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


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(6) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyInt = Pos Main.Nat  | Neg Main.Nat ;

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

predMyInt :: MyInt  ->  MyInt;
predMyInt (Main.Pos Main.Zero) = Main.Neg (Main.Succ Main.Zero);
predMyInt (Main.Neg Main.Zero) = Main.Neg (Main.Succ Main.Zero);
predMyInt (Main.Pos (Main.Succ x)) = Main.Pos x;
predMyInt (Main.Neg (Main.Succ x)) = Main.Neg (Main.Succ (Main.Succ x));

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyInt = Pos Main.Nat  | Neg Main.Nat ;

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

predMyInt :: MyInt  ->  MyInt;
predMyInt (Main.Pos Main.Zero) = Main.Neg (Main.Succ Main.Zero);
predMyInt (Main.Neg Main.Zero) = Main.Neg (Main.Succ Main.Zero);
predMyInt (Main.Pos (Main.Succ x)) = Main.Pos x;
predMyInt (Main.Neg (Main.Succ x)) = Main.Neg (Main.Succ (Main.Succ x));

}

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

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

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

predMyInt :: MyInt  ->  MyInt;
predMyInt (Main.Pos Main.Zero) = Main.Neg (Main.Succ Main.Zero);
predMyInt (Main.Neg Main.Zero) = Main.Neg (Main.Succ Main.Zero);
predMyInt (Main.Pos (Main.Succ x)) = Main.Pos x;
predMyInt (Main.Neg (Main.Succ x)) = Main.Neg (Main.Succ (Main.Succ x));

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="predMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="predMyInt vx3",fontsize=16,color="burlywood",shape="triangle"];14[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 14[label="",style="solid", color="burlywood", weight=9];
14 -> 4[label="",style="solid", color="burlywood", weight=3];
15[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 15[label="",style="solid", color="burlywood", weight=9];
15 -> 5[label="",style="solid", color="burlywood", weight=3];
4[label="predMyInt (Pos vx30)",fontsize=16,color="burlywood",shape="box"];16[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
16 -> 6[label="",style="solid", color="burlywood", weight=3];
17[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
17 -> 7[label="",style="solid", color="burlywood", weight=3];
5[label="predMyInt (Neg vx30)",fontsize=16,color="burlywood",shape="box"];18[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
18 -> 8[label="",style="solid", color="burlywood", weight=3];
19[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 9[label="",style="solid", color="burlywood", weight=3];
6[label="predMyInt (Pos (Succ vx300))",fontsize=16,color="black",shape="box"];6 -> 10[label="",style="solid", color="black", weight=3];
7[label="predMyInt (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
8[label="predMyInt (Neg (Succ vx300))",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
9[label="predMyInt (Neg Zero)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10[label="Pos vx300",fontsize=16,color="green",shape="box"];11[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];12[label="Neg (Succ (Succ vx300))",fontsize=16,color="green",shape="box"];13[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];}

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

(6)
YES