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


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 28 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 Ordering = LT  | EQ  | GT ;

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 = GT;

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

toEnum2 MyTrue vy = EQ;
toEnum2 vz wu = toEnum1 wu;

toEnum3 vy = toEnum2 (esEsMyInt vy (Main.Pos (Main.Succ Main.Zero))) vy;
toEnum3 wv = toEnum1 wv;

toEnum4 MyTrue ww = LT;
toEnum4 wx wy = toEnum3 wy;

toEnum5 ww = toEnum4 (esEsMyInt ww (Main.Pos Main.Zero)) ww;
toEnum5 wz = toEnum3 wz;

toEnumOrdering :: MyInt  ->  Ordering;
toEnumOrdering ww = toEnum5 ww;
toEnumOrdering vy = toEnum3 vy;
toEnumOrdering 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 Ordering = LT  | EQ  | GT ;

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 = GT;

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

toEnum2 MyTrue vy = EQ;
toEnum2 vz wu = toEnum1 wu;

toEnum3 vy = toEnum2 (esEsMyInt vy (Main.Pos (Main.Succ Main.Zero))) vy;
toEnum3 wv = toEnum1 wv;

toEnum4 MyTrue ww = LT;
toEnum4 wx wy = toEnum3 wy;

toEnum5 ww = toEnum4 (esEsMyInt ww (Main.Pos Main.Zero)) ww;
toEnum5 wz = toEnum3 wz;

toEnumOrdering :: MyInt  ->  Ordering;
toEnumOrdering ww = toEnum5 ww;
toEnumOrdering vy = toEnum3 vy;
toEnumOrdering 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 Ordering = LT  | EQ  | GT ;

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 = GT;

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

toEnum2 MyTrue vy = EQ;
toEnum2 vz wu = toEnum1 wu;

toEnum3 vy = toEnum2 (esEsMyInt vy (Main.Pos (Main.Succ Main.Zero))) vy;
toEnum3 wv = toEnum1 wv;

toEnum4 MyTrue ww = LT;
toEnum4 wx wy = toEnum3 wy;

toEnum5 ww = toEnum4 (esEsMyInt ww (Main.Pos Main.Zero)) ww;
toEnum5 wz = toEnum3 wz;

toEnumOrdering :: MyInt  ->  Ordering;
toEnumOrdering ww = toEnum5 ww;
toEnumOrdering vy = toEnum3 vy;
toEnumOrdering vx = toEnum1 vx;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="toEnumOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="toEnumOrdering xw3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="toEnum5 xw3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="toEnum4 (esEsMyInt xw3 (Pos Zero)) xw3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="toEnum4 (primEqInt xw3 (Pos Zero)) xw3",fontsize=16,color="burlywood",shape="box"];48[label="xw3/Pos xw30",fontsize=10,color="white",style="solid",shape="box"];6 -> 48[label="",style="solid", color="burlywood", weight=9];
48 -> 7[label="",style="solid", color="burlywood", weight=3];
49[label="xw3/Neg xw30",fontsize=10,color="white",style="solid",shape="box"];6 -> 49[label="",style="solid", color="burlywood", weight=9];
49 -> 8[label="",style="solid", color="burlywood", weight=3];
7[label="toEnum4 (primEqInt (Pos xw30) (Pos Zero)) (Pos xw30)",fontsize=16,color="burlywood",shape="box"];50[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];7 -> 50[label="",style="solid", color="burlywood", weight=9];
50 -> 9[label="",style="solid", color="burlywood", weight=3];
51[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 51[label="",style="solid", color="burlywood", weight=9];
51 -> 10[label="",style="solid", color="burlywood", weight=3];
8[label="toEnum4 (primEqInt (Neg xw30) (Pos Zero)) (Neg xw30)",fontsize=16,color="burlywood",shape="box"];52[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];8 -> 52[label="",style="solid", color="burlywood", weight=9];
52 -> 11[label="",style="solid", color="burlywood", weight=3];
53[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 53[label="",style="solid", color="burlywood", weight=9];
53 -> 12[label="",style="solid", color="burlywood", weight=3];
9[label="toEnum4 (primEqInt (Pos (Succ xw300)) (Pos Zero)) (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="toEnum4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
11[label="toEnum4 (primEqInt (Neg (Succ xw300)) (Pos Zero)) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="toEnum4 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="toEnum4 MyFalse (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="toEnum4 MyTrue (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="toEnum4 MyFalse (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="toEnum4 MyTrue (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="toEnum3 (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="LT",fontsize=16,color="green",shape="box"];19[label="toEnum3 (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3];
20[label="LT",fontsize=16,color="green",shape="box"];21[label="toEnum2 (esEsMyInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
22[label="toEnum2 (esEsMyInt (Neg (Succ xw300)) (Pos (Succ Zero))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
23[label="toEnum2 (primEqInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
24[label="toEnum2 (primEqInt (Neg (Succ xw300)) (Pos (Succ Zero))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="toEnum2 (primEqNat xw300 Zero) (Pos (Succ xw300))",fontsize=16,color="burlywood",shape="box"];54[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 54[label="",style="solid", color="burlywood", weight=9];
54 -> 27[label="",style="solid", color="burlywood", weight=3];
55[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 55[label="",style="solid", color="burlywood", weight=9];
55 -> 28[label="",style="solid", color="burlywood", weight=3];
26[label="toEnum2 MyFalse (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3];
27[label="toEnum2 (primEqNat (Succ xw3000) Zero) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
28[label="toEnum2 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
29[label="toEnum1 (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];29 -> 32[label="",style="solid", color="black", weight=3];
30[label="toEnum2 MyFalse (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];30 -> 33[label="",style="solid", color="black", weight=3];
31[label="toEnum2 MyTrue (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3];
32[label="toEnum0 (esEsMyInt (Neg (Succ xw300)) (Pos (Succ (Succ Zero)))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];32 -> 35[label="",style="solid", color="black", weight=3];
33[label="toEnum1 (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];33 -> 36[label="",style="solid", color="black", weight=3];
34[label="EQ",fontsize=16,color="green",shape="box"];35[label="toEnum0 (primEqInt (Neg (Succ xw300)) (Pos (Succ (Succ Zero)))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
36[label="toEnum0 (esEsMyInt (Pos (Succ (Succ xw3000))) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3];
37[label="toEnum0 MyFalse (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
38[label="toEnum0 (primEqInt (Pos (Succ (Succ xw3000))) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
39[label="error []",fontsize=16,color="red",shape="box"];40[label="toEnum0 (primEqNat (Succ xw3000) (Succ Zero)) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
41[label="toEnum0 (primEqNat xw3000 Zero) (Pos (Succ (Succ xw3000)))",fontsize=16,color="burlywood",shape="box"];56[label="xw3000/Succ xw30000",fontsize=10,color="white",style="solid",shape="box"];41 -> 56[label="",style="solid", color="burlywood", weight=9];
56 -> 42[label="",style="solid", color="burlywood", weight=3];
57[label="xw3000/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 57[label="",style="solid", color="burlywood", weight=9];
57 -> 43[label="",style="solid", color="burlywood", weight=3];
42[label="toEnum0 (primEqNat (Succ xw30000) Zero) (Pos (Succ (Succ (Succ xw30000))))",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
43[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
44[label="toEnum0 MyFalse (Pos (Succ (Succ (Succ xw30000))))",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
45[label="toEnum0 MyTrue (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
46[label="error []",fontsize=16,color="red",shape="box"];47[label="GT",fontsize=16,color="green",shape="box"];}

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

(6)
YES