/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 274 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 = LT;
toEnum 1 = EQ;
toEnum 2 = GT;
"
is transformed to
"toEnum xw = toEnum5 xw;
toEnum wy = toEnum3 wy;
toEnum wx = toEnum1 wx;
"
"toEnum0 True wx = GT;
"
"toEnum1 wx = toEnum0 (wx == 2) wx;
"
"toEnum2 True wy = EQ;
toEnum2 wz xu = toEnum1 xu;
"
"toEnum3 wy = toEnum2 (wy == 1) wy;
toEnum3 xv = toEnum1 xv;
"
"toEnum4 True xw = LT;
toEnum4 xx xy = toEnum3 xy;
"
"toEnum5 xw = toEnum4 (xw == 0) xw;
toEnum5 xz = toEnum3 xz;
"

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

(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 yu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="enumFromTo yu3 yu4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="map toEnum (enumFromTo (fromEnum yu3) (fromEnum yu4))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="map toEnum (numericEnumFromTo (fromEnum yu3) (fromEnum yu4))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="map toEnum (takeWhile (flip (<=) (fromEnum yu4)) (numericEnumFrom (fromEnum yu3)))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="map toEnum (takeWhile (flip (<=) (fromEnum yu4)) (fromEnum yu3 : (numericEnumFrom $! fromEnum yu3 + 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 yu4)) (fromEnum yu3 : (numericEnumFrom $! fromEnum yu3 + 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 yu4)) (fromEnum yu3) (numericEnumFrom $! fromEnum yu3 + fromInt (Pos (Succ Zero))) (flip (<=) (fromEnum yu4) (fromEnum yu3)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum yu3) (numericEnumFrom $! fromEnum yu3 + fromInt (Pos (Succ Zero))) ((<=) fromEnum yu3 fromEnum yu4))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum yu3) (numericEnumFrom $! fromEnum yu3 + fromInt (Pos (Succ Zero))) (compare (fromEnum yu3) (fromEnum yu4) /= GT))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum yu3) (numericEnumFrom $! fromEnum yu3 + fromInt (Pos (Succ Zero))) (not (compare (fromEnum yu3) (fromEnum yu4) == GT)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum yu3) (numericEnumFrom $! fromEnum yu3 + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum yu3) (fromEnum yu4) == GT)))",fontsize=16,color="burlywood",shape="box"];250[label="yu3/LT",fontsize=10,color="white",style="solid",shape="box"];14 -> 250[label="",style="solid", color="burlywood", weight=9];
250 -> 15[label="",style="solid", color="burlywood", weight=3];
251[label="yu3/EQ",fontsize=10,color="white",style="solid",shape="box"];14 -> 251[label="",style="solid", color="burlywood", weight=9];
251 -> 16[label="",style="solid", color="burlywood", weight=3];
252[label="yu3/GT",fontsize=10,color="white",style="solid",shape="box"];14 -> 252[label="",style="solid", color="burlywood", weight=9];
252 -> 17[label="",style="solid", color="burlywood", weight=3];
15[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum LT) (numericEnumFrom $! fromEnum LT + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum LT) (fromEnum yu4) == GT)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
16[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum EQ) (numericEnumFrom $! fromEnum EQ + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum EQ) (fromEnum yu4) == GT)))",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
17[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (fromEnum GT) (numericEnumFrom $! fromEnum GT + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum GT) (fromEnum yu4) == GT)))",fontsize=16,color="black",shape="box"];17 -> 20[label="",style="solid", color="black", weight=3];
18[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum yu4) == GT)))",fontsize=16,color="burlywood",shape="box"];253[label="yu4/LT",fontsize=10,color="white",style="solid",shape="box"];18 -> 253[label="",style="solid", color="burlywood", weight=9];
253 -> 21[label="",style="solid", color="burlywood", weight=3];
254[label="yu4/EQ",fontsize=10,color="white",style="solid",shape="box"];18 -> 254[label="",style="solid", color="burlywood", weight=9];
254 -> 22[label="",style="solid", color="burlywood", weight=3];
255[label="yu4/GT",fontsize=10,color="white",style="solid",shape="box"];18 -> 255[label="",style="solid", color="burlywood", weight=9];
255 -> 23[label="",style="solid", color="burlywood", weight=3];
19[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum yu4) == GT)))",fontsize=16,color="burlywood",shape="box"];256[label="yu4/LT",fontsize=10,color="white",style="solid",shape="box"];19 -> 256[label="",style="solid", color="burlywood", weight=9];
256 -> 24[label="",style="solid", color="burlywood", weight=3];
257[label="yu4/EQ",fontsize=10,color="white",style="solid",shape="box"];19 -> 257[label="",style="solid", color="burlywood", weight=9];
257 -> 25[label="",style="solid", color="burlywood", weight=3];
258[label="yu4/GT",fontsize=10,color="white",style="solid",shape="box"];19 -> 258[label="",style="solid", color="burlywood", weight=9];
258 -> 26[label="",style="solid", color="burlywood", weight=3];
20[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yu4)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (fromEnum yu4) == GT)))",fontsize=16,color="burlywood",shape="box"];259[label="yu4/LT",fontsize=10,color="white",style="solid",shape="box"];20 -> 259[label="",style="solid", color="burlywood", weight=9];
259 -> 27[label="",style="solid", color="burlywood", weight=3];
260[label="yu4/EQ",fontsize=10,color="white",style="solid",shape="box"];20 -> 260[label="",style="solid", color="burlywood", weight=9];
260 -> 28[label="",style="solid", color="burlywood", weight=3];
261[label="yu4/GT",fontsize=10,color="white",style="solid",shape="box"];20 -> 261[label="",style="solid", color="burlywood", weight=9];
261 -> 29[label="",style="solid", color="burlywood", weight=3];
21[label="map toEnum (takeWhile1 (flip (<=) (fromEnum LT)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum LT) == GT)))",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
22[label="map toEnum (takeWhile1 (flip (<=) (fromEnum EQ)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum EQ) == GT)))",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
23[label="map toEnum (takeWhile1 (flip (<=) (fromEnum GT)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum GT) == GT)))",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
24[label="map toEnum (takeWhile1 (flip (<=) (fromEnum LT)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum LT) == GT)))",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
25[label="map toEnum (takeWhile1 (flip (<=) (fromEnum EQ)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum EQ) == GT)))",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
26[label="map toEnum (takeWhile1 (flip (<=) (fromEnum GT)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum GT) == GT)))",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
27[label="map toEnum (takeWhile1 (flip (<=) (fromEnum LT)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (fromEnum LT) == GT)))",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
28[label="map toEnum (takeWhile1 (flip (<=) (fromEnum EQ)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (fromEnum EQ) == GT)))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
29[label="map toEnum (takeWhile1 (flip (<=) (fromEnum GT)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (fromEnum GT) == GT)))",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
30[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"];30 -> 39[label="",style="solid", color="black", weight=3];
31[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
32[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
33[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="triangle"];33 -> 42[label="",style="solid", color="black", weight=3];
34[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="triangle"];34 -> 43[label="",style="solid", color="black", weight=3];
35[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="triangle"];35 -> 44[label="",style="solid", color="black", weight=3];
36[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
37[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
38[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ Zero))) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
39[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"];39 -> 48[label="",style="solid", color="black", weight=3];
40[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
41[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero (Succ (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
42[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"];42 -> 51[label="",style="solid", color="black", weight=3];
43[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ Zero) (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];43 -> 52[label="",style="solid", color="black", weight=3];
44[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ Zero) (Succ (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];44 -> 53[label="",style="solid", color="black", weight=3];
45[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ Zero)) Zero == GT)))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
46[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ Zero)) (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
47[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ Zero)) (Succ (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
48[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
49[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (LT == GT)))",fontsize=16,color="black",shape="box"];49 -> 58[label="",style="solid", color="black", weight=3];
50[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (LT == GT)))",fontsize=16,color="black",shape="box"];50 -> 59[label="",style="solid", color="black", weight=3];
51[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"];51 -> 60[label="",style="solid", color="black", weight=3];
52[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];52 -> 61[label="",style="solid", color="black", weight=3];
53[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];53 -> 62[label="",style="solid", color="black", weight=3];
54[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (GT == GT)))",fontsize=16,color="black",shape="box"];54 -> 63[label="",style="solid", color="black", weight=3];
55[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ Zero) Zero == GT)))",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
56[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ Zero) (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];56 -> 65[label="",style="solid", color="black", weight=3];
57[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];57 -> 66[label="",style="solid", color="black", weight=3];
58[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];58 -> 67[label="",style="solid", color="black", weight=3];
59[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];59 -> 68[label="",style="solid", color="black", weight=3];
60[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"];60 -> 69[label="",style="solid", color="black", weight=3];
61[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];61 -> 70[label="",style="solid", color="black", weight=3];
62[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (LT == GT)))",fontsize=16,color="black",shape="box"];62 -> 71[label="",style="solid", color="black", weight=3];
63[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not True))",fontsize=16,color="black",shape="box"];63 -> 72[label="",style="solid", color="black", weight=3];
64[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (GT == GT)))",fontsize=16,color="black",shape="box"];64 -> 73[label="",style="solid", color="black", weight=3];
65[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ Zero))) (numericEnumFrom $! Pos (Succ (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="triangle"];65 -> 74[label="",style="solid", color="black", weight=3];
66[label="map toEnum (Pos Zero : takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];66 -> 75[label="",style="solid", color="black", weight=3];
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162[label="map toEnum (takeWhile (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];162 -> 170[label="",style="solid", color="black", weight=3];
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164[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom (Pos (primPlusNat (Succ Zero) (Succ Zero)))))",fontsize=16,color="black",shape="box"];164 -> 172[label="",style="solid", color="black", weight=3];
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203[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat (Succ Zero) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ Zero) (Succ Zero)) + fromInt (Pos (Succ Zero))) (compare (Pos (primPlusNat (Succ Zero) (Succ Zero))) (Pos (Succ Zero)) /= GT))",fontsize=16,color="black",shape="box"];203 -> 210[label="",style="solid", color="black", weight=3];
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211[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (primPlusNat (Succ Zero) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ Zero) (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (compare (Pos (primPlusNat (Succ Zero) (Succ Zero))) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];211 -> 217[label="",style="solid", color="black", weight=3];
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217[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (primPlusNat (Succ Zero) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ Zero) (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primPlusNat (Succ Zero) (Succ Zero))) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];217 -> 221[label="",style="solid", color="black", weight=3];
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221[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ (primPlusNat Zero Zero)))) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];221 -> 225[label="",style="solid", color="black", weight=3];
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223[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (primPlusNat (Succ (Succ Zero)) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ (Succ Zero)) (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primPlusNat (Succ (Succ Zero)) (Succ Zero))) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];223 -> 227[label="",style="solid", color="black", weight=3];
224[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ (primPlusNat Zero Zero))) (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];224 -> 228[label="",style="solid", color="black", weight=3];
225[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ (primPlusNat Zero Zero))) (Succ (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];225 -> 229[label="",style="solid", color="black", weight=3];
226[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];226 -> 230[label="",style="solid", color="black", weight=3];
227[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ (primPlusNat (Succ Zero) Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat (Succ Zero) Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ (primPlusNat (Succ Zero) Zero)))) (Pos (Succ (Succ Zero))) == GT)))",fontsize=16,color="black",shape="box"];227 -> 231[label="",style="solid", color="black", weight=3];
228[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (primPlusNat Zero Zero)) Zero == GT)))",fontsize=16,color="black",shape="box"];228 -> 232[label="",style="solid", color="black", weight=3];
229[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (primPlusNat Zero Zero)) (Succ Zero) == GT)))",fontsize=16,color="black",shape="box"];229 -> 233[label="",style="solid", color="black", weight=3];
230[label="toEnum0 True (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];230 -> 234[label="",style="solid", color="black", weight=3];
231[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ (primPlusNat (Succ Zero) Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat (Succ Zero) Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ (primPlusNat (Succ Zero) Zero))) (Succ (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];231 -> 235[label="",style="solid", color="black", weight=3];
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----------------------------------------

(8)
YES