7.70/3.48	YES
9.41/3.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.41/3.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.41/3.93	
9.41/3.93	
9.41/3.93	H-Termination with start terms of the given HASKELL could be proven:
9.41/3.93	
9.41/3.93	(0) HASKELL
9.41/3.93	(1) BR [EQUIVALENT, 0 ms]
9.41/3.93	(2) HASKELL
9.41/3.93	(3) COR [EQUIVALENT, 0 ms]
9.41/3.93	(4) HASKELL
9.41/3.93	(5) Narrow [EQUIVALENT, 0 ms]
9.41/3.93	(6) YES
9.41/3.93	
9.41/3.93	
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(0)
9.41/3.93	Obligation:
9.41/3.93	mainModule Main 
9.41/3.93	module Main where {
9.41/3.93	import qualified Prelude;
9.41/3.93	data MyBool = MyTrue  | MyFalse ;
9.41/3.93	
9.41/3.93	data Ordering = LT  | EQ  | GT ;
9.41/3.93	
9.41/3.93	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.41/3.93	ltEsOrdering LT LT = MyTrue;
9.41/3.93	ltEsOrdering LT EQ = MyTrue;
9.41/3.93	ltEsOrdering LT GT = MyTrue;
9.41/3.93	ltEsOrdering EQ LT = MyFalse;
9.41/3.93	ltEsOrdering EQ EQ = MyTrue;
9.41/3.93	ltEsOrdering EQ GT = MyTrue;
9.41/3.93	ltEsOrdering GT LT = MyFalse;
9.41/3.93	ltEsOrdering GT EQ = MyFalse;
9.41/3.93	ltEsOrdering GT GT = MyTrue;
9.41/3.93	
9.41/3.93	}
9.41/3.93	
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(1) BR (EQUIVALENT)
9.41/3.93	Replaced joker patterns by fresh variables and removed binding patterns.
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(2)
9.41/3.93	Obligation:
9.41/3.93	mainModule Main 
9.41/3.93	module Main where {
9.41/3.93	import qualified Prelude;
9.41/3.93	data MyBool = MyTrue  | MyFalse ;
9.41/3.93	
9.41/3.93	data Ordering = LT  | EQ  | GT ;
9.41/3.93	
9.41/3.93	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.41/3.93	ltEsOrdering LT LT = MyTrue;
9.41/3.93	ltEsOrdering LT EQ = MyTrue;
9.41/3.93	ltEsOrdering LT GT = MyTrue;
9.41/3.93	ltEsOrdering EQ LT = MyFalse;
9.41/3.93	ltEsOrdering EQ EQ = MyTrue;
9.41/3.93	ltEsOrdering EQ GT = MyTrue;
9.41/3.93	ltEsOrdering GT LT = MyFalse;
9.41/3.93	ltEsOrdering GT EQ = MyFalse;
9.41/3.93	ltEsOrdering GT GT = MyTrue;
9.41/3.93	
9.41/3.93	}
9.41/3.93	
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(3) COR (EQUIVALENT)
9.41/3.93	Cond Reductions:
9.41/3.93	The following Function with conditions
9.41/3.93	"undefined |Falseundefined;
9.41/3.93	"
9.41/3.93	is transformed to
9.41/3.93	"undefined  = undefined1;
9.41/3.93	"
9.41/3.93	"undefined0 True = undefined;
9.41/3.93	"
9.41/3.93	"undefined1  = undefined0 False;
9.41/3.93	"
9.41/3.93	
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(4)
9.41/3.93	Obligation:
9.41/3.93	mainModule Main 
9.41/3.93	module Main where {
9.41/3.93	import qualified Prelude;
9.41/3.93	data MyBool = MyTrue  | MyFalse ;
9.41/3.93	
9.41/3.93	data Ordering = LT  | EQ  | GT ;
9.41/3.93	
9.41/3.93	ltEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.41/3.93	ltEsOrdering LT LT = MyTrue;
9.41/3.93	ltEsOrdering LT EQ = MyTrue;
9.41/3.93	ltEsOrdering LT GT = MyTrue;
9.41/3.93	ltEsOrdering EQ LT = MyFalse;
9.41/3.93	ltEsOrdering EQ EQ = MyTrue;
9.41/3.93	ltEsOrdering EQ GT = MyTrue;
9.41/3.93	ltEsOrdering GT LT = MyFalse;
9.41/3.93	ltEsOrdering GT EQ = MyFalse;
9.41/3.93	ltEsOrdering GT GT = MyTrue;
9.41/3.93	
9.41/3.93	}
9.41/3.93	
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(5) Narrow (EQUIVALENT)
9.41/3.93	Haskell To QDPs
9.41/3.93	
9.41/3.93	digraph dp_graph {
9.41/3.93	node [outthreshold=100, inthreshold=100];1[label="ltEsOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.41/3.93	3[label="ltEsOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.41/3.93	4[label="ltEsOrdering vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];26[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];4 -> 26[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	26 -> 5[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	27[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];4 -> 27[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	27 -> 6[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	28[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];4 -> 28[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	28 -> 7[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	5[label="ltEsOrdering LT vx4",fontsize=16,color="burlywood",shape="box"];29[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];5 -> 29[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	29 -> 8[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	30[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 30[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	30 -> 9[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	31[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 31[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	31 -> 10[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	6[label="ltEsOrdering EQ vx4",fontsize=16,color="burlywood",shape="box"];32[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	32 -> 11[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	33[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	33 -> 12[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	34[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	34 -> 13[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	7[label="ltEsOrdering GT vx4",fontsize=16,color="burlywood",shape="box"];35[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	35 -> 14[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	36[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	36 -> 15[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	37[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
9.41/3.93	37 -> 16[label="",style="solid", color="burlywood", weight=3];
9.41/3.93	8[label="ltEsOrdering LT LT",fontsize=16,color="black",shape="box"];8 -> 17[label="",style="solid", color="black", weight=3];
9.41/3.93	9[label="ltEsOrdering LT EQ",fontsize=16,color="black",shape="box"];9 -> 18[label="",style="solid", color="black", weight=3];
9.41/3.93	10[label="ltEsOrdering LT GT",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.41/3.93	11[label="ltEsOrdering EQ LT",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.41/3.93	12[label="ltEsOrdering EQ EQ",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.41/3.93	13[label="ltEsOrdering EQ GT",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.41/3.93	14[label="ltEsOrdering GT LT",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.41/3.93	15[label="ltEsOrdering GT EQ",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.41/3.93	16[label="ltEsOrdering GT GT",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.41/3.93	17[label="MyTrue",fontsize=16,color="green",shape="box"];18[label="MyTrue",fontsize=16,color="green",shape="box"];19[label="MyTrue",fontsize=16,color="green",shape="box"];20[label="MyFalse",fontsize=16,color="green",shape="box"];21[label="MyTrue",fontsize=16,color="green",shape="box"];22[label="MyTrue",fontsize=16,color="green",shape="box"];23[label="MyFalse",fontsize=16,color="green",shape="box"];24[label="MyFalse",fontsize=16,color="green",shape="box"];25[label="MyTrue",fontsize=16,color="green",shape="box"];}
9.41/3.93	
9.41/3.93	----------------------------------------
9.41/3.93	
9.41/3.93	(6)
9.41/3.93	YES
9.49/5.76	EOF