7.56/3.42	YES
9.38/3.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.38/3.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.38/3.89	
9.38/3.89	
9.38/3.89	H-Termination with start terms of the given HASKELL could be proven:
9.38/3.89	
9.38/3.89	(0) HASKELL
9.38/3.89	(1) BR [EQUIVALENT, 0 ms]
9.38/3.89	(2) HASKELL
9.38/3.89	(3) COR [EQUIVALENT, 0 ms]
9.38/3.89	(4) HASKELL
9.38/3.89	(5) Narrow [EQUIVALENT, 0 ms]
9.38/3.89	(6) YES
9.38/3.89	
9.38/3.89	
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(0)
9.38/3.89	Obligation:
9.38/3.89	mainModule Main 
9.38/3.89	module Main where {
9.38/3.89	import qualified Prelude;
9.38/3.89	data MyBool = MyTrue  | MyFalse ;
9.38/3.89	
9.38/3.89	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.38/3.89	esEsMyBool MyFalse MyFalse = MyTrue;
9.38/3.89	esEsMyBool MyFalse MyTrue = MyFalse;
9.38/3.89	esEsMyBool MyTrue MyFalse = MyFalse;
9.38/3.89	esEsMyBool MyTrue MyTrue = MyTrue;
9.38/3.89	
9.38/3.89	}
9.38/3.89	
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(1) BR (EQUIVALENT)
9.38/3.89	Replaced joker patterns by fresh variables and removed binding patterns.
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(2)
9.38/3.89	Obligation:
9.38/3.89	mainModule Main 
9.38/3.89	module Main where {
9.38/3.89	import qualified Prelude;
9.38/3.89	data MyBool = MyTrue  | MyFalse ;
9.38/3.89	
9.38/3.89	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.38/3.89	esEsMyBool MyFalse MyFalse = MyTrue;
9.38/3.89	esEsMyBool MyFalse MyTrue = MyFalse;
9.38/3.89	esEsMyBool MyTrue MyFalse = MyFalse;
9.38/3.89	esEsMyBool MyTrue MyTrue = MyTrue;
9.38/3.89	
9.38/3.89	}
9.38/3.89	
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(3) COR (EQUIVALENT)
9.38/3.89	Cond Reductions:
9.38/3.89	The following Function with conditions
9.38/3.89	"undefined |Falseundefined;
9.38/3.89	"
9.38/3.89	is transformed to
9.38/3.89	"undefined  = undefined1;
9.38/3.89	"
9.38/3.89	"undefined0 True = undefined;
9.38/3.89	"
9.38/3.89	"undefined1  = undefined0 False;
9.38/3.89	"
9.38/3.89	
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(4)
9.38/3.89	Obligation:
9.38/3.89	mainModule Main 
9.38/3.89	module Main where {
9.38/3.89	import qualified Prelude;
9.38/3.89	data MyBool = MyTrue  | MyFalse ;
9.38/3.89	
9.38/3.89	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.38/3.89	esEsMyBool MyFalse MyFalse = MyTrue;
9.38/3.89	esEsMyBool MyFalse MyTrue = MyFalse;
9.38/3.89	esEsMyBool MyTrue MyFalse = MyFalse;
9.38/3.89	esEsMyBool MyTrue MyTrue = MyTrue;
9.38/3.89	
9.38/3.89	}
9.38/3.89	
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(5) Narrow (EQUIVALENT)
9.38/3.89	Haskell To QDPs
9.38/3.89	
9.38/3.89	digraph dp_graph {
9.38/3.89	node [outthreshold=100, inthreshold=100];1[label="esEsMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.38/3.89	3[label="esEsMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.38/3.89	4[label="esEsMyBool vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];15[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];4 -> 15[label="",style="solid", color="burlywood", weight=9];
9.38/3.89	15 -> 5[label="",style="solid", color="burlywood", weight=3];
9.38/3.89	16[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
9.38/3.89	16 -> 6[label="",style="solid", color="burlywood", weight=3];
9.38/3.89	5[label="esEsMyBool MyTrue vx4",fontsize=16,color="burlywood",shape="box"];17[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
9.38/3.89	17 -> 7[label="",style="solid", color="burlywood", weight=3];
9.38/3.89	18[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
9.38/3.89	18 -> 8[label="",style="solid", color="burlywood", weight=3];
9.38/3.89	6[label="esEsMyBool MyFalse vx4",fontsize=16,color="burlywood",shape="box"];19[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];6 -> 19[label="",style="solid", color="burlywood", weight=9];
9.38/3.89	19 -> 9[label="",style="solid", color="burlywood", weight=3];
9.38/3.89	20[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
9.38/3.89	20 -> 10[label="",style="solid", color="burlywood", weight=3];
9.38/3.89	7[label="esEsMyBool MyTrue MyTrue",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
9.38/3.89	8[label="esEsMyBool MyTrue MyFalse",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9.38/3.89	9[label="esEsMyBool MyFalse MyTrue",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.38/3.89	10[label="esEsMyBool MyFalse MyFalse",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.38/3.89	11[label="MyTrue",fontsize=16,color="green",shape="box"];12[label="MyFalse",fontsize=16,color="green",shape="box"];13[label="MyFalse",fontsize=16,color="green",shape="box"];14[label="MyTrue",fontsize=16,color="green",shape="box"];}
9.38/3.89	
9.38/3.89	----------------------------------------
9.38/3.89	
9.38/3.89	(6)
9.38/3.89	YES
9.38/3.93	EOF