7.94/3.49	YES
9.47/3.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.47/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.47/3.99	
9.47/3.99	
9.47/3.99	H-Termination with start terms of the given HASKELL could be proven:
9.47/3.99	
9.47/3.99	(0) HASKELL
9.47/3.99	(1) BR [EQUIVALENT, 0 ms]
9.47/3.99	(2) HASKELL
9.47/3.99	(3) COR [EQUIVALENT, 0 ms]
9.47/3.99	(4) HASKELL
9.47/3.99	(5) Narrow [EQUIVALENT, 26 ms]
9.47/3.99	(6) YES
9.47/3.99	
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(0)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	data MyBool = MyTrue  | MyFalse ;
9.47/3.99	
9.47/3.99	data Ordering = LT  | EQ  | GT ;
9.47/3.99	
9.47/3.99	data Tup0 = Tup0 ;
9.47/3.99	
9.47/3.99	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.47/3.99	compareTup0 Tup0 Tup0 = EQ;
9.47/3.99	
9.47/3.99	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.47/3.99	esEsOrdering LT LT = MyTrue;
9.47/3.99	esEsOrdering LT EQ = MyFalse;
9.47/3.99	esEsOrdering LT GT = MyFalse;
9.47/3.99	esEsOrdering EQ LT = MyFalse;
9.47/3.99	esEsOrdering EQ EQ = MyTrue;
9.47/3.99	esEsOrdering EQ GT = MyFalse;
9.47/3.99	esEsOrdering GT LT = MyFalse;
9.47/3.99	esEsOrdering GT EQ = MyFalse;
9.47/3.99	esEsOrdering GT GT = MyTrue;
9.47/3.99	
9.47/3.99	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.47/3.99	fsEsOrdering x y = not (esEsOrdering x y);
9.47/3.99	
9.47/3.99	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.47/3.99	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.47/3.99	
9.47/3.99	max0 x y MyTrue = x;
9.47/3.99	
9.47/3.99	max1 x y MyTrue = y;
9.47/3.99	max1 x y MyFalse = max0 x y otherwise;
9.47/3.99	
9.47/3.99	max2 x y = max1 x y (ltEsTup0 x y);
9.47/3.99	
9.47/3.99	maxTup0 :: Tup0  ->  Tup0  ->  Tup0;
9.47/3.99	maxTup0 x y = max2 x y;
9.47/3.99	
9.47/3.99	not :: MyBool  ->  MyBool;
9.47/3.99	not MyTrue = MyFalse;
9.47/3.99	not MyFalse = MyTrue;
9.47/3.99	
9.47/3.99	otherwise :: MyBool;
9.47/3.99	otherwise = MyTrue;
9.47/3.99	
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(1) BR (EQUIVALENT)
9.47/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(2)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	data MyBool = MyTrue  | MyFalse ;
9.47/3.99	
9.47/3.99	data Ordering = LT  | EQ  | GT ;
9.47/3.99	
9.47/3.99	data Tup0 = Tup0 ;
9.47/3.99	
9.47/3.99	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.47/3.99	compareTup0 Tup0 Tup0 = EQ;
9.47/3.99	
9.47/3.99	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.47/3.99	esEsOrdering LT LT = MyTrue;
9.47/3.99	esEsOrdering LT EQ = MyFalse;
9.47/3.99	esEsOrdering LT GT = MyFalse;
9.47/3.99	esEsOrdering EQ LT = MyFalse;
9.47/3.99	esEsOrdering EQ EQ = MyTrue;
9.47/3.99	esEsOrdering EQ GT = MyFalse;
9.47/3.99	esEsOrdering GT LT = MyFalse;
9.47/3.99	esEsOrdering GT EQ = MyFalse;
9.47/3.99	esEsOrdering GT GT = MyTrue;
9.47/3.99	
9.47/3.99	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.47/3.99	fsEsOrdering x y = not (esEsOrdering x y);
9.47/3.99	
9.47/3.99	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.47/3.99	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.47/3.99	
9.47/3.99	max0 x y MyTrue = x;
9.47/3.99	
9.47/3.99	max1 x y MyTrue = y;
9.47/3.99	max1 x y MyFalse = max0 x y otherwise;
9.47/3.99	
9.47/3.99	max2 x y = max1 x y (ltEsTup0 x y);
9.47/3.99	
9.47/3.99	maxTup0 :: Tup0  ->  Tup0  ->  Tup0;
9.47/3.99	maxTup0 x y = max2 x y;
9.47/3.99	
9.47/3.99	not :: MyBool  ->  MyBool;
9.47/3.99	not MyTrue = MyFalse;
9.47/3.99	not MyFalse = MyTrue;
9.47/3.99	
9.47/3.99	otherwise :: MyBool;
9.47/3.99	otherwise = MyTrue;
9.47/3.99	
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(3) COR (EQUIVALENT)
9.47/3.99	Cond Reductions:
9.47/3.99	The following Function with conditions
9.47/3.99	"undefined |Falseundefined;
9.47/3.99	"
9.47/3.99	is transformed to
9.47/3.99	"undefined  = undefined1;
9.47/3.99	"
9.47/3.99	"undefined0 True = undefined;
9.47/3.99	"
9.47/3.99	"undefined1  = undefined0 False;
9.47/3.99	"
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(4)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	data MyBool = MyTrue  | MyFalse ;
9.47/3.99	
9.47/3.99	data Ordering = LT  | EQ  | GT ;
9.47/3.99	
9.47/3.99	data Tup0 = Tup0 ;
9.47/3.99	
9.47/3.99	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.47/3.99	compareTup0 Tup0 Tup0 = EQ;
9.47/3.99	
9.47/3.99	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.47/3.99	esEsOrdering LT LT = MyTrue;
9.47/3.99	esEsOrdering LT EQ = MyFalse;
9.47/3.99	esEsOrdering LT GT = MyFalse;
9.47/3.99	esEsOrdering EQ LT = MyFalse;
9.47/3.99	esEsOrdering EQ EQ = MyTrue;
9.47/3.99	esEsOrdering EQ GT = MyFalse;
9.47/3.99	esEsOrdering GT LT = MyFalse;
9.47/3.99	esEsOrdering GT EQ = MyFalse;
9.47/3.99	esEsOrdering GT GT = MyTrue;
9.47/3.99	
9.47/3.99	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.47/3.99	fsEsOrdering x y = not (esEsOrdering x y);
9.47/3.99	
9.47/3.99	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.47/3.99	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.47/3.99	
9.47/3.99	max0 x y MyTrue = x;
9.47/3.99	
9.47/3.99	max1 x y MyTrue = y;
9.47/3.99	max1 x y MyFalse = max0 x y otherwise;
9.47/3.99	
9.47/3.99	max2 x y = max1 x y (ltEsTup0 x y);
9.47/3.99	
9.47/3.99	maxTup0 :: Tup0  ->  Tup0  ->  Tup0;
9.47/3.99	maxTup0 x y = max2 x y;
9.47/3.99	
9.47/3.99	not :: MyBool  ->  MyBool;
9.47/3.99	not MyTrue = MyFalse;
9.47/3.99	not MyFalse = MyTrue;
9.47/3.99	
9.47/3.99	otherwise :: MyBool;
9.47/3.99	otherwise = MyTrue;
9.47/3.99	
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(5) Narrow (EQUIVALENT)
9.47/3.99	Haskell To QDPs
9.47/3.99	
9.47/3.99	digraph dp_graph {
9.47/3.99	node [outthreshold=100, inthreshold=100];1[label="maxTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.47/3.99	3[label="maxTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.47/3.99	4[label="maxTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.47/3.99	5[label="max2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.47/3.99	6[label="max1 vx3 vx4 (ltEsTup0 vx3 vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.47/3.99	7[label="max1 vx3 vx4 (fsEsOrdering (compareTup0 vx3 vx4) GT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.47/3.99	8[label="max1 vx3 vx4 (not (esEsOrdering (compareTup0 vx3 vx4) GT))",fontsize=16,color="burlywood",shape="box"];15[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];8 -> 15[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	15 -> 9[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	9[label="max1 Tup0 vx4 (not (esEsOrdering (compareTup0 Tup0 vx4) GT))",fontsize=16,color="burlywood",shape="box"];16[label="vx4/Tup0",fontsize=10,color="white",style="solid",shape="box"];9 -> 16[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	16 -> 10[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	10[label="max1 Tup0 Tup0 (not (esEsOrdering (compareTup0 Tup0 Tup0) GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.47/3.99	11[label="max1 Tup0 Tup0 (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
9.47/3.99	12[label="max1 Tup0 Tup0 (not MyFalse)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
9.47/3.99	13[label="max1 Tup0 Tup0 MyTrue",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
9.47/3.99	14[label="Tup0",fontsize=16,color="green",shape="box"];}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(6)
9.47/3.99	YES
9.78/4.04	EOF