7.32/4.32	YES
9.00/4.80	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.00/4.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.00/4.80	
9.00/4.80	
9.00/4.80	H-Termination with start terms of the given HASKELL could be proven:
9.00/4.80	
9.00/4.80	(0) HASKELL
9.00/4.80	(1) BR [EQUIVALENT, 0 ms]
9.00/4.80	(2) HASKELL
9.00/4.80	(3) COR [EQUIVALENT, 0 ms]
9.00/4.80	(4) HASKELL
9.00/4.80	(5) Narrow [EQUIVALENT, 30 ms]
9.00/4.80	(6) YES
9.00/4.80	
9.00/4.80	
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(0)
9.00/4.80	Obligation:
9.00/4.80	mainModule Main 
9.00/4.80	module Main where {
9.00/4.80	import qualified Prelude;
9.00/4.80	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.00/4.80	
9.00/4.80	data Main.Nat = Succ Main.Nat  | Zero ;
9.00/4.80	
9.00/4.80	succMyInt :: MyInt  ->  MyInt;
9.00/4.80	succMyInt (Main.Pos Main.Zero) = Main.Pos (Main.Succ Main.Zero);
9.00/4.80	succMyInt (Main.Neg Main.Zero) = Main.Pos (Main.Succ Main.Zero);
9.00/4.80	succMyInt (Main.Pos (Main.Succ x)) = Main.Pos (Main.Succ (Main.Succ x));
9.00/4.80	succMyInt (Main.Neg (Main.Succ x)) = Main.Neg x;
9.00/4.80	
9.00/4.80	}
9.00/4.80	
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(1) BR (EQUIVALENT)
9.00/4.80	Replaced joker patterns by fresh variables and removed binding patterns.
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(2)
9.00/4.80	Obligation:
9.00/4.80	mainModule Main 
9.00/4.80	module Main where {
9.00/4.80	import qualified Prelude;
9.00/4.80	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.00/4.80	
9.00/4.80	data Main.Nat = Succ Main.Nat  | Zero ;
9.00/4.80	
9.00/4.80	succMyInt :: MyInt  ->  MyInt;
9.00/4.80	succMyInt (Main.Pos Main.Zero) = Main.Pos (Main.Succ Main.Zero);
9.00/4.80	succMyInt (Main.Neg Main.Zero) = Main.Pos (Main.Succ Main.Zero);
9.00/4.80	succMyInt (Main.Pos (Main.Succ x)) = Main.Pos (Main.Succ (Main.Succ x));
9.00/4.80	succMyInt (Main.Neg (Main.Succ x)) = Main.Neg x;
9.00/4.80	
9.00/4.80	}
9.00/4.80	
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(3) COR (EQUIVALENT)
9.00/4.80	Cond Reductions:
9.00/4.80	The following Function with conditions
9.00/4.80	"undefined |Falseundefined;
9.00/4.80	"
9.00/4.80	is transformed to
9.00/4.80	"undefined  = undefined1;
9.00/4.80	"
9.00/4.80	"undefined0 True = undefined;
9.00/4.80	"
9.00/4.80	"undefined1  = undefined0 False;
9.00/4.80	"
9.00/4.80	
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(4)
9.00/4.80	Obligation:
9.00/4.80	mainModule Main 
9.00/4.80	module Main where {
9.00/4.80	import qualified Prelude;
9.00/4.80	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.00/4.80	
9.00/4.80	data Main.Nat = Succ Main.Nat  | Zero ;
9.00/4.80	
9.00/4.80	succMyInt :: MyInt  ->  MyInt;
9.00/4.80	succMyInt (Main.Pos Main.Zero) = Main.Pos (Main.Succ Main.Zero);
9.00/4.80	succMyInt (Main.Neg Main.Zero) = Main.Pos (Main.Succ Main.Zero);
9.00/4.80	succMyInt (Main.Pos (Main.Succ x)) = Main.Pos (Main.Succ (Main.Succ x));
9.00/4.80	succMyInt (Main.Neg (Main.Succ x)) = Main.Neg x;
9.00/4.80	
9.00/4.80	}
9.00/4.80	
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(5) Narrow (EQUIVALENT)
9.00/4.80	Haskell To QDPs
9.00/4.80	
9.00/4.80	digraph dp_graph {
9.00/4.80	node [outthreshold=100, inthreshold=100];1[label="succMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.00/4.80	3[label="succMyInt vx3",fontsize=16,color="burlywood",shape="triangle"];14[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 14[label="",style="solid", color="burlywood", weight=9];
9.00/4.80	14 -> 4[label="",style="solid", color="burlywood", weight=3];
9.00/4.80	15[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 15[label="",style="solid", color="burlywood", weight=9];
9.00/4.80	15 -> 5[label="",style="solid", color="burlywood", weight=3];
9.00/4.80	4[label="succMyInt (Pos vx30)",fontsize=16,color="burlywood",shape="box"];16[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
9.00/4.80	16 -> 6[label="",style="solid", color="burlywood", weight=3];
9.00/4.80	17[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
9.00/4.80	17 -> 7[label="",style="solid", color="burlywood", weight=3];
9.00/4.80	5[label="succMyInt (Neg vx30)",fontsize=16,color="burlywood",shape="box"];18[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
9.00/4.80	18 -> 8[label="",style="solid", color="burlywood", weight=3];
9.00/4.80	19[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
9.00/4.80	19 -> 9[label="",style="solid", color="burlywood", weight=3];
9.00/4.80	6[label="succMyInt (Pos (Succ vx300))",fontsize=16,color="black",shape="box"];6 -> 10[label="",style="solid", color="black", weight=3];
9.00/4.80	7[label="succMyInt (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
9.00/4.80	8[label="succMyInt (Neg (Succ vx300))",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9.00/4.80	9[label="succMyInt (Neg Zero)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.00/4.80	10[label="Pos (Succ (Succ vx300))",fontsize=16,color="green",shape="box"];11[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];12[label="Neg vx300",fontsize=16,color="green",shape="box"];13[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];}
9.00/4.80	
9.00/4.80	----------------------------------------
9.00/4.80	
9.00/4.80	(6)
9.00/4.80	YES
9.15/4.84	EOF