/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 32 ms]
(6) YES


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

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

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

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

fromIntFloat :: MyInt  ->  Float;
fromIntFloat = primIntToFloat;

fsFloat :: Float  ->  Float  ->  Float;
fsFloat = primDivFloat;

primDivFloat :: Float  ->  Float  ->  Float;
primDivFloat (Float x1 x2) (Float y1 y2) = Float (srMyInt x1 y2) (srMyInt x2 y1);

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);

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

recipFloat :: Float  ->  Float;
recipFloat x = fsFloat (fromIntFloat (Main.Pos (Main.Succ Main.Zero))) x;

srMyInt :: MyInt  ->  MyInt  ->  MyInt;
srMyInt = primMulInt;

}

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

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

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

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

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

fromIntFloat :: MyInt  ->  Float;
fromIntFloat = primIntToFloat;

fsFloat :: Float  ->  Float  ->  Float;
fsFloat = primDivFloat;

primDivFloat :: Float  ->  Float  ->  Float;
primDivFloat (Float x1 x2) (Float y1 y2) = Float (srMyInt x1 y2) (srMyInt x2 y1);

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);

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

recipFloat :: Float  ->  Float;
recipFloat x = fsFloat (fromIntFloat (Main.Pos (Main.Succ Main.Zero))) x;

srMyInt :: MyInt  ->  MyInt  ->  MyInt;
srMyInt = primMulInt;

}

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

(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 Float = Float MyInt MyInt ;

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

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

fromIntFloat :: MyInt  ->  Float;
fromIntFloat = primIntToFloat;

fsFloat :: Float  ->  Float  ->  Float;
fsFloat = primDivFloat;

primDivFloat :: Float  ->  Float  ->  Float;
primDivFloat (Float x1 x2) (Float y1 y2) = Float (srMyInt x1 y2) (srMyInt x2 y1);

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);

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

recipFloat :: Float  ->  Float;
recipFloat x = fsFloat (fromIntFloat (Main.Pos (Main.Succ Main.Zero))) x;

srMyInt :: MyInt  ->  MyInt  ->  MyInt;
srMyInt = primMulInt;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="recipFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="recipFloat vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="fsFloat (fromIntFloat (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="primDivFloat (fromIntFloat (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="primDivFloat (primIntToFloat (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];27[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];7 -> 27[label="",style="solid", color="burlywood", weight=9];
27 -> 8[label="",style="solid", color="burlywood", weight=3];
8[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vx30 vx31)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="Float (srMyInt (Pos (Succ Zero)) vx31) (srMyInt (Pos (Succ Zero)) vx30)",fontsize=16,color="green",shape="box"];9 -> 10[label="",style="dashed", color="green", weight=3];
9 -> 11[label="",style="dashed", color="green", weight=3];
10[label="srMyInt (Pos (Succ Zero)) vx31",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3];
11 -> 10[label="",style="dashed", color="red", weight=0];
11[label="srMyInt (Pos (Succ Zero)) vx30",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3];
12[label="primMulInt (Pos (Succ Zero)) vx31",fontsize=16,color="burlywood",shape="box"];28[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];12 -> 28[label="",style="solid", color="burlywood", weight=9];
28 -> 14[label="",style="solid", color="burlywood", weight=3];
29[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];12 -> 29[label="",style="solid", color="burlywood", weight=9];
29 -> 15[label="",style="solid", color="burlywood", weight=3];
13[label="vx30",fontsize=16,color="green",shape="box"];14[label="primMulInt (Pos (Succ Zero)) (Pos vx310)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="primMulInt (Pos (Succ Zero)) (Neg vx310)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="Pos (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3];
17[label="Neg (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];17 -> 19[label="",style="dashed", color="green", weight=3];
18[label="primMulNat (Succ Zero) vx310",fontsize=16,color="burlywood",shape="triangle"];30[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];18 -> 30[label="",style="solid", color="burlywood", weight=9];
30 -> 20[label="",style="solid", color="burlywood", weight=3];
31[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 31[label="",style="solid", color="burlywood", weight=9];
31 -> 21[label="",style="solid", color="burlywood", weight=3];
19 -> 18[label="",style="dashed", color="red", weight=0];
19[label="primMulNat (Succ Zero) vx310",fontsize=16,color="magenta"];19 -> 22[label="",style="dashed", color="magenta", weight=3];
20[label="primMulNat (Succ Zero) (Succ vx3100)",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
21[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
22[label="vx310",fontsize=16,color="green",shape="box"];23[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
24[label="Zero",fontsize=16,color="green",shape="box"];25[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3];
26[label="Succ vx3100",fontsize=16,color="green",shape="box"];}

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

(6)
YES