/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 27 ms]
(6) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

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

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

data Tup0 = Tup0 ;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
primEqNat Main.Zero Main.Zero = MyTrue;
primEqNat Main.Zero (Main.Succ y) = MyFalse;
primEqNat (Main.Succ x) Main.Zero = MyFalse;
primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;

toEnum0 MyTrue vx = Tup0;

toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx;

toEnumTup0 :: MyInt  ->  Tup0;
toEnumTup0 vx = toEnum1 vx;

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

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

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

data Tup0 = Tup0 ;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
primEqNat Main.Zero Main.Zero = MyTrue;
primEqNat Main.Zero (Main.Succ y) = MyFalse;
primEqNat (Main.Succ x) Main.Zero = MyFalse;
primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;

toEnum0 MyTrue vx = Tup0;

toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx;

toEnumTup0 :: MyInt  ->  Tup0;
toEnumTup0 vx = toEnum1 vx;

}

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

(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 MyBool = MyTrue  | MyFalse ;

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

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

data Tup0 = Tup0 ;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
primEqNat Main.Zero Main.Zero = MyTrue;
primEqNat Main.Zero (Main.Succ y) = MyFalse;
primEqNat (Main.Succ x) Main.Zero = MyFalse;
primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;

toEnum0 MyTrue vx = Tup0;

toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx;

toEnumTup0 :: MyInt  ->  Tup0;
toEnumTup0 vx = toEnum1 vx;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="toEnumTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="toEnumTup0 wu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="toEnum1 wu3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="toEnum0 (esEsMyInt wu3 (Pos Zero)) wu3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="toEnum0 (primEqInt wu3 (Pos Zero)) wu3",fontsize=16,color="burlywood",shape="box"];21[label="wu3/Pos wu30",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
21 -> 7[label="",style="solid", color="burlywood", weight=3];
22[label="wu3/Neg wu30",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
22 -> 8[label="",style="solid", color="burlywood", weight=3];
7[label="toEnum0 (primEqInt (Pos wu30) (Pos Zero)) (Pos wu30)",fontsize=16,color="burlywood",shape="box"];23[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];7 -> 23[label="",style="solid", color="burlywood", weight=9];
23 -> 9[label="",style="solid", color="burlywood", weight=3];
24[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 24[label="",style="solid", color="burlywood", weight=9];
24 -> 10[label="",style="solid", color="burlywood", weight=3];
8[label="toEnum0 (primEqInt (Neg wu30) (Pos Zero)) (Neg wu30)",fontsize=16,color="burlywood",shape="box"];25[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];8 -> 25[label="",style="solid", color="burlywood", weight=9];
25 -> 11[label="",style="solid", color="burlywood", weight=3];
26[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 26[label="",style="solid", color="burlywood", weight=9];
26 -> 12[label="",style="solid", color="burlywood", weight=3];
9[label="toEnum0 (primEqInt (Pos (Succ wu300)) (Pos Zero)) (Pos (Succ wu300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="toEnum0 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="toEnum0 (primEqInt (Neg (Succ wu300)) (Pos Zero)) (Neg (Succ wu300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="toEnum0 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="toEnum0 MyFalse (Pos (Succ wu300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="toEnum0 MyTrue (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="toEnum0 MyFalse (Neg (Succ wu300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="toEnum0 MyTrue (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="error []",fontsize=16,color="red",shape="box"];18[label="Tup0",fontsize=16,color="green",shape="box"];19[label="error []",fontsize=16,color="red",shape="box"];20[label="Tup0",fontsize=16,color="green",shape="box"];}

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

(6)
YES