7.51/3.56	YES
8.96/3.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.96/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.96/3.99	
8.96/3.99	
8.96/3.99	H-Termination with start terms of the given HASKELL could be proven:
8.96/3.99	
8.96/3.99	(0) HASKELL
8.96/3.99	(1) BR [EQUIVALENT, 0 ms]
8.96/3.99	(2) HASKELL
8.96/3.99	(3) COR [EQUIVALENT, 0 ms]
8.96/3.99	(4) HASKELL
8.96/3.99	(5) Narrow [EQUIVALENT, 0 ms]
8.96/3.99	(6) YES
8.96/3.99	
8.96/3.99	
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(0)
8.96/3.99	Obligation:
8.96/3.99	mainModule Main 
8.96/3.99	module Main where {
8.96/3.99	import qualified Prelude;
8.96/3.99	data MyBool = MyTrue  | MyFalse ;
8.96/3.99	
8.96/3.99	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
8.96/3.99	esEsMyBool MyFalse MyFalse = MyTrue;
8.96/3.99	esEsMyBool MyFalse MyTrue = MyFalse;
8.96/3.99	esEsMyBool MyTrue MyFalse = MyFalse;
8.96/3.99	esEsMyBool MyTrue MyTrue = MyTrue;
8.96/3.99	
8.96/3.99	fsEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
8.96/3.99	fsEsMyBool x y = not (esEsMyBool x y);
8.96/3.99	
8.96/3.99	not :: MyBool  ->  MyBool;
8.96/3.99	not MyTrue = MyFalse;
8.96/3.99	not MyFalse = MyTrue;
8.96/3.99	
8.96/3.99	}
8.96/3.99	
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(1) BR (EQUIVALENT)
8.96/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(2)
8.96/3.99	Obligation:
8.96/3.99	mainModule Main 
8.96/3.99	module Main where {
8.96/3.99	import qualified Prelude;
8.96/3.99	data MyBool = MyTrue  | MyFalse ;
8.96/3.99	
8.96/3.99	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
8.96/3.99	esEsMyBool MyFalse MyFalse = MyTrue;
8.96/3.99	esEsMyBool MyFalse MyTrue = MyFalse;
8.96/3.99	esEsMyBool MyTrue MyFalse = MyFalse;
8.96/3.99	esEsMyBool MyTrue MyTrue = MyTrue;
8.96/3.99	
8.96/3.99	fsEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
8.96/3.99	fsEsMyBool x y = not (esEsMyBool x y);
8.96/3.99	
8.96/3.99	not :: MyBool  ->  MyBool;
8.96/3.99	not MyTrue = MyFalse;
8.96/3.99	not MyFalse = MyTrue;
8.96/3.99	
8.96/3.99	}
8.96/3.99	
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(3) COR (EQUIVALENT)
8.96/3.99	Cond Reductions:
8.96/3.99	The following Function with conditions
8.96/3.99	"undefined |Falseundefined;
8.96/3.99	"
8.96/3.99	is transformed to
8.96/3.99	"undefined  = undefined1;
8.96/3.99	"
8.96/3.99	"undefined0 True = undefined;
8.96/3.99	"
8.96/3.99	"undefined1  = undefined0 False;
8.96/3.99	"
8.96/3.99	
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(4)
8.96/3.99	Obligation:
8.96/3.99	mainModule Main 
8.96/3.99	module Main where {
8.96/3.99	import qualified Prelude;
8.96/3.99	data MyBool = MyTrue  | MyFalse ;
8.96/3.99	
8.96/3.99	esEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
8.96/3.99	esEsMyBool MyFalse MyFalse = MyTrue;
8.96/3.99	esEsMyBool MyFalse MyTrue = MyFalse;
8.96/3.99	esEsMyBool MyTrue MyFalse = MyFalse;
8.96/3.99	esEsMyBool MyTrue MyTrue = MyTrue;
8.96/3.99	
8.96/3.99	fsEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
8.96/3.99	fsEsMyBool x y = not (esEsMyBool x y);
8.96/3.99	
8.96/3.99	not :: MyBool  ->  MyBool;
8.96/3.99	not MyTrue = MyFalse;
8.96/3.99	not MyFalse = MyTrue;
8.96/3.99	
8.96/3.99	}
8.96/3.99	
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(5) Narrow (EQUIVALENT)
8.96/3.99	Haskell To QDPs
8.96/3.99	
8.96/3.99	digraph dp_graph {
8.96/3.99	node [outthreshold=100, inthreshold=100];1[label="fsEsMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.96/3.99	3[label="fsEsMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
8.96/3.99	4[label="fsEsMyBool vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
8.96/3.99	5[label="not (esEsMyBool vx3 vx4)",fontsize=16,color="burlywood",shape="box"];18[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
8.96/3.99	18 -> 6[label="",style="solid", color="burlywood", weight=3];
8.96/3.99	19[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
8.96/3.99	19 -> 7[label="",style="solid", color="burlywood", weight=3];
8.96/3.99	6[label="not (esEsMyBool MyTrue vx4)",fontsize=16,color="burlywood",shape="box"];20[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];6 -> 20[label="",style="solid", color="burlywood", weight=9];
8.96/3.99	20 -> 8[label="",style="solid", color="burlywood", weight=3];
8.96/3.99	21[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
8.96/3.99	21 -> 9[label="",style="solid", color="burlywood", weight=3];
8.96/3.99	7[label="not (esEsMyBool MyFalse vx4)",fontsize=16,color="burlywood",shape="box"];22[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 22[label="",style="solid", color="burlywood", weight=9];
8.96/3.99	22 -> 10[label="",style="solid", color="burlywood", weight=3];
8.96/3.99	23[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 23[label="",style="solid", color="burlywood", weight=9];
8.96/3.99	23 -> 11[label="",style="solid", color="burlywood", weight=3];
8.96/3.99	8[label="not (esEsMyBool MyTrue MyTrue)",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
8.96/3.99	9[label="not (esEsMyBool MyTrue MyFalse)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
8.96/3.99	10[label="not (esEsMyBool MyFalse MyTrue)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
8.96/3.99	11[label="not (esEsMyBool MyFalse MyFalse)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
8.96/3.99	12[label="not MyTrue",fontsize=16,color="black",shape="triangle"];12 -> 16[label="",style="solid", color="black", weight=3];
8.96/3.99	13[label="not MyFalse",fontsize=16,color="black",shape="triangle"];13 -> 17[label="",style="solid", color="black", weight=3];
8.96/3.99	14 -> 13[label="",style="dashed", color="red", weight=0];
8.96/3.99	14[label="not MyFalse",fontsize=16,color="magenta"];15 -> 12[label="",style="dashed", color="red", weight=0];
8.96/3.99	15[label="not MyTrue",fontsize=16,color="magenta"];16[label="MyFalse",fontsize=16,color="green",shape="box"];17[label="MyTrue",fontsize=16,color="green",shape="box"];}
8.96/3.99	
8.96/3.99	----------------------------------------
8.96/3.99	
8.96/3.99	(6)
8.96/3.99	YES
9.24/4.03	EOF