7.88/3.49	YES
9.52/3.99	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.52/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.52/3.99	
9.52/3.99	
9.52/3.99	H-Termination with start terms of the given HASKELL could be proven:
9.52/3.99	
9.52/3.99	(0) HASKELL
9.52/3.99	(1) BR [EQUIVALENT, 0 ms]
9.52/3.99	(2) HASKELL
9.52/3.99	(3) COR [EQUIVALENT, 0 ms]
9.52/3.99	(4) HASKELL
9.52/3.99	(5) Narrow [EQUIVALENT, 28 ms]
9.52/3.99	(6) YES
9.52/3.99	
9.52/3.99	
9.52/3.99	----------------------------------------
9.52/3.99	
9.52/3.99	(0)
9.52/3.99	Obligation:
9.52/3.99	mainModule Main 
9.52/3.99	module Main where {
9.52/3.99	import qualified Prelude;
9.52/3.99	data MyBool = MyTrue  | MyFalse ;
9.52/3.99	
9.52/3.99	data Ordering = LT  | EQ  | GT ;
9.52/3.99	
9.52/3.99	compare0 x y MyTrue = GT;
9.52/3.99	
9.52/3.99	compare1 x y MyTrue = LT;
9.52/3.99	compare1 x y MyFalse = compare0 x y otherwise;
9.52/3.99	
9.52/3.99	compare2 x y MyTrue = EQ;
9.52/3.99	compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);
9.52/3.99	
9.52/3.99	compare3 x y = compare2 x y (esEsMyBool x y);
9.52/3.99	
9.52/3.99	compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
9.52/3.99	compareMyBool x y = compare3 x y;
9.52/3.99	
9.52/3.99	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/3.99	esEsMyBool MyFalse MyFalse = MyTrue;
9.52/3.99	esEsMyBool MyFalse MyTrue = MyFalse;
9.52/3.99	esEsMyBool MyTrue MyFalse = MyFalse;
9.52/3.99	esEsMyBool MyTrue MyTrue = MyTrue;
9.52/3.99	
9.52/3.99	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.52/3.99	esEsOrdering LT LT = MyTrue;
9.52/3.99	esEsOrdering LT EQ = MyFalse;
9.52/3.99	esEsOrdering LT GT = MyFalse;
9.52/3.99	esEsOrdering EQ LT = MyFalse;
9.52/3.99	esEsOrdering EQ EQ = MyTrue;
9.52/3.99	esEsOrdering EQ GT = MyFalse;
9.52/3.99	esEsOrdering GT LT = MyFalse;
9.52/3.99	esEsOrdering GT EQ = MyFalse;
9.52/3.99	esEsOrdering GT GT = MyTrue;
9.52/3.99	
9.52/3.99	gtMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/3.99	gtMyBool x y = esEsOrdering (compareMyBool x y) GT;
9.52/3.99	
9.52/3.99	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/3.99	ltEsMyBool MyFalse MyFalse = MyTrue;
9.52/3.99	ltEsMyBool MyFalse MyTrue = MyTrue;
9.52/3.99	ltEsMyBool MyTrue MyFalse = MyFalse;
9.52/3.99	ltEsMyBool MyTrue MyTrue = MyTrue;
9.52/3.99	
9.52/3.99	otherwise :: MyBool;
9.52/3.99	otherwise = MyTrue;
9.52/3.99	
9.52/3.99	}
9.52/3.99	
9.52/3.99	----------------------------------------
9.52/3.99	
9.52/3.99	(1) BR (EQUIVALENT)
9.52/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
9.52/3.99	----------------------------------------
9.52/3.99	
9.52/3.99	(2)
9.52/3.99	Obligation:
9.52/3.99	mainModule Main 
9.52/3.99	module Main where {
9.52/3.99	import qualified Prelude;
9.52/3.99	data MyBool = MyTrue  | MyFalse ;
9.52/3.99	
9.52/3.99	data Ordering = LT  | EQ  | GT ;
9.52/3.99	
9.52/3.99	compare0 x y MyTrue = GT;
9.52/4.00	
9.52/4.00	compare1 x y MyTrue = LT;
9.52/4.00	compare1 x y MyFalse = compare0 x y otherwise;
9.52/4.00	
9.52/4.00	compare2 x y MyTrue = EQ;
9.52/4.00	compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);
9.52/4.00	
9.52/4.00	compare3 x y = compare2 x y (esEsMyBool x y);
9.52/4.00	
9.52/4.00	compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
9.52/4.00	compareMyBool x y = compare3 x y;
9.52/4.00	
9.52/4.00	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/4.00	esEsMyBool MyFalse MyFalse = MyTrue;
9.52/4.00	esEsMyBool MyFalse MyTrue = MyFalse;
9.52/4.00	esEsMyBool MyTrue MyFalse = MyFalse;
9.52/4.00	esEsMyBool MyTrue MyTrue = MyTrue;
9.52/4.00	
9.52/4.00	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.52/4.00	esEsOrdering LT LT = MyTrue;
9.52/4.00	esEsOrdering LT EQ = MyFalse;
9.52/4.00	esEsOrdering LT GT = MyFalse;
9.52/4.00	esEsOrdering EQ LT = MyFalse;
9.52/4.00	esEsOrdering EQ EQ = MyTrue;
9.52/4.00	esEsOrdering EQ GT = MyFalse;
9.52/4.00	esEsOrdering GT LT = MyFalse;
9.52/4.00	esEsOrdering GT EQ = MyFalse;
9.52/4.00	esEsOrdering GT GT = MyTrue;
9.52/4.00	
9.52/4.00	gtMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/4.00	gtMyBool x y = esEsOrdering (compareMyBool x y) GT;
9.52/4.00	
9.52/4.00	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/4.00	ltEsMyBool MyFalse MyFalse = MyTrue;
9.52/4.00	ltEsMyBool MyFalse MyTrue = MyTrue;
9.52/4.00	ltEsMyBool MyTrue MyFalse = MyFalse;
9.52/4.00	ltEsMyBool MyTrue MyTrue = MyTrue;
9.52/4.00	
9.52/4.00	otherwise :: MyBool;
9.52/4.00	otherwise = MyTrue;
9.52/4.00	
9.52/4.00	}
9.52/4.00	
9.52/4.00	----------------------------------------
9.52/4.00	
9.52/4.00	(3) COR (EQUIVALENT)
9.52/4.00	Cond Reductions:
9.52/4.00	The following Function with conditions
9.52/4.00	"undefined |Falseundefined;
9.52/4.00	"
9.52/4.00	is transformed to
9.52/4.00	"undefined  = undefined1;
9.52/4.00	"
9.52/4.00	"undefined0 True = undefined;
9.52/4.00	"
9.52/4.00	"undefined1  = undefined0 False;
9.52/4.00	"
9.52/4.00	
9.52/4.00	----------------------------------------
9.52/4.00	
9.52/4.00	(4)
9.52/4.00	Obligation:
9.52/4.00	mainModule Main 
9.52/4.00	module Main where {
9.52/4.00	import qualified Prelude;
9.52/4.00	data MyBool = MyTrue  | MyFalse ;
9.52/4.00	
9.52/4.00	data Ordering = LT  | EQ  | GT ;
9.52/4.00	
9.52/4.00	compare0 x y MyTrue = GT;
9.52/4.00	
9.52/4.00	compare1 x y MyTrue = LT;
9.52/4.00	compare1 x y MyFalse = compare0 x y otherwise;
9.52/4.00	
9.52/4.00	compare2 x y MyTrue = EQ;
9.52/4.00	compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);
9.52/4.00	
9.52/4.00	compare3 x y = compare2 x y (esEsMyBool x y);
9.52/4.00	
9.52/4.00	compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
9.52/4.00	compareMyBool x y = compare3 x y;
9.52/4.00	
9.52/4.00	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/4.00	esEsMyBool MyFalse MyFalse = MyTrue;
9.52/4.00	esEsMyBool MyFalse MyTrue = MyFalse;
9.52/4.00	esEsMyBool MyTrue MyFalse = MyFalse;
9.52/4.00	esEsMyBool MyTrue MyTrue = MyTrue;
9.52/4.00	
9.52/4.00	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.52/4.00	esEsOrdering LT LT = MyTrue;
9.52/4.00	esEsOrdering LT EQ = MyFalse;
9.52/4.00	esEsOrdering LT GT = MyFalse;
9.52/4.00	esEsOrdering EQ LT = MyFalse;
9.52/4.00	esEsOrdering EQ EQ = MyTrue;
9.52/4.00	esEsOrdering EQ GT = MyFalse;
9.52/4.00	esEsOrdering GT LT = MyFalse;
9.52/4.00	esEsOrdering GT EQ = MyFalse;
9.52/4.00	esEsOrdering GT GT = MyTrue;
9.52/4.00	
9.52/4.00	gtMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/4.00	gtMyBool x y = esEsOrdering (compareMyBool x y) GT;
9.52/4.00	
9.52/4.00	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.52/4.00	ltEsMyBool MyFalse MyFalse = MyTrue;
9.52/4.00	ltEsMyBool MyFalse MyTrue = MyTrue;
9.52/4.00	ltEsMyBool MyTrue MyFalse = MyFalse;
9.52/4.00	ltEsMyBool MyTrue MyTrue = MyTrue;
9.52/4.00	
9.52/4.00	otherwise :: MyBool;
9.52/4.00	otherwise = MyTrue;
9.52/4.00	
9.52/4.00	}
9.52/4.00	
9.52/4.00	----------------------------------------
9.52/4.00	
9.52/4.00	(5) Narrow (EQUIVALENT)
9.52/4.00	Haskell To QDPs
9.52/4.00	
9.52/4.00	digraph dp_graph {
9.52/4.00	node [outthreshold=100, inthreshold=100];1[label="gtMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.52/4.00	3[label="gtMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.52/4.00	4[label="gtMyBool vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.52/4.00	5[label="esEsOrdering (compareMyBool vx3 vx4) GT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.52/4.00	6[label="esEsOrdering (compare3 vx3 vx4) GT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.52/4.00	7[label="esEsOrdering (compare2 vx3 vx4 (esEsMyBool vx3 vx4)) GT",fontsize=16,color="burlywood",shape="box"];31[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 31[label="",style="solid", color="burlywood", weight=9];
9.52/4.00	31 -> 8[label="",style="solid", color="burlywood", weight=3];
9.52/4.00	32[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 32[label="",style="solid", color="burlywood", weight=9];
9.52/4.00	32 -> 9[label="",style="solid", color="burlywood", weight=3];
9.52/4.00	8[label="esEsOrdering (compare2 MyTrue vx4 (esEsMyBool MyTrue vx4)) GT",fontsize=16,color="burlywood",shape="box"];33[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];8 -> 33[label="",style="solid", color="burlywood", weight=9];
9.52/4.00	33 -> 10[label="",style="solid", color="burlywood", weight=3];
9.52/4.00	34[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];8 -> 34[label="",style="solid", color="burlywood", weight=9];
9.52/4.00	34 -> 11[label="",style="solid", color="burlywood", weight=3];
9.52/4.00	9[label="esEsOrdering (compare2 MyFalse vx4 (esEsMyBool MyFalse vx4)) GT",fontsize=16,color="burlywood",shape="box"];35[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];9 -> 35[label="",style="solid", color="burlywood", weight=9];
9.52/4.00	35 -> 12[label="",style="solid", color="burlywood", weight=3];
9.52/4.00	36[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];9 -> 36[label="",style="solid", color="burlywood", weight=9];
9.52/4.00	36 -> 13[label="",style="solid", color="burlywood", weight=3];
9.52/4.00	10[label="esEsOrdering (compare2 MyTrue MyTrue (esEsMyBool MyTrue MyTrue)) GT",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.52/4.00	11[label="esEsOrdering (compare2 MyTrue MyFalse (esEsMyBool MyTrue MyFalse)) GT",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.52/4.00	12[label="esEsOrdering (compare2 MyFalse MyTrue (esEsMyBool MyFalse MyTrue)) GT",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.52/4.00	13[label="esEsOrdering (compare2 MyFalse MyFalse (esEsMyBool MyFalse MyFalse)) GT",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.52/4.00	14[label="esEsOrdering (compare2 MyTrue MyTrue MyTrue) GT",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.52/4.00	15[label="esEsOrdering (compare2 MyTrue MyFalse MyFalse) GT",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.52/4.00	16[label="esEsOrdering (compare2 MyFalse MyTrue MyFalse) GT",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.52/4.00	17[label="esEsOrdering (compare2 MyFalse MyFalse MyTrue) GT",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
9.52/4.00	18[label="esEsOrdering EQ GT",fontsize=16,color="black",shape="triangle"];18 -> 22[label="",style="solid", color="black", weight=3];
9.52/4.00	19[label="esEsOrdering (compare1 MyTrue MyFalse (ltEsMyBool MyTrue MyFalse)) GT",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
9.52/4.00	20[label="esEsOrdering (compare1 MyFalse MyTrue (ltEsMyBool MyFalse MyTrue)) GT",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
9.52/4.00	21 -> 18[label="",style="dashed", color="red", weight=0];
9.52/4.00	21[label="esEsOrdering EQ GT",fontsize=16,color="magenta"];22[label="MyFalse",fontsize=16,color="green",shape="box"];23[label="esEsOrdering (compare1 MyTrue MyFalse MyFalse) GT",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
9.52/4.00	24[label="esEsOrdering (compare1 MyFalse MyTrue MyTrue) GT",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
9.52/4.00	25[label="esEsOrdering (compare0 MyTrue MyFalse otherwise) GT",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
9.52/4.00	26[label="esEsOrdering LT GT",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
9.52/4.00	27[label="esEsOrdering (compare0 MyTrue MyFalse MyTrue) GT",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
9.52/4.00	28[label="MyFalse",fontsize=16,color="green",shape="box"];29[label="esEsOrdering GT GT",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
9.52/4.00	30[label="MyTrue",fontsize=16,color="green",shape="box"];}
9.52/4.00	
9.52/4.00	----------------------------------------
9.52/4.00	
9.52/4.00	(6)
9.52/4.00	YES
9.80/4.03	EOF