/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 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 ;

negateMyInt :: MyInt  ->  MyInt;
negateMyInt = primNegInt;

primNegInt :: MyInt  ->  MyInt;
primNegInt (Main.Pos x) = Main.Neg x;
primNegInt (Main.Neg x) = Main.Pos 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 ;

negateMyInt :: MyInt  ->  MyInt;
negateMyInt = primNegInt;

primNegInt :: MyInt  ->  MyInt;
primNegInt (Main.Pos x) = Main.Neg x;
primNegInt (Main.Neg x) = Main.Pos 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 ;

negateMyInt :: MyInt  ->  MyInt;
negateMyInt = primNegInt;

primNegInt :: MyInt  ->  MyInt;
primNegInt (Main.Pos x) = Main.Neg x;
primNegInt (Main.Neg x) = Main.Pos x;

}

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

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="negateMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="negateMyInt vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="primNegInt vx3",fontsize=16,color="burlywood",shape="box"];9[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 9[label="",style="solid", color="burlywood", weight=9];
9 -> 5[label="",style="solid", color="burlywood", weight=3];
10[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9];
10 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="primNegInt (Pos vx30)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="primNegInt (Neg vx30)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="Neg vx30",fontsize=16,color="green",shape="box"];8[label="Pos vx30",fontsize=16,color="green",shape="box"];}

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

(6)
YES