7.85/3.86	YES
9.60/4.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.60/4.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.60/4.34	
9.60/4.34	
9.60/4.34	H-Termination with start terms of the given HASKELL could be proven:
9.60/4.34	
9.60/4.34	(0) HASKELL
9.60/4.34	(1) BR [EQUIVALENT, 0 ms]
9.60/4.34	(2) HASKELL
9.60/4.34	(3) COR [EQUIVALENT, 0 ms]
9.60/4.34	(4) HASKELL
9.60/4.34	(5) Narrow [EQUIVALENT, 0 ms]
9.60/4.34	(6) YES
9.60/4.34	
9.60/4.34	
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(0)
9.60/4.34	Obligation:
9.60/4.34	mainModule Main 
9.60/4.34	module Main where {
9.60/4.34	import qualified Prelude;
9.60/4.34	data MyBool = MyTrue  | MyFalse ;
9.60/4.34	
9.60/4.34	data Ordering = LT  | EQ  | GT ;
9.60/4.34	
9.60/4.34	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.60/4.34	esEsOrdering LT LT = MyTrue;
9.60/4.34	esEsOrdering LT EQ = MyFalse;
9.60/4.34	esEsOrdering LT GT = MyFalse;
9.60/4.34	esEsOrdering EQ LT = MyFalse;
9.60/4.34	esEsOrdering EQ EQ = MyTrue;
9.60/4.34	esEsOrdering EQ GT = MyFalse;
9.60/4.34	esEsOrdering GT LT = MyFalse;
9.60/4.34	esEsOrdering GT EQ = MyFalse;
9.60/4.34	esEsOrdering GT GT = MyTrue;
9.60/4.34	
9.60/4.34	}
9.60/4.34	
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(1) BR (EQUIVALENT)
9.60/4.34	Replaced joker patterns by fresh variables and removed binding patterns.
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(2)
9.60/4.34	Obligation:
9.60/4.34	mainModule Main 
9.60/4.34	module Main where {
9.60/4.34	import qualified Prelude;
9.60/4.34	data MyBool = MyTrue  | MyFalse ;
9.60/4.34	
9.60/4.34	data Ordering = LT  | EQ  | GT ;
9.60/4.34	
9.60/4.34	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.60/4.34	esEsOrdering LT LT = MyTrue;
9.60/4.34	esEsOrdering LT EQ = MyFalse;
9.60/4.34	esEsOrdering LT GT = MyFalse;
9.60/4.34	esEsOrdering EQ LT = MyFalse;
9.60/4.34	esEsOrdering EQ EQ = MyTrue;
9.60/4.34	esEsOrdering EQ GT = MyFalse;
9.60/4.34	esEsOrdering GT LT = MyFalse;
9.60/4.34	esEsOrdering GT EQ = MyFalse;
9.60/4.34	esEsOrdering GT GT = MyTrue;
9.60/4.34	
9.60/4.34	}
9.60/4.34	
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(3) COR (EQUIVALENT)
9.60/4.34	Cond Reductions:
9.60/4.34	The following Function with conditions
9.60/4.34	"undefined |Falseundefined;
9.60/4.34	"
9.60/4.34	is transformed to
9.60/4.34	"undefined  = undefined1;
9.60/4.34	"
9.60/4.34	"undefined0 True = undefined;
9.60/4.34	"
9.60/4.34	"undefined1  = undefined0 False;
9.60/4.34	"
9.60/4.34	
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(4)
9.60/4.34	Obligation:
9.60/4.34	mainModule Main 
9.60/4.34	module Main where {
9.60/4.34	import qualified Prelude;
9.60/4.34	data MyBool = MyTrue  | MyFalse ;
9.60/4.34	
9.60/4.34	data Ordering = LT  | EQ  | GT ;
9.60/4.34	
9.60/4.34	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
9.60/4.34	esEsOrdering LT LT = MyTrue;
9.60/4.34	esEsOrdering LT EQ = MyFalse;
9.60/4.34	esEsOrdering LT GT = MyFalse;
9.60/4.34	esEsOrdering EQ LT = MyFalse;
9.60/4.34	esEsOrdering EQ EQ = MyTrue;
9.60/4.34	esEsOrdering EQ GT = MyFalse;
9.60/4.34	esEsOrdering GT LT = MyFalse;
9.60/4.34	esEsOrdering GT EQ = MyFalse;
9.60/4.34	esEsOrdering GT GT = MyTrue;
9.60/4.34	
9.60/4.34	}
9.60/4.34	
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(5) Narrow (EQUIVALENT)
9.60/4.34	Haskell To QDPs
9.60/4.34	
9.60/4.34	digraph dp_graph {
9.60/4.34	node [outthreshold=100, inthreshold=100];1[label="esEsOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.60/4.34	3[label="esEsOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.60/4.34	4[label="esEsOrdering 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];
9.60/4.34	26 -> 5[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	27[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];4 -> 27[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	27 -> 6[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	28[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];4 -> 28[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	28 -> 7[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	5[label="esEsOrdering 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];
9.60/4.34	29 -> 8[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	30[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 30[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	30 -> 9[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	31[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 31[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	31 -> 10[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	6[label="esEsOrdering 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];
9.60/4.34	32 -> 11[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	33[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	33 -> 12[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	34[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	34 -> 13[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	7[label="esEsOrdering 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];
9.60/4.34	35 -> 14[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	36[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	36 -> 15[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	37[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
9.60/4.34	37 -> 16[label="",style="solid", color="burlywood", weight=3];
9.60/4.34	8[label="esEsOrdering LT LT",fontsize=16,color="black",shape="box"];8 -> 17[label="",style="solid", color="black", weight=3];
9.60/4.34	9[label="esEsOrdering LT EQ",fontsize=16,color="black",shape="box"];9 -> 18[label="",style="solid", color="black", weight=3];
9.60/4.34	10[label="esEsOrdering LT GT",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.60/4.34	11[label="esEsOrdering EQ LT",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.60/4.34	12[label="esEsOrdering EQ EQ",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.60/4.34	13[label="esEsOrdering EQ GT",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.60/4.34	14[label="esEsOrdering GT LT",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.60/4.34	15[label="esEsOrdering GT EQ",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.60/4.34	16[label="esEsOrdering GT GT",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.60/4.34	17[label="MyTrue",fontsize=16,color="green",shape="box"];18[label="MyFalse",fontsize=16,color="green",shape="box"];19[label="MyFalse",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="MyFalse",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"];}
9.60/4.34	
9.60/4.34	----------------------------------------
9.60/4.34	
9.60/4.34	(6)
9.60/4.34	YES
9.60/4.38	EOF