/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) NumRed [SOUND, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 0 ms]
(8) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"toEnum 0 = ();
"
is transformed to
"toEnum vz = toEnum1 vz;
"
"toEnum0 True vz = ();
"
"toEnum1 vz = toEnum0 (vz == 0) vz;
"
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;
}

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

(5) NumRed (SOUND)
Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
----------------------------------------

(6)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(7) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="pred wu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="toEnum1 ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="toEnum0 ((subtract (Pos (Succ Zero))) . fromEnum == Pos Zero) ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="toEnum0 (primEqInt ((subtract (Pos (Succ Zero))) . fromEnum) (Pos Zero)) ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="toEnum0 (primEqInt (subtract (Pos (Succ Zero)) (fromEnum wu3)) (Pos Zero)) (subtract (Pos (Succ Zero)) (fromEnum wu3))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="toEnum0 (primEqInt (flip (-) (Pos (Succ Zero)) (fromEnum wu3)) (Pos Zero)) (flip (-) (Pos (Succ Zero)) (fromEnum wu3))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="toEnum0 (primEqInt ((-) fromEnum wu3 Pos (Succ Zero)) (Pos Zero)) ((-) fromEnum wu3 Pos (Succ Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="toEnum0 (primEqInt (primMinusInt (fromEnum wu3) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum wu3) (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];19[label="wu3/()",fontsize=10,color="white",style="solid",shape="box"];12 -> 19[label="",style="solid", color="burlywood", weight=9];
19 -> 13[label="",style="solid", color="burlywood", weight=3];
13[label="toEnum0 (primEqInt (primMinusInt (fromEnum ()) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum ()) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="toEnum0 (primEqInt (primMinusInt (Pos Zero) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos Zero) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="toEnum0 (primEqInt (primMinusNat Zero (Succ Zero)) (Pos Zero)) (primMinusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
16[label="toEnum0 (primEqInt (Neg (Succ Zero)) (Pos Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
17[label="toEnum0 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
18[label="error []",fontsize=16,color="red",shape="box"];}

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

(8)
YES