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

YES 1.124 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

((lookup :: Int -> [(Int,a)] -> Maybe a) :: Int -> [(Int,a)] -> Maybe a)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

((lookup :: Int -> [(Int,a)] -> Maybe a) :: Int -> [(Int,a)] -> Maybe a)

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

lookup k [] = Nothing

lookup k ((x,y) : xys)

| k == x

= Just y

| otherwise

= lookup k xys

is transformed to

lookup k [] = lookup3 k []

lookup k ((x,y) : xys) = lookup2 k ((x,y) : xys)

lookup0 k x y xys True = lookup k xys

lookup1 k x y xys True = Just y

lookup1 k x y xys False = lookup0 k x y xys otherwise

lookup2 k ((x,y) : xys) = lookup1 k x y xys (k == x)

lookup3 k [] = Nothing

lookup3 ww wx = lookup2 ww wx

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

(lookup :: Int -> [(Int,a)] -> Maybe a)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookup",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookup wy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookup wy3 wy4",fontsize=16,color="burlywood",shape="triangle"];778[label="wy4/wy40 : wy41",fontsize=10,color="white",style="solid",shape="box"];4 -> 778[label="",style="solid", color="burlywood", weight=9];
778 -> 5[label="",style="solid", color="burlywood", weight=3];
779[label="wy4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 779[label="",style="solid", color="burlywood", weight=9];
779 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookup wy3 (wy40 : wy41)",fontsize=16,color="burlywood",shape="box"];780[label="wy40/(wy400,wy401)",fontsize=10,color="white",style="solid",shape="box"];5 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup wy3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookup wy3 ((wy400,wy401) : wy41)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 wy3 []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="lookup2 wy3 ((wy400,wy401) : wy41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 wy3 wy400 wy401 wy41 (wy3 == wy400)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="lookup1 wy3 wy400 wy401 wy41 (primEqInt wy3 wy400)",fontsize=16,color="burlywood",shape="box"];781[label="wy3/Pos wy30",fontsize=10,color="white",style="solid",shape="box"];12 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 13[label="",style="solid", color="burlywood", weight=3];
782[label="wy3/Neg wy30",fontsize=10,color="white",style="solid",shape="box"];12 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 14[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 (Pos wy30) wy400 wy401 wy41 (primEqInt (Pos wy30) wy400)",fontsize=16,color="burlywood",shape="box"];783[label="wy30/Succ wy300",fontsize=10,color="white",style="solid",shape="box"];13 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 15[label="",style="solid", color="burlywood", weight=3];
784[label="wy30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 16[label="",style="solid", color="burlywood", weight=3];
14[label="lookup1 (Neg wy30) wy400 wy401 wy41 (primEqInt (Neg wy30) wy400)",fontsize=16,color="burlywood",shape="box"];785[label="wy30/Succ wy300",fontsize=10,color="white",style="solid",shape="box"];14 -> 785[label="",style="solid", color="burlywood", weight=9];
785 -> 17[label="",style="solid", color="burlywood", weight=3];
786[label="wy30/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 786[label="",style="solid", color="burlywood", weight=9];
786 -> 18[label="",style="solid", color="burlywood", weight=3];
15[label="lookup1 (Pos (Succ wy300)) wy400 wy401 wy41 (primEqInt (Pos (Succ wy300)) wy400)",fontsize=16,color="burlywood",shape="box"];787[label="wy400/Pos wy4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 787[label="",style="solid", color="burlywood", weight=9];
787 -> 19[label="",style="solid", color="burlywood", weight=3];
788[label="wy400/Neg wy4000",fontsize=10,color="white",style="solid",shape="box"];15 -> 788[label="",style="solid", color="burlywood", weight=9];
788 -> 20[label="",style="solid", color="burlywood", weight=3];
16[label="lookup1 (Pos Zero) wy400 wy401 wy41 (primEqInt (Pos Zero) wy400)",fontsize=16,color="burlywood",shape="box"];789[label="wy400/Pos wy4000",fontsize=10,color="white",style="solid",shape="box"];16 -> 789[label="",style="solid", color="burlywood", weight=9];
789 -> 21[label="",style="solid", color="burlywood", weight=3];
790[label="wy400/Neg wy4000",fontsize=10,color="white",style="solid",shape="box"];16 -> 790[label="",style="solid", color="burlywood", weight=9];
790 -> 22[label="",style="solid", color="burlywood", weight=3];
17[label="lookup1 (Neg (Succ wy300)) wy400 wy401 wy41 (primEqInt (Neg (Succ wy300)) wy400)",fontsize=16,color="burlywood",shape="box"];791[label="wy400/Pos wy4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 791[label="",style="solid", color="burlywood", weight=9];
791 -> 23[label="",style="solid", color="burlywood", weight=3];
792[label="wy400/Neg wy4000",fontsize=10,color="white",style="solid",shape="box"];17 -> 792[label="",style="solid", color="burlywood", weight=9];
792 -> 24[label="",style="solid", color="burlywood", weight=3];
18[label="lookup1 (Neg Zero) wy400 wy401 wy41 (primEqInt (Neg Zero) wy400)",fontsize=16,color="burlywood",shape="box"];793[label="wy400/Pos wy4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 793[label="",style="solid", color="burlywood", weight=9];
793 -> 25[label="",style="solid", color="burlywood", weight=3];
794[label="wy400/Neg wy4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 794[label="",style="solid", color="burlywood", weight=9];
794 -> 26[label="",style="solid", color="burlywood", weight=3];
19[label="lookup1 (Pos (Succ wy300)) (Pos wy4000) wy401 wy41 (primEqInt (Pos (Succ wy300)) (Pos wy4000))",fontsize=16,color="burlywood",shape="box"];795[label="wy4000/Succ wy40000",fontsize=10,color="white",style="solid",shape="box"];19 -> 795[label="",style="solid", color="burlywood", weight=9];
795 -> 27[label="",style="solid", color="burlywood", weight=3];
796[label="wy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 796[label="",style="solid", color="burlywood", weight=9];
796 -> 28[label="",style="solid", color="burlywood", weight=3];
20[label="lookup1 (Pos (Succ wy300)) (Neg wy4000) wy401 wy41 (primEqInt (Pos (Succ wy300)) (Neg wy4000))",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
21[label="lookup1 (Pos Zero) (Pos wy4000) wy401 wy41 (primEqInt (Pos Zero) (Pos wy4000))",fontsize=16,color="burlywood",shape="box"];797[label="wy4000/Succ wy40000",fontsize=10,color="white",style="solid",shape="box"];21 -> 797[label="",style="solid", color="burlywood", weight=9];
797 -> 30[label="",style="solid", color="burlywood", weight=3];
798[label="wy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 798[label="",style="solid", color="burlywood", weight=9];
798 -> 31[label="",style="solid", color="burlywood", weight=3];
22[label="lookup1 (Pos Zero) (Neg wy4000) wy401 wy41 (primEqInt (Pos Zero) (Neg wy4000))",fontsize=16,color="burlywood",shape="box"];799[label="wy4000/Succ wy40000",fontsize=10,color="white",style="solid",shape="box"];22 -> 799[label="",style="solid", color="burlywood", weight=9];
799 -> 32[label="",style="solid", color="burlywood", weight=3];
800[label="wy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 800[label="",style="solid", color="burlywood", weight=9];
800 -> 33[label="",style="solid", color="burlywood", weight=3];
23[label="lookup1 (Neg (Succ wy300)) (Pos wy4000) wy401 wy41 (primEqInt (Neg (Succ wy300)) (Pos wy4000))",fontsize=16,color="black",shape="box"];23 -> 34[label="",style="solid", color="black", weight=3];
24[label="lookup1 (Neg (Succ wy300)) (Neg wy4000) wy401 wy41 (primEqInt (Neg (Succ wy300)) (Neg wy4000))",fontsize=16,color="burlywood",shape="box"];801[label="wy4000/Succ wy40000",fontsize=10,color="white",style="solid",shape="box"];24 -> 801[label="",style="solid", color="burlywood", weight=9];
801 -> 35[label="",style="solid", color="burlywood", weight=3];
802[label="wy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];24 -> 802[label="",style="solid", color="burlywood", weight=9];
802 -> 36[label="",style="solid", color="burlywood", weight=3];
25[label="lookup1 (Neg Zero) (Pos wy4000) wy401 wy41 (primEqInt (Neg Zero) (Pos wy4000))",fontsize=16,color="burlywood",shape="box"];803[label="wy4000/Succ wy40000",fontsize=10,color="white",style="solid",shape="box"];25 -> 803[label="",style="solid", color="burlywood", weight=9];
803 -> 37[label="",style="solid", color="burlywood", weight=3];
804[label="wy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 804[label="",style="solid", color="burlywood", weight=9];
804 -> 38[label="",style="solid", color="burlywood", weight=3];
26[label="lookup1 (Neg Zero) (Neg wy4000) wy401 wy41 (primEqInt (Neg Zero) (Neg wy4000))",fontsize=16,color="burlywood",shape="box"];805[label="wy4000/Succ wy40000",fontsize=10,color="white",style="solid",shape="box"];26 -> 805[label="",style="solid", color="burlywood", weight=9];
805 -> 39[label="",style="solid", color="burlywood", weight=3];
806[label="wy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 806[label="",style="solid", color="burlywood", weight=9];
806 -> 40[label="",style="solid", color="burlywood", weight=3];
27[label="lookup1 (Pos (Succ wy300)) (Pos (Succ wy40000)) wy401 wy41 (primEqInt (Pos (Succ wy300)) (Pos (Succ wy40000)))",fontsize=16,color="black",shape="box"];27 -> 41[label="",style="solid", color="black", weight=3];
28[label="lookup1 (Pos (Succ wy300)) (Pos Zero) wy401 wy41 (primEqInt (Pos (Succ wy300)) (Pos Zero))",fontsize=16,color="black",shape="box"];28 -> 42[label="",style="solid", color="black", weight=3];
29[label="lookup1 (Pos (Succ wy300)) (Neg wy4000) wy401 wy41 False",fontsize=16,color="black",shape="box"];29 -> 43[label="",style="solid", color="black", weight=3];
30[label="lookup1 (Pos Zero) (Pos (Succ wy40000)) wy401 wy41 (primEqInt (Pos Zero) (Pos (Succ wy40000)))",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3];
31[label="lookup1 (Pos Zero) (Pos Zero) wy401 wy41 (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];31 -> 45[label="",style="solid", color="black", weight=3];
32[label="lookup1 (Pos Zero) (Neg (Succ wy40000)) wy401 wy41 (primEqInt (Pos Zero) (Neg (Succ wy40000)))",fontsize=16,color="black",shape="box"];32 -> 46[label="",style="solid", color="black", weight=3];
33[label="lookup1 (Pos Zero) (Neg Zero) wy401 wy41 (primEqInt (Pos Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];33 -> 47[label="",style="solid", color="black", weight=3];
34[label="lookup1 (Neg (Succ wy300)) (Pos wy4000) wy401 wy41 False",fontsize=16,color="black",shape="box"];34 -> 48[label="",style="solid", color="black", weight=3];
35[label="lookup1 (Neg (Succ wy300)) (Neg (Succ wy40000)) wy401 wy41 (primEqInt (Neg (Succ wy300)) (Neg (Succ wy40000)))",fontsize=16,color="black",shape="box"];35 -> 49[label="",style="solid", color="black", weight=3];
36[label="lookup1 (Neg (Succ wy300)) (Neg Zero) wy401 wy41 (primEqInt (Neg (Succ wy300)) (Neg Zero))",fontsize=16,color="black",shape="box"];36 -> 50[label="",style="solid", color="black", weight=3];
37[label="lookup1 (Neg Zero) (Pos (Succ wy40000)) wy401 wy41 (primEqInt (Neg Zero) (Pos (Succ wy40000)))",fontsize=16,color="black",shape="box"];37 -> 51[label="",style="solid", color="black", weight=3];
38[label="lookup1 (Neg Zero) (Pos Zero) wy401 wy41 (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];38 -> 52[label="",style="solid", color="black", weight=3];
39[label="lookup1 (Neg Zero) (Neg (Succ wy40000)) wy401 wy41 (primEqInt (Neg Zero) (Neg (Succ wy40000)))",fontsize=16,color="black",shape="box"];39 -> 53[label="",style="solid", color="black", weight=3];
40[label="lookup1 (Neg Zero) (Neg Zero) wy401 wy41 (primEqInt (Neg Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];40 -> 54[label="",style="solid", color="black", weight=3];
41 -> 620[label="",style="dashed", color="red", weight=0];
41[label="lookup1 (Pos (Succ wy300)) (Pos (Succ wy40000)) wy401 wy41 (primEqNat wy300 wy40000)",fontsize=16,color="magenta"];41 -> 621[label="",style="dashed", color="magenta", weight=3];
41 -> 622[label="",style="dashed", color="magenta", weight=3];
41 -> 623[label="",style="dashed", color="magenta", weight=3];
41 -> 624[label="",style="dashed", color="magenta", weight=3];
41 -> 625[label="",style="dashed", color="magenta", weight=3];
41 -> 626[label="",style="dashed", color="magenta", weight=3];
42[label="lookup1 (Pos (Succ wy300)) (Pos Zero) wy401 wy41 False",fontsize=16,color="black",shape="box"];42 -> 57[label="",style="solid", color="black", weight=3];
43[label="lookup0 (Pos (Succ wy300)) (Neg wy4000) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];43 -> 58[label="",style="solid", color="black", weight=3];
44[label="lookup1 (Pos Zero) (Pos (Succ wy40000)) wy401 wy41 False",fontsize=16,color="black",shape="box"];44 -> 59[label="",style="solid", color="black", weight=3];
45[label="lookup1 (Pos Zero) (Pos Zero) wy401 wy41 True",fontsize=16,color="black",shape="box"];45 -> 60[label="",style="solid", color="black", weight=3];
46[label="lookup1 (Pos Zero) (Neg (Succ wy40000)) wy401 wy41 False",fontsize=16,color="black",shape="box"];46 -> 61[label="",style="solid", color="black", weight=3];
47[label="lookup1 (Pos Zero) (Neg Zero) wy401 wy41 True",fontsize=16,color="black",shape="box"];47 -> 62[label="",style="solid", color="black", weight=3];
48[label="lookup0 (Neg (Succ wy300)) (Pos wy4000) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];48 -> 63[label="",style="solid", color="black", weight=3];
49 -> 683[label="",style="dashed", color="red", weight=0];
49[label="lookup1 (Neg (Succ wy300)) (Neg (Succ wy40000)) wy401 wy41 (primEqNat wy300 wy40000)",fontsize=16,color="magenta"];49 -> 684[label="",style="dashed", color="magenta", weight=3];
49 -> 685[label="",style="dashed", color="magenta", weight=3];
49 -> 686[label="",style="dashed", color="magenta", weight=3];
49 -> 687[label="",style="dashed", color="magenta", weight=3];
49 -> 688[label="",style="dashed", color="magenta", weight=3];
49 -> 689[label="",style="dashed", color="magenta", weight=3];
50[label="lookup1 (Neg (Succ wy300)) (Neg Zero) wy401 wy41 False",fontsize=16,color="black",shape="box"];50 -> 66[label="",style="solid", color="black", weight=3];
51[label="lookup1 (Neg Zero) (Pos (Succ wy40000)) wy401 wy41 False",fontsize=16,color="black",shape="box"];51 -> 67[label="",style="solid", color="black", weight=3];
52[label="lookup1 (Neg Zero) (Pos Zero) wy401 wy41 True",fontsize=16,color="black",shape="box"];52 -> 68[label="",style="solid", color="black", weight=3];
53[label="lookup1 (Neg Zero) (Neg (Succ wy40000)) wy401 wy41 False",fontsize=16,color="black",shape="box"];53 -> 69[label="",style="solid", color="black", weight=3];
54[label="lookup1 (Neg Zero) (Neg Zero) wy401 wy41 True",fontsize=16,color="black",shape="box"];54 -> 70[label="",style="solid", color="black", weight=3];
621[label="wy40000",fontsize=16,color="green",shape="box"];622[label="wy41",fontsize=16,color="green",shape="box"];623[label="wy401",fontsize=16,color="green",shape="box"];624[label="wy300",fontsize=16,color="green",shape="box"];625[label="wy300",fontsize=16,color="green",shape="box"];626[label="wy40000",fontsize=16,color="green",shape="box"];620[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat wy78 wy79)",fontsize=16,color="burlywood",shape="triangle"];809[label="wy78/Succ wy780",fontsize=10,color="white",style="solid",shape="box"];620 -> 809[label="",style="solid", color="burlywood", weight=9];
809 -> 681[label="",style="solid", color="burlywood", weight=3];
810[label="wy78/Zero",fontsize=10,color="white",style="solid",shape="box"];620 -> 810[label="",style="solid", color="burlywood", weight=9];
810 -> 682[label="",style="solid", color="burlywood", weight=3];
57[label="lookup0 (Pos (Succ wy300)) (Pos Zero) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3];
58[label="lookup0 (Pos (Succ wy300)) (Neg wy4000) wy401 wy41 True",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3];
59[label="lookup0 (Pos Zero) (Pos (Succ wy40000)) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];59 -> 77[label="",style="solid", color="black", weight=3];
60[label="Just wy401",fontsize=16,color="green",shape="box"];61[label="lookup0 (Pos Zero) (Neg (Succ wy40000)) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];61 -> 78[label="",style="solid", color="black", weight=3];
62[label="Just wy401",fontsize=16,color="green",shape="box"];63[label="lookup0 (Neg (Succ wy300)) (Pos wy4000) wy401 wy41 True",fontsize=16,color="black",shape="box"];63 -> 79[label="",style="solid", color="black", weight=3];
684[label="wy41",fontsize=16,color="green",shape="box"];685[label="wy40000",fontsize=16,color="green",shape="box"];686[label="wy300",fontsize=16,color="green",shape="box"];687[label="wy40000",fontsize=16,color="green",shape="box"];688[label="wy300",fontsize=16,color="green",shape="box"];689[label="wy401",fontsize=16,color="green",shape="box"];683[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat wy85 wy86)",fontsize=16,color="burlywood",shape="triangle"];811[label="wy85/Succ wy850",fontsize=10,color="white",style="solid",shape="box"];683 -> 811[label="",style="solid", color="burlywood", weight=9];
811 -> 744[label="",style="solid", color="burlywood", weight=3];
812[label="wy85/Zero",fontsize=10,color="white",style="solid",shape="box"];683 -> 812[label="",style="solid", color="burlywood", weight=9];
812 -> 745[label="",style="solid", color="burlywood", weight=3];
66[label="lookup0 (Neg (Succ wy300)) (Neg Zero) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];66 -> 84[label="",style="solid", color="black", weight=3];
67[label="lookup0 (Neg Zero) (Pos (Succ wy40000)) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];67 -> 85[label="",style="solid", color="black", weight=3];
68[label="Just wy401",fontsize=16,color="green",shape="box"];69[label="lookup0 (Neg Zero) (Neg (Succ wy40000)) wy401 wy41 otherwise",fontsize=16,color="black",shape="box"];69 -> 86[label="",style="solid", color="black", weight=3];
70[label="Just wy401",fontsize=16,color="green",shape="box"];681[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat (Succ wy780) wy79)",fontsize=16,color="burlywood",shape="box"];813[label="wy79/Succ wy790",fontsize=10,color="white",style="solid",shape="box"];681 -> 813[label="",style="solid", color="burlywood", weight=9];
813 -> 746[label="",style="solid", color="burlywood", weight=3];
814[label="wy79/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 814[label="",style="solid", color="burlywood", weight=9];
814 -> 747[label="",style="solid", color="burlywood", weight=3];
682[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat Zero wy79)",fontsize=16,color="burlywood",shape="box"];815[label="wy79/Succ wy790",fontsize=10,color="white",style="solid",shape="box"];682 -> 815[label="",style="solid", color="burlywood", weight=9];
815 -> 748[label="",style="solid", color="burlywood", weight=3];
816[label="wy79/Zero",fontsize=10,color="white",style="solid",shape="box"];682 -> 816[label="",style="solid", color="burlywood", weight=9];
816 -> 749[label="",style="solid", color="burlywood", weight=3];
75[label="lookup0 (Pos (Succ wy300)) (Pos Zero) wy401 wy41 True",fontsize=16,color="black",shape="box"];75 -> 91[label="",style="solid", color="black", weight=3];
76 -> 4[label="",style="dashed", color="red", weight=0];
76[label="lookup (Pos (Succ wy300)) wy41",fontsize=16,color="magenta"];76 -> 92[label="",style="dashed", color="magenta", weight=3];
76 -> 93[label="",style="dashed", color="magenta", weight=3];
77[label="lookup0 (Pos Zero) (Pos (Succ wy40000)) wy401 wy41 True",fontsize=16,color="black",shape="box"];77 -> 94[label="",style="solid", color="black", weight=3];
78[label="lookup0 (Pos Zero) (Neg (Succ wy40000)) wy401 wy41 True",fontsize=16,color="black",shape="box"];78 -> 95[label="",style="solid", color="black", weight=3];
79 -> 4[label="",style="dashed", color="red", weight=0];
79[label="lookup (Neg (Succ wy300)) wy41",fontsize=16,color="magenta"];79 -> 96[label="",style="dashed", color="magenta", weight=3];
79 -> 97[label="",style="dashed", color="magenta", weight=3];
744[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat (Succ wy850) wy86)",fontsize=16,color="burlywood",shape="box"];819[label="wy86/Succ wy860",fontsize=10,color="white",style="solid",shape="box"];744 -> 819[label="",style="solid", color="burlywood", weight=9];
819 -> 750[label="",style="solid", color="burlywood", weight=3];
820[label="wy86/Zero",fontsize=10,color="white",style="solid",shape="box"];744 -> 820[label="",style="solid", color="burlywood", weight=9];
820 -> 751[label="",style="solid", color="burlywood", weight=3];
745[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat Zero wy86)",fontsize=16,color="burlywood",shape="box"];821[label="wy86/Succ wy860",fontsize=10,color="white",style="solid",shape="box"];745 -> 821[label="",style="solid", color="burlywood", weight=9];
821 -> 752[label="",style="solid", color="burlywood", weight=3];
822[label="wy86/Zero",fontsize=10,color="white",style="solid",shape="box"];745 -> 822[label="",style="solid", color="burlywood", weight=9];
822 -> 753[label="",style="solid", color="burlywood", weight=3];
84[label="lookup0 (Neg (Succ wy300)) (Neg Zero) wy401 wy41 True",fontsize=16,color="black",shape="box"];84 -> 102[label="",style="solid", color="black", weight=3];
85[label="lookup0 (Neg Zero) (Pos (Succ wy40000)) wy401 wy41 True",fontsize=16,color="black",shape="box"];85 -> 103[label="",style="solid", color="black", weight=3];
86[label="lookup0 (Neg Zero) (Neg (Succ wy40000)) wy401 wy41 True",fontsize=16,color="black",shape="box"];86 -> 104[label="",style="solid", color="black", weight=3];
746[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat (Succ wy780) (Succ wy790))",fontsize=16,color="black",shape="box"];746 -> 754[label="",style="solid", color="black", weight=3];
747[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat (Succ wy780) Zero)",fontsize=16,color="black",shape="box"];747 -> 755[label="",style="solid", color="black", weight=3];
748[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat Zero (Succ wy790))",fontsize=16,color="black",shape="box"];748 -> 756[label="",style="solid", color="black", weight=3];
749[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];749 -> 757[label="",style="solid", color="black", weight=3];
91 -> 4[label="",style="dashed", color="red", weight=0];
91[label="lookup (Pos (Succ wy300)) wy41",fontsize=16,color="magenta"];91 -> 110[label="",style="dashed", color="magenta", weight=3];
91 -> 111[label="",style="dashed", color="magenta", weight=3];
92[label="wy41",fontsize=16,color="green",shape="box"];93[label="Pos (Succ wy300)",fontsize=16,color="green",shape="box"];94 -> 4[label="",style="dashed", color="red", weight=0];
94[label="lookup (Pos Zero) wy41",fontsize=16,color="magenta"];94 -> 112[label="",style="dashed", color="magenta", weight=3];
94 -> 113[label="",style="dashed", color="magenta", weight=3];
95 -> 4[label="",style="dashed", color="red", weight=0];
95[label="lookup (Pos Zero) wy41",fontsize=16,color="magenta"];95 -> 114[label="",style="dashed", color="magenta", weight=3];
95 -> 115[label="",style="dashed", color="magenta", weight=3];
96[label="wy41",fontsize=16,color="green",shape="box"];97[label="Neg (Succ wy300)",fontsize=16,color="green",shape="box"];750[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat (Succ wy850) (Succ wy860))",fontsize=16,color="black",shape="box"];750 -> 758[label="",style="solid", color="black", weight=3];
751[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat (Succ wy850) Zero)",fontsize=16,color="black",shape="box"];751 -> 759[label="",style="solid", color="black", weight=3];
752[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat Zero (Succ wy860))",fontsize=16,color="black",shape="box"];752 -> 760[label="",style="solid", color="black", weight=3];
753[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];753 -> 761[label="",style="solid", color="black", weight=3];
102 -> 4[label="",style="dashed", color="red", weight=0];
102[label="lookup (Neg (Succ wy300)) wy41",fontsize=16,color="magenta"];102 -> 121[label="",style="dashed", color="magenta", weight=3];
102 -> 122[label="",style="dashed", color="magenta", weight=3];
103 -> 4[label="",style="dashed", color="red", weight=0];
103[label="lookup (Neg Zero) wy41",fontsize=16,color="magenta"];103 -> 123[label="",style="dashed", color="magenta", weight=3];
103 -> 124[label="",style="dashed", color="magenta", weight=3];
104 -> 4[label="",style="dashed", color="red", weight=0];
104[label="lookup (Neg Zero) wy41",fontsize=16,color="magenta"];104 -> 125[label="",style="dashed", color="magenta", weight=3];
104 -> 126[label="",style="dashed", color="magenta", weight=3];
754 -> 620[label="",style="dashed", color="red", weight=0];
754[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 (primEqNat wy780 wy790)",fontsize=16,color="magenta"];754 -> 762[label="",style="dashed", color="magenta", weight=3];
754 -> 763[label="",style="dashed", color="magenta", weight=3];
755[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 False",fontsize=16,color="black",shape="triangle"];755 -> 764[label="",style="solid", color="black", weight=3];
756 -> 755[label="",style="dashed", color="red", weight=0];
756[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 False",fontsize=16,color="magenta"];757[label="lookup1 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 True",fontsize=16,color="black",shape="box"];757 -> 765[label="",style="solid", color="black", weight=3];
110[label="wy41",fontsize=16,color="green",shape="box"];111[label="Pos (Succ wy300)",fontsize=16,color="green",shape="box"];112[label="wy41",fontsize=16,color="green",shape="box"];113[label="Pos Zero",fontsize=16,color="green",shape="box"];114[label="wy41",fontsize=16,color="green",shape="box"];115[label="Pos Zero",fontsize=16,color="green",shape="box"];758 -> 683[label="",style="dashed", color="red", weight=0];
758[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 (primEqNat wy850 wy860)",fontsize=16,color="magenta"];758 -> 766[label="",style="dashed", color="magenta", weight=3];
758 -> 767[label="",style="dashed", color="magenta", weight=3];
759[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 False",fontsize=16,color="black",shape="triangle"];759 -> 768[label="",style="solid", color="black", weight=3];
760 -> 759[label="",style="dashed", color="red", weight=0];
760[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 False",fontsize=16,color="magenta"];761[label="lookup1 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 True",fontsize=16,color="black",shape="box"];761 -> 769[label="",style="solid", color="black", weight=3];
121[label="wy41",fontsize=16,color="green",shape="box"];122[label="Neg (Succ wy300)",fontsize=16,color="green",shape="box"];123[label="wy41",fontsize=16,color="green",shape="box"];124[label="Neg Zero",fontsize=16,color="green",shape="box"];125[label="wy41",fontsize=16,color="green",shape="box"];126[label="Neg Zero",fontsize=16,color="green",shape="box"];762[label="wy790",fontsize=16,color="green",shape="box"];763[label="wy780",fontsize=16,color="green",shape="box"];764[label="lookup0 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 otherwise",fontsize=16,color="black",shape="box"];764 -> 770[label="",style="solid", color="black", weight=3];
765[label="Just wy76",fontsize=16,color="green",shape="box"];766[label="wy860",fontsize=16,color="green",shape="box"];767[label="wy850",fontsize=16,color="green",shape="box"];768[label="lookup0 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 otherwise",fontsize=16,color="black",shape="box"];768 -> 771[label="",style="solid", color="black", weight=3];
769[label="Just wy83",fontsize=16,color="green",shape="box"];770[label="lookup0 (Pos (Succ wy74)) (Pos (Succ wy75)) wy76 wy77 True",fontsize=16,color="black",shape="box"];770 -> 772[label="",style="solid", color="black", weight=3];
771[label="lookup0 (Neg (Succ wy81)) (Neg (Succ wy82)) wy83 wy84 True",fontsize=16,color="black",shape="box"];771 -> 773[label="",style="solid", color="black", weight=3];
772 -> 4[label="",style="dashed", color="red", weight=0];
772[label="lookup (Pos (Succ wy74)) wy77",fontsize=16,color="magenta"];772 -> 774[label="",style="dashed", color="magenta", weight=3];
772 -> 775[label="",style="dashed", color="magenta", weight=3];
773 -> 4[label="",style="dashed", color="red", weight=0];
773[label="lookup (Neg (Succ wy81)) wy84",fontsize=16,color="magenta"];773 -> 776[label="",style="dashed", color="magenta", weight=3];
773 -> 777[label="",style="dashed", color="magenta", weight=3];
774[label="wy77",fontsize=16,color="green",shape="box"];775[label="Pos (Succ wy74)",fontsize=16,color="green",shape="box"];776[label="wy84",fontsize=16,color="green",shape="box"];777[label="Neg (Succ wy81)",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_lookup11(wy81, wy82, wy83, wy84, Zero, Succ(wy860), bc) → new_lookup12(wy81, wy82, wy83, wy84, bc)
new_lookup(Pos(Zero), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Pos(Zero), wy41, bb)
new_lookup1(wy74, wy75, wy76, wy77, Zero, Succ(wy790), ba) → new_lookup10(wy74, wy75, wy76, wy77, ba)
new_lookup1(wy74, wy75, wy76, wy77, Succ(wy780), Succ(wy790), ba) → new_lookup1(wy74, wy75, wy76, wy77, wy780, wy790, ba)
new_lookup(Neg(Succ(wy300)), :(@2(Pos(wy4000), wy401), wy41), bb) → new_lookup(Neg(Succ(wy300)), wy41, bb)
new_lookup10(wy74, wy75, wy76, wy77, ba) → new_lookup(Pos(Succ(wy74)), wy77, ba)
new_lookup(Pos(Succ(wy300)), :(@2(Neg(wy4000), wy401), wy41), bb) → new_lookup(Pos(Succ(wy300)), wy41, bb)
new_lookup11(wy81, wy82, wy83, wy84, Succ(wy850), Zero, bc) → new_lookup(Neg(Succ(wy81)), wy84, bc)
new_lookup(Pos(Succ(wy300)), :(@2(Pos(Zero), wy401), wy41), bb) → new_lookup(Pos(Succ(wy300)), wy41, bb)
new_lookup(Pos(Zero), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Pos(Zero), wy41, bb)
new_lookup11(wy81, wy82, wy83, wy84, Succ(wy850), Succ(wy860), bc) → new_lookup11(wy81, wy82, wy83, wy84, wy850, wy860, bc)
new_lookup(Neg(Zero), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Neg(Zero), wy41, bb)
new_lookup(Neg(Succ(wy300)), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup11(wy300, wy40000, wy401, wy41, wy300, wy40000, bb)
new_lookup(Neg(Succ(wy300)), :(@2(Neg(Zero), wy401), wy41), bb) → new_lookup(Neg(Succ(wy300)), wy41, bb)
new_lookup12(wy81, wy82, wy83, wy84, bc) → new_lookup(Neg(Succ(wy81)), wy84, bc)
new_lookup1(wy74, wy75, wy76, wy77, Succ(wy780), Zero, ba) → new_lookup(Pos(Succ(wy74)), wy77, ba)
new_lookup(Pos(Succ(wy300)), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup1(wy300, wy40000, wy401, wy41, wy300, wy40000, bb)
new_lookup(Neg(Zero), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Neg(Zero), wy41, 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_lookup(Neg(Zero), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Neg(Zero), wy41, bb)
new_lookup(Neg(Zero), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Neg(Zero), wy41, 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_lookup(Neg(Zero), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Neg(Zero), wy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
new_lookup(Neg(Zero), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Neg(Zero), wy41, 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_lookup1(wy74, wy75, wy76, wy77, Zero, Succ(wy790), ba) → new_lookup10(wy74, wy75, wy76, wy77, ba)
new_lookup1(wy74, wy75, wy76, wy77, Succ(wy780), Succ(wy790), ba) → new_lookup1(wy74, wy75, wy76, wy77, wy780, wy790, ba)
new_lookup(Pos(Succ(wy300)), :(@2(Neg(wy4000), wy401), wy41), bb) → new_lookup(Pos(Succ(wy300)), wy41, bb)
new_lookup10(wy74, wy75, wy76, wy77, ba) → new_lookup(Pos(Succ(wy74)), wy77, ba)
new_lookup1(wy74, wy75, wy76, wy77, Succ(wy780), Zero, ba) → new_lookup(Pos(Succ(wy74)), wy77, ba)
new_lookup(Pos(Succ(wy300)), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup1(wy300, wy40000, wy401, wy41, wy300, wy40000, bb)
new_lookup(Pos(Succ(wy300)), :(@2(Pos(Zero), wy401), wy41), bb) → new_lookup(Pos(Succ(wy300)), wy41, bb)

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

new_lookup1(wy74, wy75, wy76, wy77, Zero, Succ(wy790), ba) → new_lookup10(wy74, wy75, wy76, wy77, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
new_lookup(Pos(Succ(wy300)), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup1(wy300, wy40000, wy401, wy41, wy300, wy40000, bb)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 1 > 5, 2 > 6, 3 >= 7
new_lookup1(wy74, wy75, wy76, wy77, Succ(wy780), Succ(wy790), ba) → new_lookup1(wy74, wy75, wy76, wy77, wy780, wy790, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7
new_lookup1(wy74, wy75, wy76, wy77, Succ(wy780), Zero, ba) → new_lookup(Pos(Succ(wy74)), wy77, ba)
The graph contains the following edges 4 >= 2, 7 >= 3
new_lookup10(wy74, wy75, wy76, wy77, ba) → new_lookup(Pos(Succ(wy74)), wy77, ba)
The graph contains the following edges 4 >= 2, 5 >= 3
new_lookup(Pos(Succ(wy300)), :(@2(Neg(wy4000), wy401), wy41), bb) → new_lookup(Pos(Succ(wy300)), wy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
new_lookup(Pos(Succ(wy300)), :(@2(Pos(Zero), wy401), wy41), bb) → new_lookup(Pos(Succ(wy300)), wy41, 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_lookup(Pos(Zero), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Pos(Zero), wy41, bb)
new_lookup(Pos(Zero), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Pos(Zero), wy41, bb)

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

new_lookup(Pos(Zero), :(@2(Pos(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Pos(Zero), wy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
new_lookup(Pos(Zero), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup(Pos(Zero), wy41, 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_lookup11(wy81, wy82, wy83, wy84, Zero, Succ(wy860), bc) → new_lookup12(wy81, wy82, wy83, wy84, bc)
new_lookup(Neg(Succ(wy300)), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup11(wy300, wy40000, wy401, wy41, wy300, wy40000, bb)
new_lookup(Neg(Succ(wy300)), :(@2(Pos(wy4000), wy401), wy41), bb) → new_lookup(Neg(Succ(wy300)), wy41, bb)
new_lookup(Neg(Succ(wy300)), :(@2(Neg(Zero), wy401), wy41), bb) → new_lookup(Neg(Succ(wy300)), wy41, bb)
new_lookup12(wy81, wy82, wy83, wy84, bc) → new_lookup(Neg(Succ(wy81)), wy84, bc)
new_lookup11(wy81, wy82, wy83, wy84, Succ(wy850), Zero, bc) → new_lookup(Neg(Succ(wy81)), wy84, bc)
new_lookup11(wy81, wy82, wy83, wy84, Succ(wy850), Succ(wy860), bc) → new_lookup11(wy81, wy82, wy83, wy84, wy850, wy860, bc)

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

new_lookup11(wy81, wy82, wy83, wy84, Zero, Succ(wy860), bc) → new_lookup12(wy81, wy82, wy83, wy84, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
new_lookup(Neg(Succ(wy300)), :(@2(Neg(Succ(wy40000)), wy401), wy41), bb) → new_lookup11(wy300, wy40000, wy401, wy41, wy300, wy40000, bb)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 1 > 5, 2 > 6, 3 >= 7
new_lookup11(wy81, wy82, wy83, wy84, Succ(wy850), Succ(wy860), bc) → new_lookup11(wy81, wy82, wy83, wy84, wy850, wy860, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7
new_lookup11(wy81, wy82, wy83, wy84, Succ(wy850), Zero, bc) → new_lookup(Neg(Succ(wy81)), wy84, bc)
The graph contains the following edges 4 >= 2, 7 >= 3
new_lookup12(wy81, wy82, wy83, wy84, bc) → new_lookup(Neg(Succ(wy81)), wy84, bc)
The graph contains the following edges 4 >= 2, 5 >= 3
new_lookup(Neg(Succ(wy300)), :(@2(Pos(wy4000), wy401), wy41), bb) → new_lookup(Neg(Succ(wy300)), wy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
new_lookup(Neg(Succ(wy300)), :(@2(Neg(Zero), wy401), wy41), bb) → new_lookup(Neg(Succ(wy300)), wy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3

lookup	k []	= lookup3 k []
lookup	k ((x,y) : xys)	= lookup2 k ((x,y) : xys)

lookup1	k x y xys True	= Just y
lookup1	k x y xys False	= lookup0 k x y xys otherwise