7.69/3.84	YES
9.44/4.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.44/4.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.44/4.35	
9.44/4.35	
9.44/4.35	H-Termination with start terms of the given HASKELL could be proven:
9.44/4.35	
9.44/4.35	(0) HASKELL
9.44/4.35	(1) BR [EQUIVALENT, 0 ms]
9.44/4.35	(2) HASKELL
9.44/4.35	(3) COR [EQUIVALENT, 0 ms]
9.44/4.35	(4) HASKELL
9.44/4.35	(5) Narrow [EQUIVALENT, 0 ms]
9.44/4.35	(6) YES
9.44/4.35	
9.44/4.35	
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(0)
9.44/4.35	Obligation:
9.44/4.35	mainModule Main 
9.44/4.35	module Main where {
9.44/4.35	import qualified Prelude;
9.44/4.35	data List a = Cons a (List a)  | Nil ;
9.44/4.35	
9.44/4.35	data Main.Maybe a = Nothing  | Just a ;
9.44/4.35	
9.44/4.35	data MyBool = MyTrue  | MyFalse ;
9.44/4.35	
9.44/4.35	data Tup0 = Tup0 ;
9.44/4.35	
9.44/4.35	data Tup2 a b = Tup2 a b ;
9.44/4.35	
9.44/4.35	esEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.44/4.35	esEsTup0 Tup0 Tup0 = MyTrue;
9.44/4.35	
9.44/4.35	lookup k Nil = lookup3 k Nil;
9.44/4.35	lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);
9.44/4.35	
9.44/4.35	lookup0 k x y xys MyTrue = lookup k xys;
9.44/4.35	
9.44/4.35	lookup1 k x y xys MyTrue = Main.Just y;
9.44/4.35	lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;
9.44/4.35	
9.44/4.35	lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsTup0 k x);
9.44/4.35	
9.44/4.35	lookup3 k Nil = Main.Nothing;
9.44/4.35	lookup3 vy vz = lookup2 vy vz;
9.44/4.35	
9.44/4.35	otherwise :: MyBool;
9.44/4.35	otherwise = MyTrue;
9.44/4.35	
9.44/4.35	}
9.44/4.35	
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(1) BR (EQUIVALENT)
9.44/4.35	Replaced joker patterns by fresh variables and removed binding patterns.
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(2)
9.44/4.35	Obligation:
9.44/4.35	mainModule Main 
9.44/4.35	module Main where {
9.44/4.35	import qualified Prelude;
9.44/4.35	data List a = Cons a (List a)  | Nil ;
9.44/4.35	
9.44/4.35	data Main.Maybe a = Nothing  | Just a ;
9.44/4.35	
9.44/4.35	data MyBool = MyTrue  | MyFalse ;
9.44/4.35	
9.44/4.35	data Tup0 = Tup0 ;
9.44/4.35	
9.44/4.35	data Tup2 a b = Tup2 a b ;
9.44/4.35	
9.44/4.35	esEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.44/4.35	esEsTup0 Tup0 Tup0 = MyTrue;
9.44/4.35	
9.44/4.35	lookup k Nil = lookup3 k Nil;
9.44/4.35	lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);
9.44/4.35	
9.44/4.35	lookup0 k x y xys MyTrue = lookup k xys;
9.44/4.35	
9.44/4.35	lookup1 k x y xys MyTrue = Main.Just y;
9.44/4.35	lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;
9.44/4.35	
9.44/4.35	lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsTup0 k x);
9.44/4.35	
9.44/4.35	lookup3 k Nil = Main.Nothing;
9.44/4.35	lookup3 vy vz = lookup2 vy vz;
9.44/4.35	
9.44/4.35	otherwise :: MyBool;
9.44/4.35	otherwise = MyTrue;
9.44/4.35	
9.44/4.35	}
9.44/4.35	
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(3) COR (EQUIVALENT)
9.44/4.35	Cond Reductions:
9.44/4.35	The following Function with conditions
9.44/4.35	"undefined |Falseundefined;
9.44/4.35	"
9.44/4.35	is transformed to
9.44/4.35	"undefined  = undefined1;
9.44/4.35	"
9.44/4.35	"undefined0 True = undefined;
9.44/4.35	"
9.44/4.35	"undefined1  = undefined0 False;
9.44/4.35	"
9.44/4.35	
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(4)
9.44/4.35	Obligation:
9.44/4.35	mainModule Main 
9.44/4.35	module Main where {
9.44/4.35	import qualified Prelude;
9.44/4.35	data List a = Cons a (List a)  | Nil ;
9.44/4.35	
9.44/4.35	data Main.Maybe a = Nothing  | Just a ;
9.44/4.35	
9.44/4.35	data MyBool = MyTrue  | MyFalse ;
9.44/4.35	
9.44/4.35	data Tup0 = Tup0 ;
9.44/4.35	
9.44/4.35	data Tup2 a b = Tup2 a b ;
9.44/4.35	
9.44/4.35	esEsTup0 :: Tup0  ->  Tup0  ->  MyBool;
9.44/4.35	esEsTup0 Tup0 Tup0 = MyTrue;
9.44/4.35	
9.44/4.35	lookup k Nil = lookup3 k Nil;
9.44/4.35	lookup k (Cons (Tup2 x y) xys) = lookup2 k (Cons (Tup2 x y) xys);
9.44/4.35	
9.44/4.35	lookup0 k x y xys MyTrue = lookup k xys;
9.44/4.35	
9.44/4.35	lookup1 k x y xys MyTrue = Main.Just y;
9.44/4.35	lookup1 k x y xys MyFalse = lookup0 k x y xys otherwise;
9.44/4.35	
9.44/4.35	lookup2 k (Cons (Tup2 x y) xys) = lookup1 k x y xys (esEsTup0 k x);
9.44/4.35	
9.44/4.35	lookup3 k Nil = Main.Nothing;
9.44/4.35	lookup3 vy vz = lookup2 vy vz;
9.44/4.35	
9.44/4.35	otherwise :: MyBool;
9.44/4.35	otherwise = MyTrue;
9.44/4.35	
9.44/4.35	}
9.44/4.35	
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(5) Narrow (EQUIVALENT)
9.44/4.35	Haskell To QDPs
9.44/4.35	
9.44/4.35	digraph dp_graph {
9.44/4.35	node [outthreshold=100, inthreshold=100];1[label="lookup",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.44/4.35	3[label="lookup vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.44/4.35	4[label="lookup vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];16[label="vx4/Cons vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
9.44/4.35	16 -> 5[label="",style="solid", color="burlywood", weight=3];
9.44/4.35	17[label="vx4/Nil",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
9.44/4.35	17 -> 6[label="",style="solid", color="burlywood", weight=3];
9.44/4.35	5[label="lookup vx3 (Cons vx40 vx41)",fontsize=16,color="burlywood",shape="box"];18[label="vx40/Tup2 vx400 vx401",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
9.44/4.35	18 -> 7[label="",style="solid", color="burlywood", weight=3];
9.44/4.35	6[label="lookup vx3 Nil",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.44/4.35	7[label="lookup vx3 (Cons (Tup2 vx400 vx401) vx41)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.44/4.35	8[label="lookup3 vx3 Nil",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9.44/4.35	9[label="lookup2 vx3 (Cons (Tup2 vx400 vx401) vx41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.44/4.35	10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 vx3 vx400 vx401 vx41 (esEsTup0 vx3 vx400)",fontsize=16,color="burlywood",shape="box"];19[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];11 -> 19[label="",style="solid", color="burlywood", weight=9];
9.44/4.35	19 -> 12[label="",style="solid", color="burlywood", weight=3];
9.44/4.35	12[label="lookup1 Tup0 vx400 vx401 vx41 (esEsTup0 Tup0 vx400)",fontsize=16,color="burlywood",shape="box"];20[label="vx400/Tup0",fontsize=10,color="white",style="solid",shape="box"];12 -> 20[label="",style="solid", color="burlywood", weight=9];
9.44/4.35	20 -> 13[label="",style="solid", color="burlywood", weight=3];
9.44/4.35	13[label="lookup1 Tup0 Tup0 vx401 vx41 (esEsTup0 Tup0 Tup0)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
9.44/4.35	14[label="lookup1 Tup0 Tup0 vx401 vx41 MyTrue",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
9.44/4.35	15[label="Just vx401",fontsize=16,color="green",shape="box"];}
9.44/4.35	
9.44/4.35	----------------------------------------
9.44/4.35	
9.44/4.35	(6)
9.44/4.35	YES
9.44/4.39	EOF