7.94/3.48	YES
9.38/3.92	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.38/3.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.38/3.92	
9.38/3.92	
9.38/3.92	H-Termination with start terms of the given HASKELL could be proven:
9.38/3.92	
9.38/3.92	(0) HASKELL
9.38/3.92	(1) BR [EQUIVALENT, 0 ms]
9.38/3.92	(2) HASKELL
9.38/3.92	(3) COR [EQUIVALENT, 0 ms]
9.38/3.92	(4) HASKELL
9.38/3.92	(5) Narrow [EQUIVALENT, 0 ms]
9.38/3.92	(6) YES
9.38/3.92	
9.38/3.92	
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(0)
9.38/3.92	Obligation:
9.38/3.92	mainModule Main 
9.38/3.92	module Main where {
9.38/3.92	import qualified Prelude;
9.38/3.92	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.38/3.92	
9.38/3.92	data Main.Nat = Succ Main.Nat  | Zero ;
9.38/3.92	
9.38/3.92	data Tup0 = Tup0 ;
9.38/3.92	
9.38/3.92	data Tup2 a b = Tup2 a b ;
9.38/3.92	
9.38/3.92	indexTup0 :: Tup2 Tup0 Tup0  ->  Tup0  ->  MyInt;
9.38/3.92	indexTup0 (Tup2 Tup0 Tup0) Tup0 = Main.Pos Main.Zero;
9.38/3.92	
9.38/3.92	}
9.38/3.92	
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(1) BR (EQUIVALENT)
9.38/3.92	Replaced joker patterns by fresh variables and removed binding patterns.
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(2)
9.38/3.92	Obligation:
9.38/3.92	mainModule Main 
9.38/3.92	module Main where {
9.38/3.92	import qualified Prelude;
9.38/3.92	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.38/3.92	
9.38/3.92	data Main.Nat = Succ Main.Nat  | Zero ;
9.38/3.92	
9.38/3.92	data Tup0 = Tup0 ;
9.38/3.92	
9.38/3.92	data Tup2 a b = Tup2 a b ;
9.38/3.92	
9.38/3.92	indexTup0 :: Tup2 Tup0 Tup0  ->  Tup0  ->  MyInt;
9.38/3.92	indexTup0 (Tup2 Tup0 Tup0) Tup0 = Main.Pos Main.Zero;
9.38/3.92	
9.38/3.92	}
9.38/3.92	
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(3) COR (EQUIVALENT)
9.38/3.92	Cond Reductions:
9.38/3.92	The following Function with conditions
9.38/3.92	"undefined |Falseundefined;
9.38/3.92	"
9.38/3.92	is transformed to
9.38/3.92	"undefined  = undefined1;
9.38/3.92	"
9.38/3.92	"undefined0 True = undefined;
9.38/3.92	"
9.38/3.92	"undefined1  = undefined0 False;
9.38/3.92	"
9.38/3.92	
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(4)
9.38/3.92	Obligation:
9.38/3.92	mainModule Main 
9.38/3.92	module Main where {
9.38/3.92	import qualified Prelude;
9.38/3.92	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.38/3.92	
9.38/3.92	data Main.Nat = Succ Main.Nat  | Zero ;
9.38/3.92	
9.38/3.92	data Tup0 = Tup0 ;
9.38/3.92	
9.38/3.92	data Tup2 a b = Tup2 a b ;
9.38/3.92	
9.38/3.92	indexTup0 :: Tup2 Tup0 Tup0  ->  Tup0  ->  MyInt;
9.38/3.92	indexTup0 (Tup2 Tup0 Tup0) Tup0 = Main.Pos Main.Zero;
9.38/3.92	
9.38/3.92	}
9.38/3.92	
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(5) Narrow (EQUIVALENT)
9.38/3.92	Haskell To QDPs
9.38/3.92	
9.38/3.92	digraph dp_graph {
9.38/3.92	node [outthreshold=100, inthreshold=100];1[label="indexTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.38/3.92	3[label="indexTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.38/3.92	4[label="indexTup0 vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];10[label="vx3/Tup2 vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9];
9.38/3.92	10 -> 5[label="",style="solid", color="burlywood", weight=3];
9.38/3.92	5[label="indexTup0 (Tup2 vx30 vx31) vx4",fontsize=16,color="burlywood",shape="box"];11[label="vx30/Tup0",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
9.38/3.92	11 -> 6[label="",style="solid", color="burlywood", weight=3];
9.38/3.92	6[label="indexTup0 (Tup2 Tup0 vx31) vx4",fontsize=16,color="burlywood",shape="box"];12[label="vx31/Tup0",fontsize=10,color="white",style="solid",shape="box"];6 -> 12[label="",style="solid", color="burlywood", weight=9];
9.38/3.92	12 -> 7[label="",style="solid", color="burlywood", weight=3];
9.38/3.92	7[label="indexTup0 (Tup2 Tup0 Tup0) vx4",fontsize=16,color="burlywood",shape="box"];13[label="vx4/Tup0",fontsize=10,color="white",style="solid",shape="box"];7 -> 13[label="",style="solid", color="burlywood", weight=9];
9.38/3.92	13 -> 8[label="",style="solid", color="burlywood", weight=3];
9.38/3.92	8[label="indexTup0 (Tup2 Tup0 Tup0) Tup0",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.38/3.92	9[label="Pos Zero",fontsize=16,color="green",shape="box"];}
9.38/3.92	
9.38/3.92	----------------------------------------
9.38/3.92	
9.38/3.92	(6)
9.38/3.92	YES
9.38/3.94	EOF