7.69/3.56	YES
9.39/4.06	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.39/4.06	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.39/4.06	
9.39/4.06	
9.39/4.06	H-Termination with start terms of the given HASKELL could be proven:
9.39/4.06	
9.39/4.06	(0) HASKELL
9.39/4.06	(1) BR [EQUIVALENT, 0 ms]
9.39/4.06	(2) HASKELL
9.39/4.06	(3) COR [EQUIVALENT, 0 ms]
9.39/4.06	(4) HASKELL
9.39/4.06	(5) Narrow [EQUIVALENT, 34 ms]
9.39/4.06	(6) YES
9.39/4.06	
9.39/4.06	
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(0)
9.39/4.06	Obligation:
9.39/4.06	mainModule Main 
9.39/4.06	module Main where {
9.39/4.06	import qualified Prelude;
9.39/4.06	data MyBool = MyTrue  | MyFalse ;
9.39/4.06	
9.39/4.06	data Ordering = LT  | EQ  | GT ;
9.39/4.06	
9.39/4.06	compare0 x y MyTrue = GT;
9.39/4.06	
9.39/4.06	compare1 x y MyTrue = LT;
9.39/4.06	compare1 x y MyFalse = compare0 x y otherwise;
9.39/4.06	
9.39/4.06	compare2 x y MyTrue = EQ;
9.39/4.06	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.39/4.06	
9.39/4.06	compare3 x y = compare2 x y (esEsOrdering x y);
9.39/4.06	
9.39/4.06	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.39/4.06	compareOrdering x y = compare3 x y;
9.39/4.06	
9.39/4.06	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	esEsOrdering LT LT = MyTrue;
9.39/4.06	esEsOrdering LT EQ = MyFalse;
9.39/4.06	esEsOrdering LT GT = MyFalse;
9.39/4.06	esEsOrdering EQ LT = MyFalse;
9.39/4.06	esEsOrdering EQ EQ = MyTrue;
9.39/4.06	esEsOrdering EQ GT = MyFalse;
9.39/4.06	esEsOrdering GT LT = MyFalse;
9.39/4.06	esEsOrdering GT EQ = MyFalse;
9.39/4.06	esEsOrdering GT GT = MyTrue;
9.39/4.06	
9.39/4.06	gtOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	gtOrdering x y = esEsOrdering (compareOrdering x y) GT;
9.39/4.06	
9.39/4.06	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	ltEsOrdering LT LT = MyTrue;
9.39/4.06	ltEsOrdering LT EQ = MyTrue;
9.39/4.06	ltEsOrdering LT GT = MyTrue;
9.39/4.06	ltEsOrdering EQ LT = MyFalse;
9.39/4.06	ltEsOrdering EQ EQ = MyTrue;
9.39/4.06	ltEsOrdering EQ GT = MyTrue;
9.39/4.06	ltEsOrdering GT LT = MyFalse;
9.39/4.06	ltEsOrdering GT EQ = MyFalse;
9.39/4.06	ltEsOrdering GT GT = MyTrue;
9.39/4.06	
9.39/4.06	otherwise :: MyBool;
9.39/4.06	otherwise = MyTrue;
9.39/4.06	
9.39/4.06	}
9.39/4.06	
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(1) BR (EQUIVALENT)
9.39/4.06	Replaced joker patterns by fresh variables and removed binding patterns.
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(2)
9.39/4.06	Obligation:
9.39/4.06	mainModule Main 
9.39/4.06	module Main where {
9.39/4.06	import qualified Prelude;
9.39/4.06	data MyBool = MyTrue  | MyFalse ;
9.39/4.06	
9.39/4.06	data Ordering = LT  | EQ  | GT ;
9.39/4.06	
9.39/4.06	compare0 x y MyTrue = GT;
9.39/4.06	
9.39/4.06	compare1 x y MyTrue = LT;
9.39/4.06	compare1 x y MyFalse = compare0 x y otherwise;
9.39/4.06	
9.39/4.06	compare2 x y MyTrue = EQ;
9.39/4.06	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.39/4.06	
9.39/4.06	compare3 x y = compare2 x y (esEsOrdering x y);
9.39/4.06	
9.39/4.06	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.39/4.06	compareOrdering x y = compare3 x y;
9.39/4.06	
9.39/4.06	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	esEsOrdering LT LT = MyTrue;
9.39/4.06	esEsOrdering LT EQ = MyFalse;
9.39/4.06	esEsOrdering LT GT = MyFalse;
9.39/4.06	esEsOrdering EQ LT = MyFalse;
9.39/4.06	esEsOrdering EQ EQ = MyTrue;
9.39/4.06	esEsOrdering EQ GT = MyFalse;
9.39/4.06	esEsOrdering GT LT = MyFalse;
9.39/4.06	esEsOrdering GT EQ = MyFalse;
9.39/4.06	esEsOrdering GT GT = MyTrue;
9.39/4.06	
9.39/4.06	gtOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	gtOrdering x y = esEsOrdering (compareOrdering x y) GT;
9.39/4.06	
9.39/4.06	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	ltEsOrdering LT LT = MyTrue;
9.39/4.06	ltEsOrdering LT EQ = MyTrue;
9.39/4.06	ltEsOrdering LT GT = MyTrue;
9.39/4.06	ltEsOrdering EQ LT = MyFalse;
9.39/4.06	ltEsOrdering EQ EQ = MyTrue;
9.39/4.06	ltEsOrdering EQ GT = MyTrue;
9.39/4.06	ltEsOrdering GT LT = MyFalse;
9.39/4.06	ltEsOrdering GT EQ = MyFalse;
9.39/4.06	ltEsOrdering GT GT = MyTrue;
9.39/4.06	
9.39/4.06	otherwise :: MyBool;
9.39/4.06	otherwise = MyTrue;
9.39/4.06	
9.39/4.06	}
9.39/4.06	
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(3) COR (EQUIVALENT)
9.39/4.06	Cond Reductions:
9.39/4.06	The following Function with conditions
9.39/4.06	"undefined |Falseundefined;
9.39/4.06	"
9.39/4.06	is transformed to
9.39/4.06	"undefined  = undefined1;
9.39/4.06	"
9.39/4.06	"undefined0 True = undefined;
9.39/4.06	"
9.39/4.06	"undefined1  = undefined0 False;
9.39/4.06	"
9.39/4.06	
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(4)
9.39/4.06	Obligation:
9.39/4.06	mainModule Main 
9.39/4.06	module Main where {
9.39/4.06	import qualified Prelude;
9.39/4.06	data MyBool = MyTrue  | MyFalse ;
9.39/4.06	
9.39/4.06	data Ordering = LT  | EQ  | GT ;
9.39/4.06	
9.39/4.06	compare0 x y MyTrue = GT;
9.39/4.06	
9.39/4.06	compare1 x y MyTrue = LT;
9.39/4.06	compare1 x y MyFalse = compare0 x y otherwise;
9.39/4.06	
9.39/4.06	compare2 x y MyTrue = EQ;
9.39/4.06	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.39/4.06	
9.39/4.06	compare3 x y = compare2 x y (esEsOrdering x y);
9.39/4.06	
9.39/4.06	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.39/4.06	compareOrdering x y = compare3 x y;
9.39/4.06	
9.39/4.06	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	esEsOrdering LT LT = MyTrue;
9.39/4.06	esEsOrdering LT EQ = MyFalse;
9.39/4.06	esEsOrdering LT GT = MyFalse;
9.39/4.06	esEsOrdering EQ LT = MyFalse;
9.39/4.06	esEsOrdering EQ EQ = MyTrue;
9.39/4.06	esEsOrdering EQ GT = MyFalse;
9.39/4.06	esEsOrdering GT LT = MyFalse;
9.39/4.06	esEsOrdering GT EQ = MyFalse;
9.39/4.06	esEsOrdering GT GT = MyTrue;
9.39/4.06	
9.39/4.06	gtOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	gtOrdering x y = esEsOrdering (compareOrdering x y) GT;
9.39/4.06	
9.39/4.06	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.39/4.06	ltEsOrdering LT LT = MyTrue;
9.39/4.06	ltEsOrdering LT EQ = MyTrue;
9.39/4.06	ltEsOrdering LT GT = MyTrue;
9.39/4.06	ltEsOrdering EQ LT = MyFalse;
9.39/4.06	ltEsOrdering EQ EQ = MyTrue;
9.39/4.06	ltEsOrdering EQ GT = MyTrue;
9.39/4.06	ltEsOrdering GT LT = MyFalse;
9.39/4.06	ltEsOrdering GT EQ = MyFalse;
9.39/4.06	ltEsOrdering GT GT = MyTrue;
9.39/4.06	
9.39/4.06	otherwise :: MyBool;
9.39/4.06	otherwise = MyTrue;
9.39/4.06	
9.39/4.06	}
9.39/4.06	
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(5) Narrow (EQUIVALENT)
9.39/4.06	Haskell To QDPs
9.39/4.06	
9.39/4.06	digraph dp_graph {
9.39/4.06	node [outthreshold=100, inthreshold=100];1[label="gtOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.39/4.06	3[label="gtOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.39/4.06	4[label="gtOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.39/4.06	5[label="esEsOrdering (compareOrdering vx3 vx4) GT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.39/4.06	6[label="esEsOrdering (compare3 vx3 vx4) GT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.39/4.06	7[label="esEsOrdering (compare2 vx3 vx4 (esEsOrdering vx3 vx4)) GT",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];
9.39/4.06	59 -> 8[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	60[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	60 -> 9[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	61[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 61[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	61 -> 10[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	8[label="esEsOrdering (compare2 LT vx4 (esEsOrdering LT vx4)) GT",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];
9.39/4.06	62 -> 11[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	63[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	63 -> 12[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	64[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 64[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	64 -> 13[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	9[label="esEsOrdering (compare2 EQ vx4 (esEsOrdering EQ vx4)) GT",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];
9.39/4.06	65 -> 14[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	66[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	66 -> 15[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	67[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 67[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	67 -> 16[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	10[label="esEsOrdering (compare2 GT vx4 (esEsOrdering GT vx4)) GT",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];
9.39/4.06	68 -> 17[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	69[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	69 -> 18[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	70[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
9.39/4.06	70 -> 19[label="",style="solid", color="burlywood", weight=3];
9.39/4.06	11[label="esEsOrdering (compare2 LT LT (esEsOrdering LT LT)) GT",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.39/4.06	12[label="esEsOrdering (compare2 LT EQ (esEsOrdering LT EQ)) GT",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.39/4.06	13[label="esEsOrdering (compare2 LT GT (esEsOrdering LT GT)) GT",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.39/4.06	14[label="esEsOrdering (compare2 EQ LT (esEsOrdering EQ LT)) GT",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.39/4.06	15[label="esEsOrdering (compare2 EQ EQ (esEsOrdering EQ EQ)) GT",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.39/4.06	16[label="esEsOrdering (compare2 EQ GT (esEsOrdering EQ GT)) GT",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.39/4.06	17[label="esEsOrdering (compare2 GT LT (esEsOrdering GT LT)) GT",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.39/4.06	18[label="esEsOrdering (compare2 GT EQ (esEsOrdering GT EQ)) GT",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.39/4.06	19[label="esEsOrdering (compare2 GT GT (esEsOrdering GT GT)) GT",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.39/4.06	20[label="esEsOrdering (compare2 LT LT MyTrue) GT",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.39/4.06	21[label="esEsOrdering (compare2 LT EQ MyFalse) GT",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.39/4.06	22[label="esEsOrdering (compare2 LT GT MyFalse) GT",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.39/4.06	23[label="esEsOrdering (compare2 EQ LT MyFalse) GT",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.39/4.06	24[label="esEsOrdering (compare2 EQ EQ MyTrue) GT",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.39/4.06	25[label="esEsOrdering (compare2 EQ GT MyFalse) GT",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.39/4.06	26[label="esEsOrdering (compare2 GT LT MyFalse) GT",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.39/4.06	27[label="esEsOrdering (compare2 GT EQ MyFalse) GT",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.39/4.06	28[label="esEsOrdering (compare2 GT GT MyTrue) GT",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
9.39/4.06	29[label="esEsOrdering EQ GT",fontsize=16,color="black",shape="triangle"];29 -> 38[label="",style="solid", color="black", weight=3];
9.39/4.06	30[label="esEsOrdering (compare1 LT EQ (ltEsOrdering LT EQ)) GT",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
9.39/4.06	31[label="esEsOrdering (compare1 LT GT (ltEsOrdering LT GT)) GT",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
9.39/4.06	32[label="esEsOrdering (compare1 EQ LT (ltEsOrdering EQ LT)) GT",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
9.39/4.06	33 -> 29[label="",style="dashed", color="red", weight=0];
9.39/4.06	33[label="esEsOrdering EQ GT",fontsize=16,color="magenta"];34[label="esEsOrdering (compare1 EQ GT (ltEsOrdering EQ GT)) GT",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3];
9.39/4.06	35[label="esEsOrdering (compare1 GT LT (ltEsOrdering GT LT)) GT",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
9.39/4.06	36[label="esEsOrdering (compare1 GT EQ (ltEsOrdering GT EQ)) GT",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
9.39/4.06	37 -> 29[label="",style="dashed", color="red", weight=0];
9.39/4.06	37[label="esEsOrdering EQ GT",fontsize=16,color="magenta"];38[label="MyFalse",fontsize=16,color="green",shape="box"];39[label="esEsOrdering (compare1 LT EQ MyTrue) GT",fontsize=16,color="black",shape="box"];39 -> 45[label="",style="solid", color="black", weight=3];
9.39/4.06	40[label="esEsOrdering (compare1 LT GT MyTrue) GT",fontsize=16,color="black",shape="box"];40 -> 46[label="",style="solid", color="black", weight=3];
9.39/4.06	41[label="esEsOrdering (compare1 EQ LT MyFalse) GT",fontsize=16,color="black",shape="box"];41 -> 47[label="",style="solid", color="black", weight=3];
9.39/4.06	42[label="esEsOrdering (compare1 EQ GT MyTrue) GT",fontsize=16,color="black",shape="box"];42 -> 48[label="",style="solid", color="black", weight=3];
9.39/4.06	43[label="esEsOrdering (compare1 GT LT MyFalse) GT",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
9.39/4.06	44[label="esEsOrdering (compare1 GT EQ MyFalse) GT",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
9.39/4.06	45[label="esEsOrdering LT GT",fontsize=16,color="black",shape="triangle"];45 -> 51[label="",style="solid", color="black", weight=3];
9.39/4.06	46 -> 45[label="",style="dashed", color="red", weight=0];
9.39/4.06	46[label="esEsOrdering LT GT",fontsize=16,color="magenta"];47[label="esEsOrdering (compare0 EQ LT otherwise) GT",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
9.39/4.06	48 -> 45[label="",style="dashed", color="red", weight=0];
9.39/4.06	48[label="esEsOrdering LT GT",fontsize=16,color="magenta"];49[label="esEsOrdering (compare0 GT LT otherwise) GT",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
9.39/4.06	50[label="esEsOrdering (compare0 GT EQ otherwise) GT",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
9.39/4.06	51[label="MyFalse",fontsize=16,color="green",shape="box"];52[label="esEsOrdering (compare0 EQ LT MyTrue) GT",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3];
9.39/4.06	53[label="esEsOrdering (compare0 GT LT MyTrue) GT",fontsize=16,color="black",shape="box"];53 -> 56[label="",style="solid", color="black", weight=3];
9.39/4.06	54[label="esEsOrdering (compare0 GT EQ MyTrue) GT",fontsize=16,color="black",shape="box"];54 -> 57[label="",style="solid", color="black", weight=3];
9.39/4.06	55[label="esEsOrdering GT GT",fontsize=16,color="black",shape="triangle"];55 -> 58[label="",style="solid", color="black", weight=3];
9.39/4.06	56 -> 55[label="",style="dashed", color="red", weight=0];
9.39/4.06	56[label="esEsOrdering GT GT",fontsize=16,color="magenta"];57 -> 55[label="",style="dashed", color="red", weight=0];
9.39/4.06	57[label="esEsOrdering GT GT",fontsize=16,color="magenta"];58[label="MyTrue",fontsize=16,color="green",shape="box"];}
9.39/4.06	
9.39/4.06	----------------------------------------
9.39/4.06	
9.39/4.06	(6)
9.39/4.06	YES
9.54/8.48	EOF