7.69/3.52	YES
9.43/4.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.43/4.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.43/4.01	
9.43/4.01	
9.43/4.01	H-Termination with start terms of the given HASKELL could be proven:
9.43/4.01	
9.43/4.01	(0) HASKELL
9.43/4.01	(1) BR [EQUIVALENT, 0 ms]
9.43/4.01	(2) HASKELL
9.43/4.01	(3) COR [EQUIVALENT, 0 ms]
9.43/4.01	(4) HASKELL
9.43/4.01	(5) Narrow [EQUIVALENT, 28 ms]
9.43/4.01	(6) YES
9.43/4.01	
9.43/4.01	
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(0)
9.43/4.01	Obligation:
9.43/4.01	mainModule Main 
9.43/4.01	module Main where {
9.43/4.01	import qualified Prelude;
9.43/4.01	data MyBool = MyTrue  | MyFalse ;
9.43/4.01	
9.43/4.01	data Ordering = LT  | EQ  | GT ;
9.43/4.01	
9.43/4.01	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.01	ltEsOrdering LT LT = MyTrue;
9.43/4.01	ltEsOrdering LT EQ = MyTrue;
9.43/4.01	ltEsOrdering LT GT = MyTrue;
9.43/4.01	ltEsOrdering EQ LT = MyFalse;
9.43/4.01	ltEsOrdering EQ EQ = MyTrue;
9.43/4.01	ltEsOrdering EQ GT = MyTrue;
9.43/4.01	ltEsOrdering GT LT = MyFalse;
9.43/4.01	ltEsOrdering GT EQ = MyFalse;
9.43/4.01	ltEsOrdering GT GT = MyTrue;
9.43/4.01	
9.43/4.01	max0 x y MyTrue = x;
9.43/4.01	
9.43/4.01	max1 x y MyTrue = y;
9.43/4.01	max1 x y MyFalse = max0 x y otherwise;
9.43/4.01	
9.43/4.01	max2 x y = max1 x y (ltEsOrdering x y);
9.43/4.01	
9.43/4.01	maxOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.43/4.01	maxOrdering x y = max2 x y;
9.43/4.01	
9.43/4.01	otherwise :: MyBool;
9.43/4.01	otherwise = MyTrue;
9.43/4.01	
9.43/4.01	}
9.43/4.01	
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(1) BR (EQUIVALENT)
9.43/4.01	Replaced joker patterns by fresh variables and removed binding patterns.
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(2)
9.43/4.01	Obligation:
9.43/4.01	mainModule Main 
9.43/4.01	module Main where {
9.43/4.01	import qualified Prelude;
9.43/4.01	data MyBool = MyTrue  | MyFalse ;
9.43/4.01	
9.43/4.01	data Ordering = LT  | EQ  | GT ;
9.43/4.01	
9.43/4.01	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.01	ltEsOrdering LT LT = MyTrue;
9.43/4.01	ltEsOrdering LT EQ = MyTrue;
9.43/4.01	ltEsOrdering LT GT = MyTrue;
9.43/4.01	ltEsOrdering EQ LT = MyFalse;
9.43/4.01	ltEsOrdering EQ EQ = MyTrue;
9.43/4.01	ltEsOrdering EQ GT = MyTrue;
9.43/4.01	ltEsOrdering GT LT = MyFalse;
9.43/4.01	ltEsOrdering GT EQ = MyFalse;
9.43/4.01	ltEsOrdering GT GT = MyTrue;
9.43/4.01	
9.43/4.01	max0 x y MyTrue = x;
9.43/4.01	
9.43/4.01	max1 x y MyTrue = y;
9.43/4.01	max1 x y MyFalse = max0 x y otherwise;
9.43/4.01	
9.43/4.01	max2 x y = max1 x y (ltEsOrdering x y);
9.43/4.01	
9.43/4.01	maxOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.43/4.01	maxOrdering x y = max2 x y;
9.43/4.01	
9.43/4.01	otherwise :: MyBool;
9.43/4.01	otherwise = MyTrue;
9.43/4.01	
9.43/4.01	}
9.43/4.01	
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(3) COR (EQUIVALENT)
9.43/4.01	Cond Reductions:
9.43/4.01	The following Function with conditions
9.43/4.01	"undefined |Falseundefined;
9.43/4.01	"
9.43/4.01	is transformed to
9.43/4.01	"undefined  = undefined1;
9.43/4.01	"
9.43/4.01	"undefined0 True = undefined;
9.43/4.01	"
9.43/4.01	"undefined1  = undefined0 False;
9.43/4.01	"
9.43/4.01	
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(4)
9.43/4.01	Obligation:
9.43/4.01	mainModule Main 
9.43/4.01	module Main where {
9.43/4.01	import qualified Prelude;
9.43/4.01	data MyBool = MyTrue  | MyFalse ;
9.43/4.01	
9.43/4.01	data Ordering = LT  | EQ  | GT ;
9.43/4.01	
9.43/4.01	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.01	ltEsOrdering LT LT = MyTrue;
9.43/4.01	ltEsOrdering LT EQ = MyTrue;
9.43/4.01	ltEsOrdering LT GT = MyTrue;
9.43/4.01	ltEsOrdering EQ LT = MyFalse;
9.43/4.01	ltEsOrdering EQ EQ = MyTrue;
9.43/4.01	ltEsOrdering EQ GT = MyTrue;
9.43/4.01	ltEsOrdering GT LT = MyFalse;
9.43/4.01	ltEsOrdering GT EQ = MyFalse;
9.43/4.01	ltEsOrdering GT GT = MyTrue;
9.43/4.01	
9.43/4.01	max0 x y MyTrue = x;
9.43/4.01	
9.43/4.01	max1 x y MyTrue = y;
9.43/4.01	max1 x y MyFalse = max0 x y otherwise;
9.43/4.01	
9.43/4.01	max2 x y = max1 x y (ltEsOrdering x y);
9.43/4.01	
9.43/4.01	maxOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.43/4.01	maxOrdering x y = max2 x y;
9.43/4.01	
9.43/4.01	otherwise :: MyBool;
9.43/4.01	otherwise = MyTrue;
9.43/4.01	
9.43/4.01	}
9.43/4.01	
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(5) Narrow (EQUIVALENT)
9.43/4.01	Haskell To QDPs
9.43/4.01	
9.43/4.01	digraph dp_graph {
9.43/4.01	node [outthreshold=100, inthreshold=100];1[label="maxOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.43/4.01	3[label="maxOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.43/4.01	4[label="maxOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.43/4.01	5[label="max2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.43/4.01	6[label="max1 vx3 vx4 (ltEsOrdering vx3 vx4)",fontsize=16,color="burlywood",shape="box"];43[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 43[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	43 -> 7[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	44[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 44[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	44 -> 8[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	45[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 45[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	45 -> 9[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	7[label="max1 LT vx4 (ltEsOrdering LT vx4)",fontsize=16,color="burlywood",shape="box"];46[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 46[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	46 -> 10[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	47[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 47[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	47 -> 11[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	48[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 48[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	48 -> 12[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	8[label="max1 EQ vx4 (ltEsOrdering EQ vx4)",fontsize=16,color="burlywood",shape="box"];49[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 49[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	49 -> 13[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	50[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 50[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	50 -> 14[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	51[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 51[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	51 -> 15[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	9[label="max1 GT vx4 (ltEsOrdering GT vx4)",fontsize=16,color="burlywood",shape="box"];52[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 52[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	52 -> 16[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	53[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 53[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	53 -> 17[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	54[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 54[label="",style="solid", color="burlywood", weight=9];
9.43/4.01	54 -> 18[label="",style="solid", color="burlywood", weight=3];
9.43/4.01	10[label="max1 LT LT (ltEsOrdering LT LT)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.43/4.01	11[label="max1 LT EQ (ltEsOrdering LT EQ)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.43/4.01	12[label="max1 LT GT (ltEsOrdering LT GT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.43/4.01	13[label="max1 EQ LT (ltEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.43/4.01	14[label="max1 EQ EQ (ltEsOrdering EQ EQ)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.43/4.01	15[label="max1 EQ GT (ltEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.43/4.01	16[label="max1 GT LT (ltEsOrdering GT LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.43/4.01	17[label="max1 GT EQ (ltEsOrdering GT EQ)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.43/4.01	18[label="max1 GT GT (ltEsOrdering GT GT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.43/4.01	19[label="max1 LT LT MyTrue",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.43/4.01	20[label="max1 LT EQ MyTrue",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.43/4.01	21[label="max1 LT GT MyTrue",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.43/4.01	22[label="max1 EQ LT MyFalse",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.43/4.01	23[label="max1 EQ EQ MyTrue",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.43/4.01	24[label="max1 EQ GT MyTrue",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.43/4.01	25[label="max1 GT LT MyFalse",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.43/4.01	26[label="max1 GT EQ MyFalse",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.43/4.01	27[label="max1 GT GT MyTrue",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.43/4.01	28[label="LT",fontsize=16,color="green",shape="box"];29[label="EQ",fontsize=16,color="green",shape="box"];30[label="GT",fontsize=16,color="green",shape="box"];31[label="max0 EQ LT otherwise",fontsize=16,color="black",shape="box"];31 -> 37[label="",style="solid", color="black", weight=3];
9.43/4.01	32[label="EQ",fontsize=16,color="green",shape="box"];33[label="GT",fontsize=16,color="green",shape="box"];34[label="max0 GT LT otherwise",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
9.43/4.01	35[label="max0 GT EQ otherwise",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
9.43/4.01	36[label="GT",fontsize=16,color="green",shape="box"];37[label="max0 EQ LT MyTrue",fontsize=16,color="black",shape="box"];37 -> 40[label="",style="solid", color="black", weight=3];
9.43/4.01	38[label="max0 GT LT MyTrue",fontsize=16,color="black",shape="box"];38 -> 41[label="",style="solid", color="black", weight=3];
9.43/4.01	39[label="max0 GT EQ MyTrue",fontsize=16,color="black",shape="box"];39 -> 42[label="",style="solid", color="black", weight=3];
9.43/4.01	40[label="EQ",fontsize=16,color="green",shape="box"];41[label="GT",fontsize=16,color="green",shape="box"];42[label="GT",fontsize=16,color="green",shape="box"];}
9.43/4.01	
9.43/4.01	----------------------------------------
9.43/4.01	
9.43/4.01	(6)
9.43/4.01	YES
9.43/4.05	EOF