H-Termination proof of /home/matraf/haskell/eval_FullyBlown

YES 0.911 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

((enumFromTo :: Bool -> Bool -> [Bool]) :: Bool -> Bool -> [Bool])

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((enumFromTo :: Bool -> Bool -> [Bool]) :: Bool -> Bool -> [Bool])

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

The following Function with conditions

takeWhile p [] = []

takeWhile p (x : xs)

| p x

= x : takeWhile p xs

| otherwise

= []

is transformed to

takeWhile p [] = takeWhile3 p []

takeWhile p (x : xs) = takeWhile2 p (x : xs)

takeWhile0 p x xs True = []

takeWhile1 p x xs True = x : takeWhile p xs

takeWhile1 p x xs False = takeWhile0 p x xs otherwise

takeWhile2 p (x : xs) = takeWhile1 p x xs (p x)

takeWhile3 p [] = []

takeWhile3 wv ww = takeWhile2 wv ww

The following Function with conditions

toEnum 0 = False

toEnum 1 = True

is transformed to

toEnum wy = toEnum3 wy

toEnum wx = toEnum1 wx

toEnum0 True wx = True

toEnum1 wx = toEnum0 (wx == 1) wx

toEnum2 True wy = False

toEnum2 wz xu = toEnum1 xu

toEnum3 wy = toEnum2 (wy == 0) wy

toEnum3 xv = toEnum1 xv

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

mainModule Main

((enumFromTo :: Bool -> Bool -> [Bool]) :: Bool -> Bool -> [Bool])

module Main where

import qualified Prelude

Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

mainModule Main

(enumFromTo :: Bool -> Bool -> [Bool])

module Main where

import qualified Prelude

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 xw3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="enumFromTo xw3 xw4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="map toEnum (enumFromTo (fromEnum xw3) (fromEnum xw4))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="map toEnum (numericEnumFromTo (fromEnum xw3) (fromEnum xw4))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="map toEnum (takeWhile (flip (<=) (fromEnum xw4)) (numericEnumFrom (fromEnum xw3)))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="map toEnum (takeWhile (flip (<=) (fromEnum xw4)) (fromEnum xw3 : (numericEnumFrom $! fromEnum xw3 + 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 xw4)) (fromEnum xw3 : (numericEnumFrom $! fromEnum xw3 + 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 xw4)) (fromEnum xw3) (numericEnumFrom $! fromEnum xw3 + fromInt (Pos (Succ Zero))) (flip (<=) (fromEnum xw4) (fromEnum xw3)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (fromEnum xw3) (numericEnumFrom $! fromEnum xw3 + fromInt (Pos (Succ Zero))) ((<=) fromEnum xw3 fromEnum xw4))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (fromEnum xw3) (numericEnumFrom $! fromEnum xw3 + fromInt (Pos (Succ Zero))) (compare (fromEnum xw3) (fromEnum xw4) /= GT))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (fromEnum xw3) (numericEnumFrom $! fromEnum xw3 + fromInt (Pos (Succ Zero))) (not (compare (fromEnum xw3) (fromEnum xw4) == GT)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (fromEnum xw3) (numericEnumFrom $! fromEnum xw3 + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum xw3) (fromEnum xw4) == GT)))",fontsize=16,color="burlywood",shape="box"];124[label="xw3/False",fontsize=10,color="white",style="solid",shape="box"];14 -> 124[label="",style="solid", color="burlywood", weight=9];
124 -> 15[label="",style="solid", color="burlywood", weight=3];
125[label="xw3/True",fontsize=10,color="white",style="solid",shape="box"];14 -> 125[label="",style="solid", color="burlywood", weight=9];
125 -> 16[label="",style="solid", color="burlywood", weight=3];
15[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (fromEnum False) (numericEnumFrom $! fromEnum False + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum False) (fromEnum xw4) == GT)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (fromEnum True) (numericEnumFrom $! fromEnum True + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum True) (fromEnum xw4) == GT)))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum xw4) == GT)))",fontsize=16,color="burlywood",shape="box"];126[label="xw4/False",fontsize=10,color="white",style="solid",shape="box"];17 -> 126[label="",style="solid", color="burlywood", weight=9];
126 -> 19[label="",style="solid", color="burlywood", weight=3];
127[label="xw4/True",fontsize=10,color="white",style="solid",shape="box"];17 -> 127[label="",style="solid", color="burlywood", weight=9];
127 -> 20[label="",style="solid", color="burlywood", weight=3];
18[label="map toEnum (takeWhile1 (flip (<=) (fromEnum xw4)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum xw4) == GT)))",fontsize=16,color="burlywood",shape="box"];128[label="xw4/False",fontsize=10,color="white",style="solid",shape="box"];18 -> 128[label="",style="solid", color="burlywood", weight=9];
128 -> 21[label="",style="solid", color="burlywood", weight=3];
129[label="xw4/True",fontsize=10,color="white",style="solid",shape="box"];18 -> 129[label="",style="solid", color="burlywood", weight=9];
129 -> 22[label="",style="solid", color="burlywood", weight=3];
19[label="map toEnum (takeWhile1 (flip (<=) (fromEnum False)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum False) == GT)))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="map toEnum (takeWhile1 (flip (<=) (fromEnum True)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum True) == GT)))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="map toEnum (takeWhile1 (flip (<=) (fromEnum False)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum False) == GT)))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="map toEnum (takeWhile1 (flip (<=) (fromEnum True)) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (fromEnum True) == GT)))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[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"];23 -> 27[label="",style="solid", color="black", weight=3];
24[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"];24 -> 28[label="",style="solid", color="black", weight=3];
25[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"];25 -> 29[label="",style="solid", color="black", weight=3];
26[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"];26 -> 30[label="",style="solid", color="black", weight=3];
27[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"];27 -> 31[label="",style="solid", color="black", weight=3];
28[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"];28 -> 32[label="",style="solid", color="black", weight=3];
29[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"];29 -> 33[label="",style="solid", color="black", weight=3];
30[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"];30 -> 34[label="",style="solid", color="black", weight=3];
31[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
32[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"];32 -> 36[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 (GT == GT)))",fontsize=16,color="black",shape="box"];33 -> 37[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 (primCmpNat Zero Zero == GT)))",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
35[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
36[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"];36 -> 40[label="",style="solid", color="black", weight=3];
37[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"];37 -> 41[label="",style="solid", color="black", weight=3];
38[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"];38 -> 42[label="",style="solid", color="black", weight=3];
39[label="map toEnum (Pos Zero : takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];39 -> 43[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))) True)",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3];
41[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"];41 -> 45[label="",style="solid", color="black", weight=3];
42[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
43[label="toEnum (Pos Zero) : map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];43 -> 47[label="",style="dashed", color="green", weight=3];
43 -> 48[label="",style="dashed", color="green", weight=3];
44[label="map toEnum (Pos Zero : takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];44 -> 49[label="",style="solid", color="black", weight=3];
45[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"];45 -> 50[label="",style="solid", color="black", weight=3];
46[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];46 -> 51[label="",style="solid", color="black", weight=3];
47[label="toEnum (Pos Zero)",fontsize=16,color="black",shape="triangle"];47 -> 52[label="",style="solid", color="black", weight=3];
48[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];48 -> 53[label="",style="solid", color="black", weight=3];
49[label="toEnum (Pos Zero) : map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];49 -> 54[label="",style="dashed", color="green", weight=3];
49 -> 55[label="",style="dashed", color="green", 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 -> 56[label="",style="solid", color="black", weight=3];
51[label="map toEnum (Pos (Succ Zero) : takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];51 -> 57[label="",style="solid", color="black", weight=3];
52[label="toEnum3 (Pos Zero)",fontsize=16,color="black",shape="box"];52 -> 58[label="",style="solid", color="black", weight=3];
53[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"];53 -> 59[label="",style="solid", color="black", weight=3];
54 -> 47[label="",style="dashed", color="red", weight=0];
54[label="toEnum (Pos Zero)",fontsize=16,color="magenta"];55[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];55 -> 60[label="",style="solid", color="black", weight=3];
56[label="map toEnum []",fontsize=16,color="black",shape="triangle"];56 -> 61[label="",style="solid", color="black", weight=3];
57[label="toEnum (Pos (Succ Zero)) : map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];57 -> 62[label="",style="dashed", color="green", weight=3];
57 -> 63[label="",style="dashed", color="green", weight=3];
58[label="toEnum2 (Pos Zero == Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];58 -> 64[label="",style="solid", color="black", weight=3];
59[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"];59 -> 65[label="",style="solid", color="black", weight=3];
60[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (Pos Zero + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];60 -> 66[label="",style="solid", color="black", weight=3];
61[label="[]",fontsize=16,color="green",shape="box"];62[label="toEnum (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];62 -> 67[label="",style="solid", color="black", weight=3];
63[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];63 -> 68[label="",style="solid", color="black", weight=3];
64[label="toEnum2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];64 -> 69[label="",style="solid", color="black", weight=3];
65[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"];65 -> 70[label="",style="solid", color="black", weight=3];
66[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (Pos Zero + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];66 -> 71[label="",style="solid", color="black", weight=3];
67[label="toEnum3 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];67 -> 72[label="",style="solid", color="black", weight=3];
68[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (Pos (Succ Zero) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (Succ Zero) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];68 -> 73[label="",style="solid", color="black", weight=3];
69[label="toEnum2 True (Pos Zero)",fontsize=16,color="black",shape="box"];69 -> 74[label="",style="solid", color="black", weight=3];
70[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"];70 -> 75[label="",style="solid", color="black", weight=3];
71[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];71 -> 76[label="",style="solid", color="black", weight=3];
72[label="toEnum2 (Pos (Succ Zero) == Pos Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];72 -> 77[label="",style="solid", color="black", weight=3];
73[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (Pos (Succ Zero) + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos (Succ Zero) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];73 -> 78[label="",style="solid", color="black", weight=3];
74[label="False",fontsize=16,color="green",shape="box"];75[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"];75 -> 79[label="",style="solid", color="black", weight=3];
76[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos Zero) (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];76 -> 80[label="",style="solid", color="black", weight=3];
77[label="toEnum2 (primEqInt (Pos (Succ Zero)) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];77 -> 81[label="",style="solid", color="black", weight=3];
78[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (primPlusInt (Pos (Succ Zero)) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos (Succ Zero)) (fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];78 -> 82[label="",style="solid", color="black", weight=3];
79[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];79 -> 83[label="",style="solid", color="black", weight=3];
80[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (Pos (primPlusNat Zero (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero))))))",fontsize=16,color="black",shape="box"];80 -> 84[label="",style="solid", color="black", weight=3];
81[label="toEnum2 False (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];81 -> 85[label="",style="solid", color="black", weight=3];
82[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (primPlusInt (Pos (Succ Zero)) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos (Succ Zero)) (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];82 -> 86[label="",style="solid", color="black", weight=3];
83[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"];83 -> 87[label="",style="solid", color="black", weight=3];
84[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];84 -> 88[label="",style="solid", color="black", weight=3];
85[label="toEnum1 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];85 -> 89[label="",style="solid", color="black", weight=3];
86[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (enforceWHNF (WHNF (Pos (primPlusNat (Succ Zero) (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat (Succ Zero) (Succ Zero))))))",fontsize=16,color="black",shape="box"];86 -> 90[label="",style="solid", color="black", weight=3];
87[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"];87 -> 91[label="",style="solid", color="black", weight=3];
88[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];88 -> 92[label="",style="solid", color="black", weight=3];
89[label="toEnum0 (Pos (Succ Zero) == Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];89 -> 93[label="",style="solid", color="black", weight=3];
90[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (numericEnumFrom (Pos (primPlusNat (Succ Zero) (Succ Zero)))))",fontsize=16,color="black",shape="box"];90 -> 94[label="",style="solid", color="black", weight=3];
91[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"];91 -> 95[label="",style="solid", color="black", weight=3];
92[label="map toEnum (takeWhile2 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];92 -> 96[label="",style="solid", color="black", weight=3];
93[label="toEnum0 (primEqInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];93 -> 97[label="",style="solid", color="black", weight=3];
94[label="map toEnum (takeWhile (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat (Succ Zero) (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat (Succ Zero) (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];94 -> 98[label="",style="solid", color="black", weight=3];
95[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"];95 -> 99[label="",style="solid", color="black", weight=3];
96[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (flip (<=) (Pos (Succ Zero)) (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];96 -> 100[label="",style="solid", color="black", weight=3];
97[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];97 -> 101[label="",style="solid", color="black", weight=3];
98[label="map toEnum (takeWhile2 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat (Succ Zero) (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat (Succ Zero) (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];98 -> 102[label="",style="solid", color="black", weight=3];
99[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"];99 -> 103[label="",style="solid", color="black", weight=3];
100[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) ((<=) Pos (primPlusNat Zero (Succ Zero)) Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];100 -> 104[label="",style="solid", color="black", weight=3];
101[label="toEnum0 True (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];101 -> 105[label="",style="solid", color="black", weight=3];
102[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))) (flip (<=) (Pos (Succ Zero)) (Pos (primPlusNat (Succ Zero) (Succ Zero)))))",fontsize=16,color="black",shape="box"];102 -> 106[label="",style="solid", color="black", weight=3];
103[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"];103 -> 107[label="",style="solid", color="black", weight=3];
104[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (compare (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ Zero)) /= GT))",fontsize=16,color="black",shape="box"];104 -> 108[label="",style="solid", color="black", weight=3];
105[label="True",fontsize=16,color="green",shape="box"];106[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))) ((<=) Pos (primPlusNat (Succ Zero) (Succ Zero)) Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];106 -> 109[label="",style="solid", color="black", weight=3];
107[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"];107 -> 110[label="",style="solid", color="black", weight=3];
108[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (compare (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];108 -> 111[label="",style="solid", color="black", weight=3];
109[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"];109 -> 112[label="",style="solid", color="black", weight=3];
110 -> 25[label="",style="dashed", color="red", weight=0];
110[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="magenta"];111[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ Zero))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];111 -> 113[label="",style="solid", color="black", weight=3];
112[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))) (not (compare (Pos (primPlusNat (Succ Zero) (Succ Zero))) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];112 -> 114[label="",style="solid", color="black", weight=3];
113 -> 26[label="",style="dashed", color="red", weight=0];
113[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="magenta"];114[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))) (not (primCmpInt (Pos (primPlusNat (Succ Zero) (Succ Zero))) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];114 -> 115[label="",style="solid", color="black", weight=3];
115[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 (primCmpInt (Pos (Succ (Succ (primPlusNat Zero Zero)))) (Pos (Succ Zero)) == GT)))",fontsize=16,color="black",shape="box"];115 -> 116[label="",style="solid", color="black", weight=3];
116[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"];116 -> 117[label="",style="solid", color="black", weight=3];
117[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"];117 -> 118[label="",style="solid", color="black", weight=3];
118[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 (GT == GT)))",fontsize=16,color="black",shape="box"];118 -> 119[label="",style="solid", color="black", weight=3];
119[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 True))",fontsize=16,color="black",shape="box"];119 -> 120[label="",style="solid", color="black", weight=3];
120[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))) False)",fontsize=16,color="black",shape="box"];120 -> 121[label="",style="solid", color="black", weight=3];
121[label="map toEnum (takeWhile0 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) otherwise)",fontsize=16,color="black",shape="box"];121 -> 122[label="",style="solid", color="black", weight=3];
122[label="map toEnum (takeWhile0 (flip (<=) (Pos (Succ Zero))) (Pos (Succ (Succ (primPlusNat Zero Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat Zero Zero))) + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];122 -> 123[label="",style="solid", color="black", weight=3];
123 -> 56[label="",style="dashed", color="red", weight=0];
123[label="map toEnum []",fontsize=16,color="magenta"];}

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