> 153[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	149[label="(xw70 : xw71) ++ (xw41 >>= gtGt0 (xw70 : xw71))",fontsize=16,color="black",shape="box"];149 -> 154[label="",style="solid", color="black", weight=3];
12.69/4.87	150[label="[] ++ (xw41 >>= gtGt0 [])",fontsize=16,color="black",shape="box"];150 -> 155[label="",style="solid", color="black", weight=3];
12.69/4.87	151[label="foldr (>>) xw5 (take0 (Pos (Succ xw3000)) (Just xw40 : repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];151 -> 156[label="",style="solid", color="black", weight=3];
12.69/4.87	152[label="foldr (>>) xw6 (take1 (Pos (Succ xw3000)) (AProVE_IO xw40 : repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];152 -> 157[label="",style="solid", color="black", weight=3];
12.69/4.87	153[label="foldr (>>) xw7 (take1 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41)))",fontsize=16,color="black",shape="box"];153 -> 158[label="",style="solid", color="black", weight=3];
12.69/4.87	154[label="xw70 : xw71 ++ (xw41 >>= gtGt0 (xw70 : xw71))",fontsize=16,color="green",shape="box"];154 -> 159[label="",style="dashed", color="green", weight=3];
12.69/4.87	155[label="xw41 >>= gtGt0 []",fontsize=16,color="burlywood",shape="triangle"];426[label="xw41/xw410 : xw411",fontsize=10,color="white",style="solid",shape="box"];155 -> 426[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	426 -> 160[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	427[label="xw41/[]",fontsize=10,color="white",style="solid",shape="box"];155 -> 427[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	427 -> 161[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	156[label="foldr (>>) xw5 (Just xw40 : take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];156 -> 162[label="",style="solid", color="black", weight=3];
12.69/4.87	157[label="foldr (>>) xw6 (take0 (Pos (Succ xw3000)) (AProVE_IO xw40 : repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];157 -> 163[label="",style="solid", color="black", weight=3];
12.69/4.87	158[label="foldr (>>) xw7 (take0 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41)))",fontsize=16,color="black",shape="box"];158 -> 164[label="",style="solid", color="black", weight=3];
12.69/4.87	159 -> 348[label="",style="dashed", color="red", weight=0];
12.69/4.87	159[label="xw71 ++ (xw41 >>= gtGt0 (xw70 : xw71))",fontsize=16,color="magenta"];159 -> 349[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	159 -> 350[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	159 -> 351[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	159 -> 352[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	160[label="xw410 : xw411 >>= gtGt0 []",fontsize=16,color="black",shape="box"];160 -> 167[label="",style="solid", color="black", weight=3];
12.69/4.87	161[label="[] >>= gtGt0 []",fontsize=16,color="black",shape="box"];161 -> 168[label="",style="solid", color="black", weight=3];
12.69/4.87	162 -> 52[label="",style="dashed", color="red", weight=0];
12.69/4.87	162[label="(>>) Just xw40 foldr (>>) xw5 (take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="magenta"];162 -> 169[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	162 -> 170[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	163[label="foldr (>>) xw6 (AProVE_IO xw40 : take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];163 -> 171[label="",style="solid", color="black", weight=3];
12.69/4.87	164[label="foldr (>>) xw7 ((xw40 : xw41) : take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))",fontsize=16,color="black",shape="box"];164 -> 172[label="",style="solid", color="black", weight=3];
12.69/4.87	349[label="xw71",fontsize=16,color="green",shape="box"];350[label="xw71",fontsize=16,color="green",shape="box"];351[label="xw70",fontsize=16,color="green",shape="box"];352[label="xw41",fontsize=16,color="green",shape="box"];348[label="xw24 ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="burlywood",shape="triangle"];428[label="xw24/xw240 : xw241",fontsize=10,color="white",style="solid",shape="box"];348 -> 428[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	428 -> 385[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	429[label="xw24/[]",fontsize=10,color="white",style="solid",shape="box"];348 -> 429[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	429 -> 386[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	167 -> 175[label="",style="dashed", color="red", weight=0];
12.69/4.87	167[label="gtGt0 [] xw410 ++ (xw411 >>= gtGt0 [])",fontsize=16,color="magenta"];167 -> 176[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	168[label="[]",fontsize=16,color="green",shape="box"];169[label="xw3000",fontsize=16,color="green",shape="box"];170[label="Just xw40",fontsize=16,color="green",shape="box"];171 -> 54[label="",style="dashed", color="red", weight=0];
12.69/4.87	171[label="(>>) AProVE_IO xw40 foldr (>>) xw6 (take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="magenta"];171 -> 177[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	171 -> 178[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	172 -> 56[label="",style="dashed", color="red", weight=0];
12.69/4.87	172[label="(>>) xw40 : xw41 foldr (>>) xw7 (take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))",fontsize=16,color="magenta"];172 -> 179[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	172 -> 180[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	385[label="(xw240 : xw241) ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="black",shape="box"];385 -> 387[label="",style="solid", color="black", weight=3];
12.69/4.87	386[label="[] ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="black",shape="box"];386 -> 388[label="",style="solid", color="black", weight=3];
12.69/4.87	176 -> 155[label="",style="dashed", color="red", weight=0];
12.69/4.87	176[label="xw411 >>= gtGt0 []",fontsize=16,color="magenta"];176 -> 184[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	175[label="gtGt0 [] xw410 ++ xw8",fontsize=16,color="black",shape="triangle"];175 -> 185[label="",style="solid", color="black", weight=3];
12.69/4.87	177[label="xw3000",fontsize=16,color="green",shape="box"];178[label="AProVE_IO xw40",fontsize=16,color="green",shape="box"];179[label="xw3000",fontsize=16,color="green",shape="box"];180[label="xw40 : xw41",fontsize=16,color="green",shape="box"];387[label="xw240 : xw241 ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="green",shape="box"];387 -> 389[label="",style="dashed", color="green", weight=3];
12.69/4.87	388[label="xw25 >>= gtGt0 (xw26 : xw27)",fontsize=16,color="burlywood",shape="box"];430[label="xw25/xw250 : xw251",fontsize=10,color="white",style="solid",shape="box"];388 -> 430[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	430 -> 390[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	431[label="xw25/[]",fontsize=10,color="white",style="solid",shape="box"];388 -> 431[label="",style="solid", color="burlywood", weight=9];
12.69/4.87	431 -> 391[label="",style="solid", color="burlywood", weight=3];
12.69/4.87	184[label="xw411",fontsize=16,color="green",shape="box"];185[label="[] ++ xw8",fontsize=16,color="black",shape="triangle"];185 -> 190[label="",style="solid", color="black", weight=3];
12.69/4.87	389 -> 348[label="",style="dashed", color="red", weight=0];
12.69/4.87	389[label="xw241 ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="magenta"];389 -> 392[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	390[label="xw250 : xw251 >>= gtGt0 (xw26 : xw27)",fontsize=16,color="black",shape="box"];390 -> 393[label="",style="solid", color="black", weight=3];
12.69/4.87	391[label="[] >>= gtGt0 (xw26 : xw27)",fontsize=16,color="black",shape="box"];391 -> 394[label="",style="solid", color="black", weight=3];
12.69/4.87	190[label="xw8",fontsize=16,color="green",shape="box"];392[label="xw241",fontsize=16,color="green",shape="box"];393 -> 348[label="",style="dashed", color="red", weight=0];
12.69/4.87	393[label="gtGt0 (xw26 : xw27) xw250 ++ (xw251 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="magenta"];393 -> 395[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	393 -> 396[label="",style="dashed", color="magenta", weight=3];
12.69/4.87	394[label="[]",fontsize=16,color="green",shape="box"];395[label="gtGt0 (xw26 : xw27) xw250",fontsize=16,color="black",shape="box"];395 -> 397[label="",style="solid", color="black", weight=3];
12.69/4.87	396[label="xw251",fontsize=16,color="green",shape="box"];397[label="xw26 : xw27",fontsize=16,color="green",shape="box"];}
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(12)
12.69/4.87	Complex Obligation (AND)
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(13)
12.69/4.87	Obligation:
12.69/4.87	Q DP problem:
12.69/4.87	The TRS P consists of the following rules:
12.69/4.87	
12.69/4.87	   new_gtGt(:(xw40, xw41), xw7, Succ(xw3000), h) -> new_gtGt(:(xw40, xw41), xw7, xw3000, h)
12.69/4.87	
12.69/4.87	R is empty.
12.69/4.87	Q is empty.
12.69/4.87	We have to consider all minimal (P,Q,R)-chains.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(14) QDPSizeChangeProof (EQUIVALENT)
12.69/4.87	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. 
12.69/4.87	
12.69/4.87	From the DPs we obtained the following set of size-change graphs:
12.69/4.87	*new_gtGt(:(xw40, xw41), xw7, Succ(xw3000), h) -> new_gtGt(:(xw40, xw41), xw7, xw3000, h)
12.69/4.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4
12.69/4.87	
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(15)
12.69/4.87	YES
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(16)
12.69/4.87	Obligation:
12.69/4.87	Q DP problem:
12.69/4.87	The TRS P consists of the following rules:
12.69/4.87	
12.69/4.87	   new_gtGt1(Just(xw40), xw5, Succ(xw3000), h) -> new_gtGt1(Just(xw40), xw5, xw3000, h)
12.69/4.87	
12.69/4.87	R is empty.
12.69/4.87	Q is empty.
12.69/4.87	We have to consider all minimal (P,Q,R)-chains.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(17) QDPSizeChangeProof (EQUIVALENT)
12.69/4.87	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. 
12.69/4.87	
12.69/4.87	From the DPs we obtained the following set of size-change graphs:
12.69/4.87	*new_gtGt1(Just(xw40), xw5, Succ(xw3000), h) -> new_gtGt1(Just(xw40), xw5, xw3000, h)
12.69/4.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4
12.69/4.87	
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(18)
12.69/4.87	YES
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(19)
12.69/4.87	Obligation:
12.69/4.87	Q DP problem:
12.69/4.87	The TRS P consists of the following rules:
12.69/4.87	
12.69/4.87	   new_gtGtEs(:(xw410, xw411), h) -> new_gtGtEs(xw411, h)
12.69/4.87	
12.69/4.87	R is empty.
12.69/4.87	Q is empty.
12.69/4.87	We have to consider all minimal (P,Q,R)-chains.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(20) QDPSizeChangeProof (EQUIVALENT)
12.69/4.87	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. 
12.69/4.87	
12.69/4.87	From the DPs we obtained the following set of size-change graphs:
12.69/4.87	*new_gtGtEs(:(xw410, xw411), h) -> new_gtGtEs(xw411, h)
12.69/4.87	The graph contains the following edges 1 > 1, 2 >= 2
12.69/4.87	
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(21)
12.69/4.87	YES
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(22)
12.69/4.87	Obligation:
12.69/4.87	Q DP problem:
12.69/4.87	The TRS P consists of the following rules:
12.69/4.87	
12.69/4.87	   new_gtGt0(AProVE_IO(xw40), xw6, Succ(xw3000), h) -> new_gtGt0(AProVE_IO(xw40), xw6, xw3000, h)
12.69/4.87	
12.69/4.87	R is empty.
12.69/4.87	Q is empty.
12.69/4.87	We have to consider all minimal (P,Q,R)-chains.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(23) QDPSizeChangeProof (EQUIVALENT)
12.69/4.87	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. 
12.69/4.87	
12.69/4.87	From the DPs we obtained the following set of size-change graphs:
12.69/4.87	*new_gtGt0(AProVE_IO(xw40), xw6, Succ(xw3000), h) -> new_gtGt0(AProVE_IO(xw40), xw6, xw3000, h)
12.69/4.87	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4
12.69/4.87	
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(24)
12.69/4.87	YES
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(25)
12.69/4.87	Obligation:
12.69/4.87	Q DP problem:
12.69/4.87	The TRS P consists of the following rules:
12.69/4.87	
12.69/4.87	   new_psPs(:(xw240, xw241), xw25, xw26, xw27, h, ba) -> new_psPs(xw241, xw25, xw26, xw27, h, ba)
12.69/4.87	   new_psPs([], :(xw250, xw251), xw26, xw27, h, ba) -> new_psPs(:(xw26, xw27), xw251, xw26, xw27, h, ba)
12.69/4.87	
12.69/4.87	R is empty.
12.69/4.87	Q is empty.
12.69/4.87	We have to consider all minimal (P,Q,R)-chains.
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(26) QDPSizeChangeProof (EQUIVALENT)
12.69/4.87	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. 
12.69/4.87	
12.69/4.87	From the DPs we obtained the following set of size-change graphs:
12.69/4.87	*new_psPs(:(xw240, xw241), xw25, xw26, xw27, h, ba) -> new_psPs(xw241, xw25, xw26, xw27, h, ba)
12.69/4.87	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6
12.69/4.87	
12.69/4.87	
12.69/4.87	*new_psPs([], :(xw250, xw251), xw26, xw27, h, ba) -> new_psPs(:(xw26, xw27), xw251, xw26, xw27, h, ba)
12.69/4.87	The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6
12.69/4.87	
12.69/4.87	
12.69/4.87	----------------------------------------
12.69/4.87	
12.69/4.87	(27)
12.69/4.87	YES
12.78/4.95	EOF