7.44/3.54	YES
9.59/4.05	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.59/4.05	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.59/4.05	
9.59/4.05	
9.59/4.05	H-Termination with start terms of the given HASKELL could be proven:
9.59/4.05	
9.59/4.05	(0) HASKELL
9.59/4.05	(1) BR [EQUIVALENT, 0 ms]
9.59/4.05	(2) HASKELL
9.59/4.05	(3) COR [EQUIVALENT, 0 ms]
9.59/4.05	(4) HASKELL
9.59/4.05	(5) Narrow [EQUIVALENT, 39 ms]
9.59/4.05	(6) YES
9.59/4.05	
9.59/4.05	
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(0)
9.59/4.05	Obligation:
9.59/4.05	mainModule Main 
9.59/4.05	module Main where {
9.59/4.05	import qualified Prelude;
9.59/4.05	data MyBool = MyTrue  | MyFalse ;
9.59/4.05	
9.59/4.05	data Ordering = LT  | EQ  | GT ;
9.59/4.05	
9.59/4.05	compare0 x y MyTrue = GT;
9.59/4.05	
9.59/4.05	compare1 x y MyTrue = LT;
9.59/4.05	compare1 x y MyFalse = compare0 x y otherwise;
9.59/4.05	
9.59/4.05	compare2 x y MyTrue = EQ;
9.59/4.05	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.59/4.05	
9.59/4.05	compare3 x y = compare2 x y (esEsOrdering x y);
9.59/4.05	
9.59/4.05	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.59/4.05	compareOrdering x y = compare3 x y;
9.59/4.05	
9.59/4.05	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.59/4.05	esEsOrdering LT LT = MyTrue;
9.59/4.05	esEsOrdering LT EQ = MyFalse;
9.59/4.05	esEsOrdering LT GT = MyFalse;
9.59/4.05	esEsOrdering EQ LT = MyFalse;
9.59/4.05	esEsOrdering EQ EQ = MyTrue;
9.59/4.05	esEsOrdering EQ GT = MyFalse;
9.59/4.05	esEsOrdering GT LT = MyFalse;
9.59/4.05	esEsOrdering GT EQ = MyFalse;
9.59/4.05	esEsOrdering GT GT = MyTrue;
9.59/4.05	
9.59/4.05	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.59/4.05	ltEsOrdering LT LT = MyTrue;
9.59/4.05	ltEsOrdering LT EQ = MyTrue;
9.59/4.05	ltEsOrdering LT GT = MyTrue;
9.59/4.05	ltEsOrdering EQ LT = MyFalse;
9.59/4.05	ltEsOrdering EQ EQ = MyTrue;
9.59/4.05	ltEsOrdering EQ GT = MyTrue;
9.59/4.05	ltEsOrdering GT LT = MyFalse;
9.59/4.05	ltEsOrdering GT EQ = MyFalse;
9.59/4.05	ltEsOrdering GT GT = MyTrue;
9.59/4.05	
9.59/4.05	otherwise :: MyBool;
9.59/4.05	otherwise = MyTrue;
9.59/4.05	
9.59/4.05	}
9.59/4.05	
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(1) BR (EQUIVALENT)
9.59/4.05	Replaced joker patterns by fresh variables and removed binding patterns.
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(2)
9.59/4.05	Obligation:
9.59/4.05	mainModule Main 
9.59/4.05	module Main where {
9.59/4.05	import qualified Prelude;
9.59/4.05	data MyBool = MyTrue  | MyFalse ;
9.59/4.05	
9.59/4.05	data Ordering = LT  | EQ  | GT ;
9.59/4.05	
9.59/4.05	compare0 x y MyTrue = GT;
9.59/4.05	
9.59/4.05	compare1 x y MyTrue = LT;
9.59/4.05	compare1 x y MyFalse = compare0 x y otherwise;
9.59/4.05	
9.59/4.05	compare2 x y MyTrue = EQ;
9.59/4.05	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.59/4.05	
9.59/4.05	compare3 x y = compare2 x y (esEsOrdering x y);
9.59/4.05	
9.59/4.05	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.59/4.05	compareOrdering x y = compare3 x y;
9.59/4.05	
9.59/4.05	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.59/4.05	esEsOrdering LT LT = MyTrue;
9.59/4.05	esEsOrdering LT EQ = MyFalse;
9.59/4.05	esEsOrdering LT GT = MyFalse;
9.59/4.05	esEsOrdering EQ LT = MyFalse;
9.59/4.05	esEsOrdering EQ EQ = MyTrue;
9.59/4.05	esEsOrdering EQ GT = MyFalse;
9.59/4.05	esEsOrdering GT LT = MyFalse;
9.59/4.05	esEsOrdering GT EQ = MyFalse;
9.59/4.05	esEsOrdering GT GT = MyTrue;
9.59/4.05	
9.59/4.05	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.59/4.05	ltEsOrdering LT LT = MyTrue;
9.59/4.05	ltEsOrdering LT EQ = MyTrue;
9.59/4.05	ltEsOrdering LT GT = MyTrue;
9.59/4.05	ltEsOrdering EQ LT = MyFalse;
9.59/4.05	ltEsOrdering EQ EQ = MyTrue;
9.59/4.05	ltEsOrdering EQ GT = MyTrue;
9.59/4.05	ltEsOrdering GT LT = MyFalse;
9.59/4.05	ltEsOrdering GT EQ = MyFalse;
9.59/4.05	ltEsOrdering GT GT = MyTrue;
9.59/4.05	
9.59/4.05	otherwise :: MyBool;
9.59/4.05	otherwise = MyTrue;
9.59/4.05	
9.59/4.05	}
9.59/4.05	
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(3) COR (EQUIVALENT)
9.59/4.05	Cond Reductions:
9.59/4.05	The following Function with conditions
9.59/4.05	"undefined |Falseundefined;
9.59/4.05	"
9.59/4.05	is transformed to
9.59/4.05	"undefined  = undefined1;
9.59/4.05	"
9.59/4.05	"undefined0 True = undefined;
9.59/4.05	"
9.59/4.05	"undefined1  = undefined0 False;
9.59/4.05	"
9.59/4.05	
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(4)
9.59/4.05	Obligation:
9.59/4.05	mainModule Main 
9.59/4.05	module Main where {
9.59/4.05	import qualified Prelude;
9.59/4.05	data MyBool = MyTrue  | MyFalse ;
9.59/4.05	
9.59/4.05	data Ordering = LT  | EQ  | GT ;
9.59/4.05	
9.59/4.05	compare0 x y MyTrue = GT;
9.59/4.05	
9.59/4.05	compare1 x y MyTrue = LT;
9.59/4.05	compare1 x y MyFalse = compare0 x y otherwise;
9.59/4.05	
9.59/4.05	compare2 x y MyTrue = EQ;
9.59/4.05	compare2 x y MyFalse = compare1 x y (ltEsOrdering x y);
9.59/4.05	
9.59/4.05	compare3 x y = compare2 x y (esEsOrdering x y);
9.59/4.05	
9.59/4.05	compareOrdering :: Ordering  ->  Ordering  ->  Ordering;
9.59/4.05	compareOrdering x y = compare3 x y;
9.59/4.05	
9.59/4.05	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.59/4.05	esEsOrdering LT LT = MyTrue;
9.59/4.05	esEsOrdering LT EQ = MyFalse;
9.59/4.05	esEsOrdering LT GT = MyFalse;
9.59/4.05	esEsOrdering EQ LT = MyFalse;
9.59/4.05	esEsOrdering EQ EQ = MyTrue;
9.59/4.05	esEsOrdering EQ GT = MyFalse;
9.59/4.05	esEsOrdering GT LT = MyFalse;
9.59/4.05	esEsOrdering GT EQ = MyFalse;
9.59/4.05	esEsOrdering GT GT = MyTrue;
9.59/4.05	
9.59/4.05	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.59/4.05	ltEsOrdering LT LT = MyTrue;
9.59/4.05	ltEsOrdering LT EQ = MyTrue;
9.59/4.05	ltEsOrdering LT GT = MyTrue;
9.59/4.05	ltEsOrdering EQ LT = MyFalse;
9.59/4.05	ltEsOrdering EQ EQ = MyTrue;
9.59/4.05	ltEsOrdering EQ GT = MyTrue;
9.59/4.05	ltEsOrdering GT LT = MyFalse;
9.59/4.05	ltEsOrdering GT EQ = MyFalse;
9.59/4.05	ltEsOrdering GT GT = MyTrue;
9.59/4.05	
9.59/4.05	otherwise :: MyBool;
9.59/4.05	otherwise = MyTrue;
9.59/4.05	
9.59/4.05	}
9.59/4.05	
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(5) Narrow (EQUIVALENT)
9.59/4.05	Haskell To QDPs
9.59/4.05	
9.59/4.05	digraph dp_graph {
9.59/4.05	node [outthreshold=100, inthreshold=100];1[label="compareOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.59/4.05	3[label="compareOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.59/4.05	4[label="compareOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.59/4.05	5[label="compare3 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.59/4.05	6[label="compare2 vx3 vx4 (esEsOrdering vx3 vx4)",fontsize=16,color="burlywood",shape="box"];55[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 55[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	55 -> 7[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	56[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 56[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	56 -> 8[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	57[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 57[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	57 -> 9[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	7[label="compare2 LT vx4 (esEsOrdering LT vx4)",fontsize=16,color="burlywood",shape="box"];58[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 58[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	58 -> 10[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	59[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 59[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	59 -> 11[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	60[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	60 -> 12[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	8[label="compare2 EQ vx4 (esEsOrdering EQ vx4)",fontsize=16,color="burlywood",shape="box"];61[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 61[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	61 -> 13[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	62[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 62[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	62 -> 14[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	63[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	63 -> 15[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	9[label="compare2 GT vx4 (esEsOrdering GT vx4)",fontsize=16,color="burlywood",shape="box"];64[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 64[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	64 -> 16[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	65[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 65[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	65 -> 17[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	66[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
9.59/4.05	66 -> 18[label="",style="solid", color="burlywood", weight=3];
9.59/4.05	10[label="compare2 LT LT (esEsOrdering LT LT)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.59/4.05	11[label="compare2 LT EQ (esEsOrdering LT EQ)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.59/4.05	12[label="compare2 LT GT (esEsOrdering LT GT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.59/4.05	13[label="compare2 EQ LT (esEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.59/4.05	14[label="compare2 EQ EQ (esEsOrdering EQ EQ)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.59/4.05	15[label="compare2 EQ GT (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.59/4.05	16[label="compare2 GT LT (esEsOrdering GT LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.59/4.05	17[label="compare2 GT EQ (esEsOrdering GT EQ)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.59/4.05	18[label="compare2 GT GT (esEsOrdering GT GT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.59/4.05	19[label="compare2 LT LT MyTrue",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.59/4.05	20[label="compare2 LT EQ MyFalse",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.59/4.05	21[label="compare2 LT GT MyFalse",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.59/4.05	22[label="compare2 EQ LT MyFalse",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.59/4.05	23[label="compare2 EQ EQ MyTrue",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.59/4.05	24[label="compare2 EQ GT MyFalse",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.59/4.05	25[label="compare2 GT LT MyFalse",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.59/4.05	26[label="compare2 GT EQ MyFalse",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.59/4.05	27[label="compare2 GT GT MyTrue",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.59/4.05	28[label="EQ",fontsize=16,color="green",shape="box"];29[label="compare1 LT EQ (ltEsOrdering LT EQ)",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3];
9.59/4.05	30[label="compare1 LT GT (ltEsOrdering LT GT)",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3];
9.59/4.05	31[label="compare1 EQ LT (ltEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3];
9.59/4.05	32[label="EQ",fontsize=16,color="green",shape="box"];33[label="compare1 EQ GT (ltEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3];
9.59/4.05	34[label="compare1 GT LT (ltEsOrdering GT LT)",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3];
9.59/4.05	35[label="compare1 GT EQ (ltEsOrdering GT EQ)",fontsize=16,color="black",shape="box"];35 -> 42[label="",style="solid", color="black", weight=3];
9.59/4.05	36[label="EQ",fontsize=16,color="green",shape="box"];37[label="compare1 LT EQ MyTrue",fontsize=16,color="black",shape="box"];37 -> 43[label="",style="solid", color="black", weight=3];
9.59/4.05	38[label="compare1 LT GT MyTrue",fontsize=16,color="black",shape="box"];38 -> 44[label="",style="solid", color="black", weight=3];
9.59/4.05	39[label="compare1 EQ LT MyFalse",fontsize=16,color="black",shape="box"];39 -> 45[label="",style="solid", color="black", weight=3];
9.59/4.05	40[label="compare1 EQ GT MyTrue",fontsize=16,color="black",shape="box"];40 -> 46[label="",style="solid", color="black", weight=3];
9.59/4.05	41[label="compare1 GT LT MyFalse",fontsize=16,color="black",shape="box"];41 -> 47[label="",style="solid", color="black", weight=3];
9.59/4.05	42[label="compare1 GT EQ MyFalse",fontsize=16,color="black",shape="box"];42 -> 48[label="",style="solid", color="black", weight=3];
9.59/4.05	43[label="LT",fontsize=16,color="green",shape="box"];44[label="LT",fontsize=16,color="green",shape="box"];45[label="compare0 EQ LT otherwise",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3];
9.59/4.05	46[label="LT",fontsize=16,color="green",shape="box"];47[label="compare0 GT LT otherwise",fontsize=16,color="black",shape="box"];47 -> 50[label="",style="solid", color="black", weight=3];
9.59/4.05	48[label="compare0 GT EQ otherwise",fontsize=16,color="black",shape="box"];48 -> 51[label="",style="solid", color="black", weight=3];
9.59/4.05	49[label="compare0 EQ LT MyTrue",fontsize=16,color="black",shape="box"];49 -> 52[label="",style="solid", color="black", weight=3];
9.59/4.05	50[label="compare0 GT LT MyTrue",fontsize=16,color="black",shape="box"];50 -> 53[label="",style="solid", color="black", weight=3];
9.59/4.05	51[label="compare0 GT EQ MyTrue",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
9.59/4.05	52[label="GT",fontsize=16,color="green",shape="box"];53[label="GT",fontsize=16,color="green",shape="box"];54[label="GT",fontsize=16,color="green",shape="box"];}
9.59/4.05	
9.59/4.05	----------------------------------------
9.59/4.05	
9.59/4.05	(6)
9.59/4.05	YES
9.59/4.09	EOF