/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) NumRed [SOUND, 0 ms]
(6) HASKELL
(7) Narrow [EQUIVALENT, 63 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
"takeWhile p [] = [];
takeWhile p (x : xs)|p xx : takeWhile p xs|otherwise[];
"
is transformed to
"takeWhile p [] = takeWhile3 p [];
takeWhile p (x : xs) = takeWhile2 p (x : xs);
"
"takeWhile1 p x xs True = x : takeWhile p xs;
takeWhile1 p x xs False = takeWhile0 p x xs otherwise;
"
"takeWhile0 p x xs True = [];
"
"takeWhile2 p (x : xs) = takeWhile1 p x xs (p x);
"
"takeWhile3 p [] = [];
takeWhile3 wv ww = takeWhile2 wv ww;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"toEnum 0 = ();
"
is transformed to
"toEnum wx = toEnum1 wx;
"
"toEnum0 True wx = ();
"
"toEnum1 wx = toEnum0 (wx == 0) wx;
"

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

(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="enumFromTo",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="enumFromTo wy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="enumFromTo wy3 wy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="map toEnum (enumFromTo (fromEnum wy3) (fromEnum wy4))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="map toEnum (numericEnumFromTo (fromEnum wy3) (fromEnum wy4))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="map toEnum (takeWhile (flip (<=) (fromEnum wy4)) (numericEnumFrom (fromEnum wy3)))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="map toEnum (takeWhile (flip (<=) (fromEnum wy4)) (fromEnum wy3 : (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="map toEnum (takeWhile2 (flip (<=) (fromEnum wy4)) (fromEnum wy3 : (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (fromEnum wy3) (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero))) (flip (<=) (fromEnum wy4) (fromEnum wy3)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (fromEnum wy3) (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero))) ((<=) fromEnum wy3 fromEnum wy4))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (fromEnum wy3) (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero))) (compare (fromEnum wy3) (fromEnum wy4) /= GT))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (fromEnum wy3) (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero))) (not (compare (fromEnum wy3) (fromEnum wy4) == GT)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (fromEnum wy3) (numericEnumFrom $! fromEnum wy3 + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum wy3) (fromEnum wy4) == GT)))",fontsize=16,color="burlywood",shape="box"];53[label="wy3/()",fontsize=10,color="white",style="solid",shape="box"];14 -> 53[label="",style="solid", color="burlywood", weight=9];
53 -> 15[label="",style="solid", color="burlywood", weight=3];
15[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (fromEnum ()) (numericEnumFrom $! fromEnum () + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum ()) (fromEnum wy4) == GT)))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
16[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wy4)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum wy4) == GT)))",fontsize=16,color="burlywood",shape="box"];54[label="wy4/()",fontsize=10,color="white",style="solid",shape="box"];16 -> 54[label="",style="solid", color="burlywood", weight=9];
54 -> 17[label="",style="solid", color="burlywood", weight=3];
17[label="map toEnum (takeWhile1 (flip (<=) (fromEnum ())) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum ()) == GT)))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
18[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
19[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
20[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
21[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
22[label="map toEnum (Pos Zero : takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
23[label="toEnum (Pos Zero) : map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];23 -> 24[label="",style="dashed", color="green", weight=3];
23 -> 25[label="",style="dashed", color="green", weight=3];
24[label="toEnum (Pos Zero)",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="toEnum1 (Pos Zero)",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
27[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (Pos Zero + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
28[label="toEnum0 (Pos Zero == Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
29[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (Pos Zero + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
30[label="toEnum0 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
31[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
32[label="toEnum0 True (Pos Zero)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
33[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos Zero) (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
34[label="()",fontsize=16,color="green",shape="box"];35[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (Pos (primPlusNat Zero (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero))))))",fontsize=16,color="black",shape="box"];35 -> 36[label="",style="solid", color="black", weight=3];
36[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];36 -> 37[label="",style="solid", color="black", weight=3];
37[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3];
38[label="map toEnum (takeWhile2 (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
39[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (flip (<=) (Pos Zero) (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3];
40[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) ((<=) Pos (primPlusNat Zero (Succ Zero)) Pos Zero))",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
41[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (compare (Pos (primPlusNat Zero (Succ Zero))) (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3];
42[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (compare (Pos (primPlusNat Zero (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3];
43[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primPlusNat Zero (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3];
44[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3];
45[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ Zero) Zero == GT)))",fontsize=16,color="black",shape="box"];45 -> 46[label="",style="solid", color="black", weight=3];
46[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (GT == GT)))",fontsize=16,color="black",shape="box"];46 -> 47[label="",style="solid", color="black", weight=3];
47[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not True))",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
48[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) False)",fontsize=16,color="black",shape="box"];48 -> 49[label="",style="solid", color="black", weight=3];
49[label="map toEnum (takeWhile0 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) otherwise)",fontsize=16,color="black",shape="box"];49 -> 50[label="",style="solid", color="black", weight=3];
50[label="map toEnum (takeWhile0 (flip (<=) (Pos Zero)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];50 -> 51[label="",style="solid", color="black", weight=3];
51[label="map toEnum []",fontsize=16,color="black",shape="box"];51 -> 52[label="",style="solid", color="black", weight=3];
52[label="[]",fontsize=16,color="green",shape="box"];}

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

(8)
YES