7.54/3.47	YES
9.15/3.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.15/3.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.15/3.94	
9.15/3.94	
9.15/3.94	H-Termination with start terms of the given HASKELL could be proven:
9.15/3.94	
9.15/3.94	(0) HASKELL
9.15/3.94	(1) BR [EQUIVALENT, 0 ms]
9.15/3.94	(2) HASKELL
9.15/3.94	(3) COR [EQUIVALENT, 0 ms]
9.15/3.94	(4) HASKELL
9.15/3.94	(5) Narrow [EQUIVALENT, 31 ms]
9.15/3.94	(6) YES
9.15/3.94	
9.15/3.94	
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(0)
9.15/3.94	Obligation:
9.15/3.94	mainModule Main 
9.15/3.94	module Main where {
9.15/3.94	import qualified Prelude;
9.15/3.94	data MyBool = MyTrue  | MyFalse ;
9.15/3.94	
9.15/3.94	data Ordering = LT  | EQ  | GT ;
9.15/3.94	
9.15/3.94	data Tup0 = Tup0 ;
9.15/3.94	
9.15/3.94	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.15/3.94	compareTup0 Tup0 Tup0 = EQ;
9.15/3.94	
9.15/3.94	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.15/3.94	esEsOrdering LT LT = MyTrue;
9.15/3.94	esEsOrdering LT EQ = MyFalse;
9.15/3.94	esEsOrdering LT GT = MyFalse;
9.15/3.94	esEsOrdering EQ LT = MyFalse;
9.15/3.94	esEsOrdering EQ EQ = MyTrue;
9.15/3.94	esEsOrdering EQ GT = MyFalse;
9.15/3.94	esEsOrdering GT LT = MyFalse;
9.15/3.94	esEsOrdering GT EQ = MyFalse;
9.15/3.94	esEsOrdering GT GT = MyTrue;
9.15/3.94	
9.15/3.94	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.15/3.94	fsEsOrdering x y = not (esEsOrdering x y);
9.15/3.94	
9.15/3.94	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.15/3.94	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.15/3.94	
9.15/3.94	not :: MyBool  ->  MyBool;
9.15/3.94	not MyTrue = MyFalse;
9.15/3.94	not MyFalse = MyTrue;
9.15/3.94	
9.15/3.94	}
9.15/3.94	
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(1) BR (EQUIVALENT)
9.15/3.94	Replaced joker patterns by fresh variables and removed binding patterns.
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(2)
9.15/3.94	Obligation:
9.15/3.94	mainModule Main 
9.15/3.94	module Main where {
9.15/3.94	import qualified Prelude;
9.15/3.94	data MyBool = MyTrue  | MyFalse ;
9.15/3.94	
9.15/3.94	data Ordering = LT  | EQ  | GT ;
9.15/3.94	
9.15/3.94	data Tup0 = Tup0 ;
9.15/3.94	
9.15/3.94	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.15/3.94	compareTup0 Tup0 Tup0 = EQ;
9.15/3.94	
9.15/3.94	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.15/3.94	esEsOrdering LT LT = MyTrue;
9.15/3.94	esEsOrdering LT EQ = MyFalse;
9.15/3.94	esEsOrdering LT GT = MyFalse;
9.15/3.94	esEsOrdering EQ LT = MyFalse;
9.15/3.94	esEsOrdering EQ EQ = MyTrue;
9.15/3.94	esEsOrdering EQ GT = MyFalse;
9.15/3.94	esEsOrdering GT LT = MyFalse;
9.15/3.94	esEsOrdering GT EQ = MyFalse;
9.15/3.94	esEsOrdering GT GT = MyTrue;
9.15/3.94	
9.15/3.94	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.15/3.94	fsEsOrdering x y = not (esEsOrdering x y);
9.15/3.94	
9.15/3.94	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.15/3.94	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.15/3.94	
9.15/3.94	not :: MyBool  ->  MyBool;
9.15/3.94	not MyTrue = MyFalse;
9.15/3.94	not MyFalse = MyTrue;
9.15/3.94	
9.15/3.94	}
9.15/3.94	
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(3) COR (EQUIVALENT)
9.15/3.94	Cond Reductions:
9.15/3.94	The following Function with conditions
9.15/3.94	"undefined |Falseundefined;
9.15/3.94	"
9.15/3.94	is transformed to
9.15/3.94	"undefined  = undefined1;
9.15/3.94	"
9.15/3.94	"undefined0 True = undefined;
9.15/3.94	"
9.15/3.94	"undefined1  = undefined0 False;
9.15/3.94	"
9.15/3.94	
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(4)
9.15/3.94	Obligation:
9.15/3.94	mainModule Main 
9.15/3.94	module Main where {
9.15/3.94	import qualified Prelude;
9.15/3.94	data MyBool = MyTrue  | MyFalse ;
9.15/3.94	
9.15/3.94	data Ordering = LT  | EQ  | GT ;
9.15/3.94	
9.15/3.94	data Tup0 = Tup0 ;
9.15/3.94	
9.15/3.94	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.15/3.94	compareTup0 Tup0 Tup0 = EQ;
9.15/3.94	
9.15/3.94	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.15/3.94	esEsOrdering LT LT = MyTrue;
9.15/3.94	esEsOrdering LT EQ = MyFalse;
9.15/3.94	esEsOrdering LT GT = MyFalse;
9.15/3.94	esEsOrdering EQ LT = MyFalse;
9.15/3.94	esEsOrdering EQ EQ = MyTrue;
9.15/3.94	esEsOrdering EQ GT = MyFalse;
9.15/3.94	esEsOrdering GT LT = MyFalse;
9.15/3.94	esEsOrdering GT EQ = MyFalse;
9.15/3.94	esEsOrdering GT GT = MyTrue;
9.15/3.94	
9.15/3.94	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.15/3.94	fsEsOrdering x y = not (esEsOrdering x y);
9.15/3.94	
9.15/3.94	ltEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.15/3.94	ltEsTup0 x y = fsEsOrdering (compareTup0 x y) GT;
9.15/3.94	
9.15/3.94	not :: MyBool  ->  MyBool;
9.15/3.94	not MyTrue = MyFalse;
9.15/3.94	not MyFalse = MyTrue;
9.15/3.94	
9.15/3.94	}
9.15/3.94	
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(5) Narrow (EQUIVALENT)
9.15/3.94	Haskell To QDPs
9.15/3.94	
9.15/3.94	digraph dp_graph {
9.15/3.94	node [outthreshold=100, inthreshold=100];1[label="ltEsTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.15/3.94	3[label="ltEsTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.15/3.94	4[label="ltEsTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.15/3.94	5[label="fsEsOrdering (compareTup0 vx3 vx4) GT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.15/3.94	6[label="not (esEsOrdering (compareTup0 vx3 vx4) GT)",fontsize=16,color="burlywood",shape="box"];12[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];6 -> 12[label="",style="solid", color="burlywood", weight=9];
9.15/3.94	12 -> 7[label="",style="solid", color="burlywood", weight=3];
9.15/3.94	7[label="not (esEsOrdering (compareTup0 Tup0 vx4) GT)",fontsize=16,color="burlywood",shape="box"];13[label="vx4/Tup0",fontsize=10,color="white",style="solid",shape="box"];7 -> 13[label="",style="solid", color="burlywood", weight=9];
9.15/3.94	13 -> 8[label="",style="solid", color="burlywood", weight=3];
9.15/3.94	8[label="not (esEsOrdering (compareTup0 Tup0 Tup0) GT)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.15/3.94	9[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.15/3.94	10[label="not MyFalse",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.15/3.94	11[label="MyTrue",fontsize=16,color="green",shape="box"];}
9.15/3.94	
9.15/3.94	----------------------------------------
9.15/3.94	
9.15/3.94	(6)
9.15/3.94	YES
9.42/3.98	EOF