8.06/3.66	YES
9.83/4.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.83/4.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.83/4.15	
9.83/4.15	
9.83/4.15	H-Termination with start terms of the given HASKELL could be proven:
9.83/4.15	
9.83/4.15	(0) HASKELL
9.83/4.15	(1) BR [EQUIVALENT, 0 ms]
9.83/4.15	(2) HASKELL
9.83/4.15	(3) COR [EQUIVALENT, 0 ms]
9.83/4.15	(4) HASKELL
9.83/4.15	(5) Narrow [EQUIVALENT, 30 ms]
9.83/4.15	(6) YES
9.83/4.15	
9.83/4.15	
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(0)
9.83/4.15	Obligation:
9.83/4.15	mainModule Main 
9.83/4.15	module Main where {
9.83/4.15	import qualified Prelude;
9.83/4.15	data MyBool = MyTrue  | MyFalse ;
9.83/4.15	
9.83/4.15	data Ordering = LT  | EQ  | GT ;
9.83/4.15	
9.83/4.15	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.83/4.15	ltEsOrdering LT LT = MyTrue;
9.83/4.15	ltEsOrdering LT EQ = MyTrue;
9.83/4.15	ltEsOrdering LT GT = MyTrue;
9.83/4.15	ltEsOrdering EQ LT = MyFalse;
9.83/4.15	ltEsOrdering EQ EQ = MyTrue;
9.83/4.15	ltEsOrdering EQ GT = MyTrue;
9.83/4.15	ltEsOrdering GT LT = MyFalse;
9.83/4.15	ltEsOrdering GT EQ = MyFalse;
9.83/4.15	ltEsOrdering GT GT = MyTrue;
9.83/4.15	
9.83/4.15	min0 x y MyTrue = y;
9.83/4.15	
9.83/4.15	min1 x y MyTrue = x;
9.83/4.15	min1 x y MyFalse = min0 x y otherwise;
9.83/4.15	
9.83/4.15	min2 x y = min1 x y (ltEsOrdering x y);
9.83/4.15	
9.83/4.15	minOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.83/4.15	minOrdering x y = min2 x y;
9.83/4.15	
9.83/4.15	otherwise :: MyBool;
9.83/4.15	otherwise = MyTrue;
9.83/4.15	
9.83/4.15	}
9.83/4.15	
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(1) BR (EQUIVALENT)
9.83/4.15	Replaced joker patterns by fresh variables and removed binding patterns.
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(2)
9.83/4.15	Obligation:
9.83/4.15	mainModule Main 
9.83/4.15	module Main where {
9.83/4.15	import qualified Prelude;
9.83/4.15	data MyBool = MyTrue  | MyFalse ;
9.83/4.15	
9.83/4.15	data Ordering = LT  | EQ  | GT ;
9.83/4.15	
9.83/4.15	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.83/4.15	ltEsOrdering LT LT = MyTrue;
9.83/4.15	ltEsOrdering LT EQ = MyTrue;
9.83/4.15	ltEsOrdering LT GT = MyTrue;
9.83/4.15	ltEsOrdering EQ LT = MyFalse;
9.83/4.15	ltEsOrdering EQ EQ = MyTrue;
9.83/4.15	ltEsOrdering EQ GT = MyTrue;
9.83/4.15	ltEsOrdering GT LT = MyFalse;
9.83/4.15	ltEsOrdering GT EQ = MyFalse;
9.83/4.15	ltEsOrdering GT GT = MyTrue;
9.83/4.15	
9.83/4.15	min0 x y MyTrue = y;
9.83/4.15	
9.83/4.15	min1 x y MyTrue = x;
9.83/4.15	min1 x y MyFalse = min0 x y otherwise;
9.83/4.15	
9.83/4.15	min2 x y = min1 x y (ltEsOrdering x y);
9.83/4.15	
9.83/4.15	minOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.83/4.15	minOrdering x y = min2 x y;
9.83/4.15	
9.83/4.15	otherwise :: MyBool;
9.83/4.15	otherwise = MyTrue;
9.83/4.15	
9.83/4.15	}
9.83/4.15	
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(3) COR (EQUIVALENT)
9.83/4.15	Cond Reductions:
9.83/4.15	The following Function with conditions
9.83/4.15	"undefined |Falseundefined;
9.83/4.15	"
9.83/4.15	is transformed to
9.83/4.15	"undefined  = undefined1;
9.83/4.15	"
9.83/4.15	"undefined0 True = undefined;
9.83/4.15	"
9.83/4.15	"undefined1  = undefined0 False;
9.83/4.15	"
9.83/4.15	
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(4)
9.83/4.15	Obligation:
9.83/4.15	mainModule Main 
9.83/4.15	module Main where {
9.83/4.15	import qualified Prelude;
9.83/4.15	data MyBool = MyTrue  | MyFalse ;
9.83/4.15	
9.83/4.15	data Ordering = LT  | EQ  | GT ;
9.83/4.15	
9.83/4.15	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.83/4.15	ltEsOrdering LT LT = MyTrue;
9.83/4.15	ltEsOrdering LT EQ = MyTrue;
9.83/4.15	ltEsOrdering LT GT = MyTrue;
9.83/4.15	ltEsOrdering EQ LT = MyFalse;
9.83/4.15	ltEsOrdering EQ EQ = MyTrue;
9.83/4.15	ltEsOrdering EQ GT = MyTrue;
9.83/4.15	ltEsOrdering GT LT = MyFalse;
9.83/4.15	ltEsOrdering GT EQ = MyFalse;
9.83/4.15	ltEsOrdering GT GT = MyTrue;
9.83/4.15	
9.83/4.15	min0 x y MyTrue = y;
9.83/4.15	
9.83/4.15	min1 x y MyTrue = x;
9.83/4.15	min1 x y MyFalse = min0 x y otherwise;
9.83/4.15	
9.83/4.15	min2 x y = min1 x y (ltEsOrdering x y);
9.83/4.15	
9.83/4.15	minOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.83/4.15	minOrdering x y = min2 x y;
9.83/4.15	
9.83/4.15	otherwise :: MyBool;
9.83/4.15	otherwise = MyTrue;
9.83/4.15	
9.83/4.15	}
9.83/4.15	
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(5) Narrow (EQUIVALENT)
9.83/4.15	Haskell To QDPs
9.83/4.15	
9.83/4.15	digraph dp_graph {
9.83/4.15	node [outthreshold=100, inthreshold=100];1[label="minOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.83/4.15	3[label="minOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.83/4.15	4[label="minOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.83/4.15	5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.83/4.15	6[label="min1 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];
9.83/4.15	43 -> 7[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	44[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 44[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	44 -> 8[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	45[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 45[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	45 -> 9[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	7[label="min1 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];
9.83/4.15	46 -> 10[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	47[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 47[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	47 -> 11[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	48[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 48[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	48 -> 12[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	8[label="min1 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];
9.83/4.15	49 -> 13[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	50[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 50[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	50 -> 14[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	51[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 51[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	51 -> 15[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	9[label="min1 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];
9.83/4.15	52 -> 16[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	53[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 53[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	53 -> 17[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	54[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 54[label="",style="solid", color="burlywood", weight=9];
9.83/4.15	54 -> 18[label="",style="solid", color="burlywood", weight=3];
9.83/4.15	10[label="min1 LT LT (ltEsOrdering LT LT)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.83/4.15	11[label="min1 LT EQ (ltEsOrdering LT EQ)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.83/4.15	12[label="min1 LT GT (ltEsOrdering LT GT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.83/4.15	13[label="min1 EQ LT (ltEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.83/4.15	14[label="min1 EQ EQ (ltEsOrdering EQ EQ)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.83/4.15	15[label="min1 EQ GT (ltEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.83/4.15	16[label="min1 GT LT (ltEsOrdering GT LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.83/4.15	17[label="min1 GT EQ (ltEsOrdering GT EQ)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.83/4.15	18[label="min1 GT GT (ltEsOrdering GT GT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.83/4.15	19[label="min1 LT LT MyTrue",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.83/4.15	20[label="min1 LT EQ MyTrue",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.83/4.15	21[label="min1 LT GT MyTrue",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.83/4.15	22[label="min1 EQ LT MyFalse",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.83/4.15	23[label="min1 EQ EQ MyTrue",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.83/4.15	24[label="min1 EQ GT MyTrue",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.83/4.15	25[label="min1 GT LT MyFalse",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.83/4.15	26[label="min1 GT EQ MyFalse",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.83/4.15	27[label="min1 GT GT MyTrue",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.83/4.15	28[label="LT",fontsize=16,color="green",shape="box"];29[label="LT",fontsize=16,color="green",shape="box"];30[label="LT",fontsize=16,color="green",shape="box"];31[label="min0 EQ LT otherwise",fontsize=16,color="black",shape="box"];31 -> 37[label="",style="solid", color="black", weight=3];
9.83/4.15	32[label="EQ",fontsize=16,color="green",shape="box"];33[label="EQ",fontsize=16,color="green",shape="box"];34[label="min0 GT LT otherwise",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
9.83/4.15	35[label="min0 GT EQ otherwise",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
9.83/4.15	36[label="GT",fontsize=16,color="green",shape="box"];37[label="min0 EQ LT MyTrue",fontsize=16,color="black",shape="box"];37 -> 40[label="",style="solid", color="black", weight=3];
9.83/4.15	38[label="min0 GT LT MyTrue",fontsize=16,color="black",shape="box"];38 -> 41[label="",style="solid", color="black", weight=3];
9.83/4.15	39[label="min0 GT EQ MyTrue",fontsize=16,color="black",shape="box"];39 -> 42[label="",style="solid", color="black", weight=3];
9.83/4.15	40[label="LT",fontsize=16,color="green",shape="box"];41[label="LT",fontsize=16,color="green",shape="box"];42[label="EQ",fontsize=16,color="green",shape="box"];}
9.83/4.15	
9.83/4.15	----------------------------------------
9.83/4.15	
9.83/4.15	(6)
9.83/4.15	YES
9.98/4.24	EOF