/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [EQUIVALENT, 35 ms]
(6) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Main.Char = Char MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

flip :: (a  ->  b  ->  c)  ->  b  ->  a  ->  c;
flip f x y = f y x;

fromEnumChar :: Main.Char  ->  MyInt;
fromEnumChar = primCharToInt;

msMyInt :: MyInt  ->  MyInt  ->  MyInt;
msMyInt = primMinusInt;

predChar :: Main.Char  ->  Main.Char;
predChar = pt toEnumChar (pt (subtractMyInt (Main.Pos (Main.Succ Main.Zero))) fromEnumChar);

primCharToInt :: Main.Char  ->  MyInt;
primCharToInt (Main.Char x) = x;

primIntToChar :: MyInt  ->  Main.Char;
primIntToChar x = Main.Char x;

primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
primMinusInt (Main.Pos x) (Main.Neg y) = Main.Pos (primPlusNat x y);
primMinusInt (Main.Neg x) (Main.Pos y) = Main.Neg (primPlusNat x y);
primMinusInt (Main.Neg x) (Main.Neg y) = primMinusNat y x;
primMinusInt (Main.Pos x) (Main.Pos y) = primMinusNat x y;

primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;

primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primPlusNat Main.Zero Main.Zero = Main.Zero;
primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));

pt :: (a  ->  c)  ->  (b  ->  a)  ->  b  ->  c;
pt f g x = f (g x);

subtractMyInt :: MyInt  ->  MyInt  ->  MyInt;
subtractMyInt = flip msMyInt;

toEnumChar :: MyInt  ->  Main.Char;
toEnumChar = primIntToChar;

}

----------------------------------------

(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Main.Char = Char MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

flip :: (a  ->  b  ->  c)  ->  b  ->  a  ->  c;
flip f x y = f y x;

fromEnumChar :: Main.Char  ->  MyInt;
fromEnumChar = primCharToInt;

msMyInt :: MyInt  ->  MyInt  ->  MyInt;
msMyInt = primMinusInt;

predChar :: Main.Char  ->  Main.Char;
predChar = pt toEnumChar (pt (subtractMyInt (Main.Pos (Main.Succ Main.Zero))) fromEnumChar);

primCharToInt :: Main.Char  ->  MyInt;
primCharToInt (Main.Char x) = x;

primIntToChar :: MyInt  ->  Main.Char;
primIntToChar x = Main.Char x;

primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
primMinusInt (Main.Pos x) (Main.Neg y) = Main.Pos (primPlusNat x y);
primMinusInt (Main.Neg x) (Main.Pos y) = Main.Neg (primPlusNat x y);
primMinusInt (Main.Neg x) (Main.Neg y) = primMinusNat y x;
primMinusInt (Main.Pos x) (Main.Pos y) = primMinusNat x y;

primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;

primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primPlusNat Main.Zero Main.Zero = Main.Zero;
primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));

pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
pt f g x = f (g x);

subtractMyInt :: MyInt  ->  MyInt  ->  MyInt;
subtractMyInt = flip msMyInt;

toEnumChar :: MyInt  ->  Main.Char;
toEnumChar = primIntToChar;

}

----------------------------------------

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Main.Char = Char MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

flip :: (b  ->  c  ->  a)  ->  c  ->  b  ->  a;
flip f x y = f y x;

fromEnumChar :: Main.Char  ->  MyInt;
fromEnumChar = primCharToInt;

msMyInt :: MyInt  ->  MyInt  ->  MyInt;
msMyInt = primMinusInt;

predChar :: Main.Char  ->  Main.Char;
predChar = pt toEnumChar (pt (subtractMyInt (Main.Pos (Main.Succ Main.Zero))) fromEnumChar);

primCharToInt :: Main.Char  ->  MyInt;
primCharToInt (Main.Char x) = x;

primIntToChar :: MyInt  ->  Main.Char;
primIntToChar x = Main.Char x;

primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
primMinusInt (Main.Pos x) (Main.Neg y) = Main.Pos (primPlusNat x y);
primMinusInt (Main.Neg x) (Main.Pos y) = Main.Neg (primPlusNat x y);
primMinusInt (Main.Neg x) (Main.Neg y) = primMinusNat y x;
primMinusInt (Main.Pos x) (Main.Pos y) = primMinusNat x y;

primMinusNat :: Main.Nat  ->  Main.Nat  ->  MyInt;
primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero;
primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y);
primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x);
primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y;

primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primPlusNat Main.Zero Main.Zero = Main.Zero;
primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));

pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
pt f g x = f (g x);

subtractMyInt :: MyInt  ->  MyInt  ->  MyInt;
subtractMyInt = flip msMyInt;

toEnumChar :: MyInt  ->  Main.Char;
toEnumChar = primIntToChar;

}

----------------------------------------

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="predChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="predChar vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="pt toEnumChar (pt (subtractMyInt (Pos (Succ Zero))) fromEnumChar) vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="toEnumChar (pt (subtractMyInt (Pos (Succ Zero))) fromEnumChar vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="primIntToChar (pt (subtractMyInt (Pos (Succ Zero))) fromEnumChar vx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="Char (pt (subtractMyInt (Pos (Succ Zero))) fromEnumChar vx3)",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
8[label="pt (subtractMyInt (Pos (Succ Zero))) fromEnumChar vx3",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="subtractMyInt (Pos (Succ Zero)) (fromEnumChar vx3)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="flip msMyInt (Pos (Succ Zero)) (fromEnumChar vx3)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="msMyInt (fromEnumChar vx3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="primMinusInt (fromEnumChar vx3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="primMinusInt (primCharToInt vx3) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];38[label="vx3/Char vx30",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="burlywood", weight=9];
38 -> 14[label="",style="solid", color="burlywood", weight=3];
14[label="primMinusInt (primCharToInt (Char vx30)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="primMinusInt vx30 (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];39[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 39[label="",style="solid", color="burlywood", weight=9];
39 -> 16[label="",style="solid", color="burlywood", weight=3];
40[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 40[label="",style="solid", color="burlywood", weight=9];
40 -> 17[label="",style="solid", color="burlywood", weight=3];
16[label="primMinusInt (Pos vx300) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="primMinusInt (Neg vx300) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
18[label="primMinusNat vx300 (Succ Zero)",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];
41 -> 20[label="",style="solid", color="burlywood", weight=3];
42[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 42[label="",style="solid", color="burlywood", weight=9];
42 -> 21[label="",style="solid", color="burlywood", weight=3];
19[label="Neg (primPlusNat vx300 (Succ Zero))",fontsize=16,color="green",shape="box"];19 -> 22[label="",style="dashed", color="green", weight=3];
20[label="primMinusNat (Succ vx3000) (Succ Zero)",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
21[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
22[label="primPlusNat vx300 (Succ Zero)",fontsize=16,color="burlywood",shape="box"];43[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];22 -> 43[label="",style="solid", color="burlywood", weight=9];
43 -> 25[label="",style="solid", color="burlywood", weight=3];
44[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 44[label="",style="solid", color="burlywood", weight=9];
44 -> 26[label="",style="solid", color="burlywood", weight=3];
23[label="primMinusNat vx3000 Zero",fontsize=16,color="burlywood",shape="box"];45[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];23 -> 45[label="",style="solid", color="burlywood", weight=9];
45 -> 27[label="",style="solid", color="burlywood", weight=3];
46[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 46[label="",style="solid", color="burlywood", weight=9];
46 -> 28[label="",style="solid", color="burlywood", weight=3];
24[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];25[label="primPlusNat (Succ vx3000) (Succ Zero)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
27[label="primMinusNat (Succ vx30000) Zero",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
29[label="Succ (Succ (primPlusNat vx3000 Zero))",fontsize=16,color="green",shape="box"];29 -> 33[label="",style="dashed", color="green", weight=3];
30[label="Succ Zero",fontsize=16,color="green",shape="box"];31[label="Pos (Succ vx30000)",fontsize=16,color="green",shape="box"];32[label="Pos Zero",fontsize=16,color="green",shape="box"];33[label="primPlusNat vx3000 Zero",fontsize=16,color="burlywood",shape="box"];47[label="vx3000/Succ vx30000",fontsize=10,color="white",style="solid",shape="box"];33 -> 47[label="",style="solid", color="burlywood", weight=9];
47 -> 34[label="",style="solid", color="burlywood", weight=3];
48[label="vx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 48[label="",style="solid", color="burlywood", weight=9];
48 -> 35[label="",style="solid", color="burlywood", weight=3];
34[label="primPlusNat (Succ vx30000) Zero",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
35[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
36[label="Succ vx30000",fontsize=16,color="green",shape="box"];37[label="Zero",fontsize=16,color="green",shape="box"];}

----------------------------------------

(6)
YES