8.27/3.61	YES
10.27/4.14	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.27/4.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.27/4.14	
10.27/4.14	
10.27/4.14	H-Termination with start terms of the given HASKELL could be proven:
10.27/4.14	
10.27/4.14	(0) HASKELL
10.27/4.14	(1) BR [EQUIVALENT, 0 ms]
10.27/4.14	(2) HASKELL
10.27/4.14	(3) COR [EQUIVALENT, 0 ms]
10.27/4.14	(4) HASKELL
10.27/4.14	(5) NumRed [SOUND, 0 ms]
10.27/4.14	(6) HASKELL
10.27/4.14	(7) Narrow [EQUIVALENT, 0 ms]
10.27/4.14	(8) YES
10.27/4.14	
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(0)
10.27/4.14	Obligation:
10.27/4.14	mainModule Main 
10.27/4.14	module Main where {
10.27/4.14	import qualified Prelude;
10.27/4.14	}
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(1) BR (EQUIVALENT)
10.27/4.14	Replaced joker patterns by fresh variables and removed binding patterns.
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(2)
10.27/4.14	Obligation:
10.27/4.14	mainModule Main 
10.27/4.14	module Main where {
10.27/4.14	import qualified Prelude;
10.27/4.14	}
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(3) COR (EQUIVALENT)
10.27/4.14	Cond Reductions:
10.27/4.14	The following Function with conditions
10.27/4.14	"absReal x|x >= 0x|otherwise`negate` x;
10.27/4.14	"
10.27/4.14	is transformed to
10.27/4.14	"absReal x = absReal2 x;
10.27/4.14	"
10.27/4.14	"absReal0 x True = `negate` x;
10.27/4.14	"
10.27/4.14	"absReal1 x True = x;
10.27/4.14	absReal1 x False = absReal0 x otherwise;
10.27/4.14	"
10.27/4.14	"absReal2 x = absReal1 x (x >= 0);
10.27/4.14	"
10.27/4.14	The following Function with conditions
10.27/4.14	"undefined |Falseundefined;
10.27/4.14	"
10.27/4.14	is transformed to
10.27/4.14	"undefined  = undefined1;
10.27/4.14	"
10.27/4.14	"undefined0 True = undefined;
10.27/4.14	"
10.27/4.14	"undefined1  = undefined0 False;
10.27/4.14	"
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(4)
10.27/4.14	Obligation:
10.27/4.14	mainModule Main 
10.27/4.14	module Main where {
10.27/4.14	import qualified Prelude;
10.27/4.14	}
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(5) NumRed (SOUND)
10.27/4.14	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(6)
10.27/4.14	Obligation:
10.27/4.14	mainModule Main 
10.27/4.14	module Main where {
10.27/4.14	import qualified Prelude;
10.27/4.14	}
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(7) Narrow (EQUIVALENT)
10.27/4.14	Haskell To QDPs
10.27/4.14	
10.27/4.14	digraph dp_graph {
10.27/4.14	node [outthreshold=100, inthreshold=100];1[label="abs",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.27/4.14	3[label="abs vx3",fontsize=16,color="burlywood",shape="triangle"];44[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 44[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	44 -> 4[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	4[label="abs (vx30 :% vx31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.27/4.14	5[label="abs vx30 :% vx31",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
10.27/4.14	6[label="abs vx30",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.27/4.14	7[label="absReal vx30",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
10.27/4.14	8[label="absReal2 vx30",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
10.27/4.14	9[label="absReal1 vx30 (vx30 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10.27/4.14	10[label="absReal1 vx30 (compare vx30 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.27/4.14	11[label="absReal1 vx30 (not (compare vx30 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
10.27/4.14	12[label="absReal1 vx30 (not (primCmpInt vx30 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];45[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];12 -> 45[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	45 -> 13[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	46[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];12 -> 46[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	46 -> 14[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	13[label="absReal1 (Pos vx300) (not (primCmpInt (Pos vx300) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];47[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];13 -> 47[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	47 -> 15[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	48[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 48[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	48 -> 16[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	14[label="absReal1 (Neg vx300) (not (primCmpInt (Neg vx300) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];49[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];14 -> 49[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	49 -> 17[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	50[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 50[label="",style="solid", color="burlywood", weight=9];
10.27/4.14	50 -> 18[label="",style="solid", color="burlywood", weight=3];
10.27/4.14	15[label="absReal1 (Pos (Succ vx3000)) (not (primCmpInt (Pos (Succ vx3000)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
10.27/4.14	16[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
10.27/4.14	17[label="absReal1 (Neg (Succ vx3000)) (not (primCmpInt (Neg (Succ vx3000)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
10.27/4.14	18[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
10.27/4.14	19[label="absReal1 (Pos (Succ vx3000)) (not (primCmpInt (Pos (Succ vx3000)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
10.27/4.14	20[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
10.27/4.14	21[label="absReal1 (Neg (Succ vx3000)) (not (primCmpInt (Neg (Succ vx3000)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
10.27/4.14	22[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
10.27/4.14	23[label="absReal1 (Pos (Succ vx3000)) (not (primCmpNat (Succ vx3000) Zero == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
10.27/4.14	24[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
10.27/4.14	25[label="absReal1 (Neg (Succ vx3000)) (not (LT == LT))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
10.27/4.14	26[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
10.27/4.14	27[label="absReal1 (Pos (Succ vx3000)) (not (GT == LT))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
10.27/4.14	28[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
10.27/4.14	29[label="absReal1 (Neg (Succ vx3000)) (not True)",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
10.27/4.14	30[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
10.27/4.14	31[label="absReal1 (Pos (Succ vx3000)) (not False)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
10.27/4.14	32[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
10.27/4.14	33[label="absReal1 (Neg (Succ vx3000)) False",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
10.27/4.14	34[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
10.27/4.14	35[label="absReal1 (Pos (Succ vx3000)) True",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
10.27/4.14	36[label="Pos Zero",fontsize=16,color="green",shape="box"];37[label="absReal0 (Neg (Succ vx3000)) otherwise",fontsize=16,color="black",shape="box"];37 -> 40[label="",style="solid", color="black", weight=3];
10.27/4.14	38[label="Neg Zero",fontsize=16,color="green",shape="box"];39[label="Pos (Succ vx3000)",fontsize=16,color="green",shape="box"];40[label="absReal0 (Neg (Succ vx3000)) True",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
10.27/4.14	41[label="`negate` Neg (Succ vx3000)",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3];
10.27/4.14	42[label="primNegInt (Neg (Succ vx3000))",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3];
10.27/4.14	43[label="Pos (Succ vx3000)",fontsize=16,color="green",shape="box"];}
10.27/4.14	
10.27/4.14	----------------------------------------
10.27/4.14	
10.27/4.14	(8)
10.27/4.14	YES
10.27/4.18	EOF