7.45/3.46	YES
9.23/3.92	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.23/3.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.23/3.92	
9.23/3.92	
9.23/3.92	H-Termination with start terms of the given HASKELL could be proven:
9.23/3.92	
9.23/3.92	(0) HASKELL
9.23/3.92	(1) BR [EQUIVALENT, 0 ms]
9.23/3.92	(2) HASKELL
9.23/3.92	(3) COR [EQUIVALENT, 0 ms]
9.23/3.92	(4) HASKELL
9.23/3.92	(5) Narrow [EQUIVALENT, 0 ms]
9.23/3.92	(6) YES
9.23/3.92	
9.23/3.92	
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(0)
9.23/3.92	Obligation:
9.23/3.92	mainModule Main 
9.23/3.92	module Main where {
9.23/3.92	import qualified Prelude;
9.23/3.92	data MyBool = MyTrue  | MyFalse ;
9.23/3.92	
9.23/3.92	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.23/3.92	ltEsMyBool MyFalse MyFalse = MyTrue;
9.23/3.92	ltEsMyBool MyFalse MyTrue = MyTrue;
9.23/3.92	ltEsMyBool MyTrue MyFalse = MyFalse;
9.23/3.92	ltEsMyBool MyTrue MyTrue = MyTrue;
9.23/3.92	
9.23/3.92	min0 x y MyTrue = y;
9.23/3.92	
9.23/3.92	min1 x y MyTrue = x;
9.23/3.92	min1 x y MyFalse = min0 x y otherwise;
9.23/3.92	
9.23/3.92	min2 x y = min1 x y (ltEsMyBool x y);
9.23/3.92	
9.23/3.92	minMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.23/3.92	minMyBool x y = min2 x y;
9.23/3.92	
9.23/3.92	otherwise :: MyBool;
9.23/3.92	otherwise = MyTrue;
9.23/3.92	
9.23/3.92	}
9.23/3.92	
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(1) BR (EQUIVALENT)
9.23/3.92	Replaced joker patterns by fresh variables and removed binding patterns.
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(2)
9.23/3.92	Obligation:
9.23/3.92	mainModule Main 
9.23/3.92	module Main where {
9.23/3.92	import qualified Prelude;
9.23/3.92	data MyBool = MyTrue  | MyFalse ;
9.23/3.92	
9.23/3.92	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.23/3.92	ltEsMyBool MyFalse MyFalse = MyTrue;
9.23/3.92	ltEsMyBool MyFalse MyTrue = MyTrue;
9.23/3.92	ltEsMyBool MyTrue MyFalse = MyFalse;
9.23/3.92	ltEsMyBool MyTrue MyTrue = MyTrue;
9.23/3.92	
9.23/3.92	min0 x y MyTrue = y;
9.23/3.92	
9.23/3.92	min1 x y MyTrue = x;
9.23/3.92	min1 x y MyFalse = min0 x y otherwise;
9.23/3.92	
9.23/3.92	min2 x y = min1 x y (ltEsMyBool x y);
9.23/3.92	
9.23/3.92	minMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.23/3.92	minMyBool x y = min2 x y;
9.23/3.92	
9.23/3.92	otherwise :: MyBool;
9.23/3.92	otherwise = MyTrue;
9.23/3.92	
9.23/3.92	}
9.23/3.92	
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(3) COR (EQUIVALENT)
9.23/3.92	Cond Reductions:
9.23/3.92	The following Function with conditions
9.23/3.92	"undefined |Falseundefined;
9.23/3.92	"
9.23/3.92	is transformed to
9.23/3.92	"undefined  = undefined1;
9.23/3.92	"
9.23/3.92	"undefined0 True = undefined;
9.23/3.92	"
9.23/3.92	"undefined1  = undefined0 False;
9.23/3.92	"
9.23/3.92	
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(4)
9.23/3.92	Obligation:
9.23/3.92	mainModule Main 
9.23/3.92	module Main where {
9.23/3.92	import qualified Prelude;
9.23/3.92	data MyBool = MyTrue  | MyFalse ;
9.23/3.92	
9.23/3.92	ltEsMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.23/3.92	ltEsMyBool MyFalse MyFalse = MyTrue;
9.23/3.92	ltEsMyBool MyFalse MyTrue = MyTrue;
9.23/3.92	ltEsMyBool MyTrue MyFalse = MyFalse;
9.23/3.92	ltEsMyBool MyTrue MyTrue = MyTrue;
9.23/3.92	
9.23/3.92	min0 x y MyTrue = y;
9.23/3.92	
9.23/3.92	min1 x y MyTrue = x;
9.23/3.92	min1 x y MyFalse = min0 x y otherwise;
9.23/3.92	
9.23/3.92	min2 x y = min1 x y (ltEsMyBool x y);
9.23/3.92	
9.23/3.92	minMyBool :: MyBool  ->  MyBool  ->  MyBool;
9.23/3.92	minMyBool x y = min2 x y;
9.23/3.92	
9.23/3.92	otherwise :: MyBool;
9.23/3.92	otherwise = MyTrue;
9.23/3.92	
9.23/3.92	}
9.23/3.92	
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(5) Narrow (EQUIVALENT)
9.23/3.92	Haskell To QDPs
9.23/3.92	
9.23/3.92	digraph dp_graph {
9.23/3.92	node [outthreshold=100, inthreshold=100];1[label="minMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.23/3.92	3[label="minMyBool vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.23/3.92	4[label="minMyBool vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.23/3.92	5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.23/3.92	6[label="min1 vx3 vx4 (ltEsMyBool vx3 vx4)",fontsize=16,color="burlywood",shape="box"];23[label="vx3/MyTrue",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9];
9.23/3.92	23 -> 7[label="",style="solid", color="burlywood", weight=3];
9.23/3.92	24[label="vx3/MyFalse",fontsize=10,color="white",style="solid",shape="box"];6 -> 24[label="",style="solid", color="burlywood", weight=9];
9.23/3.92	24 -> 8[label="",style="solid", color="burlywood", weight=3];
9.23/3.92	7[label="min1 MyTrue vx4 (ltEsMyBool MyTrue vx4)",fontsize=16,color="burlywood",shape="box"];25[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 25[label="",style="solid", color="burlywood", weight=9];
9.23/3.92	25 -> 9[label="",style="solid", color="burlywood", weight=3];
9.23/3.92	26[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 26[label="",style="solid", color="burlywood", weight=9];
9.23/3.92	26 -> 10[label="",style="solid", color="burlywood", weight=3];
9.23/3.92	8[label="min1 MyFalse vx4 (ltEsMyBool MyFalse vx4)",fontsize=16,color="burlywood",shape="box"];27[label="vx4/MyTrue",fontsize=10,color="white",style="solid",shape="box"];8 -> 27[label="",style="solid", color="burlywood", weight=9];
9.23/3.92	27 -> 11[label="",style="solid", color="burlywood", weight=3];
9.23/3.92	28[label="vx4/MyFalse",fontsize=10,color="white",style="solid",shape="box"];8 -> 28[label="",style="solid", color="burlywood", weight=9];
9.23/3.92	28 -> 12[label="",style="solid", color="burlywood", weight=3];
9.23/3.92	9[label="min1 MyTrue MyTrue (ltEsMyBool MyTrue MyTrue)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.23/3.92	10[label="min1 MyTrue MyFalse (ltEsMyBool MyTrue MyFalse)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.23/3.92	11[label="min1 MyFalse MyTrue (ltEsMyBool MyFalse MyTrue)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.23/3.92	12[label="min1 MyFalse MyFalse (ltEsMyBool MyFalse MyFalse)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.23/3.92	13[label="min1 MyTrue MyTrue MyTrue",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.23/3.92	14[label="min1 MyTrue MyFalse MyFalse",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.23/3.92	15[label="min1 MyFalse MyTrue MyTrue",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.23/3.92	16[label="min1 MyFalse MyFalse MyTrue",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.23/3.92	17[label="MyTrue",fontsize=16,color="green",shape="box"];18[label="min0 MyTrue MyFalse otherwise",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3];
9.23/3.92	19[label="MyFalse",fontsize=16,color="green",shape="box"];20[label="MyFalse",fontsize=16,color="green",shape="box"];21[label="min0 MyTrue MyFalse MyTrue",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
9.23/3.92	22[label="MyFalse",fontsize=16,color="green",shape="box"];}
9.23/3.92	
9.23/3.92	----------------------------------------
9.23/3.92	
9.23/3.92	(6)
9.23/3.92	YES
9.28/3.97	EOF