7.79/3.53	YES
9.34/4.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.34/4.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.34/4.02	
9.34/4.02	
9.34/4.02	H-Termination with start terms of the given HASKELL could be proven:
9.34/4.02	
9.34/4.02	(0) HASKELL
9.34/4.02	(1) BR [EQUIVALENT, 0 ms]
9.34/4.02	(2) HASKELL
9.34/4.02	(3) COR [EQUIVALENT, 0 ms]
9.34/4.02	(4) HASKELL
9.34/4.02	(5) Narrow [EQUIVALENT, 0 ms]
9.34/4.02	(6) YES
9.34/4.02	
9.34/4.02	
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(0)
9.34/4.02	Obligation:
9.34/4.02	mainModule Main 
9.34/4.02	module Main where {
9.34/4.02	import qualified Prelude;
9.34/4.02	data MyBool = MyTrue  | MyFalse ;
9.34/4.02	
9.34/4.02	data Ordering = LT  | EQ  | GT ;
9.34/4.02	
9.34/4.02	data Tup0 = Tup0 ;
9.34/4.02	
9.34/4.02	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.34/4.02	compareTup0 Tup0 Tup0 = EQ;
9.34/4.02	
9.34/4.02	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.34/4.02	esEsOrdering LT LT = MyTrue;
9.34/4.02	esEsOrdering LT EQ = MyFalse;
9.34/4.02	esEsOrdering LT GT = MyFalse;
9.34/4.02	esEsOrdering EQ LT = MyFalse;
9.34/4.02	esEsOrdering EQ EQ = MyTrue;
9.34/4.02	esEsOrdering EQ GT = MyFalse;
9.34/4.02	esEsOrdering GT LT = MyFalse;
9.34/4.02	esEsOrdering GT EQ = MyFalse;
9.34/4.02	esEsOrdering GT GT = MyTrue;
9.34/4.02	
9.34/4.02	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.34/4.02	fsEsOrdering x y = not (esEsOrdering x y);
9.34/4.02	
9.34/4.02	gtEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.34/4.02	gtEsTup0 x y = fsEsOrdering (compareTup0 x y) LT;
9.34/4.02	
9.34/4.02	not :: MyBool  ->  MyBool;
9.34/4.02	not MyTrue = MyFalse;
9.34/4.02	not MyFalse = MyTrue;
9.34/4.02	
9.34/4.02	}
9.34/4.02	
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(1) BR (EQUIVALENT)
9.34/4.02	Replaced joker patterns by fresh variables and removed binding patterns.
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(2)
9.34/4.02	Obligation:
9.34/4.02	mainModule Main 
9.34/4.02	module Main where {
9.34/4.02	import qualified Prelude;
9.34/4.02	data MyBool = MyTrue  | MyFalse ;
9.34/4.02	
9.34/4.02	data Ordering = LT  | EQ  | GT ;
9.34/4.02	
9.34/4.02	data Tup0 = Tup0 ;
9.34/4.02	
9.34/4.02	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.34/4.02	compareTup0 Tup0 Tup0 = EQ;
9.34/4.02	
9.34/4.02	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.34/4.02	esEsOrdering LT LT = MyTrue;
9.34/4.02	esEsOrdering LT EQ = MyFalse;
9.34/4.02	esEsOrdering LT GT = MyFalse;
9.34/4.02	esEsOrdering EQ LT = MyFalse;
9.34/4.02	esEsOrdering EQ EQ = MyTrue;
9.34/4.02	esEsOrdering EQ GT = MyFalse;
9.34/4.02	esEsOrdering GT LT = MyFalse;
9.34/4.02	esEsOrdering GT EQ = MyFalse;
9.34/4.02	esEsOrdering GT GT = MyTrue;
9.34/4.02	
9.34/4.02	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.34/4.02	fsEsOrdering x y = not (esEsOrdering x y);
9.34/4.02	
9.34/4.02	gtEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.34/4.02	gtEsTup0 x y = fsEsOrdering (compareTup0 x y) LT;
9.34/4.02	
9.34/4.02	not :: MyBool  ->  MyBool;
9.34/4.02	not MyTrue = MyFalse;
9.34/4.02	not MyFalse = MyTrue;
9.34/4.02	
9.34/4.02	}
9.34/4.02	
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(3) COR (EQUIVALENT)
9.34/4.02	Cond Reductions:
9.34/4.02	The following Function with conditions
9.34/4.02	"undefined |Falseundefined;
9.34/4.02	"
9.34/4.02	is transformed to
9.34/4.02	"undefined  = undefined1;
9.34/4.02	"
9.34/4.02	"undefined0 True = undefined;
9.34/4.02	"
9.34/4.02	"undefined1  = undefined0 False;
9.34/4.02	"
9.34/4.02	
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(4)
9.34/4.02	Obligation:
9.34/4.02	mainModule Main 
9.34/4.02	module Main where {
9.34/4.02	import qualified Prelude;
9.34/4.02	data MyBool = MyTrue  | MyFalse ;
9.34/4.02	
9.34/4.02	data Ordering = LT  | EQ  | GT ;
9.34/4.02	
9.34/4.02	data Tup0 = Tup0 ;
9.34/4.02	
9.34/4.02	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.34/4.02	compareTup0 Tup0 Tup0 = EQ;
9.34/4.02	
9.34/4.02	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.34/4.02	esEsOrdering LT LT = MyTrue;
9.34/4.02	esEsOrdering LT EQ = MyFalse;
9.34/4.02	esEsOrdering LT GT = MyFalse;
9.34/4.02	esEsOrdering EQ LT = MyFalse;
9.34/4.02	esEsOrdering EQ EQ = MyTrue;
9.34/4.02	esEsOrdering EQ GT = MyFalse;
9.34/4.02	esEsOrdering GT LT = MyFalse;
9.34/4.02	esEsOrdering GT EQ = MyFalse;
9.34/4.02	esEsOrdering GT GT = MyTrue;
9.34/4.02	
9.34/4.02	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.34/4.02	fsEsOrdering x y = not (esEsOrdering x y);
9.34/4.02	
9.34/4.02	gtEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.34/4.02	gtEsTup0 x y = fsEsOrdering (compareTup0 x y) LT;
9.34/4.02	
9.34/4.02	not :: MyBool  ->  MyBool;
9.34/4.02	not MyTrue = MyFalse;
9.34/4.02	not MyFalse = MyTrue;
9.34/4.02	
9.34/4.02	}
9.34/4.02	
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(5) Narrow (EQUIVALENT)
9.34/4.02	Haskell To QDPs
9.34/4.02	
9.34/4.02	digraph dp_graph {
9.34/4.02	node [outthreshold=100, inthreshold=100];1[label="gtEsTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.34/4.02	3[label="gtEsTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.34/4.02	4[label="gtEsTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.34/4.02	5[label="fsEsOrdering (compareTup0 vx3 vx4) LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.34/4.02	6[label="not (esEsOrdering (compareTup0 vx3 vx4) LT)",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];
9.34/4.02	12 -> 7[label="",style="solid", color="burlywood", weight=3];
9.34/4.02	7[label="not (esEsOrdering (compareTup0 Tup0 vx4) LT)",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];
9.34/4.02	13 -> 8[label="",style="solid", color="burlywood", weight=3];
9.34/4.02	8[label="not (esEsOrdering (compareTup0 Tup0 Tup0) LT)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.34/4.02	9[label="not (esEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.34/4.02	10[label="not MyFalse",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.34/4.02	11[label="MyTrue",fontsize=16,color="green",shape="box"];}
9.34/4.02	
9.34/4.02	----------------------------------------
9.34/4.02	
9.34/4.02	(6)
9.34/4.02	YES
9.34/4.06	EOF