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

MAYBE 19.66 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could not be shown:

↳ HASKELL

  ↳ BR

mainModule Main

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

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

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

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)

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 vz wu = takeWhile2 vz wu

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

mainModule Main

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

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

              ↳ Narrow

mainModule Main

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

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 wv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="enumFromTo wv3 wv4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="map toEnum (enumFromTo (fromEnum wv3) (fromEnum wv4))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="map toEnum (numericEnumFromTo (fromEnum wv3) (fromEnum wv4))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="map toEnum (takeWhile (flip (<=) (fromEnum wv4)) (numericEnumFrom (fromEnum wv3)))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="map toEnum (takeWhile (flip (<=) (fromEnum wv4)) (fromEnum wv3 : (numericEnumFrom $! fromEnum wv3 + 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 wv4)) (fromEnum wv3 : (numericEnumFrom $! fromEnum wv3 + 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 wv4)) (fromEnum wv3) (numericEnumFrom $! fromEnum wv3 + fromInt (Pos (Succ Zero))) (flip (<=) (fromEnum wv4) (fromEnum wv3)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (fromEnum wv3) (numericEnumFrom $! fromEnum wv3 + fromInt (Pos (Succ Zero))) ((<=) fromEnum wv3 fromEnum wv4))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (fromEnum wv3) (numericEnumFrom $! fromEnum wv3 + fromInt (Pos (Succ Zero))) (compare (fromEnum wv3) (fromEnum wv4) /= GT))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (fromEnum wv3) (numericEnumFrom $! fromEnum wv3 + fromInt (Pos (Succ Zero))) (not (compare (fromEnum wv3) (fromEnum wv4) == GT)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (fromEnum wv3) (numericEnumFrom $! fromEnum wv3 + fromInt (Pos (Succ Zero))) (not (primCmpInt (fromEnum wv3) (fromEnum wv4) == GT)))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (primCharToInt wv3) (numericEnumFrom $! primCharToInt wv3 + fromInt (Pos (Succ Zero))) (not (primCmpInt (primCharToInt wv3) (fromEnum wv4) == GT)))",fontsize=16,color="burlywood",shape="box"];559[label="wv3/Char wv30",fontsize=10,color="white",style="solid",shape="box"];15 -> 559[label="",style="solid", color="burlywood", weight=9];
559 -> 16[label="",style="solid", color="burlywood", weight=3];
16[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (primCharToInt (Char wv30)) (numericEnumFrom $! primCharToInt (Char wv30) + fromInt (Pos (Succ Zero))) (not (primCmpInt (primCharToInt (Char wv30)) (fromEnum wv4) == GT)))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
17[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (Pos wv30) (numericEnumFrom $! Pos wv30 + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos wv30) (fromEnum wv4) == GT)))",fontsize=16,color="burlywood",shape="box"];560[label="wv30/Succ wv300",fontsize=10,color="white",style="solid",shape="box"];17 -> 560[label="",style="solid", color="burlywood", weight=9];
560 -> 18[label="",style="solid", color="burlywood", weight=3];
561[label="wv30/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 561[label="",style="solid", color="burlywood", weight=9];
561 -> 19[label="",style="solid", color="burlywood", weight=3];
18[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ wv300)) (fromEnum wv4) == GT)))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
19[label="map toEnum (takeWhile1 (flip (<=) (fromEnum wv4)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (fromEnum wv4) == GT)))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
20[label="map toEnum (takeWhile1 (flip (<=) (primCharToInt wv4)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ wv300)) (primCharToInt wv4) == GT)))",fontsize=16,color="burlywood",shape="box"];562[label="wv4/Char wv40",fontsize=10,color="white",style="solid",shape="box"];20 -> 562[label="",style="solid", color="burlywood", weight=9];
562 -> 22[label="",style="solid", color="burlywood", weight=3];
21[label="map toEnum (takeWhile1 (flip (<=) (primCharToInt wv4)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (primCharToInt wv4) == GT)))",fontsize=16,color="burlywood",shape="box"];563[label="wv4/Char wv40",fontsize=10,color="white",style="solid",shape="box"];21 -> 563[label="",style="solid", color="burlywood", weight=9];
563 -> 23[label="",style="solid", color="burlywood", weight=3];
22[label="map toEnum (takeWhile1 (flip (<=) (primCharToInt (Char wv40))) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ wv300)) (primCharToInt (Char wv40)) == GT)))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
23[label="map toEnum (takeWhile1 (flip (<=) (primCharToInt (Char wv40))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (primCharToInt (Char wv40)) == GT)))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
24[label="map toEnum (takeWhile1 (flip (<=) (Pos wv40)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ wv300)) (Pos wv40) == GT)))",fontsize=16,color="black",shape="triangle"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="map toEnum (takeWhile1 (flip (<=) (Pos wv40)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (Pos wv40) == GT)))",fontsize=16,color="burlywood",shape="box"];564[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];25 -> 564[label="",style="solid", color="burlywood", weight=9];
564 -> 27[label="",style="solid", color="burlywood", weight=3];
565[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 565[label="",style="solid", color="burlywood", weight=9];
565 -> 28[label="",style="solid", color="burlywood", weight=3];
26[label="map toEnum (takeWhile1 (flip (<=) (Pos wv40)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ wv300) wv40 == GT)))",fontsize=16,color="burlywood",shape="box"];566[label="wv40/Succ wv400",fontsize=10,color="white",style="solid",shape="box"];26 -> 566[label="",style="solid", color="burlywood", weight=9];
566 -> 29[label="",style="solid", color="burlywood", weight=3];
567[label="wv40/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 567[label="",style="solid", color="burlywood", weight=9];
567 -> 30[label="",style="solid", color="burlywood", weight=3];
27[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos Zero) (Pos (Succ wv400)) == GT)))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28[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"];28 -> 32[label="",style="solid", color="black", weight=3];
29[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ wv300) (Succ wv400) == GT)))",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
30[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ wv300) Zero == GT)))",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
31[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero (Succ wv400) == GT)))",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
32[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"];32 -> 36[label="",style="solid", color="black", weight=3];
33 -> 450[label="",style="dashed", color="red", weight=0];
33[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (primCmpNat wv300 wv400 == GT)))",fontsize=16,color="magenta"];33 -> 451[label="",style="dashed", color="magenta", weight=3];
33 -> 452[label="",style="dashed", color="magenta", weight=3];
33 -> 453[label="",style="dashed", color="magenta", weight=3];
33 -> 454[label="",style="dashed", color="magenta", weight=3];
34[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not (GT == GT)))",fontsize=16,color="black",shape="box"];34 -> 39[label="",style="solid", color="black", weight=3];
35[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not (LT == GT)))",fontsize=16,color="black",shape="box"];35 -> 40[label="",style="solid", color="black", weight=3];
36[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];36 -> 41[label="",style="solid", color="black", weight=3];
451[label="wv300",fontsize=16,color="green",shape="box"];452[label="wv300",fontsize=16,color="green",shape="box"];453[label="wv400",fontsize=16,color="green",shape="box"];454[label="wv400",fontsize=16,color="green",shape="box"];450[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat wv24 wv25 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];569[label="wv24/Succ wv240",fontsize=10,color="white",style="solid",shape="box"];450 -> 569[label="",style="solid", color="burlywood", weight=9];
569 -> 491[label="",style="solid", color="burlywood", weight=3];
570[label="wv24/Zero",fontsize=10,color="white",style="solid",shape="box"];450 -> 570[label="",style="solid", color="burlywood", weight=9];
570 -> 492[label="",style="solid", color="burlywood", weight=3];
39[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) (not True))",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3];
40[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) (not False))",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3];
41[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3];
491[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ wv240) wv25 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];571[label="wv25/Succ wv250",fontsize=10,color="white",style="solid",shape="box"];491 -> 571[label="",style="solid", color="burlywood", weight=9];
571 -> 493[label="",style="solid", color="burlywood", weight=3];
572[label="wv25/Zero",fontsize=10,color="white",style="solid",shape="box"];491 -> 572[label="",style="solid", color="burlywood", weight=9];
572 -> 494[label="",style="solid", color="burlywood", weight=3];
492[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero wv25 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];573[label="wv25/Succ wv250",fontsize=10,color="white",style="solid",shape="box"];492 -> 573[label="",style="solid", color="burlywood", weight=9];
573 -> 495[label="",style="solid", color="burlywood", weight=3];
574[label="wv25/Zero",fontsize=10,color="white",style="solid",shape="box"];492 -> 574[label="",style="solid", color="burlywood", weight=9];
574 -> 496[label="",style="solid", color="burlywood", weight=3];
46[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) False)",fontsize=16,color="black",shape="box"];46 -> 53[label="",style="solid", color="black", weight=3];
47[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos Zero) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];47 -> 54[label="",style="solid", color="black", weight=3];
48[label="map toEnum (Pos Zero : takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];48 -> 55[label="",style="solid", color="black", weight=3];
493[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ wv240) (Succ wv250) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];493 -> 497[label="",style="solid", color="black", weight=3];
494[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ wv240) Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];494 -> 498[label="",style="solid", color="black", weight=3];
495[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero (Succ wv250) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];495 -> 499[label="",style="solid", color="black", weight=3];
496[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat Zero Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];496 -> 500[label="",style="solid", color="black", weight=3];
53[label="map toEnum (takeWhile0 (flip (<=) (Pos Zero)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) otherwise)",fontsize=16,color="black",shape="box"];53 -> 61[label="",style="solid", color="black", weight=3];
54[label="map toEnum (Pos Zero : takeWhile (flip (<=) (Pos (Succ wv400))) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];54 -> 62[label="",style="solid", color="black", weight=3];
55[label="toEnum (Pos Zero) : map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];55 -> 63[label="",style="dashed", color="green", weight=3];
55 -> 64[label="",style="dashed", color="green", weight=3];
497 -> 450[label="",style="dashed", color="red", weight=0];
497[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (primCmpNat wv240 wv250 == GT)))\n  Enum a",fontsize=16,color="magenta"];497 -> 501[label="",style="dashed", color="magenta", weight=3];
497 -> 502[label="",style="dashed", color="magenta", weight=3];
498[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (GT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];498 -> 503[label="",style="solid", color="black", weight=3];
499[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (LT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];499 -> 504[label="",style="solid", color="black", weight=3];
500[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not (EQ == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];500 -> 505[label="",style="solid", color="black", weight=3];
61[label="map toEnum (takeWhile0 (flip (<=) (Pos Zero)) (Pos (Succ wv300)) (numericEnumFrom $! Pos (Succ wv300) + fromInt (Pos (Succ Zero))) True)",fontsize=16,color="black",shape="box"];61 -> 72[label="",style="solid", color="black", weight=3];
62[label="toEnum (Pos Zero) : map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="green",shape="box"];62 -> 73[label="",style="dashed", color="green", weight=3];
62 -> 74[label="",style="dashed", color="green", weight=3];
63[label="toEnum (Pos Zero)",fontsize=16,color="black",shape="triangle"];63 -> 75[label="",style="solid", color="black", weight=3];
64[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];64 -> 76[label="",style="solid", color="black", weight=3];
501[label="wv240",fontsize=16,color="green",shape="box"];502[label="wv250",fontsize=16,color="green",shape="box"];503[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not True))\n  Enum a",fontsize=16,color="black",shape="box"];503 -> 506[label="",style="solid", color="black", weight=3];
504[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not False))\n  Enum a",fontsize=16,color="black",shape="triangle"];504 -> 507[label="",style="solid", color="black", weight=3];
505 -> 504[label="",style="dashed", color="red", weight=0];
505[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) (not False))\n  Enum a",fontsize=16,color="magenta"];72[label="map toEnum []",fontsize=16,color="black",shape="triangle"];72 -> 84[label="",style="solid", color="black", weight=3];
73 -> 63[label="",style="dashed", color="red", weight=0];
73[label="toEnum (Pos Zero)",fontsize=16,color="magenta"];74[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];74 -> 85[label="",style="solid", color="black", weight=3];
75[label="primIntToChar (Pos Zero)",fontsize=16,color="black",shape="box"];75 -> 86[label="",style="solid", color="black", weight=3];
76[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"];76 -> 87[label="",style="solid", color="black", weight=3];
506[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) False)\n  Enum a",fontsize=16,color="black",shape="box"];506 -> 508[label="",style="solid", color="black", weight=3];
507[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) True)\n  Enum a",fontsize=16,color="black",shape="box"];507 -> 509[label="",style="solid", color="black", weight=3];
84[label="[]",fontsize=16,color="green",shape="box"];85[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (Pos Zero + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];85 -> 96[label="",style="solid", color="black", weight=3];
86[label="Char Zero",fontsize=16,color="green",shape="box"];87[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"];87 -> 97[label="",style="solid", color="black", weight=3];
508[label="map toEnum (takeWhile0 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) otherwise)\n  Enum a",fontsize=16,color="black",shape="box"];508 -> 510[label="",style="solid", color="black", weight=3];
509[label="map toEnum (Pos (Succ wv23) : takeWhile (flip (<=) (Pos (Succ wv22))) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))))\n  Enum a",fontsize=16,color="black",shape="box"];509 -> 511[label="",style="solid", color="black", weight=3];
96[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (enforceWHNF (WHNF (Pos Zero + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];96 -> 110[label="",style="solid", color="black", weight=3];
97[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"];97 -> 111[label="",style="solid", color="black", weight=3];
510[label="map toEnum (takeWhile0 (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23)) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))) True)\n  Enum a",fontsize=16,color="black",shape="box"];510 -> 512[label="",style="solid", color="black", weight=3];
511[label="toEnum (Pos (Succ wv23)) : map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))))\n  Enum a",fontsize=16,color="green",shape="box"];511 -> 513[label="",style="dashed", color="green", weight=3];
511 -> 514[label="",style="dashed", color="green", weight=3];
110[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos Zero) (fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];110 -> 122[label="",style="solid", color="black", weight=3];
111[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"];111 -> 123[label="",style="solid", color="black", weight=3];
512[label="map toEnum []\n  Enum a",fontsize=16,color="black",shape="box"];512 -> 515[label="",style="solid", color="black", weight=3];
513[label="toEnum (Pos (Succ wv23))\n  Enum a",fontsize=16,color="blue",shape="box"];578[label="toEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];513 -> 578[label="",style="solid", color="blue", weight=9];
578 -> 516[label="",style="solid", color="blue", weight=3];
579[label="toEnum :: Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];513 -> 579[label="",style="solid", color="blue", weight=9];
579 -> 517[label="",style="solid", color="blue", weight=3];
580[label="toEnum :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];513 -> 580[label="",style="solid", color="blue", weight=9];
580 -> 518[label="",style="solid", color="blue", weight=3];
581[label="toEnum :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];513 -> 581[label="",style="solid", color="blue", weight=9];
581 -> 519[label="",style="solid", color="blue", weight=3];
582[label="toEnum :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];513 -> 582[label="",style="solid", color="blue", weight=9];
582 -> 520[label="",style="solid", color="blue", weight=3];
583[label="toEnum :: Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];513 -> 583[label="",style="solid", color="blue", weight=9];
583 -> 521[label="",style="solid", color="blue", weight=3];
584[label="toEnum :: Int -> ()",fontsize=10,color="white",style="solid",shape="box"];513 -> 584[label="",style="solid", color="blue", weight=9];
584 -> 522[label="",style="solid", color="blue", weight=3];
585[label="toEnum :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];513 -> 585[label="",style="solid", color="blue", weight=9];
585 -> 523[label="",style="solid", color="blue", weight=3];
586[label="toEnum :: Int -> Char",fontsize=10,color="white",style="solid",shape="box"];513 -> 586[label="",style="solid", color="blue", weight=9];
586 -> 524[label="",style="solid", color="blue", weight=3];
514[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (numericEnumFrom $! Pos (Succ wv23) + fromInt (Pos (Succ Zero))))\n  Enum a",fontsize=16,color="black",shape="box"];514 -> 525[label="",style="solid", color="black", weight=3];
122[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (enforceWHNF (WHNF (primPlusInt (Pos Zero) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos Zero) (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];122 -> 135[label="",style="solid", color="black", weight=3];
123[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"];123 -> 136[label="",style="solid", color="black", weight=3];
515[label="[]\n  Enum a",fontsize=16,color="green",shape="box"];516[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];516 -> 526[label="",style="solid", color="black", weight=3];
517[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];517 -> 527[label="",style="solid", color="black", weight=3];
518[label="toEnum (Pos (Succ wv23))\n  Integral a",fontsize=16,color="black",shape="box"];518 -> 528[label="",style="solid", color="black", weight=3];
519[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];519 -> 529[label="",style="solid", color="black", weight=3];
520[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];520 -> 530[label="",style="solid", color="black", weight=3];
521[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];521 -> 531[label="",style="solid", color="black", weight=3];
522[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];522 -> 532[label="",style="solid", color="black", weight=3];
523[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];523 -> 533[label="",style="solid", color="black", weight=3];
524[label="toEnum (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];524 -> 534[label="",style="solid", color="black", weight=3];
525[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (Pos (Succ wv23) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (Succ wv23) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="black",shape="box"];525 -> 535[label="",style="solid", color="black", weight=3];
135[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (enforceWHNF (WHNF (Pos (primPlusNat Zero (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero))))))",fontsize=16,color="black",shape="box"];135 -> 151[label="",style="solid", color="black", weight=3];
136[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];136 -> 152[label="",style="solid", color="black", weight=3];
526[label="error []",fontsize=16,color="red",shape="box"];527[label="error []",fontsize=16,color="red",shape="box"];528[label="error []",fontsize=16,color="red",shape="box"];529[label="error []",fontsize=16,color="red",shape="box"];530[label="error []",fontsize=16,color="red",shape="box"];531[label="error []",fontsize=16,color="red",shape="box"];532[label="error []",fontsize=16,color="red",shape="box"];533[label="error []",fontsize=16,color="red",shape="box"];534[label="primIntToChar (Pos (Succ wv23))",fontsize=16,color="black",shape="box"];534 -> 536[label="",style="solid", color="black", weight=3];
535[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (enforceWHNF (WHNF (Pos (Succ wv23) + fromInt (Pos (Succ Zero)))) (numericEnumFrom (Pos (Succ wv23) + fromInt (Pos (Succ Zero))))))\n  Enum a",fontsize=16,color="black",shape="box"];535 -> 537[label="",style="solid", color="black", weight=3];
151[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (numericEnumFrom (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];151 -> 165[label="",style="solid", color="black", weight=3];
152[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"];152 -> 166[label="",style="solid", color="black", weight=3];
536[label="Char (Succ wv23)",fontsize=16,color="green",shape="box"];537[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (enforceWHNF (WHNF (primPlusInt (Pos (Succ wv23)) (fromInt (Pos (Succ Zero))))) (numericEnumFrom (primPlusInt (Pos (Succ wv23)) (fromInt (Pos (Succ Zero)))))))\n  Enum a",fontsize=16,color="black",shape="box"];537 -> 538[label="",style="solid", color="black", weight=3];
165[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];165 -> 180[label="",style="solid", color="black", weight=3];
166[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"];166 -> 181[label="",style="solid", color="black", weight=3];
538[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (enforceWHNF (WHNF (primPlusInt (Pos (Succ wv23)) (Pos (Succ Zero)))) (numericEnumFrom (primPlusInt (Pos (Succ wv23)) (Pos (Succ Zero))))))\n  Enum a",fontsize=16,color="black",shape="box"];538 -> 539[label="",style="solid", color="black", weight=3];
180[label="map toEnum (takeWhile2 (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="black",shape="box"];180 -> 198[label="",style="solid", color="black", weight=3];
181[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"];181 -> 199[label="",style="solid", color="black", weight=3];
539[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (enforceWHNF (WHNF (Pos (primPlusNat (Succ wv23) (Succ Zero)))) (numericEnumFrom (Pos (primPlusNat (Succ wv23) (Succ Zero))))))\n  Enum a",fontsize=16,color="black",shape="box"];539 -> 540[label="",style="solid", color="black", weight=3];
198[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (flip (<=) (Pos (Succ wv400)) (Pos (primPlusNat Zero (Succ Zero)))))",fontsize=16,color="black",shape="box"];198 -> 214[label="",style="solid", color="black", weight=3];
199[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"];199 -> 215[label="",style="solid", color="black", weight=3];
540[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (numericEnumFrom (Pos (primPlusNat (Succ wv23) (Succ Zero)))))\n  Enum a",fontsize=16,color="black",shape="box"];540 -> 541[label="",style="solid", color="black", weight=3];
214[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) ((<=) Pos (primPlusNat Zero (Succ Zero)) Pos (Succ wv400)))",fontsize=16,color="black",shape="box"];214 -> 231[label="",style="solid", color="black", weight=3];
215[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"];215 -> 232[label="",style="solid", color="black", weight=3];
541[label="map toEnum (takeWhile (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="black",shape="box"];541 -> 542[label="",style="solid", color="black", weight=3];
231[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (compare (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ wv400)) /= GT))",fontsize=16,color="black",shape="box"];231 -> 253[label="",style="solid", color="black", weight=3];
232[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"];232 -> 254[label="",style="solid", color="black", weight=3];
542[label="map toEnum (takeWhile2 (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero)) : (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="black",shape="box"];542 -> 543[label="",style="solid", color="black", weight=3];
253[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (compare (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ wv400)) == GT)))",fontsize=16,color="black",shape="box"];253 -> 270[label="",style="solid", color="black", weight=3];
254[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"];254 -> 271[label="",style="solid", color="black", weight=3];
543[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero))) (flip (<=) (Pos (Succ wv22)) (Pos (primPlusNat (Succ wv23) (Succ Zero)))))\n  Enum a",fontsize=16,color="black",shape="box"];543 -> 544[label="",style="solid", color="black", weight=3];
270[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (primPlusNat Zero (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat Zero (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primPlusNat Zero (Succ Zero))) (Pos (Succ wv400)) == GT)))",fontsize=16,color="black",shape="box"];270 -> 288[label="",style="solid", color="black", weight=3];
271 -> 24[label="",style="dashed", color="red", weight=0];
271[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"];271 -> 289[label="",style="dashed", color="magenta", weight=3];
271 -> 290[label="",style="dashed", color="magenta", weight=3];
544[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero))) ((<=) Pos (primPlusNat (Succ wv23) (Succ Zero)) Pos (Succ wv22)))\n  Enum a",fontsize=16,color="black",shape="box"];544 -> 545[label="",style="solid", color="black", weight=3];
288 -> 24[label="",style="dashed", color="red", weight=0];
288[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv400))) (Pos (Succ Zero)) (numericEnumFrom $! Pos (Succ Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ Zero)) (Pos (Succ wv400)) == GT)))",fontsize=16,color="magenta"];288 -> 310[label="",style="dashed", color="magenta", weight=3];
288 -> 311[label="",style="dashed", color="magenta", weight=3];
289[label="Zero",fontsize=16,color="green",shape="box"];290[label="Zero",fontsize=16,color="green",shape="box"];545[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero))) (compare (Pos (primPlusNat (Succ wv23) (Succ Zero))) (Pos (Succ wv22)) /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];545 -> 546[label="",style="solid", color="black", weight=3];
310[label="Zero",fontsize=16,color="green",shape="box"];311[label="Succ wv400",fontsize=16,color="green",shape="box"];546[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (compare (Pos (primPlusNat (Succ wv23) (Succ Zero))) (Pos (Succ wv22)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];546 -> 547[label="",style="solid", color="black", weight=3];
547[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (primPlusNat (Succ wv23) (Succ Zero))) (numericEnumFrom $! Pos (primPlusNat (Succ wv23) (Succ Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primPlusNat (Succ wv23) (Succ Zero))) (Pos (Succ wv22)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];547 -> 548[label="",style="solid", color="black", weight=3];
548[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ (Succ (primPlusNat wv23 Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat wv23 Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (Succ (Succ (primPlusNat wv23 Zero)))) (Pos (Succ wv22)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];548 -> 549[label="",style="solid", color="black", weight=3];
549 -> 450[label="",style="dashed", color="red", weight=0];
549[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ wv22))) (Pos (Succ (Succ (primPlusNat wv23 Zero)))) (numericEnumFrom $! Pos (Succ (Succ (primPlusNat wv23 Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpNat (Succ (Succ (primPlusNat wv23 Zero))) (Succ wv22) == GT)))\n  Enum a",fontsize=16,color="magenta"];549 -> 550[label="",style="dashed", color="magenta", weight=3];
549 -> 551[label="",style="dashed", color="magenta", weight=3];
549 -> 552[label="",style="dashed", color="magenta", weight=3];
550[label="Succ (Succ (primPlusNat wv23 Zero))",fontsize=16,color="green",shape="box"];550 -> 553[label="",style="dashed", color="green", weight=3];
551[label="Succ (primPlusNat wv23 Zero)",fontsize=16,color="green",shape="box"];551 -> 554[label="",style="dashed", color="green", weight=3];
552[label="Succ wv22",fontsize=16,color="green",shape="box"];553[label="primPlusNat wv23 Zero",fontsize=16,color="burlywood",shape="triangle"];590[label="wv23/Succ wv230",fontsize=10,color="white",style="solid",shape="box"];553 -> 590[label="",style="solid", color="burlywood", weight=9];
590 -> 555[label="",style="solid", color="burlywood", weight=3];
591[label="wv23/Zero",fontsize=10,color="white",style="solid",shape="box"];553 -> 591[label="",style="solid", color="burlywood", weight=9];
591 -> 556[label="",style="solid", color="burlywood", weight=3];
554 -> 553[label="",style="dashed", color="red", weight=0];
554[label="primPlusNat wv23 Zero",fontsize=16,color="magenta"];555[label="primPlusNat (Succ wv230) Zero",fontsize=16,color="black",shape="box"];555 -> 557[label="",style="solid", color="black", weight=3];
556[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];556 -> 558[label="",style="solid", color="black", weight=3];
557[label="Succ wv230",fontsize=16,color="green",shape="box"];558[label="Zero",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ QDP

                  ↳ ForwardInstantiation

              ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_map(wv22, wv23, Zero, Succ(wv250), ba) → new_map(wv22, Succ(new_primPlusNat(wv23)), Succ(Succ(new_primPlusNat(wv23))), Succ(wv22), ba)
new_map(wv22, wv23, Zero, Zero, ba) → new_map0(wv22, wv23, ba)
new_map0(wv22, wv23, ba) → new_map(wv22, Succ(new_primPlusNat(wv23)), Succ(Succ(new_primPlusNat(wv23))), Succ(wv22), ba)
new_map(wv22, wv23, Succ(wv240), Succ(wv250), ba) → new_map(wv22, wv23, wv240, wv250, ba)

The TRS R consists of the following rules:

new_primPlusNat(Succ(wv230)) → Succ(wv230)
new_primPlusNat(Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat(Zero)
new_primPlusNat(Succ(x0))

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map(wv22, wv23, Succ(wv240), Succ(wv250), ba) → new_map(wv22, wv23, wv240, wv250, ba) we obtained the following new rules:

new_map(x0, x1, Succ(Zero), Succ(Zero), x4) → new_map(x0, x1, Zero, Zero, x4)
new_map(x0, x1, Succ(Zero), Succ(Succ(y_2)), x4) → new_map(x0, x1, Zero, Succ(y_2), x4)
new_map(x0, x1, Succ(Succ(y_2)), Succ(Succ(y_3)), x4) → new_map(x0, x1, Succ(y_2), Succ(y_3), x4)

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ MNOCProof

              ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_map(wv22, wv23, Zero, Succ(wv250), ba) → new_map(wv22, Succ(new_primPlusNat(wv23)), Succ(Succ(new_primPlusNat(wv23))), Succ(wv22), ba)
new_map(x0, x1, Succ(Zero), Succ(Zero), x4) → new_map(x0, x1, Zero, Zero, x4)
new_map(wv22, wv23, Zero, Zero, ba) → new_map0(wv22, wv23, ba)
new_map(x0, x1, Succ(Zero), Succ(Succ(y_2)), x4) → new_map(x0, x1, Zero, Succ(y_2), x4)
new_map0(wv22, wv23, ba) → new_map(wv22, Succ(new_primPlusNat(wv23)), Succ(Succ(new_primPlusNat(wv23))), Succ(wv22), ba)
new_map(x0, x1, Succ(Succ(y_2)), Succ(Succ(y_3)), x4) → new_map(x0, x1, Succ(y_2), Succ(y_3), x4)

The TRS R consists of the following rules:

new_primPlusNat(Succ(wv230)) → Succ(wv230)
new_primPlusNat(Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat(Zero)
new_primPlusNat(Succ(x0))

We have to consider all minimal (P,Q,R)-chains.
We use the modular non-overlap check [17] to decrease Q to the empty set.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ QDP

                  ↳ ForwardInstantiation

                    ↳ QDP

                      ↳ MNOCProof

                        ↳ QDP

              ↳ Narrow

Q DP problem:
The TRS P consists of the following rules:

new_map(wv22, wv23, Zero, Succ(wv250), ba) → new_map(wv22, Succ(new_primPlusNat(wv23)), Succ(Succ(new_primPlusNat(wv23))), Succ(wv22), ba)
new_map(wv22, wv23, Zero, Zero, ba) → new_map0(wv22, wv23, ba)
new_map(x0, x1, Succ(Zero), Succ(Zero), x4) → new_map(x0, x1, Zero, Zero, x4)
new_map0(wv22, wv23, ba) → new_map(wv22, Succ(new_primPlusNat(wv23)), Succ(Succ(new_primPlusNat(wv23))), Succ(wv22), ba)
new_map(x0, x1, Succ(Zero), Succ(Succ(y_2)), x4) → new_map(x0, x1, Zero, Succ(y_2), x4)
new_map(x0, x1, Succ(Succ(y_2)), Succ(Succ(y_3)), x4) → new_map(x0, x1, Succ(y_2), Succ(y_3), x4)

The TRS R consists of the following rules:

new_primPlusNat(Succ(wv230)) → Succ(wv230)
new_primPlusNat(Zero) → Zero

Q is empty.
We have to consider all (P,Q,R)-chains.
Haskell To QDPs

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

              ↳ Narrow

                ↳ QDP

                  ↳ PisEmptyProof

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.
The TRS P is empty. Hence, there is no (P,Q,R) chain.

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