7.67/3.55	YES
9.46/4.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.46/4.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.46/4.01	
9.46/4.01	
9.46/4.01	H-Termination with start terms of the given HASKELL could be proven:
9.46/4.01	
9.46/4.01	(0) HASKELL
9.46/4.01	(1) BR [EQUIVALENT, 0 ms]
9.46/4.01	(2) HASKELL
9.46/4.01	(3) COR [EQUIVALENT, 0 ms]
9.46/4.01	(4) HASKELL
9.46/4.01	(5) Narrow [EQUIVALENT, 29 ms]
9.46/4.01	(6) YES
9.46/4.01	
9.46/4.01	
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(0)
9.46/4.01	Obligation:
9.46/4.01	mainModule Main 
9.46/4.01	module Main where {
9.46/4.01	import qualified Prelude;
9.46/4.01	data MyBool = MyTrue  | MyFalse ;
9.46/4.01	
9.46/4.01	data Ordering = LT  | EQ  | GT ;
9.46/4.01	
9.46/4.01	compare0 x y MyTrue = GT;
9.46/4.01	
9.46/4.01	compare1 x y MyTrue = LT;
9.46/4.01	compare1 x y MyFalse = compare0 x y otherwise;
9.46/4.01	
9.46/4.01	compare2 x y MyTrue = EQ;
9.46/4.01	compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);
9.46/4.01	
9.46/4.01	compare3 x y = compare2 x y (esEsMyBool x y);
9.46/4.01	
9.46/4.01	compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
9.46/4.01	compareMyBool x y = compare3 x y;
9.46/4.01	
9.46/4.01	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.46/4.01	esEsMyBool MyFalse MyFalse = MyTrue;
9.46/4.01	esEsMyBool MyFalse MyTrue = MyFalse;
9.46/4.01	esEsMyBool MyTrue MyFalse = MyFalse;
9.46/4.01	esEsMyBool MyTrue MyTrue = MyTrue;
9.46/4.01	
9.46/4.01	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.46/4.01	ltEsMyBool MyFalse MyFalse = MyTrue;
9.46/4.01	ltEsMyBool MyFalse MyTrue = MyTrue;
9.46/4.01	ltEsMyBool MyTrue MyFalse = MyFalse;
9.46/4.01	ltEsMyBool MyTrue MyTrue = MyTrue;
9.46/4.01	
9.46/4.01	otherwise :: MyBool;
9.46/4.01	otherwise = MyTrue;
9.46/4.01	
9.46/4.01	}
9.46/4.01	
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(1) BR (EQUIVALENT)
9.46/4.01	Replaced joker patterns by fresh variables and removed binding patterns.
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(2)
9.46/4.01	Obligation:
9.46/4.01	mainModule Main 
9.46/4.01	module Main where {
9.46/4.01	import qualified Prelude;
9.46/4.01	data MyBool = MyTrue  | MyFalse ;
9.46/4.01	
9.46/4.01	data Ordering = LT  | EQ  | GT ;
9.46/4.01	
9.46/4.01	compare0 x y MyTrue = GT;
9.46/4.01	
9.46/4.01	compare1 x y MyTrue = LT;
9.46/4.01	compare1 x y MyFalse = compare0 x y otherwise;
9.46/4.01	
9.46/4.01	compare2 x y MyTrue = EQ;
9.46/4.01	compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);
9.46/4.01	
9.46/4.01	compare3 x y = compare2 x y (esEsMyBool x y);
9.46/4.01	
9.46/4.01	compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
9.46/4.01	compareMyBool x y = compare3 x y;
9.46/4.01	
9.46/4.01	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.46/4.01	esEsMyBool MyFalse MyFalse = MyTrue;
9.46/4.01	esEsMyBool MyFalse MyTrue = MyFalse;
9.46/4.01	esEsMyBool MyTrue MyFalse = MyFalse;
9.46/4.01	esEsMyBool MyTrue MyTrue = MyTrue;
9.46/4.01	
9.46/4.01	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.46/4.01	ltEsMyBool MyFalse MyFalse = MyTrue;
9.46/4.01	ltEsMyBool MyFalse MyTrue = MyTrue;
9.46/4.01	ltEsMyBool MyTrue MyFalse = MyFalse;
9.46/4.01	ltEsMyBool MyTrue MyTrue = MyTrue;
9.46/4.01	
9.46/4.01	otherwise :: MyBool;
9.46/4.01	otherwise = MyTrue;
9.46/4.01	
9.46/4.01	}
9.46/4.01	
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(3) COR (EQUIVALENT)
9.46/4.01	Cond Reductions:
9.46/4.01	The following Function with conditions
9.46/4.01	"undefined |Falseundefined;
9.46/4.01	"
9.46/4.01	is transformed to
9.46/4.01	"undefined  = undefined1;
9.46/4.01	"
9.46/4.01	"undefined0 True = undefined;
9.46/4.01	"
9.46/4.01	"undefined1  = undefined0 False;
9.46/4.01	"
9.46/4.01	
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(4)
9.46/4.01	Obligation:
9.46/4.01	mainModule Main 
9.46/4.01	module Main where {
9.46/4.01	import qualified Prelude;
9.46/4.01	data MyBool = MyTrue  | MyFalse ;
9.46/4.01	
9.46/4.01	data Ordering = LT  | EQ  | GT ;
9.46/4.01	
9.46/4.01	compare0 x y MyTrue = GT;
9.46/4.01	
9.46/4.01	compare1 x y MyTrue = LT;
9.46/4.01	compare1 x y MyFalse = compare0 x y otherwise;
9.46/4.01	
9.46/4.01	compare2 x y MyTrue = EQ;
9.46/4.01	compare2 x y MyFalse = compare1 x y (ltEsMyBool x y);
9.46/4.01	
9.46/4.01	compare3 x y = compare2 x y (esEsMyBool x y);
9.46/4.01	
9.46/4.01	compareMyBool :: MyBool  ->  MyBool  ->  Ordering;
9.46/4.01	compareMyBool x y = compare3 x y;
9.46/4.01	
9.46/4.01	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.46/4.01	esEsMyBool MyFalse MyFalse = MyTrue;
9.46/4.01	esEsMyBool MyFalse MyTrue = MyFalse;
9.46/4.01	esEsMyBool MyTrue MyFalse = MyFalse;
9.46/4.01	esEsMyBool MyTrue MyTrue = MyTrue;
9.46/4.01	
9.46/4.01	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.46/4.01	ltEsMyBool MyFalse MyFalse = MyTrue;
9.46/4.01	ltEsMyBool MyFalse MyTrue = MyTrue;
9.46/4.01	ltEsMyBool MyTrue MyFalse = MyFalse;
9.46/4.01	ltEsMyBool MyTrue MyTrue = MyTrue;
9.46/4.01	
9.46/4.01	otherwise :: MyBool;
9.46/4.01	otherwise = MyTrue;
9.46/4.01	
9.46/4.01	}
9.46/4.01	
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(5) Narrow (EQUIVALENT)
9.46/4.01	Haskell To QDPs
9.46/4.01	
9.46/4.01	digraph dp_graph {
9.46/4.01	node [outthreshold=100, inthreshold=100];1[label="compareMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.46/4.01	3[label="compareMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.46/4.01	4[label="compareMyBool vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.46/4.01	5[label="compare3 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.46/4.01	6[label="compare2 vx3 vx4 (esEsMyBool vx3 vx4)",fontsize=16,color="burlywood",shape="box"];27[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];6 -> 27[label="",style="solid", color="burlywood", weight=9];
9.46/4.01	27 -> 7[label="",style="solid", color="burlywood", weight=3];
9.46/4.01	28[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];6 -> 28[label="",style="solid", color="burlywood", weight=9];
9.46/4.01	28 -> 8[label="",style="solid", color="burlywood", weight=3];
9.46/4.01	7[label="compare2 MyTrue vx4 (esEsMyBool MyTrue vx4)",fontsize=16,color="burlywood",shape="box"];29[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 29[label="",style="solid", color="burlywood", weight=9];
9.46/4.01	29 -> 9[label="",style="solid", color="burlywood", weight=3];
9.46/4.01	30[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 30[label="",style="solid", color="burlywood", weight=9];
9.46/4.01	30 -> 10[label="",style="solid", color="burlywood", weight=3];
9.46/4.01	8[label="compare2 MyFalse vx4 (esEsMyBool MyFalse vx4)",fontsize=16,color="burlywood",shape="box"];31[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];8 -> 31[label="",style="solid", color="burlywood", weight=9];
9.46/4.01	31 -> 11[label="",style="solid", color="burlywood", weight=3];
9.46/4.01	32[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];8 -> 32[label="",style="solid", color="burlywood", weight=9];
9.46/4.01	32 -> 12[label="",style="solid", color="burlywood", weight=3];
9.46/4.01	9[label="compare2 MyTrue MyTrue (esEsMyBool MyTrue MyTrue)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.46/4.01	10[label="compare2 MyTrue MyFalse (esEsMyBool MyTrue MyFalse)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.46/4.01	11[label="compare2 MyFalse MyTrue (esEsMyBool MyFalse MyTrue)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.46/4.01	12[label="compare2 MyFalse MyFalse (esEsMyBool MyFalse MyFalse)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.46/4.01	13[label="compare2 MyTrue MyTrue MyTrue",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.46/4.01	14[label="compare2 MyTrue MyFalse MyFalse",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.46/4.01	15[label="compare2 MyFalse MyTrue MyFalse",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.46/4.01	16[label="compare2 MyFalse MyFalse MyTrue",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.46/4.01	17[label="EQ",fontsize=16,color="green",shape="box"];18[label="compare1 MyTrue MyFalse (ltEsMyBool MyTrue MyFalse)",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3];
9.46/4.01	19[label="compare1 MyFalse MyTrue (ltEsMyBool MyFalse MyTrue)",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3];
9.46/4.01	20[label="EQ",fontsize=16,color="green",shape="box"];21[label="compare1 MyTrue MyFalse MyFalse",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
9.46/4.01	22[label="compare1 MyFalse MyTrue MyTrue",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
9.46/4.01	23[label="compare0 MyTrue MyFalse otherwise",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
9.46/4.01	24[label="LT",fontsize=16,color="green",shape="box"];25[label="compare0 MyTrue MyFalse MyTrue",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3];
9.46/4.01	26[label="GT",fontsize=16,color="green",shape="box"];}
9.46/4.01	
9.46/4.01	----------------------------------------
9.46/4.01	
9.46/4.01	(6)
9.46/4.01	YES
9.46/4.04	EOF