7.45/3.50	YES
8.82/3.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.82/3.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.82/3.94	
8.82/3.94	
8.82/3.94	H-Termination with start terms of the given HASKELL could be proven:
8.82/3.94	
8.82/3.94	(0) HASKELL
8.82/3.94	(1) BR [EQUIVALENT, 0 ms]
8.82/3.94	(2) HASKELL
8.82/3.94	(3) COR [EQUIVALENT, 0 ms]
8.82/3.94	(4) HASKELL
8.82/3.94	(5) Narrow [EQUIVALENT, 0 ms]
8.82/3.94	(6) YES
8.82/3.94	
8.82/3.94	
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(0)
8.82/3.94	Obligation:
8.82/3.94	mainModule Main 
8.82/3.94	module Main where {
8.82/3.94	import qualified Prelude;
8.82/3.94	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.82/3.94	
8.82/3.94	data Main.Nat = Succ Main.Nat  | Zero ;
8.82/3.94	
8.82/3.94	negateMyInt :: MyInt  ->  MyInt;
8.82/3.94	negateMyInt = primNegInt;
8.82/3.94	
8.82/3.94	primNegInt :: MyInt  ->  MyInt;
8.82/3.94	primNegInt (Main.Pos x) = Main.Neg x;
8.82/3.94	primNegInt (Main.Neg x) = Main.Pos x;
8.82/3.94	
8.82/3.94	}
8.82/3.94	
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(1) BR (EQUIVALENT)
8.82/3.94	Replaced joker patterns by fresh variables and removed binding patterns.
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(2)
8.82/3.94	Obligation:
8.82/3.94	mainModule Main 
8.82/3.94	module Main where {
8.82/3.94	import qualified Prelude;
8.82/3.94	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.82/3.94	
8.82/3.94	data Main.Nat = Succ Main.Nat  | Zero ;
8.82/3.94	
8.82/3.94	negateMyInt :: MyInt  ->  MyInt;
8.82/3.94	negateMyInt = primNegInt;
8.82/3.94	
8.82/3.94	primNegInt :: MyInt  ->  MyInt;
8.82/3.94	primNegInt (Main.Pos x) = Main.Neg x;
8.82/3.94	primNegInt (Main.Neg x) = Main.Pos x;
8.82/3.94	
8.82/3.94	}
8.82/3.94	
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(3) COR (EQUIVALENT)
8.82/3.94	Cond Reductions:
8.82/3.94	The following Function with conditions
8.82/3.94	"undefined |Falseundefined;
8.82/3.94	"
8.82/3.94	is transformed to
8.82/3.94	"undefined  = undefined1;
8.82/3.94	"
8.82/3.94	"undefined0 True = undefined;
8.82/3.94	"
8.82/3.94	"undefined1  = undefined0 False;
8.82/3.94	"
8.82/3.94	
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(4)
8.82/3.94	Obligation:
8.82/3.94	mainModule Main 
8.82/3.94	module Main where {
8.82/3.94	import qualified Prelude;
8.82/3.94	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.82/3.94	
8.82/3.94	data Main.Nat = Succ Main.Nat  | Zero ;
8.82/3.94	
8.82/3.94	negateMyInt :: MyInt  ->  MyInt;
8.82/3.94	negateMyInt = primNegInt;
8.82/3.94	
8.82/3.94	primNegInt :: MyInt  ->  MyInt;
8.82/3.94	primNegInt (Main.Pos x) = Main.Neg x;
8.82/3.94	primNegInt (Main.Neg x) = Main.Pos x;
8.82/3.94	
8.82/3.94	}
8.82/3.94	
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(5) Narrow (EQUIVALENT)
8.82/3.94	Haskell To QDPs
8.82/3.94	
8.82/3.94	digraph dp_graph {
8.82/3.94	node [outthreshold=100, inthreshold=100];1[label="negateMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.82/3.94	3[label="negateMyInt vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
8.82/3.94	4[label="primNegInt vx3",fontsize=16,color="burlywood",shape="box"];9[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 9[label="",style="solid", color="burlywood", weight=9];
8.82/3.94	9 -> 5[label="",style="solid", color="burlywood", weight=3];
8.82/3.94	10[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9];
8.82/3.94	10 -> 6[label="",style="solid", color="burlywood", weight=3];
8.82/3.94	5[label="primNegInt (Pos vx30)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
8.82/3.94	6[label="primNegInt (Neg vx30)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
8.82/3.94	7[label="Neg vx30",fontsize=16,color="green",shape="box"];8[label="Pos vx30",fontsize=16,color="green",shape="box"];}
8.82/3.94	
8.82/3.94	----------------------------------------
8.82/3.94	
8.82/3.94	(6)
8.82/3.94	YES
9.11/3.98	EOF