7.80/3.63	YES
9.43/4.09	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.43/4.09	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.43/4.09	
9.43/4.09	
9.43/4.09	H-Termination with start terms of the given HASKELL could be proven:
9.43/4.09	
9.43/4.09	(0) HASKELL
9.43/4.09	(1) BR [EQUIVALENT, 0 ms]
9.43/4.09	(2) HASKELL
9.43/4.09	(3) COR [EQUIVALENT, 0 ms]
9.43/4.09	(4) HASKELL
9.43/4.09	(5) Narrow [EQUIVALENT, 32 ms]
9.43/4.09	(6) YES
9.43/4.09	
9.43/4.09	
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(0)
9.43/4.09	Obligation:
9.43/4.09	mainModule Main 
9.43/4.09	module Main where {
9.43/4.09	import qualified Prelude;
9.43/4.09	data MyBool = MyTrue  | MyFalse ;
9.43/4.09	
9.43/4.09	data Ordering = LT  | EQ  | GT ;
9.43/4.09	
9.43/4.09	data Tup0 = Tup0 ;
9.43/4.09	
9.43/4.09	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.43/4.09	compareTup0 Tup0 Tup0 = EQ;
9.43/4.09	
9.43/4.09	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.09	esEsOrdering LT LT = MyTrue;
9.43/4.09	esEsOrdering LT EQ = MyFalse;
9.43/4.09	esEsOrdering LT GT = MyFalse;
9.43/4.09	esEsOrdering EQ LT = MyFalse;
9.43/4.09	esEsOrdering EQ EQ = MyTrue;
9.43/4.09	esEsOrdering EQ GT = MyFalse;
9.43/4.09	esEsOrdering GT LT = MyFalse;
9.43/4.09	esEsOrdering GT EQ = MyFalse;
9.43/4.09	esEsOrdering GT GT = MyTrue;
9.43/4.09	
9.43/4.09	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.09	fsEsOrdering x y = not (esEsOrdering x y);
9.43/4.09	
9.43/4.09	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.43/4.09	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.43/4.09	
9.43/4.09	min0 x y MyTrue = y;
9.43/4.09	
9.43/4.09	min1 x y MyTrue = x;
9.43/4.09	min1 x y MyFalse = min0 x y otherwise;
9.43/4.09	
9.43/4.09	min2 x y = min1 x y (ltEsTup0 x y);
9.43/4.09	
9.43/4.09	minTup0 :: Tup0  ->  Tup0  ->  Tup0;
9.43/4.09	minTup0 x y = min2 x y;
9.43/4.09	
9.43/4.09	not :: MyBool  ->  MyBool;
9.43/4.09	not MyTrue = MyFalse;
9.43/4.09	not MyFalse = MyTrue;
9.43/4.09	
9.43/4.09	otherwise :: MyBool;
9.43/4.09	otherwise = MyTrue;
9.43/4.09	
9.43/4.09	}
9.43/4.09	
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(1) BR (EQUIVALENT)
9.43/4.09	Replaced joker patterns by fresh variables and removed binding patterns.
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(2)
9.43/4.09	Obligation:
9.43/4.09	mainModule Main 
9.43/4.09	module Main where {
9.43/4.09	import qualified Prelude;
9.43/4.09	data MyBool = MyTrue  | MyFalse ;
9.43/4.09	
9.43/4.09	data Ordering = LT  | EQ  | GT ;
9.43/4.09	
9.43/4.09	data Tup0 = Tup0 ;
9.43/4.09	
9.43/4.09	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.43/4.09	compareTup0 Tup0 Tup0 = EQ;
9.43/4.09	
9.43/4.09	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.09	esEsOrdering LT LT = MyTrue;
9.43/4.09	esEsOrdering LT EQ = MyFalse;
9.43/4.09	esEsOrdering LT GT = MyFalse;
9.43/4.09	esEsOrdering EQ LT = MyFalse;
9.43/4.09	esEsOrdering EQ EQ = MyTrue;
9.43/4.09	esEsOrdering EQ GT = MyFalse;
9.43/4.09	esEsOrdering GT LT = MyFalse;
9.43/4.09	esEsOrdering GT EQ = MyFalse;
9.43/4.09	esEsOrdering GT GT = MyTrue;
9.43/4.09	
9.43/4.09	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.09	fsEsOrdering x y = not (esEsOrdering x y);
9.43/4.09	
9.43/4.09	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.43/4.09	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.43/4.09	
9.43/4.09	min0 x y MyTrue = y;
9.43/4.09	
9.43/4.09	min1 x y MyTrue = x;
9.43/4.09	min1 x y MyFalse = min0 x y otherwise;
9.43/4.09	
9.43/4.09	min2 x y = min1 x y (ltEsTup0 x y);
9.43/4.09	
9.43/4.09	minTup0 :: Tup0  ->  Tup0  ->  Tup0;
9.43/4.09	minTup0 x y = min2 x y;
9.43/4.09	
9.43/4.09	not :: MyBool  ->  MyBool;
9.43/4.09	not MyTrue = MyFalse;
9.43/4.09	not MyFalse = MyTrue;
9.43/4.09	
9.43/4.09	otherwise :: MyBool;
9.43/4.09	otherwise = MyTrue;
9.43/4.09	
9.43/4.09	}
9.43/4.09	
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(3) COR (EQUIVALENT)
9.43/4.09	Cond Reductions:
9.43/4.09	The following Function with conditions
9.43/4.09	"undefined |Falseundefined;
9.43/4.09	"
9.43/4.09	is transformed to
9.43/4.09	"undefined  = undefined1;
9.43/4.09	"
9.43/4.09	"undefined0 True = undefined;
9.43/4.09	"
9.43/4.09	"undefined1  = undefined0 False;
9.43/4.09	"
9.43/4.09	
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(4)
9.43/4.09	Obligation:
9.43/4.09	mainModule Main 
9.43/4.09	module Main where {
9.43/4.09	import qualified Prelude;
9.43/4.09	data MyBool = MyTrue  | MyFalse ;
9.43/4.09	
9.43/4.09	data Ordering = LT  | EQ  | GT ;
9.43/4.09	
9.43/4.09	data Tup0 = Tup0 ;
9.43/4.09	
9.43/4.09	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.43/4.09	compareTup0 Tup0 Tup0 = EQ;
9.43/4.09	
9.43/4.09	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.09	esEsOrdering LT LT = MyTrue;
9.43/4.09	esEsOrdering LT EQ = MyFalse;
9.43/4.09	esEsOrdering LT GT = MyFalse;
9.43/4.09	esEsOrdering EQ LT = MyFalse;
9.43/4.09	esEsOrdering EQ EQ = MyTrue;
9.43/4.09	esEsOrdering EQ GT = MyFalse;
9.43/4.09	esEsOrdering GT LT = MyFalse;
9.43/4.09	esEsOrdering GT EQ = MyFalse;
9.43/4.09	esEsOrdering GT GT = MyTrue;
9.43/4.09	
9.43/4.09	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.43/4.09	fsEsOrdering x y = not (esEsOrdering x y);
9.43/4.09	
9.43/4.09	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.43/4.09	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.43/4.09	
9.43/4.09	min0 x y MyTrue = y;
9.43/4.09	
9.43/4.09	min1 x y MyTrue = x;
9.43/4.09	min1 x y MyFalse = min0 x y otherwise;
9.43/4.09	
9.43/4.09	min2 x y = min1 x y (ltEsTup0 x y);
9.43/4.09	
9.43/4.09	minTup0 :: Tup0  ->  Tup0  ->  Tup0;
9.43/4.09	minTup0 x y = min2 x y;
9.43/4.09	
9.43/4.09	not :: MyBool  ->  MyBool;
9.43/4.09	not MyTrue = MyFalse;
9.43/4.09	not MyFalse = MyTrue;
9.43/4.09	
9.43/4.09	otherwise :: MyBool;
9.43/4.09	otherwise = MyTrue;
9.43/4.09	
9.43/4.09	}
9.43/4.09	
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(5) Narrow (EQUIVALENT)
9.43/4.09	Haskell To QDPs
9.43/4.09	
9.43/4.09	digraph dp_graph {
9.43/4.09	node [outthreshold=100, inthreshold=100];1[label="minTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.43/4.09	3[label="minTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.43/4.09	4[label="minTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.43/4.09	5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.43/4.09	6[label="min1 vx3 vx4 (ltEsTup0 vx3 vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.43/4.09	7[label="min1 vx3 vx4 (fsEsOrdering (compareTup0 vx3 vx4) GT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.43/4.09	8[label="min1 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];
9.43/4.09	15 -> 9[label="",style="solid", color="burlywood", weight=3];
9.43/4.09	9[label="min1 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];
9.43/4.09	16 -> 10[label="",style="solid", color="burlywood", weight=3];
9.43/4.09	10[label="min1 Tup0 Tup0 (not (esEsOrdering (compareTup0 Tup0 Tup0) GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.43/4.09	11[label="min1 Tup0 Tup0 (not (esEsOrdering EQ GT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
9.43/4.09	12[label="min1 Tup0 Tup0 (not MyFalse)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
9.43/4.09	13[label="min1 Tup0 Tup0 MyTrue",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
9.43/4.09	14[label="Tup0",fontsize=16,color="green",shape="box"];}
9.43/4.09	
9.43/4.09	----------------------------------------
9.43/4.09	
9.43/4.09	(6)
9.43/4.09	YES
9.54/4.12	EOF