11.31/4.62	YES
13.45/5.24	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
13.45/5.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.45/5.24	
13.45/5.24	
13.45/5.24	H-Termination with start terms of the given HASKELL could be proven:
13.45/5.24	
13.45/5.24	(0) HASKELL
13.45/5.24	(1) BR [EQUIVALENT, 0 ms]
13.45/5.24	(2) HASKELL
13.45/5.24	(3) COR [EQUIVALENT, 0 ms]
13.45/5.24	(4) HASKELL
13.45/5.24	(5) LetRed [EQUIVALENT, 0 ms]
13.45/5.24	(6) HASKELL
13.45/5.24	(7) NumRed [SOUND, 8 ms]
13.45/5.24	(8) HASKELL
13.45/5.24	(9) Narrow [SOUND, 0 ms]
13.45/5.24	(10) QDP
13.45/5.24	(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.45/5.24	(12) YES
13.45/5.24	
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(0)
13.45/5.24	Obligation:
13.45/5.24	mainModule Main 
13.45/5.24	module Maybe where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	module List where {
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	genericReplicate :: Integral b => b  ->  a  ->  [a];
13.45/5.24	genericReplicate n x = genericTake n (repeat x);
13.45/5.24	
13.45/5.24	genericTake :: Integral b => b  ->  [a]  ->  [a];
13.45/5.24	genericTake 0 _ = [];
13.45/5.24	genericTake _ [] = [];
13.45/5.24	genericTake n (x : xs)  | n > 0 = x : genericTake (n - 1) xs;
13.45/5.24	genericTake _ _ = error [];
13.45/5.24	
13.45/5.24	}
13.45/5.24	module Main where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(1) BR (EQUIVALENT)
13.45/5.24	Replaced joker patterns by fresh variables and removed binding patterns.
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(2)
13.45/5.24	Obligation:
13.45/5.24	mainModule Main 
13.45/5.24	module Maybe where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	module List where {
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	genericReplicate :: Integral a => a  ->  b  ->  [b];
13.45/5.24	genericReplicate n x = genericTake n (repeat x);
13.45/5.24	
13.45/5.24	genericTake :: Integral b => b  ->  [a]  ->  [a];
13.45/5.24	genericTake 0 xw = [];
13.45/5.24	genericTake xx [] = [];
13.45/5.24	genericTake n (x : xs)  | n > 0 = x : genericTake (n - 1) xs;
13.45/5.24	genericTake xy xz = error [];
13.45/5.24	
13.45/5.24	}
13.45/5.24	module Main where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(3) COR (EQUIVALENT)
13.45/5.24	Cond Reductions:
13.45/5.24	The following Function with conditions
13.45/5.24	"undefined |Falseundefined;
13.45/5.24	"
13.45/5.24	is transformed to
13.45/5.24	"undefined  = undefined1;
13.45/5.24	"
13.45/5.24	"undefined0 True = undefined;
13.45/5.24	"
13.45/5.24	"undefined1  = undefined0 False;
13.45/5.24	"
13.45/5.24	The following Function with conditions
13.45/5.24	"genericTake 0 xw = [];
13.45/5.24	genericTake xx [] = [];
13.45/5.24	genericTake n (x : xs)|n > 0x : genericTake (n - 1) xs;
13.45/5.24	genericTake xy xz = error [];
13.45/5.24	"
13.45/5.24	is transformed to
13.45/5.24	"genericTake zu xw = genericTake5 zu xw;
13.45/5.24	genericTake xx [] = genericTake3 xx [];
13.45/5.24	genericTake n (x : xs) = genericTake2 n (x : xs);
13.45/5.24	genericTake xy xz = genericTake0 xy xz;
13.45/5.24	"
13.45/5.24	"genericTake0 xy xz = error [];
13.45/5.24	"
13.45/5.24	"genericTake1 n x xs True = x : genericTake (n - 1) xs;
13.45/5.24	genericTake1 n x xs False = genericTake0 n (x : xs);
13.45/5.24	"
13.45/5.24	"genericTake2 n (x : xs) = genericTake1 n x xs (n > 0);
13.45/5.24	genericTake2 yv yw = genericTake0 yv yw;
13.45/5.24	"
13.45/5.24	"genericTake3 xx [] = [];
13.45/5.24	genericTake3 yy yz = genericTake2 yy yz;
13.45/5.24	"
13.45/5.24	"genericTake4 True zu xw = [];
13.45/5.24	genericTake4 zv zw zx = genericTake3 zw zx;
13.45/5.24	"
13.45/5.24	"genericTake5 zu xw = genericTake4 (zu == 0) zu xw;
13.45/5.24	genericTake5 zy zz = genericTake3 zy zz;
13.45/5.24	"
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(4)
13.45/5.24	Obligation:
13.45/5.24	mainModule Main 
13.45/5.24	module Maybe where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	module List where {
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	genericReplicate :: Integral b => b  ->  a  ->  [a];
13.45/5.24	genericReplicate n x = genericTake n (repeat x);
13.45/5.24	
13.45/5.24	genericTake :: Integral b => b  ->  [a]  ->  [a];
13.45/5.24	genericTake zu xw = genericTake5 zu xw;
13.45/5.24	genericTake xx [] = genericTake3 xx [];
13.45/5.24	genericTake n (x : xs) = genericTake2 n (x : xs);
13.45/5.24	genericTake xy xz = genericTake0 xy xz;
13.45/5.24	
13.45/5.24	genericTake0 xy xz = error [];
13.45/5.24	
13.45/5.24	genericTake1 n x xs True = x : genericTake (n - 1) xs;
13.45/5.24	genericTake1 n x xs False = genericTake0 n (x : xs);
13.45/5.24	
13.45/5.24	genericTake2 n (x : xs) = genericTake1 n x xs (n > 0);
13.45/5.24	genericTake2 yv yw = genericTake0 yv yw;
13.45/5.24	
13.45/5.24	genericTake3 xx [] = [];
13.45/5.24	genericTake3 yy yz = genericTake2 yy yz;
13.45/5.24	
13.45/5.24	genericTake4 True zu xw = [];
13.45/5.24	genericTake4 zv zw zx = genericTake3 zw zx;
13.45/5.24	
13.45/5.24	genericTake5 zu xw = genericTake4 (zu == 0) zu xw;
13.45/5.24	genericTake5 zy zz = genericTake3 zy zz;
13.45/5.24	
13.45/5.24	}
13.45/5.24	module Main where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(5) LetRed (EQUIVALENT)
13.45/5.24	Let/Where Reductions:
13.45/5.24	The bindings of the following Let/Where expression
13.45/5.24	"xs where {
13.45/5.24	xs  = x : xs;
13.45/5.24	} 
13.45/5.24	"
13.45/5.24	are unpacked to the following functions on top level
13.45/5.24	"repeatXs vuu = vuu : repeatXs vuu;
13.45/5.24	"
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(6)
13.45/5.24	Obligation:
13.45/5.24	mainModule Main 
13.45/5.24	module Maybe where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	module List where {
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	genericReplicate :: Integral b => b  ->  a  ->  [a];
13.45/5.24	genericReplicate n x = genericTake n (repeat x);
13.45/5.24	
13.45/5.24	genericTake :: Integral a => a  ->  [b]  ->  [b];
13.45/5.24	genericTake zu xw = genericTake5 zu xw;
13.45/5.24	genericTake xx [] = genericTake3 xx [];
13.45/5.24	genericTake n (x : xs) = genericTake2 n (x : xs);
13.45/5.24	genericTake xy xz = genericTake0 xy xz;
13.45/5.24	
13.45/5.24	genericTake0 xy xz = error [];
13.45/5.24	
13.45/5.24	genericTake1 n x xs True = x : genericTake (n - 1) xs;
13.45/5.24	genericTake1 n x xs False = genericTake0 n (x : xs);
13.45/5.24	
13.45/5.24	genericTake2 n (x : xs) = genericTake1 n x xs (n > 0);
13.45/5.24	genericTake2 yv yw = genericTake0 yv yw;
13.45/5.24	
13.45/5.24	genericTake3 xx [] = [];
13.45/5.24	genericTake3 yy yz = genericTake2 yy yz;
13.45/5.24	
13.45/5.24	genericTake4 True zu xw = [];
13.45/5.24	genericTake4 zv zw zx = genericTake3 zw zx;
13.45/5.24	
13.45/5.24	genericTake5 zu xw = genericTake4 (zu == 0) zu xw;
13.45/5.24	genericTake5 zy zz = genericTake3 zy zz;
13.45/5.24	
13.45/5.24	}
13.45/5.24	module Main where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(7) NumRed (SOUND)
13.45/5.24	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(8)
13.45/5.24	Obligation:
13.45/5.24	mainModule Main 
13.45/5.24	module Maybe where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	module List where {
13.45/5.24	import qualified Main;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	genericReplicate :: Integral b => b  ->  a  ->  [a];
13.45/5.24	genericReplicate n x = genericTake n (repeat x);
13.45/5.24	
13.45/5.24	genericTake :: Integral a => a  ->  [b]  ->  [b];
13.45/5.24	genericTake zu xw = genericTake5 zu xw;
13.45/5.24	genericTake xx [] = genericTake3 xx [];
13.45/5.24	genericTake n (x : xs) = genericTake2 n (x : xs);
13.45/5.24	genericTake xy xz = genericTake0 xy xz;
13.45/5.24	
13.45/5.24	genericTake0 xy xz = error [];
13.45/5.24	
13.45/5.24	genericTake1 n x xs True = x : genericTake (n - fromInt (Pos (Succ Zero))) xs;
13.45/5.24	genericTake1 n x xs False = genericTake0 n (x : xs);
13.45/5.24	
13.45/5.24	genericTake2 n (x : xs) = genericTake1 n x xs (n > fromInt (Pos Zero));
13.45/5.24	genericTake2 yv yw = genericTake0 yv yw;
13.45/5.24	
13.45/5.24	genericTake3 xx [] = [];
13.45/5.24	genericTake3 yy yz = genericTake2 yy yz;
13.45/5.24	
13.45/5.24	genericTake4 True zu xw = [];
13.45/5.24	genericTake4 zv zw zx = genericTake3 zw zx;
13.45/5.24	
13.45/5.24	genericTake5 zu xw = genericTake4 (zu == fromInt (Pos Zero)) zu xw;
13.45/5.24	genericTake5 zy zz = genericTake3 zy zz;
13.45/5.24	
13.45/5.24	}
13.45/5.24	module Main where {
13.45/5.24	import qualified List;
13.45/5.24	import qualified Maybe;
13.45/5.24	import qualified Prelude;
13.45/5.24	}
13.45/5.24	
13.45/5.24	----------------------------------------
13.45/5.24	
13.45/5.24	(9) Narrow (SOUND)
13.45/5.24	Haskell To QDPs
13.45/5.24	
13.45/5.24	digraph dp_graph {
13.45/5.24	node [outthreshold=100, inthreshold=100];1[label="List.genericReplicate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.45/5.24	3[label="List.genericReplicate vuv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.45/5.24	4[label="List.genericReplicate vuv3 vuv4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
13.45/5.24	5[label="List.genericTake vuv3 (repeat vuv4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
13.45/5.24	6[label="List.genericTake5 vuv3 (repeat vuv4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
13.45/5.24	7[label="List.genericTake4 (vuv3 == fromInt (Pos Zero)) vuv3 (repeat vuv4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
13.45/5.24	8[label="List.genericTake4 (primEqInt vuv3 (fromInt (Pos Zero))) vuv3 (repeat vuv4)",fontsize=16,color="burlywood",shape="box"];69[label="vuv3/Pos vuv30",fontsize=10,color="white",style="solid",shape="box"];8 -> 69[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	69 -> 9[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	70[label="vuv3/Neg vuv30",fontsize=10,color="white",style="solid",shape="box"];8 -> 70[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	70 -> 10[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	9[label="List.genericTake4 (primEqInt (Pos vuv30) (fromInt (Pos Zero))) (Pos vuv30) (repeat vuv4)",fontsize=16,color="burlywood",shape="box"];71[label="vuv30/Succ vuv300",fontsize=10,color="white",style="solid",shape="box"];9 -> 71[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	71 -> 11[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	72[label="vuv30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 72[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	72 -> 12[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	10[label="List.genericTake4 (primEqInt (Neg vuv30) (fromInt (Pos Zero))) (Neg vuv30) (repeat vuv4)",fontsize=16,color="burlywood",shape="box"];73[label="vuv30/Succ vuv300",fontsize=10,color="white",style="solid",shape="box"];10 -> 73[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	73 -> 13[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	74[label="vuv30/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 74[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	74 -> 14[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	11[label="List.genericTake4 (primEqInt (Pos (Succ vuv300)) (fromInt (Pos Zero))) (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
13.45/5.25	12[label="List.genericTake4 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13.45/5.25	13[label="List.genericTake4 (primEqInt (Neg (Succ vuv300)) (fromInt (Pos Zero))) (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
13.45/5.25	14[label="List.genericTake4 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
13.45/5.25	15[label="List.genericTake4 (primEqInt (Pos (Succ vuv300)) (Pos Zero)) (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
13.45/5.25	16[label="List.genericTake4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
13.45/5.25	17[label="List.genericTake4 (primEqInt (Neg (Succ vuv300)) (Pos Zero)) (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
13.45/5.25	18[label="List.genericTake4 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
13.45/5.25	19[label="List.genericTake4 False (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
13.45/5.25	20[label="List.genericTake4 True (Pos Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
13.45/5.25	21[label="List.genericTake4 False (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
13.45/5.25	22[label="List.genericTake4 True (Neg Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
13.45/5.25	23[label="List.genericTake3 (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
13.45/5.25	24[label="[]",fontsize=16,color="green",shape="box"];25[label="List.genericTake3 (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
13.45/5.25	26[label="[]",fontsize=16,color="green",shape="box"];27[label="List.genericTake3 (Pos (Succ vuv300)) (repeatXs vuv4)",fontsize=16,color="black",shape="triangle"];27 -> 29[label="",style="solid", color="black", weight=3];
13.45/5.25	28[label="List.genericTake3 (Neg (Succ vuv300)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
13.45/5.25	29[label="List.genericTake3 (Pos (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
13.45/5.25	30[label="List.genericTake3 (Neg (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
13.45/5.25	31[label="List.genericTake2 (Pos (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
13.45/5.25	32[label="List.genericTake2 (Neg (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
13.45/5.25	33[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (Pos (Succ vuv300) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
13.45/5.25	34[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (Neg (Succ vuv300) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
13.45/5.25	35[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (compare (Pos (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
13.45/5.25	36[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (compare (Neg (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3];
13.45/5.25	37[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Pos (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
13.45/5.25	38[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Neg (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
13.45/5.25	39[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Pos (Succ vuv300)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3];
13.45/5.25	40[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Neg (Succ vuv300)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];40 -> 42[label="",style="solid", color="black", weight=3];
13.45/5.25	41[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpNat (Succ vuv300) Zero == GT)",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3];
13.45/5.25	42[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (LT == GT)",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
13.45/5.25	43[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (GT == GT)",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
13.45/5.25	44[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) False",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
13.45/5.25	45[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) True",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
13.45/5.25	46[label="List.genericTake0 (Neg (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];46 -> 48[label="",style="solid", color="black", weight=3];
13.45/5.25	47[label="vuv4 : List.genericTake (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="green",shape="box"];47 -> 49[label="",style="dashed", color="green", weight=3];
13.45/5.25	48[label="error []",fontsize=16,color="black",shape="box"];48 -> 50[label="",style="solid", color="black", weight=3];
13.45/5.25	49[label="List.genericTake (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];49 -> 51[label="",style="solid", color="black", weight=3];
13.45/5.25	50[label="error []",fontsize=16,color="red",shape="box"];51[label="List.genericTake5 (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];51 -> 52[label="",style="solid", color="black", weight=3];
13.45/5.25	52[label="List.genericTake4 (Pos (Succ vuv300) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];52 -> 53[label="",style="solid", color="black", weight=3];
13.45/5.25	53[label="List.genericTake4 (primEqInt (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];53 -> 54[label="",style="solid", color="black", weight=3];
13.45/5.25	54[label="List.genericTake4 (primEqInt (primMinusInt (Pos (Succ vuv300)) (fromInt (Pos (Succ Zero)))) (fromInt (Pos Zero))) (primMinusInt (Pos (Succ vuv300)) (fromInt (Pos (Succ Zero)))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];54 -> 55[label="",style="solid", color="black", weight=3];
13.45/5.25	55[label="List.genericTake4 (primEqInt (primMinusInt (Pos (Succ vuv300)) (Pos (Succ Zero))) (fromInt (Pos Zero))) (primMinusInt (Pos (Succ vuv300)) (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];55 -> 56[label="",style="solid", color="black", weight=3];
13.45/5.25	56[label="List.genericTake4 (primEqInt (primMinusNat (Succ vuv300) (Succ Zero)) (fromInt (Pos Zero))) (primMinusNat (Succ vuv300) (Succ Zero)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];56 -> 57[label="",style="solid", color="black", weight=3];
13.45/5.25	57[label="List.genericTake4 (primEqInt (primMinusNat vuv300 Zero) (fromInt (Pos Zero))) (primMinusNat vuv300 Zero) (repeatXs vuv4)",fontsize=16,color="burlywood",shape="box"];75[label="vuv300/Succ vuv3000",fontsize=10,color="white",style="solid",shape="box"];57 -> 75[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	75 -> 58[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	76[label="vuv300/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 76[label="",style="solid", color="burlywood", weight=9];
13.45/5.25	76 -> 59[label="",style="solid", color="burlywood", weight=3];
13.45/5.25	58[label="List.genericTake4 (primEqInt (primMinusNat (Succ vuv3000) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuv3000) Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];58 -> 60[label="",style="solid", color="black", weight=3];
13.45/5.25	59[label="List.genericTake4 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];59 -> 61[label="",style="solid", color="black", weight=3];
13.45/5.25	60[label="List.genericTake4 (primEqInt (Pos (Succ vuv3000)) (fromInt (Pos Zero))) (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
13.45/5.25	61[label="List.genericTake4 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];61 -> 63[label="",style="solid", color="black", weight=3];
13.45/5.25	62[label="List.genericTake4 (primEqInt (Pos (Succ vuv3000)) (Pos Zero)) (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];62 -> 64[label="",style="solid", color="black", weight=3];
13.45/5.25	63[label="List.genericTake4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];63 -> 65[label="",style="solid", color="black", weight=3];
13.45/5.25	64[label="List.genericTake4 False (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];64 -> 66[label="",style="solid", color="black", weight=3];
13.45/5.25	65[label="List.genericTake4 True (Pos Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3];
13.45/5.25	66 -> 27[label="",style="dashed", color="red", weight=0];
13.45/5.25	66[label="List.genericTake3 (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="magenta"];66 -> 68[label="",style="dashed", color="magenta", weight=3];
13.45/5.25	67[label="[]",fontsize=16,color="green",shape="box"];68[label="vuv3000",fontsize=16,color="green",shape="box"];}
13.45/5.25	
13.45/5.25	----------------------------------------
13.45/5.25	
13.45/5.25	(10)
13.45/5.25	Obligation:
13.45/5.25	Q DP problem:
13.45/5.25	The TRS P consists of the following rules:
13.45/5.25	
13.45/5.25	   new_genericTake3(Succ(vuv3000), vuv4, ba) -> new_genericTake3(vuv3000, vuv4, ba)
13.45/5.25	
13.45/5.25	R is empty.
13.45/5.25	Q is empty.
13.45/5.25	We have to consider all minimal (P,Q,R)-chains.
13.45/5.25	----------------------------------------
13.45/5.25	
13.45/5.25	(11) QDPSizeChangeProof (EQUIVALENT)
13.45/5.25	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. 
13.45/5.25	
13.45/5.25	From the DPs we obtained the following set of size-change graphs:
13.45/5.25	*new_genericTake3(Succ(vuv3000), vuv4, ba) -> new_genericTake3(vuv3000, vuv4, ba)
13.45/5.25	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
13.45/5.25	
13.45/5.25	
13.45/5.25	----------------------------------------
13.45/5.25	
13.45/5.25	(12)
13.45/5.25	YES
13.62/5.28	EOF