7.54/3.42	YES
8.84/3.87	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.84/3.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.84/3.87	
8.84/3.87	
8.84/3.87	H-Termination with start terms of the given HASKELL could be proven:
8.84/3.87	
8.84/3.87	(0) HASKELL
8.84/3.87	(1) BR [EQUIVALENT, 0 ms]
8.84/3.87	(2) HASKELL
8.84/3.87	(3) COR [EQUIVALENT, 0 ms]
8.84/3.87	(4) HASKELL
8.84/3.87	(5) Narrow [EQUIVALENT, 0 ms]
8.84/3.87	(6) YES
8.84/3.87	
8.84/3.87	
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(0)
8.84/3.87	Obligation:
8.84/3.87	mainModule Main 
8.84/3.87	module Main where {
8.84/3.87	import qualified Prelude;
8.84/3.87	data MyBool = MyTrue  | MyFalse ;
8.84/3.87	
8.84/3.87	data Ordering = LT  | EQ  | GT ;
8.84/3.87	
8.84/3.87	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
8.84/3.87	esEsOrdering LT LT = MyTrue;
8.84/3.87	esEsOrdering LT EQ = MyFalse;
8.84/3.87	esEsOrdering LT GT = MyFalse;
8.84/3.87	esEsOrdering EQ LT = MyFalse;
8.84/3.87	esEsOrdering EQ EQ = MyTrue;
8.84/3.87	esEsOrdering EQ GT = MyFalse;
8.84/3.87	esEsOrdering GT LT = MyFalse;
8.84/3.87	esEsOrdering GT EQ = MyFalse;
8.84/3.87	esEsOrdering GT GT = MyTrue;
8.84/3.87	
8.84/3.87	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
8.84/3.87	fsEsOrdering x y = not (esEsOrdering x y);
8.84/3.87	
8.84/3.87	not :: MyBool  ->  MyBool;
8.84/3.87	not MyTrue = MyFalse;
8.84/3.87	not MyFalse = MyTrue;
8.84/3.87	
8.84/3.87	}
8.84/3.87	
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(1) BR (EQUIVALENT)
8.84/3.87	Replaced joker patterns by fresh variables and removed binding patterns.
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(2)
8.84/3.87	Obligation:
8.84/3.87	mainModule Main 
8.84/3.87	module Main where {
8.84/3.87	import qualified Prelude;
8.84/3.87	data MyBool = MyTrue  | MyFalse ;
8.84/3.87	
8.84/3.87	data Ordering = LT  | EQ  | GT ;
8.84/3.87	
8.84/3.87	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
8.84/3.87	esEsOrdering LT LT = MyTrue;
8.84/3.87	esEsOrdering LT EQ = MyFalse;
8.84/3.87	esEsOrdering LT GT = MyFalse;
8.84/3.87	esEsOrdering EQ LT = MyFalse;
8.84/3.87	esEsOrdering EQ EQ = MyTrue;
8.84/3.87	esEsOrdering EQ GT = MyFalse;
8.84/3.87	esEsOrdering GT LT = MyFalse;
8.84/3.87	esEsOrdering GT EQ = MyFalse;
8.84/3.87	esEsOrdering GT GT = MyTrue;
8.84/3.87	
8.84/3.87	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
8.84/3.87	fsEsOrdering x y = not (esEsOrdering x y);
8.84/3.87	
8.84/3.87	not :: MyBool  ->  MyBool;
8.84/3.87	not MyTrue = MyFalse;
8.84/3.87	not MyFalse = MyTrue;
8.84/3.87	
8.84/3.87	}
8.84/3.87	
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(3) COR (EQUIVALENT)
8.84/3.87	Cond Reductions:
8.84/3.87	The following Function with conditions
8.84/3.87	"undefined |Falseundefined;
8.84/3.87	"
8.84/3.87	is transformed to
8.84/3.87	"undefined  = undefined1;
8.84/3.87	"
8.84/3.87	"undefined0 True = undefined;
8.84/3.87	"
8.84/3.87	"undefined1  = undefined0 False;
8.84/3.87	"
8.84/3.87	
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(4)
8.84/3.87	Obligation:
8.84/3.87	mainModule Main 
8.84/3.87	module Main where {
8.84/3.87	import qualified Prelude;
8.84/3.87	data MyBool = MyTrue  | MyFalse ;
8.84/3.87	
8.84/3.87	data Ordering = LT  | EQ  | GT ;
8.84/3.87	
8.84/3.87	esEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
8.84/3.87	esEsOrdering LT LT = MyTrue;
8.84/3.87	esEsOrdering LT EQ = MyFalse;
8.84/3.87	esEsOrdering LT GT = MyFalse;
8.84/3.87	esEsOrdering EQ LT = MyFalse;
8.84/3.87	esEsOrdering EQ EQ = MyTrue;
8.84/3.87	esEsOrdering EQ GT = MyFalse;
8.84/3.87	esEsOrdering GT LT = MyFalse;
8.84/3.87	esEsOrdering GT EQ = MyFalse;
8.84/3.87	esEsOrdering GT GT = MyTrue;
8.84/3.87	
8.84/3.87	fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
8.84/3.87	fsEsOrdering x y = not (esEsOrdering x y);
8.84/3.87	
8.84/3.87	not :: MyBool  ->  MyBool;
8.84/3.87	not MyTrue = MyFalse;
8.84/3.87	not MyFalse = MyTrue;
8.84/3.87	
8.84/3.87	}
8.84/3.87	
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(5) Narrow (EQUIVALENT)
8.84/3.87	Haskell To QDPs
8.84/3.87	
8.84/3.87	digraph dp_graph {
8.84/3.87	node [outthreshold=100, inthreshold=100];1[label="fsEsOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.84/3.87	3[label="fsEsOrdering vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
8.84/3.87	4[label="fsEsOrdering vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
8.84/3.87	5[label="not (esEsOrdering vx3 vx4)",fontsize=16,color="burlywood",shape="box"];29[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];5 -> 29[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	29 -> 6[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	30[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 30[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	30 -> 7[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	31[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 31[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	31 -> 8[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	6[label="not (esEsOrdering LT 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];
8.84/3.87	32 -> 9[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	33[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	33 -> 10[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	34[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	34 -> 11[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	7[label="not (esEsOrdering EQ 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];
8.84/3.87	35 -> 12[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	36[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	36 -> 13[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	37[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	37 -> 14[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	8[label="not (esEsOrdering GT vx4)",fontsize=16,color="burlywood",shape="box"];38[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 38[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	38 -> 15[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	39[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 39[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	39 -> 16[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	40[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 40[label="",style="solid", color="burlywood", weight=9];
8.84/3.87	40 -> 17[label="",style="solid", color="burlywood", weight=3];
8.84/3.87	9[label="not (esEsOrdering LT LT)",fontsize=16,color="black",shape="box"];9 -> 18[label="",style="solid", color="black", weight=3];
8.84/3.87	10[label="not (esEsOrdering LT EQ)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
8.84/3.87	11[label="not (esEsOrdering LT GT)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
8.84/3.87	12[label="not (esEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
8.84/3.87	13[label="not (esEsOrdering EQ EQ)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
8.84/3.87	14[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
8.84/3.87	15[label="not (esEsOrdering GT LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
8.84/3.87	16[label="not (esEsOrdering GT EQ)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
8.84/3.87	17[label="not (esEsOrdering GT GT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
8.84/3.87	18[label="not MyTrue",fontsize=16,color="black",shape="triangle"];18 -> 27[label="",style="solid", color="black", weight=3];
8.84/3.87	19[label="not MyFalse",fontsize=16,color="black",shape="triangle"];19 -> 28[label="",style="solid", color="black", weight=3];
8.84/3.87	20 -> 19[label="",style="dashed", color="red", weight=0];
8.84/3.87	20[label="not MyFalse",fontsize=16,color="magenta"];21 -> 19[label="",style="dashed", color="red", weight=0];
8.84/3.87	21[label="not MyFalse",fontsize=16,color="magenta"];22 -> 18[label="",style="dashed", color="red", weight=0];
8.84/3.87	22[label="not MyTrue",fontsize=16,color="magenta"];23 -> 19[label="",style="dashed", color="red", weight=0];
8.84/3.87	23[label="not MyFalse",fontsize=16,color="magenta"];24 -> 19[label="",style="dashed", color="red", weight=0];
8.84/3.87	24[label="not MyFalse",fontsize=16,color="magenta"];25 -> 19[label="",style="dashed", color="red", weight=0];
8.84/3.87	25[label="not MyFalse",fontsize=16,color="magenta"];26 -> 18[label="",style="dashed", color="red", weight=0];
8.84/3.87	26[label="not MyTrue",fontsize=16,color="magenta"];27[label="MyFalse",fontsize=16,color="green",shape="box"];28[label="MyTrue",fontsize=16,color="green",shape="box"];}
8.84/3.87	
8.84/3.87	----------------------------------------
8.84/3.87	
8.84/3.87	(6)
8.84/3.87	YES
9.14/3.94	EOF