7.67/3.90	YES
9.23/4.37	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.23/4.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.23/4.37	
9.23/4.37	
9.23/4.37	H-Termination with start terms of the given HASKELL could be proven:
9.23/4.37	
9.23/4.37	(0) HASKELL
9.23/4.37	(1) BR [EQUIVALENT, 0 ms]
9.23/4.37	(2) HASKELL
9.23/4.37	(3) COR [EQUIVALENT, 0 ms]
9.23/4.37	(4) HASKELL
9.23/4.37	(5) Narrow [EQUIVALENT, 29 ms]
9.23/4.37	(6) YES
9.23/4.37	
9.23/4.37	
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(0)
9.23/4.37	Obligation:
9.23/4.37	mainModule Main 
9.23/4.37	module Main where {
9.23/4.37	import qualified Prelude;
9.23/4.37	data MyBool = MyTrue  | MyFalse ;
9.23/4.37	
9.23/4.37	data Ordering = LT  | EQ  | GT ;
9.23/4.37	
9.23/4.37	data Tup0 = Tup0 ;
9.23/4.37	
9.23/4.37	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.23/4.37	compareTup0 Tup0 Tup0 = EQ;
9.23/4.37	
9.23/4.37	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.23/4.37	esEsOrdering LT LT = MyTrue;
9.23/4.37	esEsOrdering LT EQ = MyFalse;
9.23/4.37	esEsOrdering LT GT = MyFalse;
9.23/4.37	esEsOrdering EQ LT = MyFalse;
9.23/4.37	esEsOrdering EQ EQ = MyTrue;
9.23/4.37	esEsOrdering EQ GT = MyFalse;
9.23/4.37	esEsOrdering GT LT = MyFalse;
9.23/4.37	esEsOrdering GT EQ = MyFalse;
9.23/4.37	esEsOrdering GT GT = MyTrue;
9.23/4.37	
9.23/4.37	ltTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.23/4.37	ltTup0 x y = esEsOrdering (compareTup0 x y) LT;
9.23/4.37	
9.23/4.37	}
9.23/4.37	
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(1) BR (EQUIVALENT)
9.23/4.37	Replaced joker patterns by fresh variables and removed binding patterns.
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(2)
9.23/4.37	Obligation:
9.23/4.37	mainModule Main 
9.23/4.37	module Main where {
9.23/4.37	import qualified Prelude;
9.23/4.37	data MyBool = MyTrue  | MyFalse ;
9.23/4.37	
9.23/4.37	data Ordering = LT  | EQ  | GT ;
9.23/4.37	
9.23/4.37	data Tup0 = Tup0 ;
9.23/4.37	
9.23/4.37	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.23/4.37	compareTup0 Tup0 Tup0 = EQ;
9.23/4.37	
9.23/4.37	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.23/4.37	esEsOrdering LT LT = MyTrue;
9.23/4.37	esEsOrdering LT EQ = MyFalse;
9.23/4.37	esEsOrdering LT GT = MyFalse;
9.23/4.37	esEsOrdering EQ LT = MyFalse;
9.23/4.37	esEsOrdering EQ EQ = MyTrue;
9.23/4.37	esEsOrdering EQ GT = MyFalse;
9.23/4.37	esEsOrdering GT LT = MyFalse;
9.23/4.37	esEsOrdering GT EQ = MyFalse;
9.23/4.37	esEsOrdering GT GT = MyTrue;
9.23/4.37	
9.23/4.37	ltTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.23/4.37	ltTup0 x y = esEsOrdering (compareTup0 x y) LT;
9.23/4.37	
9.23/4.37	}
9.23/4.37	
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(3) COR (EQUIVALENT)
9.23/4.37	Cond Reductions:
9.23/4.37	The following Function with conditions
9.23/4.37	"undefined |Falseundefined;
9.23/4.37	"
9.23/4.37	is transformed to
9.23/4.37	"undefined  = undefined1;
9.23/4.37	"
9.23/4.37	"undefined0 True = undefined;
9.23/4.37	"
9.23/4.37	"undefined1  = undefined0 False;
9.23/4.37	"
9.23/4.37	
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(4)
9.23/4.37	Obligation:
9.23/4.37	mainModule Main 
9.23/4.37	module Main where {
9.23/4.37	import qualified Prelude;
9.23/4.37	data MyBool = MyTrue  | MyFalse ;
9.23/4.37	
9.23/4.37	data Ordering = LT  | EQ  | GT ;
9.23/4.37	
9.23/4.37	data Tup0 = Tup0 ;
9.23/4.37	
9.23/4.37	compareTup0 :: Tup0  ->  Tup0  ->  Ordering;
9.23/4.37	compareTup0 Tup0 Tup0 = EQ;
9.23/4.37	
9.23/4.37	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.23/4.37	esEsOrdering LT LT = MyTrue;
9.23/4.37	esEsOrdering LT EQ = MyFalse;
9.23/4.37	esEsOrdering LT GT = MyFalse;
9.23/4.37	esEsOrdering EQ LT = MyFalse;
9.23/4.37	esEsOrdering EQ EQ = MyTrue;
9.23/4.37	esEsOrdering EQ GT = MyFalse;
9.23/4.37	esEsOrdering GT LT = MyFalse;
9.23/4.37	esEsOrdering GT EQ = MyFalse;
9.23/4.37	esEsOrdering GT GT = MyTrue;
9.23/4.37	
9.23/4.37	ltTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.23/4.37	ltTup0 x y = esEsOrdering (compareTup0 x y) LT;
9.23/4.37	
9.23/4.37	}
9.23/4.37	
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(5) Narrow (EQUIVALENT)
9.23/4.37	Haskell To QDPs
9.23/4.37	
9.23/4.37	digraph dp_graph {
9.23/4.37	node [outthreshold=100, inthreshold=100];1[label="ltTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.23/4.37	3[label="ltTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.23/4.37	4[label="ltTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.23/4.37	5[label="esEsOrdering (compareTup0 vx3 vx4) LT",fontsize=16,color="burlywood",shape="box"];10[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9];
9.23/4.37	10 -> 6[label="",style="solid", color="burlywood", weight=3];
9.23/4.37	6[label="esEsOrdering (compareTup0 Tup0 vx4) LT",fontsize=16,color="burlywood",shape="box"];11[label="vx4/Tup0",fontsize=10,color="white",style="solid",shape="box"];6 -> 11[label="",style="solid", color="burlywood", weight=9];
9.23/4.37	11 -> 7[label="",style="solid", color="burlywood", weight=3];
9.23/4.37	7[label="esEsOrdering (compareTup0 Tup0 Tup0) LT",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.23/4.37	8[label="esEsOrdering EQ LT",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.23/4.37	9[label="MyFalse",fontsize=16,color="green",shape="box"];}
9.23/4.37	
9.23/4.37	----------------------------------------
9.23/4.37	
9.23/4.37	(6)
9.23/4.37	YES
9.37/4.41	EOF