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

YES 2.611 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule FiniteMap

((lookupFM :: FiniteMap Int a -> Int -> Maybe a) :: FiniteMap Int a -> Int -> Maybe a)

module FiniteMap where

import qualified Maybe
import qualified Prelude

data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)

instance (Eq a, Eq b) => Eq (FiniteMap b a) where

lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a

lookupFM

EmptyFM key

Nothing

lookupFM

(Branch key elt _ fm_l fm_r) key_to_find

key_to_find < key

lookupFM fm_l key_to_find

key_to_find > key

lookupFM fm_r key_to_find

otherwise

Just elt

module Maybe where

import qualified FiniteMap
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule FiniteMap

((lookupFM :: FiniteMap Int a -> Int -> Maybe a) :: FiniteMap Int a -> Int -> Maybe a)

module FiniteMap where

import qualified Maybe
import qualified Prelude

data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)

instance (Eq a, Eq b) => Eq (FiniteMap a b) where

lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b

lookupFM

EmptyFM key

Nothing

lookupFM

(Branch key elt vw fm_l fm_r) key_to_find

key_to_find < key

lookupFM fm_l key_to_find

key_to_find > key

lookupFM fm_r key_to_find

otherwise

Just elt

module Maybe where

import qualified FiniteMap
import qualified Prelude

Cond Reductions:
The following Function with conditions

lookupFM EmptyFM key = Nothing

lookupFM (Branch key elt vw fm_l fm_r) key_to_find

| key_to_find < key

= lookupFM fm_l key_to_find

| key_to_find > key

= lookupFM fm_r key_to_find

| otherwise

= Just elt

is transformed to

lookupFM EmptyFM key = lookupFM4 EmptyFM key

lookupFM (Branch key elt vw fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find

lookupFM2 key elt vw fm_l fm_r key_to_find True = lookupFM fm_l key_to_find

lookupFM2 key elt vw fm_l fm_r key_to_find False = lookupFM1 key elt vw fm_l fm_r key_to_find (key_to_find > key)

lookupFM1 key elt vw fm_l fm_r key_to_find True = lookupFM fm_r key_to_find

lookupFM1 key elt vw fm_l fm_r key_to_find False = lookupFM0 key elt vw fm_l fm_r key_to_find otherwise

lookupFM0 key elt vw fm_l fm_r key_to_find True = Just elt

lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find = lookupFM2 key elt vw fm_l fm_r key_to_find (key_to_find < key)

lookupFM4 EmptyFM key = Nothing

lookupFM4 wv ww = lookupFM3 wv ww

The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule FiniteMap

(lookupFM :: FiniteMap Int a -> Int -> Maybe a)

module FiniteMap where

import qualified Maybe
import qualified Prelude

data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b)

instance (Eq a, Eq b) => Eq (FiniteMap b a) where

lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a

lookupFM	EmptyFM key	=	lookupFM4 EmptyFM key
lookupFM	(Branch key elt vw fm_l fm_r) key_to_find	=	lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find

lookupFM0

key elt vw fm_l fm_r key_to_find True

Just elt

lookupFM1	key elt vw fm_l fm_r key_to_find True	=	lookupFM fm_r key_to_find
lookupFM1	key elt vw fm_l fm_r key_to_find False	=	lookupFM0 key elt vw fm_l fm_r key_to_find otherwise

lookupFM2	key elt vw fm_l fm_r key_to_find True	=	lookupFM fm_l key_to_find
lookupFM2	key elt vw fm_l fm_r key_to_find False	=	lookupFM1 key elt vw fm_l fm_r key_to_find (key_to_find > key)

lookupFM3

(Branch key elt vw fm_l fm_r) key_to_find

lookupFM2 key elt vw fm_l fm_r key_to_find (key_to_find < key)

lookupFM4	EmptyFM key	=	Nothing
lookupFM4	wv ww	=	lookupFM3 wv ww

module Maybe where

import qualified FiniteMap
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookupFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookupFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookupFM wx3 wx4",fontsize=16,color="burlywood",shape="triangle"];2076[label="wx3/EmptyFM",fontsize=10,color="white",style="solid",shape="box"];4 -> 2076[label="",style="solid", color="burlywood", weight=9];
2076 -> 5[label="",style="solid", color="burlywood", weight=3];
2077[label="wx3/Branch wx30 wx31 wx32 wx33 wx34",fontsize=10,color="white",style="solid",shape="box"];4 -> 2077[label="",style="solid", color="burlywood", weight=9];
2077 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookupFM EmptyFM wx4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6[label="lookupFM (Branch wx30 wx31 wx32 wx33 wx34) wx4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookupFM4 EmptyFM wx4",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookupFM3 (Branch wx30 wx31 wx32 wx33 wx34) wx4",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="Nothing",fontsize=16,color="green",shape="box"];10[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (wx4 < wx30)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (compare wx4 wx30 == LT)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (primCmpInt wx4 wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2078[label="wx4/Pos wx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 2078[label="",style="solid", color="burlywood", weight=9];
2078 -> 13[label="",style="solid", color="burlywood", weight=3];
2079[label="wx4/Neg wx40",fontsize=10,color="white",style="solid",shape="box"];12 -> 2079[label="",style="solid", color="burlywood", weight=9];
2079 -> 14[label="",style="solid", color="burlywood", weight=3];
13[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 (Pos wx40) (primCmpInt (Pos wx40) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2080[label="wx40/Succ wx400",fontsize=10,color="white",style="solid",shape="box"];13 -> 2080[label="",style="solid", color="burlywood", weight=9];
2080 -> 15[label="",style="solid", color="burlywood", weight=3];
2081[label="wx40/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 2081[label="",style="solid", color="burlywood", weight=9];
2081 -> 16[label="",style="solid", color="burlywood", weight=3];
14[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 (Neg wx40) (primCmpInt (Neg wx40) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2082[label="wx40/Succ wx400",fontsize=10,color="white",style="solid",shape="box"];14 -> 2082[label="",style="solid", color="burlywood", weight=9];
2082 -> 17[label="",style="solid", color="burlywood", weight=3];
2083[label="wx40/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 2083[label="",style="solid", color="burlywood", weight=9];
2083 -> 18[label="",style="solid", color="burlywood", weight=3];
15[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2084[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 2084[label="",style="solid", color="burlywood", weight=9];
2084 -> 19[label="",style="solid", color="burlywood", weight=3];
2085[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];15 -> 2085[label="",style="solid", color="burlywood", weight=9];
2085 -> 20[label="",style="solid", color="burlywood", weight=3];
16[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2086[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 2086[label="",style="solid", color="burlywood", weight=9];
2086 -> 21[label="",style="solid", color="burlywood", weight=3];
2087[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 2087[label="",style="solid", color="burlywood", weight=9];
2087 -> 22[label="",style="solid", color="burlywood", weight=3];
17[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpInt (Neg (Succ wx400)) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2088[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];17 -> 2088[label="",style="solid", color="burlywood", weight=9];
2088 -> 23[label="",style="solid", color="burlywood", weight=3];
2089[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];17 -> 2089[label="",style="solid", color="burlywood", weight=9];
2089 -> 24[label="",style="solid", color="burlywood", weight=3];
18[label="lookupFM2 wx30 wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) wx30 == LT)",fontsize=16,color="burlywood",shape="box"];2090[label="wx30/Pos wx300",fontsize=10,color="white",style="solid",shape="box"];18 -> 2090[label="",style="solid", color="burlywood", weight=9];
2090 -> 25[label="",style="solid", color="burlywood", weight=3];
2091[label="wx30/Neg wx300",fontsize=10,color="white",style="solid",shape="box"];18 -> 2091[label="",style="solid", color="burlywood", weight=9];
2091 -> 26[label="",style="solid", color="burlywood", weight=3];
19[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Pos wx300) == LT)",fontsize=16,color="black",shape="box"];19 -> 27[label="",style="solid", color="black", weight=3];
20[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Neg wx300) == LT)",fontsize=16,color="black",shape="box"];20 -> 28[label="",style="solid", color="black", weight=3];
21[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2092[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];21 -> 2092[label="",style="solid", color="burlywood", weight=9];
2092 -> 29[label="",style="solid", color="burlywood", weight=3];
2093[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 2093[label="",style="solid", color="burlywood", weight=9];
2093 -> 30[label="",style="solid", color="burlywood", weight=3];
22[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2094[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];22 -> 2094[label="",style="solid", color="burlywood", weight=9];
2094 -> 31[label="",style="solid", color="burlywood", weight=3];
2095[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 2095[label="",style="solid", color="burlywood", weight=9];
2095 -> 32[label="",style="solid", color="burlywood", weight=3];
23[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpInt (Neg (Succ wx400)) (Pos wx300) == LT)",fontsize=16,color="black",shape="box"];23 -> 33[label="",style="solid", color="black", weight=3];
24[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpInt (Neg (Succ wx400)) (Neg wx300) == LT)",fontsize=16,color="black",shape="box"];24 -> 34[label="",style="solid", color="black", weight=3];
25[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2096[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 2096[label="",style="solid", color="burlywood", weight=9];
2096 -> 35[label="",style="solid", color="burlywood", weight=3];
2097[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 2097[label="",style="solid", color="burlywood", weight=9];
2097 -> 36[label="",style="solid", color="burlywood", weight=3];
26[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg wx300) == LT)",fontsize=16,color="burlywood",shape="box"];2098[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];26 -> 2098[label="",style="solid", color="burlywood", weight=9];
2098 -> 37[label="",style="solid", color="burlywood", weight=3];
2099[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 2099[label="",style="solid", color="burlywood", weight=9];
2099 -> 38[label="",style="solid", color="burlywood", weight=3];
27[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) wx300 == LT)",fontsize=16,color="burlywood",shape="box"];2100[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];27 -> 2100[label="",style="solid", color="burlywood", weight=9];
2100 -> 39[label="",style="solid", color="burlywood", weight=3];
2101[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 2101[label="",style="solid", color="burlywood", weight=9];
2101 -> 40[label="",style="solid", color="burlywood", weight=3];
28[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == LT)",fontsize=16,color="black",shape="box"];28 -> 41[label="",style="solid", color="black", weight=3];
29[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];29 -> 42[label="",style="solid", color="black", weight=3];
30[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];30 -> 43[label="",style="solid", color="black", weight=3];
31[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];31 -> 44[label="",style="solid", color="black", weight=3];
32[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
33[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (LT == LT)",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
34[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat wx300 (Succ wx400) == LT)",fontsize=16,color="burlywood",shape="box"];2102[label="wx300/Succ wx3000",fontsize=10,color="white",style="solid",shape="box"];34 -> 2102[label="",style="solid", color="burlywood", weight=9];
2102 -> 47[label="",style="solid", color="burlywood", weight=3];
2103[label="wx300/Zero",fontsize=10,color="white",style="solid",shape="box"];34 -> 2103[label="",style="solid", color="burlywood", weight=9];
2103 -> 48[label="",style="solid", color="burlywood", weight=3];
35[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3];
36[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3];
37[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx3000)) == LT)",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
38[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
39[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) (Succ wx3000) == LT)",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
40[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) Zero == LT)",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
41[label="lookupFM2 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) False",fontsize=16,color="black",shape="box"];41 -> 55[label="",style="solid", color="black", weight=3];
42[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpNat Zero (Succ wx3000) == LT)",fontsize=16,color="black",shape="box"];42 -> 56[label="",style="solid", color="black", weight=3];
43[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];43 -> 57[label="",style="solid", color="black", weight=3];
44[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (GT == LT)",fontsize=16,color="black",shape="box"];44 -> 58[label="",style="solid", color="black", weight=3];
45[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];45 -> 59[label="",style="solid", color="black", weight=3];
46[label="lookupFM2 (Pos wx300) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) True",fontsize=16,color="black",shape="box"];46 -> 60[label="",style="solid", color="black", weight=3];
47[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat (Succ wx3000) (Succ wx400) == LT)",fontsize=16,color="black",shape="box"];47 -> 61[label="",style="solid", color="black", weight=3];
48[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat Zero (Succ wx400) == LT)",fontsize=16,color="black",shape="box"];48 -> 62[label="",style="solid", color="black", weight=3];
49[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (LT == LT)",fontsize=16,color="black",shape="box"];49 -> 63[label="",style="solid", color="black", weight=3];
50[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];50 -> 64[label="",style="solid", color="black", weight=3];
51[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpNat (Succ wx3000) Zero == LT)",fontsize=16,color="black",shape="box"];51 -> 65[label="",style="solid", color="black", weight=3];
52[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];52 -> 66[label="",style="solid", color="black", weight=3];
53 -> 973[label="",style="dashed", color="red", weight=0];
53[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat wx400 wx3000 == LT)",fontsize=16,color="magenta"];53 -> 974[label="",style="dashed", color="magenta", weight=3];
53 -> 975[label="",style="dashed", color="magenta", weight=3];
53 -> 976[label="",style="dashed", color="magenta", weight=3];
53 -> 977[label="",style="dashed", color="magenta", weight=3];
53 -> 978[label="",style="dashed", color="magenta", weight=3];
53 -> 979[label="",style="dashed", color="magenta", weight=3];
53 -> 980[label="",style="dashed", color="magenta", weight=3];
53 -> 981[label="",style="dashed", color="magenta", weight=3];
54[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == LT)",fontsize=16,color="black",shape="box"];54 -> 69[label="",style="solid", color="black", weight=3];
55[label="lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (Pos (Succ wx400) > Neg wx300)",fontsize=16,color="black",shape="box"];55 -> 70[label="",style="solid", color="black", weight=3];
56[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];56 -> 71[label="",style="solid", color="black", weight=3];
57[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];57 -> 72[label="",style="solid", color="black", weight=3];
58[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];58 -> 73[label="",style="solid", color="black", weight=3];
59[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];59 -> 74[label="",style="solid", color="black", weight=3];
60 -> 4[label="",style="dashed", color="red", weight=0];
60[label="lookupFM wx33 (Neg (Succ wx400))",fontsize=16,color="magenta"];60 -> 75[label="",style="dashed", color="magenta", weight=3];
60 -> 76[label="",style="dashed", color="magenta", weight=3];
61 -> 1060[label="",style="dashed", color="red", weight=0];
61[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (primCmpNat wx3000 wx400 == LT)",fontsize=16,color="magenta"];61 -> 1061[label="",style="dashed", color="magenta", weight=3];
61 -> 1062[label="",style="dashed", color="magenta", weight=3];
61 -> 1063[label="",style="dashed", color="magenta", weight=3];
61 -> 1064[label="",style="dashed", color="magenta", weight=3];
61 -> 1065[label="",style="dashed", color="magenta", weight=3];
61 -> 1066[label="",style="dashed", color="magenta", weight=3];
61 -> 1067[label="",style="dashed", color="magenta", weight=3];
61 -> 1068[label="",style="dashed", color="magenta", weight=3];
62[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) (LT == LT)",fontsize=16,color="black",shape="box"];62 -> 79[label="",style="solid", color="black", weight=3];
63[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];63 -> 80[label="",style="solid", color="black", weight=3];
64[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];64 -> 81[label="",style="solid", color="black", weight=3];
65[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (GT == LT)",fontsize=16,color="black",shape="box"];65 -> 82[label="",style="solid", color="black", weight=3];
66[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];66 -> 83[label="",style="solid", color="black", weight=3];
974[label="wx400",fontsize=16,color="green",shape="box"];975[label="wx32",fontsize=16,color="green",shape="box"];976[label="wx3000",fontsize=16,color="green",shape="box"];977[label="wx33",fontsize=16,color="green",shape="box"];978[label="wx3000",fontsize=16,color="green",shape="box"];979[label="wx31",fontsize=16,color="green",shape="box"];980[label="wx400",fontsize=16,color="green",shape="box"];981[label="wx34",fontsize=16,color="green",shape="box"];973[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat wx114 wx115 == LT)",fontsize=16,color="burlywood",shape="triangle"];2107[label="wx114/Succ wx1140",fontsize=10,color="white",style="solid",shape="box"];973 -> 2107[label="",style="solid", color="burlywood", weight=9];
2107 -> 1054[label="",style="solid", color="burlywood", weight=3];
2108[label="wx114/Zero",fontsize=10,color="white",style="solid",shape="box"];973 -> 2108[label="",style="solid", color="burlywood", weight=9];
2108 -> 1055[label="",style="solid", color="burlywood", weight=3];
69[label="lookupFM2 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) False",fontsize=16,color="black",shape="box"];69 -> 88[label="",style="solid", color="black", weight=3];
70[label="lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (compare (Pos (Succ wx400)) (Neg wx300) == GT)",fontsize=16,color="black",shape="box"];70 -> 89[label="",style="solid", color="black", weight=3];
71[label="lookupFM2 (Pos (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];71 -> 90[label="",style="solid", color="black", weight=3];
72[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (Pos Zero > Pos Zero)",fontsize=16,color="black",shape="box"];72 -> 91[label="",style="solid", color="black", weight=3];
73[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (Pos Zero > Neg (Succ wx3000))",fontsize=16,color="black",shape="box"];73 -> 92[label="",style="solid", color="black", weight=3];
74[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (Pos Zero > Neg Zero)",fontsize=16,color="black",shape="box"];74 -> 93[label="",style="solid", color="black", weight=3];
75[label="Neg (Succ wx400)",fontsize=16,color="green",shape="box"];76[label="wx33",fontsize=16,color="green",shape="box"];1061[label="wx400",fontsize=16,color="green",shape="box"];1062[label="wx32",fontsize=16,color="green",shape="box"];1063[label="wx31",fontsize=16,color="green",shape="box"];1064[label="wx3000",fontsize=16,color="green",shape="box"];1065[label="wx3000",fontsize=16,color="green",shape="box"];1066[label="wx34",fontsize=16,color="green",shape="box"];1067[label="wx400",fontsize=16,color="green",shape="box"];1068[label="wx33",fontsize=16,color="green",shape="box"];1060[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat wx123 wx124 == LT)",fontsize=16,color="burlywood",shape="triangle"];2109[label="wx123/Succ wx1230",fontsize=10,color="white",style="solid",shape="box"];1060 -> 2109[label="",style="solid", color="burlywood", weight=9];
2109 -> 1141[label="",style="solid", color="burlywood", weight=3];
2110[label="wx123/Zero",fontsize=10,color="white",style="solid",shape="box"];1060 -> 2110[label="",style="solid", color="burlywood", weight=9];
2110 -> 1142[label="",style="solid", color="burlywood", weight=3];
79[label="lookupFM2 (Neg Zero) wx31 wx32 wx33 wx34 (Neg (Succ wx400)) True",fontsize=16,color="black",shape="box"];79 -> 98[label="",style="solid", color="black", weight=3];
80 -> 4[label="",style="dashed", color="red", weight=0];
80[label="lookupFM wx33 (Neg Zero)",fontsize=16,color="magenta"];80 -> 99[label="",style="dashed", color="magenta", weight=3];
80 -> 100[label="",style="dashed", color="magenta", weight=3];
81[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (Neg Zero > Pos Zero)",fontsize=16,color="black",shape="box"];81 -> 101[label="",style="solid", color="black", weight=3];
82[label="lookupFM2 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];82 -> 102[label="",style="solid", color="black", weight=3];
83[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (Neg Zero > Neg Zero)",fontsize=16,color="black",shape="box"];83 -> 103[label="",style="solid", color="black", weight=3];
1054[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat (Succ wx1140) wx115 == LT)",fontsize=16,color="burlywood",shape="box"];2112[label="wx115/Succ wx1150",fontsize=10,color="white",style="solid",shape="box"];1054 -> 2112[label="",style="solid", color="burlywood", weight=9];
2112 -> 1143[label="",style="solid", color="burlywood", weight=3];
2113[label="wx115/Zero",fontsize=10,color="white",style="solid",shape="box"];1054 -> 2113[label="",style="solid", color="burlywood", weight=9];
2113 -> 1144[label="",style="solid", color="burlywood", weight=3];
1055[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat Zero wx115 == LT)",fontsize=16,color="burlywood",shape="box"];2114[label="wx115/Succ wx1150",fontsize=10,color="white",style="solid",shape="box"];1055 -> 2114[label="",style="solid", color="burlywood", weight=9];
2114 -> 1145[label="",style="solid", color="burlywood", weight=3];
2115[label="wx115/Zero",fontsize=10,color="white",style="solid",shape="box"];1055 -> 2115[label="",style="solid", color="burlywood", weight=9];
2115 -> 1146[label="",style="solid", color="burlywood", weight=3];
88[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (Pos (Succ wx400) > Pos Zero)",fontsize=16,color="black",shape="box"];88 -> 108[label="",style="solid", color="black", weight=3];
89[label="lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Neg wx300) == GT)",fontsize=16,color="black",shape="box"];89 -> 109[label="",style="solid", color="black", weight=3];
90 -> 4[label="",style="dashed", color="red", weight=0];
90[label="lookupFM wx33 (Pos Zero)",fontsize=16,color="magenta"];90 -> 110[label="",style="dashed", color="magenta", weight=3];
90 -> 111[label="",style="dashed", color="magenta", weight=3];
91[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];91 -> 112[label="",style="solid", color="black", weight=3];
92[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (compare (Pos Zero) (Neg (Succ wx3000)) == GT)",fontsize=16,color="black",shape="box"];92 -> 113[label="",style="solid", color="black", weight=3];
93[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];93 -> 114[label="",style="solid", color="black", weight=3];
1141[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx1230) wx124 == LT)",fontsize=16,color="burlywood",shape="box"];2117[label="wx124/Succ wx1240",fontsize=10,color="white",style="solid",shape="box"];1141 -> 2117[label="",style="solid", color="burlywood", weight=9];
2117 -> 1147[label="",style="solid", color="burlywood", weight=3];
2118[label="wx124/Zero",fontsize=10,color="white",style="solid",shape="box"];1141 -> 2118[label="",style="solid", color="burlywood", weight=9];
2118 -> 1148[label="",style="solid", color="burlywood", weight=3];
1142[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat Zero wx124 == LT)",fontsize=16,color="burlywood",shape="box"];2119[label="wx124/Succ wx1240",fontsize=10,color="white",style="solid",shape="box"];1142 -> 2119[label="",style="solid", color="burlywood", weight=9];
2119 -> 1149[label="",style="solid", color="burlywood", weight=3];
2120[label="wx124/Zero",fontsize=10,color="white",style="solid",shape="box"];1142 -> 2120[label="",style="solid", color="burlywood", weight=9];
2120 -> 1150[label="",style="solid", color="burlywood", weight=3];
98 -> 4[label="",style="dashed", color="red", weight=0];
98[label="lookupFM wx33 (Neg (Succ wx400))",fontsize=16,color="magenta"];98 -> 119[label="",style="dashed", color="magenta", weight=3];
98 -> 120[label="",style="dashed", color="magenta", weight=3];
99[label="Neg Zero",fontsize=16,color="green",shape="box"];100[label="wx33",fontsize=16,color="green",shape="box"];101[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];101 -> 121[label="",style="solid", color="black", weight=3];
102[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (Neg Zero > Neg (Succ wx3000))",fontsize=16,color="black",shape="box"];102 -> 122[label="",style="solid", color="black", weight=3];
103[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];103 -> 123[label="",style="solid", color="black", weight=3];
1143[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat (Succ wx1140) (Succ wx1150) == LT)",fontsize=16,color="black",shape="box"];1143 -> 1151[label="",style="solid", color="black", weight=3];
1144[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat (Succ wx1140) Zero == LT)",fontsize=16,color="black",shape="box"];1144 -> 1152[label="",style="solid", color="black", weight=3];
1145[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat Zero (Succ wx1150) == LT)",fontsize=16,color="black",shape="box"];1145 -> 1153[label="",style="solid", color="black", weight=3];
1146[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];1146 -> 1154[label="",style="solid", color="black", weight=3];
108[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (compare (Pos (Succ wx400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];108 -> 129[label="",style="solid", color="black", weight=3];
109[label="lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == GT)",fontsize=16,color="black",shape="box"];109 -> 130[label="",style="solid", color="black", weight=3];
110[label="Pos Zero",fontsize=16,color="green",shape="box"];111[label="wx33",fontsize=16,color="green",shape="box"];112[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];112 -> 131[label="",style="solid", color="black", weight=3];
113[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ wx3000)) == GT)",fontsize=16,color="black",shape="box"];113 -> 132[label="",style="solid", color="black", weight=3];
114[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];114 -> 133[label="",style="solid", color="black", weight=3];
1147[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx1230) (Succ wx1240) == LT)",fontsize=16,color="black",shape="box"];1147 -> 1155[label="",style="solid", color="black", weight=3];
1148[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx1230) Zero == LT)",fontsize=16,color="black",shape="box"];1148 -> 1156[label="",style="solid", color="black", weight=3];
1149[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat Zero (Succ wx1240) == LT)",fontsize=16,color="black",shape="box"];1149 -> 1157[label="",style="solid", color="black", weight=3];
1150[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];1150 -> 1158[label="",style="solid", color="black", weight=3];
119[label="Neg (Succ wx400)",fontsize=16,color="green",shape="box"];120[label="wx33",fontsize=16,color="green",shape="box"];121[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];121 -> 139[label="",style="solid", color="black", weight=3];
122[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (compare (Neg Zero) (Neg (Succ wx3000)) == GT)",fontsize=16,color="black",shape="box"];122 -> 140[label="",style="solid", color="black", weight=3];
123[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];123 -> 141[label="",style="solid", color="black", weight=3];
1151 -> 973[label="",style="dashed", color="red", weight=0];
1151[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat wx1140 wx1150 == LT)",fontsize=16,color="magenta"];1151 -> 1159[label="",style="dashed", color="magenta", weight=3];
1151 -> 1160[label="",style="dashed", color="magenta", weight=3];
1152[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (GT == LT)",fontsize=16,color="black",shape="box"];1152 -> 1161[label="",style="solid", color="black", weight=3];
1153[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (LT == LT)",fontsize=16,color="black",shape="box"];1153 -> 1162[label="",style="solid", color="black", weight=3];
1154[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (EQ == LT)",fontsize=16,color="black",shape="box"];1154 -> 1163[label="",style="solid", color="black", weight=3];
129[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpInt (Pos (Succ wx400)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];129 -> 149[label="",style="solid", color="black", weight=3];
130[label="lookupFM1 (Neg wx300) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) True",fontsize=16,color="black",shape="box"];130 -> 150[label="",style="solid", color="black", weight=3];
131[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];131 -> 151[label="",style="solid", color="black", weight=3];
132[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];132 -> 152[label="",style="solid", color="black", weight=3];
133[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];133 -> 153[label="",style="solid", color="black", weight=3];
1155 -> 1060[label="",style="dashed", color="red", weight=0];
1155[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat wx1230 wx1240 == LT)",fontsize=16,color="magenta"];1155 -> 1164[label="",style="dashed", color="magenta", weight=3];
1155 -> 1165[label="",style="dashed", color="magenta", weight=3];
1156[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (GT == LT)",fontsize=16,color="black",shape="box"];1156 -> 1166[label="",style="solid", color="black", weight=3];
1157[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (LT == LT)",fontsize=16,color="black",shape="box"];1157 -> 1167[label="",style="solid", color="black", weight=3];
1158[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (EQ == LT)",fontsize=16,color="black",shape="box"];1158 -> 1168[label="",style="solid", color="black", weight=3];
139[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];139 -> 161[label="",style="solid", color="black", weight=3];
140[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ wx3000)) == GT)",fontsize=16,color="black",shape="box"];140 -> 162[label="",style="solid", color="black", weight=3];
141[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];141 -> 163[label="",style="solid", color="black", weight=3];
1159[label="wx1150",fontsize=16,color="green",shape="box"];1160[label="wx1140",fontsize=16,color="green",shape="box"];1161[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) False",fontsize=16,color="black",shape="triangle"];1161 -> 1169[label="",style="solid", color="black", weight=3];
1162[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) True",fontsize=16,color="black",shape="box"];1162 -> 1170[label="",style="solid", color="black", weight=3];
1163 -> 1161[label="",style="dashed", color="red", weight=0];
1163[label="lookupFM2 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) False",fontsize=16,color="magenta"];149[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (primCmpNat (Succ wx400) Zero == GT)",fontsize=16,color="black",shape="box"];149 -> 172[label="",style="solid", color="black", weight=3];
150 -> 4[label="",style="dashed", color="red", weight=0];
150[label="lookupFM wx34 (Pos (Succ wx400))",fontsize=16,color="magenta"];150 -> 173[label="",style="dashed", color="magenta", weight=3];
150 -> 174[label="",style="dashed", color="magenta", weight=3];
151[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];151 -> 175[label="",style="solid", color="black", weight=3];
152[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];152 -> 176[label="",style="solid", color="black", weight=3];
153[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) False",fontsize=16,color="black",shape="box"];153 -> 177[label="",style="solid", color="black", weight=3];
1164[label="wx1230",fontsize=16,color="green",shape="box"];1165[label="wx1240",fontsize=16,color="green",shape="box"];1166[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) False",fontsize=16,color="black",shape="triangle"];1166 -> 1171[label="",style="solid", color="black", weight=3];
1167[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) True",fontsize=16,color="black",shape="box"];1167 -> 1172[label="",style="solid", color="black", weight=3];
1168 -> 1166[label="",style="dashed", color="red", weight=0];
1168[label="lookupFM2 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) False",fontsize=16,color="magenta"];161[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];161 -> 186[label="",style="solid", color="black", weight=3];
162[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (primCmpNat (Succ wx3000) Zero == GT)",fontsize=16,color="black",shape="box"];162 -> 187[label="",style="solid", color="black", weight=3];
163[label="lookupFM1 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) False",fontsize=16,color="black",shape="box"];163 -> 188[label="",style="solid", color="black", weight=3];
1169[label="lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (Pos (Succ wx113) > Pos (Succ wx108))",fontsize=16,color="black",shape="box"];1169 -> 1173[label="",style="solid", color="black", weight=3];
1170 -> 4[label="",style="dashed", color="red", weight=0];
1170[label="lookupFM wx111 (Pos (Succ wx113))",fontsize=16,color="magenta"];1170 -> 1174[label="",style="dashed", color="magenta", weight=3];
1170 -> 1175[label="",style="dashed", color="magenta", weight=3];
172[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) (GT == GT)",fontsize=16,color="black",shape="box"];172 -> 196[label="",style="solid", color="black", weight=3];
173[label="Pos (Succ wx400)",fontsize=16,color="green",shape="box"];174[label="wx34",fontsize=16,color="green",shape="box"];175[label="lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];175 -> 197[label="",style="solid", color="black", weight=3];
176 -> 4[label="",style="dashed", color="red", weight=0];
176[label="lookupFM wx34 (Pos Zero)",fontsize=16,color="magenta"];176 -> 198[label="",style="dashed", color="magenta", weight=3];
176 -> 199[label="",style="dashed", color="magenta", weight=3];
177[label="lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];177 -> 200[label="",style="solid", color="black", weight=3];
1171[label="lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (Neg (Succ wx122) > Neg (Succ wx117))",fontsize=16,color="black",shape="box"];1171 -> 1176[label="",style="solid", color="black", weight=3];
1172 -> 4[label="",style="dashed", color="red", weight=0];
1172[label="lookupFM wx120 (Neg (Succ wx122))",fontsize=16,color="magenta"];1172 -> 1177[label="",style="dashed", color="magenta", weight=3];
1172 -> 1178[label="",style="dashed", color="magenta", weight=3];
186[label="lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];186 -> 208[label="",style="solid", color="black", weight=3];
187[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];187 -> 209[label="",style="solid", color="black", weight=3];
188[label="lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];188 -> 210[label="",style="solid", color="black", weight=3];
1173[label="lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (compare (Pos (Succ wx113)) (Pos (Succ wx108)) == GT)",fontsize=16,color="black",shape="box"];1173 -> 1179[label="",style="solid", color="black", weight=3];
1174[label="Pos (Succ wx113)",fontsize=16,color="green",shape="box"];1175[label="wx111",fontsize=16,color="green",shape="box"];196[label="lookupFM1 (Pos Zero) wx31 wx32 wx33 wx34 (Pos (Succ wx400)) True",fontsize=16,color="black",shape="box"];196 -> 220[label="",style="solid", color="black", weight=3];
197[label="lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];197 -> 221[label="",style="solid", color="black", weight=3];
198[label="Pos Zero",fontsize=16,color="green",shape="box"];199[label="wx34",fontsize=16,color="green",shape="box"];200[label="lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Pos Zero) True",fontsize=16,color="black",shape="box"];200 -> 222[label="",style="solid", color="black", weight=3];
1176[label="lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (compare (Neg (Succ wx122)) (Neg (Succ wx117)) == GT)",fontsize=16,color="black",shape="box"];1176 -> 1180[label="",style="solid", color="black", weight=3];
1177[label="Neg (Succ wx122)",fontsize=16,color="green",shape="box"];1178[label="wx120",fontsize=16,color="green",shape="box"];208[label="lookupFM0 (Pos Zero) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];208 -> 232[label="",style="solid", color="black", weight=3];
209[label="lookupFM1 (Neg (Succ wx3000)) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];209 -> 233[label="",style="solid", color="black", weight=3];
210[label="lookupFM0 (Neg Zero) wx31 wx32 wx33 wx34 (Neg Zero) True",fontsize=16,color="black",shape="box"];210 -> 234[label="",style="solid", color="black", weight=3];
1179[label="lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpInt (Pos (Succ wx113)) (Pos (Succ wx108)) == GT)",fontsize=16,color="black",shape="box"];1179 -> 1181[label="",style="solid", color="black", weight=3];
220 -> 4[label="",style="dashed", color="red", weight=0];
220[label="lookupFM wx34 (Pos (Succ wx400))",fontsize=16,color="magenta"];220 -> 245[label="",style="dashed", color="magenta", weight=3];
220 -> 246[label="",style="dashed", color="magenta", weight=3];
221[label="Just wx31",fontsize=16,color="green",shape="box"];222[label="Just wx31",fontsize=16,color="green",shape="box"];1180[label="lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpInt (Neg (Succ wx122)) (Neg (Succ wx117)) == GT)",fontsize=16,color="black",shape="box"];1180 -> 1182[label="",style="solid", color="black", weight=3];
232[label="Just wx31",fontsize=16,color="green",shape="box"];233 -> 4[label="",style="dashed", color="red", weight=0];
233[label="lookupFM wx34 (Neg Zero)",fontsize=16,color="magenta"];233 -> 257[label="",style="dashed", color="magenta", weight=3];
233 -> 258[label="",style="dashed", color="magenta", weight=3];
234[label="Just wx31",fontsize=16,color="green",shape="box"];1181 -> 1856[label="",style="dashed", color="red", weight=0];
1181[label="lookupFM1 (Pos (Succ wx108)) wx109 wx110 wx111 wx112 (Pos (Succ wx113)) (primCmpNat (Succ wx113) (Succ wx108) == GT)",fontsize=16,color="magenta"];1181 -> 1857[label="",style="dashed", color="magenta", weight=3];
1181 -> 1858[label="",style="dashed", color="magenta", weight=3];
1181 -> 1859[label="",style="dashed", color="magenta", weight=3];
1181 -> 1860[label="",style="dashed", color="magenta", weight=3];
1181 -> 1861[label="",style="dashed", color="magenta", weight=3];
1181 -> 1862[label="",style="dashed", color="magenta", weight=3];
1181 -> 1863[label="",style="dashed", color="magenta", weight=3];
1181 -> 1864[label="",style="dashed", color="magenta", weight=3];
245[label="Pos (Succ wx400)",fontsize=16,color="green",shape="box"];246[label="wx34",fontsize=16,color="green",shape="box"];1182 -> 1947[label="",style="dashed", color="red", weight=0];
1182[label="lookupFM1 (Neg (Succ wx117)) wx118 wx119 wx120 wx121 (Neg (Succ wx122)) (primCmpNat (Succ wx117) (Succ wx122) == GT)",fontsize=16,color="magenta"];1182 -> 1948[label="",style="dashed", color="magenta", weight=3];
1182 -> 1949[label="",style="dashed", color="magenta", weight=3];
1182 -> 1950[label="",style="dashed", color="magenta", weight=3];
1182 -> 1951[label="",style="dashed", color="magenta", weight=3];
1182 -> 1952[label="",style="dashed", color="magenta", weight=3];
1182 -> 1953[label="",style="dashed", color="magenta", weight=3];
1182 -> 1954[label="",style="dashed", color="magenta", weight=3];
1182 -> 1955[label="",style="dashed", color="magenta", weight=3];
257[label="Neg Zero",fontsize=16,color="green",shape="box"];258[label="wx34",fontsize=16,color="green",shape="box"];1857[label="wx111",fontsize=16,color="green",shape="box"];1858[label="Succ wx113",fontsize=16,color="green",shape="box"];1859[label="wx110",fontsize=16,color="green",shape="box"];1860[label="Succ wx108",fontsize=16,color="green",shape="box"];1861[label="wx112",fontsize=16,color="green",shape="box"];1862[label="wx108",fontsize=16,color="green",shape="box"];1863[label="wx113",fontsize=16,color="green",shape="box"];1864[label="wx109",fontsize=16,color="green",shape="box"];1856[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat wx234 wx235 == GT)",fontsize=16,color="burlywood",shape="triangle"];2134[label="wx234/Succ wx2340",fontsize=10,color="white",style="solid",shape="box"];1856 -> 2134[label="",style="solid", color="burlywood", weight=9];
2134 -> 1945[label="",style="solid", color="burlywood", weight=3];
2135[label="wx234/Zero",fontsize=10,color="white",style="solid",shape="box"];1856 -> 2135[label="",style="solid", color="burlywood", weight=9];
2135 -> 1946[label="",style="solid", color="burlywood", weight=3];
1948[label="wx122",fontsize=16,color="green",shape="box"];1949[label="wx119",fontsize=16,color="green",shape="box"];1950[label="wx118",fontsize=16,color="green",shape="box"];1951[label="Succ wx117",fontsize=16,color="green",shape="box"];1952[label="wx117",fontsize=16,color="green",shape="box"];1953[label="Succ wx122",fontsize=16,color="green",shape="box"];1954[label="wx120",fontsize=16,color="green",shape="box"];1955[label="wx121",fontsize=16,color="green",shape="box"];1947[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat wx243 wx244 == GT)",fontsize=16,color="burlywood",shape="triangle"];2136[label="wx243/Succ wx2430",fontsize=10,color="white",style="solid",shape="box"];1947 -> 2136[label="",style="solid", color="burlywood", weight=9];
2136 -> 2036[label="",style="solid", color="burlywood", weight=3];
2137[label="wx243/Zero",fontsize=10,color="white",style="solid",shape="box"];1947 -> 2137[label="",style="solid", color="burlywood", weight=9];
2137 -> 2037[label="",style="solid", color="burlywood", weight=3];
1945[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat (Succ wx2340) wx235 == GT)",fontsize=16,color="burlywood",shape="box"];2138[label="wx235/Succ wx2350",fontsize=10,color="white",style="solid",shape="box"];1945 -> 2138[label="",style="solid", color="burlywood", weight=9];
2138 -> 2038[label="",style="solid", color="burlywood", weight=3];
2139[label="wx235/Zero",fontsize=10,color="white",style="solid",shape="box"];1945 -> 2139[label="",style="solid", color="burlywood", weight=9];
2139 -> 2039[label="",style="solid", color="burlywood", weight=3];
1946[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat Zero wx235 == GT)",fontsize=16,color="burlywood",shape="box"];2140[label="wx235/Succ wx2350",fontsize=10,color="white",style="solid",shape="box"];1946 -> 2140[label="",style="solid", color="burlywood", weight=9];
2140 -> 2040[label="",style="solid", color="burlywood", weight=3];
2141[label="wx235/Zero",fontsize=10,color="white",style="solid",shape="box"];1946 -> 2141[label="",style="solid", color="burlywood", weight=9];
2141 -> 2041[label="",style="solid", color="burlywood", weight=3];
2036[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat (Succ wx2430) wx244 == GT)",fontsize=16,color="burlywood",shape="box"];2142[label="wx244/Succ wx2440",fontsize=10,color="white",style="solid",shape="box"];2036 -> 2142[label="",style="solid", color="burlywood", weight=9];
2142 -> 2042[label="",style="solid", color="burlywood", weight=3];
2143[label="wx244/Zero",fontsize=10,color="white",style="solid",shape="box"];2036 -> 2143[label="",style="solid", color="burlywood", weight=9];
2143 -> 2043[label="",style="solid", color="burlywood", weight=3];
2037[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat Zero wx244 == GT)",fontsize=16,color="burlywood",shape="box"];2144[label="wx244/Succ wx2440",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2144[label="",style="solid", color="burlywood", weight=9];
2144 -> 2044[label="",style="solid", color="burlywood", weight=3];
2145[label="wx244/Zero",fontsize=10,color="white",style="solid",shape="box"];2037 -> 2145[label="",style="solid", color="burlywood", weight=9];
2145 -> 2045[label="",style="solid", color="burlywood", weight=3];
2038[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat (Succ wx2340) (Succ wx2350) == GT)",fontsize=16,color="black",shape="box"];2038 -> 2046[label="",style="solid", color="black", weight=3];
2039[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat (Succ wx2340) Zero == GT)",fontsize=16,color="black",shape="box"];2039 -> 2047[label="",style="solid", color="black", weight=3];
2040[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat Zero (Succ wx2350) == GT)",fontsize=16,color="black",shape="box"];2040 -> 2048[label="",style="solid", color="black", weight=3];
2041[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];2041 -> 2049[label="",style="solid", color="black", weight=3];
2042[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat (Succ wx2430) (Succ wx2440) == GT)",fontsize=16,color="black",shape="box"];2042 -> 2050[label="",style="solid", color="black", weight=3];
2043[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat (Succ wx2430) Zero == GT)",fontsize=16,color="black",shape="box"];2043 -> 2051[label="",style="solid", color="black", weight=3];
2044[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat Zero (Succ wx2440) == GT)",fontsize=16,color="black",shape="box"];2044 -> 2052[label="",style="solid", color="black", weight=3];
2045[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];2045 -> 2053[label="",style="solid", color="black", weight=3];
2046 -> 1856[label="",style="dashed", color="red", weight=0];
2046[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (primCmpNat wx2340 wx2350 == GT)",fontsize=16,color="magenta"];2046 -> 2054[label="",style="dashed", color="magenta", weight=3];
2046 -> 2055[label="",style="dashed", color="magenta", weight=3];
2047[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (GT == GT)",fontsize=16,color="black",shape="box"];2047 -> 2056[label="",style="solid", color="black", weight=3];
2048[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (LT == GT)",fontsize=16,color="black",shape="box"];2048 -> 2057[label="",style="solid", color="black", weight=3];
2049[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) (EQ == GT)",fontsize=16,color="black",shape="box"];2049 -> 2058[label="",style="solid", color="black", weight=3];
2050 -> 1947[label="",style="dashed", color="red", weight=0];
2050[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (primCmpNat wx2430 wx2440 == GT)",fontsize=16,color="magenta"];2050 -> 2059[label="",style="dashed", color="magenta", weight=3];
2050 -> 2060[label="",style="dashed", color="magenta", weight=3];
2051[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (GT == GT)",fontsize=16,color="black",shape="box"];2051 -> 2061[label="",style="solid", color="black", weight=3];
2052[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (LT == GT)",fontsize=16,color="black",shape="box"];2052 -> 2062[label="",style="solid", color="black", weight=3];
2053[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) (EQ == GT)",fontsize=16,color="black",shape="box"];2053 -> 2063[label="",style="solid", color="black", weight=3];
2054[label="wx2340",fontsize=16,color="green",shape="box"];2055[label="wx2350",fontsize=16,color="green",shape="box"];2056[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) True",fontsize=16,color="black",shape="box"];2056 -> 2064[label="",style="solid", color="black", weight=3];
2057[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) False",fontsize=16,color="black",shape="triangle"];2057 -> 2065[label="",style="solid", color="black", weight=3];
2058 -> 2057[label="",style="dashed", color="red", weight=0];
2058[label="lookupFM1 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) False",fontsize=16,color="magenta"];2059[label="wx2430",fontsize=16,color="green",shape="box"];2060[label="wx2440",fontsize=16,color="green",shape="box"];2061[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) True",fontsize=16,color="black",shape="box"];2061 -> 2066[label="",style="solid", color="black", weight=3];
2062[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) False",fontsize=16,color="black",shape="triangle"];2062 -> 2067[label="",style="solid", color="black", weight=3];
2063 -> 2062[label="",style="dashed", color="red", weight=0];
2063[label="lookupFM1 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) False",fontsize=16,color="magenta"];2064 -> 4[label="",style="dashed", color="red", weight=0];
2064[label="lookupFM wx232 (Pos (Succ wx233))",fontsize=16,color="magenta"];2064 -> 2068[label="",style="dashed", color="magenta", weight=3];
2064 -> 2069[label="",style="dashed", color="magenta", weight=3];
2065[label="lookupFM0 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) otherwise",fontsize=16,color="black",shape="box"];2065 -> 2070[label="",style="solid", color="black", weight=3];
2066 -> 4[label="",style="dashed", color="red", weight=0];
2066[label="lookupFM wx241 (Neg (Succ wx242))",fontsize=16,color="magenta"];2066 -> 2071[label="",style="dashed", color="magenta", weight=3];
2066 -> 2072[label="",style="dashed", color="magenta", weight=3];
2067[label="lookupFM0 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) otherwise",fontsize=16,color="black",shape="box"];2067 -> 2073[label="",style="solid", color="black", weight=3];
2068[label="Pos (Succ wx233)",fontsize=16,color="green",shape="box"];2069[label="wx232",fontsize=16,color="green",shape="box"];2070[label="lookupFM0 (Pos (Succ wx228)) wx229 wx230 wx231 wx232 (Pos (Succ wx233)) True",fontsize=16,color="black",shape="box"];2070 -> 2074[label="",style="solid", color="black", weight=3];
2071[label="Neg (Succ wx242)",fontsize=16,color="green",shape="box"];2072[label="wx241",fontsize=16,color="green",shape="box"];2073[label="lookupFM0 (Neg (Succ wx237)) wx238 wx239 wx240 wx241 (Neg (Succ wx242)) True",fontsize=16,color="black",shape="box"];2073 -> 2075[label="",style="solid", color="black", weight=3];
2074[label="Just wx229",fontsize=16,color="green",shape="box"];2075[label="Just wx238",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

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

new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) → new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) → new_lookupFM(wx33, Pos(Zero), bb)
new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) → new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) → new_lookupFM(wx232, Pos(Succ(wx233)), ba)
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM2(wx3000, wx31, wx32, wx33, wx34, wx400, wx400, wx3000, bb)
new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM(wx34, Pos(Succ(wx400)), bb)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) → new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) → new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) → new_lookupFM(wx34, Pos(Zero), bb)
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM21(wx3000, wx31, wx32, wx33, wx34, wx400, wx3000, wx400, bb)
new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) → new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM(wx33, Neg(Succ(wx400)), bb)
new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) → new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) → new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM(wx33, Neg(Succ(wx400)), bb)
new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) → new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) → new_lookupFM(wx111, Pos(Succ(wx113)), h)
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) → new_lookupFM(wx33, Neg(Zero), bb)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) → new_lookupFM(wx120, Neg(Succ(wx122)), bc)
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Zero, h) → new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM(wx34, Pos(Succ(wx400)), bb)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Zero, bc) → new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) → new_lookupFM(wx241, Neg(Succ(wx242)), bd)
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) → new_lookupFM(wx34, Neg(Zero), bb)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) → new_lookupFM(wx33, Neg(Zero), bb)
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) → new_lookupFM(wx34, Neg(Zero), bb)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) → new_lookupFM(wx34, Neg(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Zero), bb) → new_lookupFM(wx33, Neg(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM(wx33, Neg(Succ(wx400)), bb)
new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) → new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) → new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) → new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) → new_lookupFM(wx120, Neg(Succ(wx122)), bc)
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM21(wx3000, wx31, wx32, wx33, wx34, wx400, wx3000, wx400, bb)
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Zero, bc) → new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM(wx33, Neg(Succ(wx400)), bb)
new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) → new_lookupFM(wx241, Neg(Succ(wx242)), bd)
new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) → new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)

From the DPs we obtained the following set of size-change graphs:

new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Succ(wx2440), bd) → new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, wx2430, wx2440, bd)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Zero, bc) → new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7
new_lookupFM10(wx237, wx238, wx239, wx240, wx241, wx242, Succ(wx2430), Zero, bd) → new_lookupFM(wx241, Neg(Succ(wx242)), bd)
The graph contains the following edges 5 >= 1, 9 >= 3
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Zero, bc) → new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9
new_lookupFM22(wx117, wx118, wx119, wx120, wx121, wx122, bc) → new_lookupFM10(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx117), Succ(wx122), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM21(wx3000, wx31, wx32, wx33, wx34, wx400, wx3000, wx400, bb)
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 1 > 7, 2 > 8, 3 >= 9
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Zero, Succ(wx1240), bc) → new_lookupFM(wx120, Neg(Succ(wx122)), bc)
The graph contains the following edges 4 >= 1, 9 >= 3
new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, Succ(wx1230), Succ(wx1240), bc) → new_lookupFM21(wx117, wx118, wx119, wx120, wx121, wx122, wx1230, wx1240, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
new_lookupFM(Branch(Neg(Zero), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM(wx33, Neg(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
new_lookupFM(Branch(Pos(wx300), wx31, wx32, wx33, wx34), Neg(Succ(wx400)), bb) → new_lookupFM(wx33, Neg(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) → new_lookupFM(wx33, Pos(Zero), bb)
new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) → new_lookupFM(wx34, Pos(Zero), bb)

From the DPs we obtained the following set of size-change graphs:

new_lookupFM(Branch(Neg(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) → new_lookupFM(wx34, Pos(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Zero), bb) → new_lookupFM(wx33, Pos(Zero), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ QDP

              ↳ DependencyGraphProof

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) → new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) → new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) → new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) → new_lookupFM(wx232, Pos(Succ(wx233)), ba)
new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) → new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM(wx34, Pos(Succ(wx400)), bb)
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) → new_lookupFM(wx111, Pos(Succ(wx113)), h)
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM2(wx3000, wx31, wx32, wx33, wx34, wx400, wx400, wx3000, bb)
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Zero, h) → new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM(wx34, Pos(Succ(wx400)), bb)

From the DPs we obtained the following set of size-change graphs:

new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Succ(wx2350), ba) → new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, wx2340, wx2350, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Zero, h) → new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7
new_lookupFM1(wx228, wx229, wx230, wx231, wx232, wx233, Succ(wx2340), Zero, ba) → new_lookupFM(wx232, Pos(Succ(wx233)), ba)
The graph contains the following edges 5 >= 1, 9 >= 3
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Zero, h) → new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9
new_lookupFM20(wx108, wx109, wx110, wx111, wx112, wx113, h) → new_lookupFM1(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx113), Succ(wx108), h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9
new_lookupFM(Branch(Pos(Succ(wx3000)), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM2(wx3000, wx31, wx32, wx33, wx34, wx400, wx400, wx3000, bb)
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 > 6, 2 > 7, 1 > 8, 3 >= 9
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Zero, Succ(wx1150), h) → new_lookupFM(wx111, Pos(Succ(wx113)), h)
The graph contains the following edges 4 >= 1, 9 >= 3
new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, Succ(wx1140), Succ(wx1150), h) → new_lookupFM2(wx108, wx109, wx110, wx111, wx112, wx113, wx1140, wx1150, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9
new_lookupFM(Branch(Neg(wx300), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM(wx34, Pos(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
new_lookupFM(Branch(Pos(Zero), wx31, wx32, wx33, wx34), Pos(Succ(wx400)), bb) → new_lookupFM(wx34, Pos(Succ(wx400)), bb)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

lookupFM	EmptyFM key	= lookupFM4 EmptyFM key
lookupFM	(Branch key elt vw fm_l fm_r) key_to_find	= lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find

lookupFM2	key elt vw fm_l fm_r key_to_find True	= lookupFM fm_l key_to_find
lookupFM2	key elt vw fm_l fm_r key_to_find False	= lookupFM1 key elt vw fm_l fm_r key_to_find (key_to_find > key)

lookupFM1	key elt vw fm_l fm_r key_to_find True	= lookupFM fm_r key_to_find
lookupFM1	key elt vw fm_l fm_r key_to_find False	= lookupFM0 key elt vw fm_l fm_r key_to_find otherwise

lookupFM4	EmptyFM key	= Nothing
lookupFM4	wv ww	= lookupFM3 wv ww