7.79/3.53	YES
9.43/4.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.43/4.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.43/4.03	
9.43/4.03	
9.43/4.03	H-Termination with start terms of the given HASKELL could be proven:
9.43/4.03	
9.43/4.03	(0) HASKELL
9.43/4.03	(1) BR [EQUIVALENT, 0 ms]
9.43/4.03	(2) HASKELL
9.43/4.03	(3) COR [EQUIVALENT, 0 ms]
9.43/4.03	(4) HASKELL
9.43/4.03	(5) Narrow [EQUIVALENT, 34 ms]
9.43/4.03	(6) YES
9.43/4.03	
9.43/4.03	
9.43/4.03	----------------------------------------
9.43/4.03	
9.43/4.03	(0)
9.43/4.03	Obligation:
9.43/4.03	mainModule Main 
9.43/4.03	module Main where {
9.43/4.03	import qualified Prelude;
9.43/4.03	data MyBool = MyTrue  | MyFalse ;
9.43/4.03	
9.43/4.03	data Ordering = LT  | EQ  | GT ;
9.43/4.03	
9.43/4.03	compare0 x y MyTrue = GT;
9.43/4.03	
9.43/4.03	compare1 x y MyTrue = LT;
9.43/4.03	compare1 x y MyFalse = compare0 x y otherwise;
9.43/4.03	
9.43/4.03	compare2 x y MyTrue = EQ;
9.43/4.03	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.43/4.03	
9.43/4.03	compare3 x y = compare2 x y (esEsOrdering x y);
9.43/4.03	
9.43/4.03	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.43/4.03	compareOrdering x y = compare3 x y;
9.43/4.03	
9.43/4.03	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.03	esEsOrdering LT LT = MyTrue;
9.43/4.03	esEsOrdering LT EQ = MyFalse;
9.43/4.03	esEsOrdering LT GT = MyFalse;
9.43/4.03	esEsOrdering EQ LT = MyFalse;
9.43/4.04	esEsOrdering EQ EQ = MyTrue;
9.43/4.04	esEsOrdering EQ GT = MyFalse;
9.43/4.04	esEsOrdering GT LT = MyFalse;
9.43/4.04	esEsOrdering GT EQ = MyFalse;
9.43/4.04	esEsOrdering GT GT = MyTrue;
9.43/4.04	
9.43/4.04	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	ltEsOrdering LT LT = MyTrue;
9.43/4.04	ltEsOrdering LT EQ = MyTrue;
9.43/4.04	ltEsOrdering LT GT = MyTrue;
9.43/4.04	ltEsOrdering EQ LT = MyFalse;
9.43/4.04	ltEsOrdering EQ EQ = MyTrue;
9.43/4.04	ltEsOrdering EQ GT = MyTrue;
9.43/4.04	ltEsOrdering GT LT = MyFalse;
9.43/4.04	ltEsOrdering GT EQ = MyFalse;
9.43/4.04	ltEsOrdering GT GT = MyTrue;
9.43/4.04	
9.43/4.04	ltOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	ltOrdering x y = esEsOrdering (compareOrdering x y) LT;
9.43/4.04	
9.43/4.04	otherwise :: MyBool;
9.43/4.04	otherwise = MyTrue;
9.43/4.04	
9.43/4.04	}
9.43/4.04	
9.43/4.04	----------------------------------------
9.43/4.04	
9.43/4.04	(1) BR (EQUIVALENT)
9.43/4.04	Replaced joker patterns by fresh variables and removed binding patterns.
9.43/4.04	----------------------------------------
9.43/4.04	
9.43/4.04	(2)
9.43/4.04	Obligation:
9.43/4.04	mainModule Main 
9.43/4.04	module Main where {
9.43/4.04	import qualified Prelude;
9.43/4.04	data MyBool = MyTrue  | MyFalse ;
9.43/4.04	
9.43/4.04	data Ordering = LT  | EQ  | GT ;
9.43/4.04	
9.43/4.04	compare0 x y MyTrue = GT;
9.43/4.04	
9.43/4.04	compare1 x y MyTrue = LT;
9.43/4.04	compare1 x y MyFalse = compare0 x y otherwise;
9.43/4.04	
9.43/4.04	compare2 x y MyTrue = EQ;
9.43/4.04	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.43/4.04	
9.43/4.04	compare3 x y = compare2 x y (esEsOrdering x y);
9.43/4.04	
9.43/4.04	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.43/4.04	compareOrdering x y = compare3 x y;
9.43/4.04	
9.43/4.04	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	esEsOrdering LT LT = MyTrue;
9.43/4.04	esEsOrdering LT EQ = MyFalse;
9.43/4.04	esEsOrdering LT GT = MyFalse;
9.43/4.04	esEsOrdering EQ LT = MyFalse;
9.43/4.04	esEsOrdering EQ EQ = MyTrue;
9.43/4.04	esEsOrdering EQ GT = MyFalse;
9.43/4.04	esEsOrdering GT LT = MyFalse;
9.43/4.04	esEsOrdering GT EQ = MyFalse;
9.43/4.04	esEsOrdering GT GT = MyTrue;
9.43/4.04	
9.43/4.04	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	ltEsOrdering LT LT = MyTrue;
9.43/4.04	ltEsOrdering LT EQ = MyTrue;
9.43/4.04	ltEsOrdering LT GT = MyTrue;
9.43/4.04	ltEsOrdering EQ LT = MyFalse;
9.43/4.04	ltEsOrdering EQ EQ = MyTrue;
9.43/4.04	ltEsOrdering EQ GT = MyTrue;
9.43/4.04	ltEsOrdering GT LT = MyFalse;
9.43/4.04	ltEsOrdering GT EQ = MyFalse;
9.43/4.04	ltEsOrdering GT GT = MyTrue;
9.43/4.04	
9.43/4.04	ltOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	ltOrdering x y = esEsOrdering (compareOrdering x y) LT;
9.43/4.04	
9.43/4.04	otherwise :: MyBool;
9.43/4.04	otherwise = MyTrue;
9.43/4.04	
9.43/4.04	}
9.43/4.04	
9.43/4.04	----------------------------------------
9.43/4.04	
9.43/4.04	(3) COR (EQUIVALENT)
9.43/4.04	Cond Reductions:
9.43/4.04	The following Function with conditions
9.43/4.04	"undefined |Falseundefined;
9.43/4.04	"
9.43/4.04	is transformed to
9.43/4.04	"undefined  = undefined1;
9.43/4.04	"
9.43/4.04	"undefined0 True = undefined;
9.43/4.04	"
9.43/4.04	"undefined1  = undefined0 False;
9.43/4.04	"
9.43/4.04	
9.43/4.04	----------------------------------------
9.43/4.04	
9.43/4.04	(4)
9.43/4.04	Obligation:
9.43/4.04	mainModule Main 
9.43/4.04	module Main where {
9.43/4.04	import qualified Prelude;
9.43/4.04	data MyBool = MyTrue  | MyFalse ;
9.43/4.04	
9.43/4.04	data Ordering = LT  | EQ  | GT ;
9.43/4.04	
9.43/4.04	compare0 x y MyTrue = GT;
9.43/4.04	
9.43/4.04	compare1 x y MyTrue = LT;
9.43/4.04	compare1 x y MyFalse = compare0 x y otherwise;
9.43/4.04	
9.43/4.04	compare2 x y MyTrue = EQ;
9.43/4.04	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.43/4.04	
9.43/4.04	compare3 x y = compare2 x y (esEsOrdering x y);
9.43/4.04	
9.43/4.04	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.43/4.04	compareOrdering x y = compare3 x y;
9.43/4.04	
9.43/4.04	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	esEsOrdering LT LT = MyTrue;
9.43/4.04	esEsOrdering LT EQ = MyFalse;
9.43/4.04	esEsOrdering LT GT = MyFalse;
9.43/4.04	esEsOrdering EQ LT = MyFalse;
9.43/4.04	esEsOrdering EQ EQ = MyTrue;
9.43/4.04	esEsOrdering EQ GT = MyFalse;
9.43/4.04	esEsOrdering GT LT = MyFalse;
9.43/4.04	esEsOrdering GT EQ = MyFalse;
9.43/4.04	esEsOrdering GT GT = MyTrue;
9.43/4.04	
9.43/4.04	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	ltEsOrdering LT LT = MyTrue;
9.43/4.04	ltEsOrdering LT EQ = MyTrue;
9.43/4.04	ltEsOrdering LT GT = MyTrue;
9.43/4.04	ltEsOrdering EQ LT = MyFalse;
9.43/4.04	ltEsOrdering EQ EQ = MyTrue;
9.43/4.04	ltEsOrdering EQ GT = MyTrue;
9.43/4.04	ltEsOrdering GT LT = MyFalse;
9.43/4.04	ltEsOrdering GT EQ = MyFalse;
9.43/4.04	ltEsOrdering GT GT = MyTrue;
9.43/4.04	
9.43/4.04	ltOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.04	ltOrdering x y = esEsOrdering (compareOrdering x y) LT;
9.43/4.04	
9.43/4.04	otherwise :: MyBool;
9.43/4.04	otherwise = MyTrue;
9.43/4.04	
9.43/4.04	}
9.43/4.04	
9.43/4.04	----------------------------------------
9.43/4.04	
9.43/4.04	(5) Narrow (EQUIVALENT)
9.43/4.04	Haskell To QDPs
9.43/4.04	
9.43/4.04	digraph dp_graph {
9.43/4.04	node [outthreshold=100, inthreshold=100];1[label="ltOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.43/4.04	3[label="ltOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.43/4.04	4[label="ltOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.43/4.04	5[label="esEsOrdering (compareOrdering vx3 vx4) LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.43/4.04	6[label="esEsOrdering (compare3 vx3 vx4) LT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.43/4.04	7[label="esEsOrdering (compare2 vx3 vx4 (esEsOrdering vx3 vx4)) LT",fontsize=16,color="burlywood",shape="box"];59[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 59[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	59 -> 8[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	60[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	60 -> 9[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	61[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 61[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	61 -> 10[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	8[label="esEsOrdering (compare2 LT vx4 (esEsOrdering LT vx4)) LT",fontsize=16,color="burlywood",shape="box"];62[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 62[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	62 -> 11[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	63[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	63 -> 12[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	64[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 64[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	64 -> 13[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	9[label="esEsOrdering (compare2 EQ vx4 (esEsOrdering EQ vx4)) LT",fontsize=16,color="burlywood",shape="box"];65[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 65[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	65 -> 14[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	66[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	66 -> 15[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	67[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 67[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	67 -> 16[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	10[label="esEsOrdering (compare2 GT vx4 (esEsOrdering GT vx4)) LT",fontsize=16,color="burlywood",shape="box"];68[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];10 -> 68[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	68 -> 17[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	69[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	69 -> 18[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	70[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
9.43/4.04	70 -> 19[label="",style="solid", color="burlywood", weight=3];
9.43/4.04	11[label="esEsOrdering (compare2 LT LT (esEsOrdering LT LT)) LT",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.43/4.04	12[label="esEsOrdering (compare2 LT EQ (esEsOrdering LT EQ)) LT",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.43/4.04	13[label="esEsOrdering (compare2 LT GT (esEsOrdering LT GT)) LT",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.43/4.04	14[label="esEsOrdering (compare2 EQ LT (esEsOrdering EQ LT)) LT",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.43/4.04	15[label="esEsOrdering (compare2 EQ EQ (esEsOrdering EQ EQ)) LT",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.43/4.04	16[label="esEsOrdering (compare2 EQ GT (esEsOrdering EQ GT)) LT",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.43/4.04	17[label="esEsOrdering (compare2 GT LT (esEsOrdering GT LT)) LT",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.43/4.04	18[label="esEsOrdering (compare2 GT EQ (esEsOrdering GT EQ)) LT",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.43/4.04	19[label="esEsOrdering (compare2 GT GT (esEsOrdering GT GT)) LT",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.43/4.04	20[label="esEsOrdering (compare2 LT LT MyTrue) LT",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.43/4.04	21[label="esEsOrdering (compare2 LT EQ MyFalse) LT",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.43/4.04	22[label="esEsOrdering (compare2 LT GT MyFalse) LT",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.43/4.04	23[label="esEsOrdering (compare2 EQ LT MyFalse) LT",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.43/4.04	24[label="esEsOrdering (compare2 EQ EQ MyTrue) LT",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.43/4.04	25[label="esEsOrdering (compare2 EQ GT MyFalse) LT",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.43/4.04	26[label="esEsOrdering (compare2 GT LT MyFalse) LT",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.43/4.04	27[label="esEsOrdering (compare2 GT EQ MyFalse) LT",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.43/4.04	28[label="esEsOrdering (compare2 GT GT MyTrue) LT",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
9.43/4.04	29[label="esEsOrdering EQ LT",fontsize=16,color="black",shape="triangle"];29 -> 38[label="",style="solid", color="black", weight=3];
9.43/4.04	30[label="esEsOrdering (compare1 LT EQ (ltEsOrdering LT EQ)) LT",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
9.43/4.04	31[label="esEsOrdering (compare1 LT GT (ltEsOrdering LT GT)) LT",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
9.43/4.04	32[label="esEsOrdering (compare1 EQ LT (ltEsOrdering EQ LT)) LT",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
9.43/4.04	33 -> 29[label="",style="dashed", color="red", weight=0];
9.43/4.04	33[label="esEsOrdering EQ LT",fontsize=16,color="magenta"];34[label="esEsOrdering (compare1 EQ GT (ltEsOrdering EQ GT)) LT",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3];
9.43/4.04	35[label="esEsOrdering (compare1 GT LT (ltEsOrdering GT LT)) LT",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
9.43/4.04	36[label="esEsOrdering (compare1 GT EQ (ltEsOrdering GT EQ)) LT",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
9.43/4.04	37 -> 29[label="",style="dashed", color="red", weight=0];
9.43/4.04	37[label="esEsOrdering EQ LT",fontsize=16,color="magenta"];38[label="MyFalse",fontsize=16,color="green",shape="box"];39[label="esEsOrdering (compare1 LT EQ MyTrue) LT",fontsize=16,color="black",shape="box"];39 -> 45[label="",style="solid", color="black", weight=3];
9.43/4.04	40[label="esEsOrdering (compare1 LT GT MyTrue) LT",fontsize=16,color="black",shape="box"];40 -> 46[label="",style="solid", color="black", weight=3];
9.43/4.04	41[label="esEsOrdering (compare1 EQ LT MyFalse) LT",fontsize=16,color="black",shape="box"];41 -> 47[label="",style="solid", color="black", weight=3];
9.43/4.04	42[label="esEsOrdering (compare1 EQ GT MyTrue) LT",fontsize=16,color="black",shape="box"];42 -> 48[label="",style="solid", color="black", weight=3];
9.43/4.04	43[label="esEsOrdering (compare1 GT LT MyFalse) LT",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
9.43/4.04	44[label="esEsOrdering (compare1 GT EQ MyFalse) LT",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
9.43/4.04	45[label="esEsOrdering LT LT",fontsize=16,color="black",shape="triangle"];45 -> 51[label="",style="solid", color="black", weight=3];
9.43/4.04	46 -> 45[label="",style="dashed", color="red", weight=0];
9.43/4.04	46[label="esEsOrdering LT LT",fontsize=16,color="magenta"];47[label="esEsOrdering (compare0 EQ LT otherwise) LT",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
9.43/4.04	48 -> 45[label="",style="dashed", color="red", weight=0];
9.43/4.04	48[label="esEsOrdering LT LT",fontsize=16,color="magenta"];49[label="esEsOrdering (compare0 GT LT otherwise) LT",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
9.43/4.04	50[label="esEsOrdering (compare0 GT EQ otherwise) LT",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
9.43/4.04	51[label="MyTrue",fontsize=16,color="green",shape="box"];52[label="esEsOrdering (compare0 EQ LT MyTrue) LT",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3];
9.43/4.04	53[label="esEsOrdering (compare0 GT LT MyTrue) LT",fontsize=16,color="black",shape="box"];53 -> 56[label="",style="solid", color="black", weight=3];
9.43/4.04	54[label="esEsOrdering (compare0 GT EQ MyTrue) LT",fontsize=16,color="black",shape="box"];54 -> 57[label="",style="solid", color="black", weight=3];
9.43/4.04	55[label="esEsOrdering GT LT",fontsize=16,color="black",shape="triangle"];55 -> 58[label="",style="solid", color="black", weight=3];
9.43/4.04	56 -> 55[label="",style="dashed", color="red", weight=0];
9.43/4.04	56[label="esEsOrdering GT LT",fontsize=16,color="magenta"];57 -> 55[label="",style="dashed", color="red", weight=0];
9.43/4.04	57[label="esEsOrdering GT LT",fontsize=16,color="magenta"];58[label="MyFalse",fontsize=16,color="green",shape="box"];}
9.43/4.04	
9.43/4.04	----------------------------------------
9.43/4.04	
9.43/4.04	(6)
9.43/4.04	YES
9.66/4.09	EOF