8.01/3.55	YES
9.92/4.05	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.92/4.05	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.92/4.05	
9.92/4.05	
9.92/4.05	H-Termination with start terms of the given HASKELL could be proven:
9.92/4.05	
9.92/4.05	(0) HASKELL
9.92/4.05	(1) BR [EQUIVALENT, 0 ms]
9.92/4.05	(2) HASKELL
9.92/4.05	(3) COR [EQUIVALENT, 0 ms]
9.92/4.05	(4) HASKELL
9.92/4.05	(5) Narrow [EQUIVALENT, 32 ms]
9.92/4.05	(6) YES
9.92/4.05	
9.92/4.05	
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(0)
9.92/4.05	Obligation:
9.92/4.05	mainModule Main 
9.92/4.05	module Main where {
9.92/4.05	import qualified Prelude;
9.92/4.05	data Main.Char = Char MyInt ;
9.92/4.05	
9.92/4.05	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.92/4.05	
9.92/4.05	data Main.Nat = Succ Main.Nat  | Zero ;
9.92/4.05	
9.92/4.05	fromEnumChar :: Main.Char  ->  MyInt;
9.92/4.05	fromEnumChar = primCharToInt;
9.92/4.05	
9.92/4.05	primCharToInt :: Main.Char  ->  MyInt;
9.92/4.05	primCharToInt (Main.Char x) = x;
9.92/4.05	
9.92/4.05	primIntToChar :: MyInt  ->  Main.Char;
9.92/4.05	primIntToChar x = Main.Char x;
9.92/4.05	
9.92/4.05	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
9.92/4.05	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
9.92/4.05	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
9.92/4.05	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
9.92/4.05	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
9.92/4.05	
9.92/4.05	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
9.92/4.05	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
9.92/4.05	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
9.92/4.05	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
9.92/4.05	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
9.92/4.05	
9.92/4.05	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.92/4.05	primPlusNat Main.Zero Main.Zero = Main.Zero;
9.92/4.05	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
9.92/4.05	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
9.92/4.05	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
9.92/4.05	
9.92/4.05	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
9.92/4.05	psMyInt = primPlusInt;
9.92/4.05	
9.92/4.05	pt :: (b  ->  c)  ->  (a  ->  b)  ->  a  ->  c;
9.92/4.05	pt f g x = f (g x);
9.92/4.05	
9.92/4.05	succChar :: Main.Char  ->  Main.Char;
9.92/4.05	succChar = pt toEnumChar (pt (psMyInt (Main.Pos (Main.Succ Main.Zero))) fromEnumChar);
9.92/4.05	
9.92/4.05	toEnumChar :: MyInt  ->  Main.Char;
9.92/4.05	toEnumChar = primIntToChar;
9.92/4.05	
9.92/4.05	}
9.92/4.05	
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(1) BR (EQUIVALENT)
9.92/4.05	Replaced joker patterns by fresh variables and removed binding patterns.
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(2)
9.92/4.05	Obligation:
9.92/4.05	mainModule Main 
9.92/4.05	module Main where {
9.92/4.05	import qualified Prelude;
9.92/4.05	data Main.Char = Char MyInt ;
9.92/4.05	
9.92/4.05	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.92/4.05	
9.92/4.05	data Main.Nat = Succ Main.Nat  | Zero ;
9.92/4.05	
9.92/4.05	fromEnumChar :: Main.Char  ->  MyInt;
9.92/4.05	fromEnumChar = primCharToInt;
9.92/4.05	
9.92/4.05	primCharToInt :: Main.Char  ->  MyInt;
9.92/4.05	primCharToInt (Main.Char x) = x;
9.92/4.05	
9.92/4.05	primIntToChar :: MyInt  ->  Main.Char;
9.92/4.05	primIntToChar x = Main.Char x;
9.92/4.05	
9.92/4.05	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
9.92/4.05	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
9.92/4.05	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
9.92/4.05	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
9.92/4.05	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
9.92/4.05	
9.92/4.05	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
9.92/4.05	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
9.92/4.05	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
9.92/4.05	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
9.92/4.05	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
9.92/4.05	
9.92/4.05	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.92/4.05	primPlusNat Main.Zero Main.Zero = Main.Zero;
9.92/4.05	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
9.92/4.05	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
9.92/4.05	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
9.92/4.05	
9.92/4.05	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
9.92/4.05	psMyInt = primPlusInt;
9.92/4.05	
9.92/4.05	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
9.92/4.05	pt f g x = f (g x);
9.92/4.05	
9.92/4.05	succChar :: Main.Char  ->  Main.Char;
9.92/4.05	succChar = pt toEnumChar (pt (psMyInt (Main.Pos (Main.Succ Main.Zero))) fromEnumChar);
9.92/4.05	
9.92/4.05	toEnumChar :: MyInt  ->  Main.Char;
9.92/4.05	toEnumChar = primIntToChar;
9.92/4.05	
9.92/4.05	}
9.92/4.05	
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(3) COR (EQUIVALENT)
9.92/4.05	Cond Reductions:
9.92/4.05	The following Function with conditions
9.92/4.05	"undefined |Falseundefined;
9.92/4.05	"
9.92/4.05	is transformed to
9.92/4.05	"undefined  = undefined1;
9.92/4.05	"
9.92/4.05	"undefined0 True = undefined;
9.92/4.05	"
9.92/4.05	"undefined1  = undefined0 False;
9.92/4.05	"
9.92/4.05	
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(4)
9.92/4.05	Obligation:
9.92/4.05	mainModule Main 
9.92/4.05	module Main where {
9.92/4.05	import qualified Prelude;
9.92/4.05	data Main.Char = Char MyInt ;
9.92/4.05	
9.92/4.05	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.92/4.05	
9.92/4.05	data Main.Nat = Succ Main.Nat  | Zero ;
9.92/4.05	
9.92/4.05	fromEnumChar :: Main.Char  ->  MyInt;
9.92/4.05	fromEnumChar = primCharToInt;
9.92/4.05	
9.92/4.05	primCharToInt :: Main.Char  ->  MyInt;
9.92/4.05	primCharToInt (Main.Char x) = x;
9.92/4.05	
9.92/4.05	primIntToChar :: MyInt  ->  Main.Char;
9.92/4.05	primIntToChar x = Main.Char x;
9.92/4.05	
9.92/4.05	primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
9.92/4.05	primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
9.92/4.05	primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
9.92/4.05	primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
9.92/4.05	primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;
9.92/4.05	
9.92/4.05	primPlusInt :: MyInt  ->  MyInt  ->  MyInt;
9.92/4.05	primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y;
9.92/4.05	primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x;
9.92/4.05	primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y);
9.92/4.05	primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y);
9.92/4.05	
9.92/4.05	primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
9.92/4.05	primPlusNat Main.Zero Main.Zero = Main.Zero;
9.92/4.05	primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
9.92/4.05	primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
9.92/4.05	primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));
9.92/4.05	
9.92/4.05	psMyInt :: MyInt  ->  MyInt  ->  MyInt;
9.92/4.05	psMyInt = primPlusInt;
9.92/4.05	
9.92/4.05	pt :: (c  ->  b)  ->  (a  ->  c)  ->  a  ->  b;
9.92/4.05	pt f g x = f (g x);
9.92/4.05	
9.92/4.05	succChar :: Main.Char  ->  Main.Char;
9.92/4.05	succChar = pt toEnumChar (pt (psMyInt (Main.Pos (Main.Succ Main.Zero))) fromEnumChar);
9.92/4.05	
9.92/4.05	toEnumChar :: MyInt  ->  Main.Char;
9.92/4.05	toEnumChar = primIntToChar;
9.92/4.05	
9.92/4.05	}
9.92/4.05	
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(5) Narrow (EQUIVALENT)
9.92/4.05	Haskell To QDPs
9.92/4.05	
9.92/4.05	digraph dp_graph {
9.92/4.05	node [outthreshold=100, inthreshold=100];1[label="succChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.92/4.05	3[label="succChar vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.92/4.05	4[label="pt toEnumChar (pt (psMyInt (Pos (Succ Zero))) fromEnumChar) vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.92/4.05	5[label="toEnumChar (pt (psMyInt (Pos (Succ Zero))) fromEnumChar vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.92/4.05	6[label="primIntToChar (pt (psMyInt (Pos (Succ Zero))) fromEnumChar vx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.92/4.05	7[label="Char (pt (psMyInt (Pos (Succ Zero))) fromEnumChar vx3)",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
9.92/4.05	8[label="pt (psMyInt (Pos (Succ Zero))) fromEnumChar vx3",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.92/4.05	9[label="psMyInt (Pos (Succ Zero)) (fromEnumChar vx3)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.92/4.05	10[label="primPlusInt (Pos (Succ Zero)) (fromEnumChar vx3)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.92/4.05	11[label="primPlusInt (Pos (Succ Zero)) (primCharToInt vx3)",fontsize=16,color="burlywood",shape="box"];36[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];11 -> 36[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	36 -> 12[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	12[label="primPlusInt (Pos (Succ Zero)) (primCharToInt (Char vx30))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
9.92/4.05	13[label="primPlusInt (Pos (Succ Zero)) vx30",fontsize=16,color="burlywood",shape="box"];37[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];13 -> 37[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	37 -> 14[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	38[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	38 -> 15[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	14[label="primPlusInt (Pos (Succ Zero)) (Pos vx300)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
9.92/4.05	15[label="primPlusInt (Pos (Succ Zero)) (Neg vx300)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
9.92/4.05	16[label="Pos (primPlusNat (Succ Zero) vx300)",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3];
9.92/4.05	17[label="primMinusNat (Succ Zero) vx300",fontsize=16,color="burlywood",shape="box"];39[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];17 -> 39[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	39 -> 19[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	40[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 40[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	40 -> 20[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	18[label="primPlusNat (Succ Zero) vx300",fontsize=16,color="burlywood",shape="box"];41[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];18 -> 41[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	41 -> 21[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	42[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 42[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	42 -> 22[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	19[label="primMinusNat (Succ Zero) (Succ vx3000)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
9.92/4.05	20[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
9.92/4.05	21[label="primPlusNat (Succ Zero) (Succ vx3000)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
9.92/4.05	22[label="primPlusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
9.92/4.05	23[label="primMinusNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];43[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];23 -> 43[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	43 -> 27[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	44[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 44[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	44 -> 28[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	24[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];25[label="Succ (Succ (primPlusNat Zero vx3000))",fontsize=16,color="green",shape="box"];25 -> 29[label="",style="dashed", color="green", weight=3];
9.92/4.05	26[label="Succ Zero",fontsize=16,color="green",shape="box"];27[label="primMinusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
9.92/4.05	28[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
9.92/4.05	29[label="primPlusNat Zero vx3000",fontsize=16,color="burlywood",shape="box"];45[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];29 -> 45[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	45 -> 32[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	46[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 46[label="",style="solid", color="burlywood", weight=9];
9.92/4.05	46 -> 33[label="",style="solid", color="burlywood", weight=3];
9.92/4.05	30[label="Neg (Succ vx30000)",fontsize=16,color="green",shape="box"];31[label="Pos Zero",fontsize=16,color="green",shape="box"];32[label="primPlusNat Zero (Succ vx30000)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
9.92/4.05	33[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
9.92/4.05	34[label="Succ vx30000",fontsize=16,color="green",shape="box"];35[label="Zero",fontsize=16,color="green",shape="box"];}
9.92/4.05	
9.92/4.05	----------------------------------------
9.92/4.05	
9.92/4.05	(6)
9.92/4.05	YES
10.06/4.10	EOF