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

YES 1.72 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 :: Eq b => Maybe b -> [(Maybe b,a)] -> Maybe a) :: Eq b => Maybe b -> [(Maybe b,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 :: Eq a => Maybe a -> [(Maybe a,b)] -> Maybe b) :: Eq a => Maybe a -> [(Maybe a,b)] -> Maybe b)

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)

lookup1 k x y xys True = Just y

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

lookup0 k x y xys True = lookup k xys

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

lookup3 k [] = Nothing

lookup3 xy xz = lookup2 xy xz

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

(lookup :: Eq a => Maybe a -> [(Maybe a,b)] -> Maybe b)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookup\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookup yu3\n  Eq a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookup yu3 yu4\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];703[label="yu4/yu40 : yu41",fontsize=10,color="white",style="solid",shape="box"];4 -> 703[label="",style="solid", color="burlywood", weight=9];
703 -> 5[label="",style="solid", color="burlywood", weight=3];
704[label="yu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 704[label="",style="solid", color="burlywood", weight=9];
704 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookup yu3 (yu40 : yu41)\n  Eq a",fontsize=16,color="burlywood",shape="box"];705[label="yu40/(yu400,yu401)",fontsize=10,color="white",style="solid",shape="box"];5 -> 705[label="",style="solid", color="burlywood", weight=9];
705 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup yu3 []\n  Eq a",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookup yu3 ((yu400,yu401) : yu41)\n  Eq a",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 yu3 []\n  Eq a",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="lookup2 yu3 ((yu400,yu401) : yu41)\n  Eq a",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 yu3 yu400 yu401 yu41 (yu3 == yu400)\n  Eq a",fontsize=16,color="burlywood",shape="box"];706[label="yu3/Nothing",fontsize=10,color="white",style="solid",shape="box"];11 -> 706[label="",style="solid", color="burlywood", weight=9];
706 -> 12[label="",style="solid", color="burlywood", weight=3];
707[label="yu3/Just yu30",fontsize=10,color="white",style="solid",shape="box"];11 -> 707[label="",style="solid", color="burlywood", weight=9];
707 -> 13[label="",style="solid", color="burlywood", weight=3];
12[label="lookup1 Nothing yu400 yu401 yu41 (Nothing == yu400)\n  Eq a",fontsize=16,color="burlywood",shape="box"];708[label="yu400/Nothing",fontsize=10,color="white",style="solid",shape="box"];12 -> 708[label="",style="solid", color="burlywood", weight=9];
708 -> 14[label="",style="solid", color="burlywood", weight=3];
709[label="yu400/Just yu4000",fontsize=10,color="white",style="solid",shape="box"];12 -> 709[label="",style="solid", color="burlywood", weight=9];
709 -> 15[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 (Just yu30) yu400 yu401 yu41 (Just yu30 == yu400)\n  Eq a",fontsize=16,color="burlywood",shape="box"];710[label="yu400/Nothing",fontsize=10,color="white",style="solid",shape="box"];13 -> 710[label="",style="solid", color="burlywood", weight=9];
710 -> 16[label="",style="solid", color="burlywood", weight=3];
711[label="yu400/Just yu4000",fontsize=10,color="white",style="solid",shape="box"];13 -> 711[label="",style="solid", color="burlywood", weight=9];
711 -> 17[label="",style="solid", color="burlywood", weight=3];
14[label="lookup1 Nothing Nothing yu401 yu41 (Nothing == Nothing)\n  Eq a",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="lookup1 Nothing (Just yu4000) yu401 yu41 (Nothing == Just yu4000)\n  Eq a",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="lookup1 (Just yu30) Nothing yu401 yu41 (Just yu30 == Nothing)\n  Eq a",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="lookup1 (Just yu30) (Just yu4000) yu401 yu41 (Just yu30 == Just yu4000)\n  Eq a",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="lookup1 Nothing Nothing yu401 yu41 True\n  Eq a",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="lookup1 Nothing (Just yu4000) yu401 yu41 False\n  Eq a",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="lookup1 (Just yu30) Nothing yu401 yu41 False\n  Eq a",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21 -> 25[label="",style="dashed", color="red", weight=0];
21[label="lookup1 (Just yu30) (Just yu4000) yu401 yu41 (yu30 == yu4000)\n  Eq a",fontsize=16,color="magenta"];21 -> 26[label="",style="dashed", color="magenta", weight=3];
21 -> 27[label="",style="dashed", color="magenta", weight=3];
21 -> 28[label="",style="dashed", color="magenta", weight=3];
21 -> 29[label="",style="dashed", color="magenta", weight=3];
21 -> 30[label="",style="dashed", color="magenta", weight=3];
22[label="Just yu401",fontsize=16,color="green",shape="box"];23[label="lookup0 Nothing (Just yu4000) yu401 yu41 otherwise\n  Eq a",fontsize=16,color="black",shape="box"];23 -> 31[label="",style="solid", color="black", weight=3];
24[label="lookup0 (Just yu30) Nothing yu401 yu41 otherwise\n  Eq a",fontsize=16,color="black",shape="box"];24 -> 32[label="",style="solid", color="black", weight=3];
26[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];27[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];28[label="yu41\n  Eq a",fontsize=16,color="green",shape="box"];29[label="yu401",fontsize=16,color="green",shape="box"];30[label="yu30 == yu4000\n  Eq a",fontsize=16,color="blue",shape="box"];713[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 713[label="",style="solid", color="blue", weight=9];
713 -> 33[label="",style="solid", color="blue", weight=3];
714[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 714[label="",style="solid", color="blue", weight=9];
714 -> 34[label="",style="solid", color="blue", weight=3];
715[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 715[label="",style="solid", color="blue", weight=9];
715 -> 35[label="",style="solid", color="blue", weight=3];
716[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 716[label="",style="solid", color="blue", weight=9];
716 -> 36[label="",style="solid", color="blue", weight=3];
717[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 717[label="",style="solid", color="blue", weight=9];
717 -> 37[label="",style="solid", color="blue", weight=3];
718[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 718[label="",style="solid", color="blue", weight=9];
718 -> 38[label="",style="solid", color="blue", weight=3];
719[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 719[label="",style="solid", color="blue", weight=9];
719 -> 39[label="",style="solid", color="blue", weight=3];
720[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 720[label="",style="solid", color="blue", weight=9];
720 -> 40[label="",style="solid", color="blue", weight=3];
721[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 721[label="",style="solid", color="blue", weight=9];
721 -> 41[label="",style="solid", color="blue", weight=3];
722[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 722[label="",style="solid", color="blue", weight=9];
722 -> 42[label="",style="solid", color="blue", weight=3];
723[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 723[label="",style="solid", color="blue", weight=9];
723 -> 43[label="",style="solid", color="blue", weight=3];
724[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 724[label="",style="solid", color="blue", weight=9];
724 -> 44[label="",style="solid", color="blue", weight=3];
725[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 725[label="",style="solid", color="blue", weight=9];
725 -> 45[label="",style="solid", color="blue", weight=3];
726[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];30 -> 726[label="",style="solid", color="blue", weight=9];
726 -> 46[label="",style="solid", color="blue", weight=3];
25[label="lookup1 (Just yu11) (Just yu12) yu13 yu14 yu15\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];727[label="yu15/False",fontsize=10,color="white",style="solid",shape="box"];25 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 47[label="",style="solid", color="burlywood", weight=3];
728[label="yu15/True",fontsize=10,color="white",style="solid",shape="box"];25 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 48[label="",style="solid", color="burlywood", weight=3];
31[label="lookup0 Nothing (Just yu4000) yu401 yu41 True\n  Eq a",fontsize=16,color="black",shape="box"];31 -> 49[label="",style="solid", color="black", weight=3];
32[label="lookup0 (Just yu30) Nothing yu401 yu41 True\n  Eq a",fontsize=16,color="black",shape="box"];32 -> 50[label="",style="solid", color="black", weight=3];
33[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];33 -> 51[label="",style="solid", color="black", weight=3];
34[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];34 -> 52[label="",style="solid", color="black", weight=3];
35[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];729[label="yu30/()",fontsize=10,color="white",style="solid",shape="box"];35 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 53[label="",style="solid", color="burlywood", weight=3];
36[label="yu30 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];730[label="yu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];36 -> 730[label="",style="solid", color="burlywood", weight=9];
730 -> 54[label="",style="solid", color="burlywood", weight=3];
731[label="yu30/Just yu300",fontsize=10,color="white",style="solid",shape="box"];36 -> 731[label="",style="solid", color="burlywood", weight=9];
731 -> 55[label="",style="solid", color="burlywood", weight=3];
37[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];732[label="yu30/LT",fontsize=10,color="white",style="solid",shape="box"];37 -> 732[label="",style="solid", color="burlywood", weight=9];
732 -> 56[label="",style="solid", color="burlywood", weight=3];
733[label="yu30/EQ",fontsize=10,color="white",style="solid",shape="box"];37 -> 733[label="",style="solid", color="burlywood", weight=9];
733 -> 57[label="",style="solid", color="burlywood", weight=3];
734[label="yu30/GT",fontsize=10,color="white",style="solid",shape="box"];37 -> 734[label="",style="solid", color="burlywood", weight=9];
734 -> 58[label="",style="solid", color="burlywood", weight=3];
38[label="yu30 == yu4000\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];735[label="yu30/yu300 :% yu301",fontsize=10,color="white",style="solid",shape="box"];38 -> 735[label="",style="solid", color="burlywood", weight=9];
735 -> 59[label="",style="solid", color="burlywood", weight=3];
39[label="yu30 == yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];736[label="yu30/(yu300,yu301,yu302)",fontsize=10,color="white",style="solid",shape="box"];39 -> 736[label="",style="solid", color="burlywood", weight=9];
736 -> 60[label="",style="solid", color="burlywood", weight=3];
40[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];737[label="yu30/Integer yu300",fontsize=10,color="white",style="solid",shape="box"];40 -> 737[label="",style="solid", color="burlywood", weight=9];
737 -> 61[label="",style="solid", color="burlywood", weight=3];
41[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];738[label="yu30/(yu300,yu301)",fontsize=10,color="white",style="solid",shape="box"];41 -> 738[label="",style="solid", color="burlywood", weight=9];
738 -> 62[label="",style="solid", color="burlywood", weight=3];
42[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];42 -> 63[label="",style="solid", color="black", weight=3];
43[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];43 -> 64[label="",style="solid", color="black", weight=3];
44[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];739[label="yu30/Left yu300",fontsize=10,color="white",style="solid",shape="box"];44 -> 739[label="",style="solid", color="burlywood", weight=9];
739 -> 65[label="",style="solid", color="burlywood", weight=3];
740[label="yu30/Right yu300",fontsize=10,color="white",style="solid",shape="box"];44 -> 740[label="",style="solid", color="burlywood", weight=9];
740 -> 66[label="",style="solid", color="burlywood", weight=3];
45[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];741[label="yu30/False",fontsize=10,color="white",style="solid",shape="box"];45 -> 741[label="",style="solid", color="burlywood", weight=9];
741 -> 67[label="",style="solid", color="burlywood", weight=3];
742[label="yu30/True",fontsize=10,color="white",style="solid",shape="box"];45 -> 742[label="",style="solid", color="burlywood", weight=9];
742 -> 68[label="",style="solid", color="burlywood", weight=3];
46[label="yu30 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];743[label="yu30/yu300 : yu301",fontsize=10,color="white",style="solid",shape="box"];46 -> 743[label="",style="solid", color="burlywood", weight=9];
743 -> 69[label="",style="solid", color="burlywood", weight=3];
744[label="yu30/[]",fontsize=10,color="white",style="solid",shape="box"];46 -> 744[label="",style="solid", color="burlywood", weight=9];
744 -> 70[label="",style="solid", color="burlywood", weight=3];
47[label="lookup1 (Just yu11) (Just yu12) yu13 yu14 False\n  Eq a",fontsize=16,color="black",shape="box"];47 -> 71[label="",style="solid", color="black", weight=3];
48[label="lookup1 (Just yu11) (Just yu12) yu13 yu14 True\n  Eq a",fontsize=16,color="black",shape="box"];48 -> 72[label="",style="solid", color="black", weight=3];
49 -> 4[label="",style="dashed", color="red", weight=0];
49[label="lookup Nothing yu41\n  Eq a",fontsize=16,color="magenta"];49 -> 73[label="",style="dashed", color="magenta", weight=3];
49 -> 74[label="",style="dashed", color="magenta", weight=3];
50 -> 4[label="",style="dashed", color="red", weight=0];
50[label="lookup (Just yu30) yu41\n  Eq a",fontsize=16,color="magenta"];50 -> 75[label="",style="dashed", color="magenta", weight=3];
50 -> 76[label="",style="dashed", color="magenta", weight=3];
51[label="primEqFloat yu30 yu4000",fontsize=16,color="burlywood",shape="box"];747[label="yu30/Float yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];51 -> 747[label="",style="solid", color="burlywood", weight=9];
747 -> 77[label="",style="solid", color="burlywood", weight=3];
52[label="primEqDouble yu30 yu4000",fontsize=16,color="burlywood",shape="box"];748[label="yu30/Double yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];52 -> 748[label="",style="solid", color="burlywood", weight=9];
748 -> 78[label="",style="solid", color="burlywood", weight=3];
53[label="() == yu4000",fontsize=16,color="burlywood",shape="box"];749[label="yu4000/()",fontsize=10,color="white",style="solid",shape="box"];53 -> 749[label="",style="solid", color="burlywood", weight=9];
749 -> 79[label="",style="solid", color="burlywood", weight=3];
54[label="Nothing == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];750[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];54 -> 750[label="",style="solid", color="burlywood", weight=9];
750 -> 80[label="",style="solid", color="burlywood", weight=3];
751[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];54 -> 751[label="",style="solid", color="burlywood", weight=9];
751 -> 81[label="",style="solid", color="burlywood", weight=3];
55[label="Just yu300 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];752[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];55 -> 752[label="",style="solid", color="burlywood", weight=9];
752 -> 82[label="",style="solid", color="burlywood", weight=3];
753[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];55 -> 753[label="",style="solid", color="burlywood", weight=9];
753 -> 83[label="",style="solid", color="burlywood", weight=3];
56[label="LT == yu4000",fontsize=16,color="burlywood",shape="box"];754[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];56 -> 754[label="",style="solid", color="burlywood", weight=9];
754 -> 84[label="",style="solid", color="burlywood", weight=3];
755[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];56 -> 755[label="",style="solid", color="burlywood", weight=9];
755 -> 85[label="",style="solid", color="burlywood", weight=3];
756[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];56 -> 756[label="",style="solid", color="burlywood", weight=9];
756 -> 86[label="",style="solid", color="burlywood", weight=3];
57[label="EQ == yu4000",fontsize=16,color="burlywood",shape="box"];757[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];57 -> 757[label="",style="solid", color="burlywood", weight=9];
757 -> 87[label="",style="solid", color="burlywood", weight=3];
758[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];57 -> 758[label="",style="solid", color="burlywood", weight=9];
758 -> 88[label="",style="solid", color="burlywood", weight=3];
759[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];57 -> 759[label="",style="solid", color="burlywood", weight=9];
759 -> 89[label="",style="solid", color="burlywood", weight=3];
58[label="GT == yu4000",fontsize=16,color="burlywood",shape="box"];760[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];58 -> 760[label="",style="solid", color="burlywood", weight=9];
760 -> 90[label="",style="solid", color="burlywood", weight=3];
761[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];58 -> 761[label="",style="solid", color="burlywood", weight=9];
761 -> 91[label="",style="solid", color="burlywood", weight=3];
762[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];58 -> 762[label="",style="solid", color="burlywood", weight=9];
762 -> 92[label="",style="solid", color="burlywood", weight=3];
59[label="yu300 :% yu301 == yu4000\n  Integral a",fontsize=16,color="burlywood",shape="box"];763[label="yu4000/yu40000 :% yu40001",fontsize=10,color="white",style="solid",shape="box"];59 -> 763[label="",style="solid", color="burlywood", weight=9];
763 -> 93[label="",style="solid", color="burlywood", weight=3];
60[label="(yu300,yu301,yu302) == yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];764[label="yu4000/(yu40000,yu40001,yu40002)",fontsize=10,color="white",style="solid",shape="box"];60 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 94[label="",style="solid", color="burlywood", weight=3];
61[label="Integer yu300 == yu4000",fontsize=16,color="burlywood",shape="box"];765[label="yu4000/Integer yu40000",fontsize=10,color="white",style="solid",shape="box"];61 -> 765[label="",style="solid", color="burlywood", weight=9];
765 -> 95[label="",style="solid", color="burlywood", weight=3];
62[label="(yu300,yu301) == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];766[label="yu4000/(yu40000,yu40001)",fontsize=10,color="white",style="solid",shape="box"];62 -> 766[label="",style="solid", color="burlywood", weight=9];
766 -> 96[label="",style="solid", color="burlywood", weight=3];
63[label="primEqInt yu30 yu4000",fontsize=16,color="burlywood",shape="triangle"];767[label="yu30/Pos yu300",fontsize=10,color="white",style="solid",shape="box"];63 -> 767[label="",style="solid", color="burlywood", weight=9];
767 -> 97[label="",style="solid", color="burlywood", weight=3];
768[label="yu30/Neg yu300",fontsize=10,color="white",style="solid",shape="box"];63 -> 768[label="",style="solid", color="burlywood", weight=9];
768 -> 98[label="",style="solid", color="burlywood", weight=3];
64[label="primEqChar yu30 yu4000",fontsize=16,color="burlywood",shape="box"];769[label="yu30/Char yu300",fontsize=10,color="white",style="solid",shape="box"];64 -> 769[label="",style="solid", color="burlywood", weight=9];
769 -> 99[label="",style="solid", color="burlywood", weight=3];
65[label="Left yu300 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];770[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];65 -> 770[label="",style="solid", color="burlywood", weight=9];
770 -> 100[label="",style="solid", color="burlywood", weight=3];
771[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];65 -> 771[label="",style="solid", color="burlywood", weight=9];
771 -> 101[label="",style="solid", color="burlywood", weight=3];
66[label="Right yu300 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];772[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];66 -> 772[label="",style="solid", color="burlywood", weight=9];
772 -> 102[label="",style="solid", color="burlywood", weight=3];
773[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];66 -> 773[label="",style="solid", color="burlywood", weight=9];
773 -> 103[label="",style="solid", color="burlywood", weight=3];
67[label="False == yu4000",fontsize=16,color="burlywood",shape="box"];774[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];67 -> 774[label="",style="solid", color="burlywood", weight=9];
774 -> 104[label="",style="solid", color="burlywood", weight=3];
775[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];67 -> 775[label="",style="solid", color="burlywood", weight=9];
775 -> 105[label="",style="solid", color="burlywood", weight=3];
68[label="True == yu4000",fontsize=16,color="burlywood",shape="box"];776[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];68 -> 776[label="",style="solid", color="burlywood", weight=9];
776 -> 106[label="",style="solid", color="burlywood", weight=3];
777[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];68 -> 777[label="",style="solid", color="burlywood", weight=9];
777 -> 107[label="",style="solid", color="burlywood", weight=3];
69[label="yu300 : yu301 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];778[label="yu4000/yu40000 : yu40001",fontsize=10,color="white",style="solid",shape="box"];69 -> 778[label="",style="solid", color="burlywood", weight=9];
778 -> 108[label="",style="solid", color="burlywood", weight=3];
779[label="yu4000/[]",fontsize=10,color="white",style="solid",shape="box"];69 -> 779[label="",style="solid", color="burlywood", weight=9];
779 -> 109[label="",style="solid", color="burlywood", weight=3];
70[label="[] == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];780[label="yu4000/yu40000 : yu40001",fontsize=10,color="white",style="solid",shape="box"];70 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 110[label="",style="solid", color="burlywood", weight=3];
781[label="yu4000/[]",fontsize=10,color="white",style="solid",shape="box"];70 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 111[label="",style="solid", color="burlywood", weight=3];
71[label="lookup0 (Just yu11) (Just yu12) yu13 yu14 otherwise\n  Eq a",fontsize=16,color="black",shape="box"];71 -> 112[label="",style="solid", color="black", weight=3];
72[label="Just yu13",fontsize=16,color="green",shape="box"];73[label="Nothing\n  Eq a",fontsize=16,color="green",shape="box"];74[label="yu41\n  Eq a",fontsize=16,color="green",shape="box"];75[label="Just yu30\n  Eq a",fontsize=16,color="green",shape="box"];76[label="yu41\n  Eq a",fontsize=16,color="green",shape="box"];77[label="primEqFloat (Float yu300 yu301) yu4000",fontsize=16,color="burlywood",shape="box"];782[label="yu4000/Float yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];77 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 113[label="",style="solid", color="burlywood", weight=3];
78[label="primEqDouble (Double yu300 yu301) yu4000",fontsize=16,color="burlywood",shape="box"];783[label="yu4000/Double yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];78 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 114[label="",style="solid", color="burlywood", weight=3];
79[label="() == ()",fontsize=16,color="black",shape="box"];79 -> 115[label="",style="solid", color="black", weight=3];
80[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];80 -> 116[label="",style="solid", color="black", weight=3];
81[label="Nothing == Just yu40000\n  Eq a",fontsize=16,color="black",shape="box"];81 -> 117[label="",style="solid", color="black", weight=3];
82[label="Just yu300 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];82 -> 118[label="",style="solid", color="black", weight=3];
83[label="Just yu300 == Just yu40000\n  Eq a",fontsize=16,color="black",shape="box"];83 -> 119[label="",style="solid", color="black", weight=3];
84[label="LT == LT",fontsize=16,color="black",shape="box"];84 -> 120[label="",style="solid", color="black", weight=3];
85[label="LT == EQ",fontsize=16,color="black",shape="box"];85 -> 121[label="",style="solid", color="black", weight=3];
86[label="LT == GT",fontsize=16,color="black",shape="box"];86 -> 122[label="",style="solid", color="black", weight=3];
87[label="EQ == LT",fontsize=16,color="black",shape="box"];87 -> 123[label="",style="solid", color="black", weight=3];
88[label="EQ == EQ",fontsize=16,color="black",shape="box"];88 -> 124[label="",style="solid", color="black", weight=3];
89[label="EQ == GT",fontsize=16,color="black",shape="box"];89 -> 125[label="",style="solid", color="black", weight=3];
90[label="GT == LT",fontsize=16,color="black",shape="box"];90 -> 126[label="",style="solid", color="black", weight=3];
91[label="GT == EQ",fontsize=16,color="black",shape="box"];91 -> 127[label="",style="solid", color="black", weight=3];
92[label="GT == GT",fontsize=16,color="black",shape="box"];92 -> 128[label="",style="solid", color="black", weight=3];
93[label="yu300 :% yu301 == yu40000 :% yu40001\n  Integral a",fontsize=16,color="black",shape="box"];93 -> 129[label="",style="solid", color="black", weight=3];
94[label="(yu300,yu301,yu302) == (yu40000,yu40001,yu40002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];94 -> 130[label="",style="solid", color="black", weight=3];
95[label="Integer yu300 == Integer yu40000",fontsize=16,color="black",shape="box"];95 -> 131[label="",style="solid", color="black", weight=3];
96[label="(yu300,yu301) == (yu40000,yu40001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];96 -> 132[label="",style="solid", color="black", weight=3];
97[label="primEqInt (Pos yu300) yu4000",fontsize=16,color="burlywood",shape="box"];784[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];97 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 133[label="",style="solid", color="burlywood", weight=3];
785[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];97 -> 785[label="",style="solid", color="burlywood", weight=9];
785 -> 134[label="",style="solid", color="burlywood", weight=3];
98[label="primEqInt (Neg yu300) yu4000",fontsize=16,color="burlywood",shape="box"];786[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];98 -> 786[label="",style="solid", color="burlywood", weight=9];
786 -> 135[label="",style="solid", color="burlywood", weight=3];
787[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];98 -> 787[label="",style="solid", color="burlywood", weight=9];
787 -> 136[label="",style="solid", color="burlywood", weight=3];
99[label="primEqChar (Char yu300) yu4000",fontsize=16,color="burlywood",shape="box"];788[label="yu4000/Char yu40000",fontsize=10,color="white",style="solid",shape="box"];99 -> 788[label="",style="solid", color="burlywood", weight=9];
788 -> 137[label="",style="solid", color="burlywood", weight=3];
100[label="Left yu300 == Left yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];100 -> 138[label="",style="solid", color="black", weight=3];
101[label="Left yu300 == Right yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];101 -> 139[label="",style="solid", color="black", weight=3];
102[label="Right yu300 == Left yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];102 -> 140[label="",style="solid", color="black", weight=3];
103[label="Right yu300 == Right yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];103 -> 141[label="",style="solid", color="black", weight=3];
104[label="False == False",fontsize=16,color="black",shape="box"];104 -> 142[label="",style="solid", color="black", weight=3];
105[label="False == True",fontsize=16,color="black",shape="box"];105 -> 143[label="",style="solid", color="black", weight=3];
106[label="True == False",fontsize=16,color="black",shape="box"];106 -> 144[label="",style="solid", color="black", weight=3];
107[label="True == True",fontsize=16,color="black",shape="box"];107 -> 145[label="",style="solid", color="black", weight=3];
108[label="yu300 : yu301 == yu40000 : yu40001\n  Eq a",fontsize=16,color="black",shape="box"];108 -> 146[label="",style="solid", color="black", weight=3];
109[label="yu300 : yu301 == []\n  Eq a",fontsize=16,color="black",shape="box"];109 -> 147[label="",style="solid", color="black", weight=3];
110[label="[] == yu40000 : yu40001\n  Eq a",fontsize=16,color="black",shape="box"];110 -> 148[label="",style="solid", color="black", weight=3];
111[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];111 -> 149[label="",style="solid", color="black", weight=3];
112[label="lookup0 (Just yu11) (Just yu12) yu13 yu14 True\n  Eq a",fontsize=16,color="black",shape="box"];112 -> 150[label="",style="solid", color="black", weight=3];
113[label="primEqFloat (Float yu300 yu301) (Float yu40000 yu40001)",fontsize=16,color="black",shape="box"];113 -> 151[label="",style="solid", color="black", weight=3];
114[label="primEqDouble (Double yu300 yu301) (Double yu40000 yu40001)",fontsize=16,color="black",shape="box"];114 -> 152[label="",style="solid", color="black", weight=3];
115[label="True",fontsize=16,color="green",shape="box"];116[label="True",fontsize=16,color="green",shape="box"];117[label="False",fontsize=16,color="green",shape="box"];118[label="False",fontsize=16,color="green",shape="box"];119[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];789[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 789[label="",style="solid", color="blue", weight=9];
789 -> 153[label="",style="solid", color="blue", weight=3];
790[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 790[label="",style="solid", color="blue", weight=9];
790 -> 154[label="",style="solid", color="blue", weight=3];
791[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 791[label="",style="solid", color="blue", weight=9];
791 -> 155[label="",style="solid", color="blue", weight=3];
792[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 792[label="",style="solid", color="blue", weight=9];
792 -> 156[label="",style="solid", color="blue", weight=3];
793[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 793[label="",style="solid", color="blue", weight=9];
793 -> 157[label="",style="solid", color="blue", weight=3];
794[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 794[label="",style="solid", color="blue", weight=9];
794 -> 158[label="",style="solid", color="blue", weight=3];
795[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 795[label="",style="solid", color="blue", weight=9];
795 -> 159[label="",style="solid", color="blue", weight=3];
796[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 796[label="",style="solid", color="blue", weight=9];
796 -> 160[label="",style="solid", color="blue", weight=3];
797[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 797[label="",style="solid", color="blue", weight=9];
797 -> 161[label="",style="solid", color="blue", weight=3];
798[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 798[label="",style="solid", color="blue", weight=9];
798 -> 162[label="",style="solid", color="blue", weight=3];
799[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 799[label="",style="solid", color="blue", weight=9];
799 -> 163[label="",style="solid", color="blue", weight=3];
800[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 800[label="",style="solid", color="blue", weight=9];
800 -> 164[label="",style="solid", color="blue", weight=3];
801[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 801[label="",style="solid", color="blue", weight=9];
801 -> 165[label="",style="solid", color="blue", weight=3];
802[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];119 -> 802[label="",style="solid", color="blue", weight=9];
802 -> 166[label="",style="solid", color="blue", weight=3];
120[label="True",fontsize=16,color="green",shape="box"];121[label="False",fontsize=16,color="green",shape="box"];122[label="False",fontsize=16,color="green",shape="box"];123[label="False",fontsize=16,color="green",shape="box"];124[label="True",fontsize=16,color="green",shape="box"];125[label="False",fontsize=16,color="green",shape="box"];126[label="False",fontsize=16,color="green",shape="box"];127[label="False",fontsize=16,color="green",shape="box"];128[label="True",fontsize=16,color="green",shape="box"];129 -> 263[label="",style="dashed", color="red", weight=0];
129[label="yu300 == yu40000 && yu301 == yu40001\n  Integral a",fontsize=16,color="magenta"];129 -> 264[label="",style="dashed", color="magenta", weight=3];
129 -> 265[label="",style="dashed", color="magenta", weight=3];
130 -> 263[label="",style="dashed", color="red", weight=0];
130[label="yu300 == yu40000 && yu301 == yu40001 && yu302 == yu40002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];130 -> 266[label="",style="dashed", color="magenta", weight=3];
130 -> 267[label="",style="dashed", color="magenta", weight=3];
131 -> 63[label="",style="dashed", color="red", weight=0];
131[label="primEqInt yu300 yu40000",fontsize=16,color="magenta"];131 -> 188[label="",style="dashed", color="magenta", weight=3];
131 -> 189[label="",style="dashed", color="magenta", weight=3];
132 -> 263[label="",style="dashed", color="red", weight=0];
132[label="yu300 == yu40000 && yu301 == yu40001\n  Eq a  Eq b",fontsize=16,color="magenta"];132 -> 268[label="",style="dashed", color="magenta", weight=3];
132 -> 269[label="",style="dashed", color="magenta", weight=3];
133[label="primEqInt (Pos (Succ yu3000)) yu4000",fontsize=16,color="burlywood",shape="box"];807[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];133 -> 807[label="",style="solid", color="burlywood", weight=9];
807 -> 190[label="",style="solid", color="burlywood", weight=3];
808[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];133 -> 808[label="",style="solid", color="burlywood", weight=9];
808 -> 191[label="",style="solid", color="burlywood", weight=3];
134[label="primEqInt (Pos Zero) yu4000",fontsize=16,color="burlywood",shape="box"];809[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];134 -> 809[label="",style="solid", color="burlywood", weight=9];
809 -> 192[label="",style="solid", color="burlywood", weight=3];
810[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];134 -> 810[label="",style="solid", color="burlywood", weight=9];
810 -> 193[label="",style="solid", color="burlywood", weight=3];
135[label="primEqInt (Neg (Succ yu3000)) yu4000",fontsize=16,color="burlywood",shape="box"];811[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];135 -> 811[label="",style="solid", color="burlywood", weight=9];
811 -> 194[label="",style="solid", color="burlywood", weight=3];
812[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];135 -> 812[label="",style="solid", color="burlywood", weight=9];
812 -> 195[label="",style="solid", color="burlywood", weight=3];
136[label="primEqInt (Neg Zero) yu4000",fontsize=16,color="burlywood",shape="box"];813[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];136 -> 813[label="",style="solid", color="burlywood", weight=9];
813 -> 196[label="",style="solid", color="burlywood", weight=3];
814[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];136 -> 814[label="",style="solid", color="burlywood", weight=9];
814 -> 197[label="",style="solid", color="burlywood", weight=3];
137[label="primEqChar (Char yu300) (Char yu40000)",fontsize=16,color="black",shape="box"];137 -> 198[label="",style="solid", color="black", weight=3];
138[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];815[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 815[label="",style="solid", color="blue", weight=9];
815 -> 199[label="",style="solid", color="blue", weight=3];
816[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 816[label="",style="solid", color="blue", weight=9];
816 -> 200[label="",style="solid", color="blue", weight=3];
817[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 817[label="",style="solid", color="blue", weight=9];
817 -> 201[label="",style="solid", color="blue", weight=3];
818[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 818[label="",style="solid", color="blue", weight=9];
818 -> 202[label="",style="solid", color="blue", weight=3];
819[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 819[label="",style="solid", color="blue", weight=9];
819 -> 203[label="",style="solid", color="blue", weight=3];
820[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 820[label="",style="solid", color="blue", weight=9];
820 -> 204[label="",style="solid", color="blue", weight=3];
821[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 821[label="",style="solid", color="blue", weight=9];
821 -> 205[label="",style="solid", color="blue", weight=3];
822[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 822[label="",style="solid", color="blue", weight=9];
822 -> 206[label="",style="solid", color="blue", weight=3];
823[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 823[label="",style="solid", color="blue", weight=9];
823 -> 207[label="",style="solid", color="blue", weight=3];
824[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 824[label="",style="solid", color="blue", weight=9];
824 -> 208[label="",style="solid", color="blue", weight=3];
825[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 825[label="",style="solid", color="blue", weight=9];
825 -> 209[label="",style="solid", color="blue", weight=3];
826[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 826[label="",style="solid", color="blue", weight=9];
826 -> 210[label="",style="solid", color="blue", weight=3];
827[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 827[label="",style="solid", color="blue", weight=9];
827 -> 211[label="",style="solid", color="blue", weight=3];
828[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];138 -> 828[label="",style="solid", color="blue", weight=9];
828 -> 212[label="",style="solid", color="blue", weight=3];
139[label="False",fontsize=16,color="green",shape="box"];140[label="False",fontsize=16,color="green",shape="box"];141[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];829[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 829[label="",style="solid", color="blue", weight=9];
829 -> 213[label="",style="solid", color="blue", weight=3];
830[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 830[label="",style="solid", color="blue", weight=9];
830 -> 214[label="",style="solid", color="blue", weight=3];
831[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 831[label="",style="solid", color="blue", weight=9];
831 -> 215[label="",style="solid", color="blue", weight=3];
832[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 832[label="",style="solid", color="blue", weight=9];
832 -> 216[label="",style="solid", color="blue", weight=3];
833[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 833[label="",style="solid", color="blue", weight=9];
833 -> 217[label="",style="solid", color="blue", weight=3];
834[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 834[label="",style="solid", color="blue", weight=9];
834 -> 218[label="",style="solid", color="blue", weight=3];
835[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 835[label="",style="solid", color="blue", weight=9];
835 -> 219[label="",style="solid", color="blue", weight=3];
836[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];141 -> 836[label="",style="solid", color="blue", weight=9];
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668[label="primMulNat Zero yu400010",fontsize=16,color="burlywood",shape="box"];1106[label="yu400010/Succ yu4000100",fontsize=10,color="white",style="solid",shape="box"];668 -> 1106[label="",style="solid", color="burlywood", weight=9];
1106 -> 675[label="",style="solid", color="burlywood", weight=3];
1107[label="yu400010/Zero",fontsize=10,color="white",style="solid",shape="box"];668 -> 1107[label="",style="solid", color="burlywood", weight=9];
1107 -> 676[label="",style="solid", color="burlywood", weight=3];
669[label="yu400010",fontsize=16,color="green",shape="box"];670[label="yu3010",fontsize=16,color="green",shape="box"];671[label="yu3010",fontsize=16,color="green",shape="box"];672[label="yu400010",fontsize=16,color="green",shape="box"];673[label="primMulNat (Succ yu30100) (Succ yu4000100)",fontsize=16,color="black",shape="box"];673 -> 677[label="",style="solid", color="black", weight=3];
674[label="primMulNat (Succ yu30100) Zero",fontsize=16,color="black",shape="box"];674 -> 678[label="",style="solid", color="black", weight=3];
675[label="primMulNat Zero (Succ yu4000100)",fontsize=16,color="black",shape="box"];675 -> 679[label="",style="solid", color="black", weight=3];
676[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];676 -> 680[label="",style="solid", color="black", weight=3];
677 -> 681[label="",style="dashed", color="red", weight=0];
677[label="primPlusNat (primMulNat yu30100 (Succ yu4000100)) (Succ yu4000100)",fontsize=16,color="magenta"];677 -> 682[label="",style="dashed", color="magenta", weight=3];
678[label="Zero",fontsize=16,color="green",shape="box"];679[label="Zero",fontsize=16,color="green",shape="box"];680[label="Zero",fontsize=16,color="green",shape="box"];682 -> 663[label="",style="dashed", color="red", weight=0];
682[label="primMulNat yu30100 (Succ yu4000100)",fontsize=16,color="magenta"];682 -> 683[label="",style="dashed", color="magenta", weight=3];
682 -> 684[label="",style="dashed", color="magenta", weight=3];
681[label="primPlusNat yu29 (Succ yu4000100)",fontsize=16,color="burlywood",shape="triangle"];1110[label="yu29/Succ yu290",fontsize=10,color="white",style="solid",shape="box"];681 -> 1110[label="",style="solid", color="burlywood", weight=9];
1110 -> 685[label="",style="solid", color="burlywood", weight=3];
1111[label="yu29/Zero",fontsize=10,color="white",style="solid",shape="box"];681 -> 1111[label="",style="solid", color="burlywood", weight=9];
1111 -> 686[label="",style="solid", color="burlywood", weight=3];
683[label="yu30100",fontsize=16,color="green",shape="box"];684[label="Succ yu4000100",fontsize=16,color="green",shape="box"];685[label="primPlusNat (Succ yu290) (Succ yu4000100)",fontsize=16,color="black",shape="box"];685 -> 687[label="",style="solid", color="black", weight=3];
686[label="primPlusNat Zero (Succ yu4000100)",fontsize=16,color="black",shape="box"];686 -> 688[label="",style="solid", color="black", weight=3];
687[label="Succ (Succ (primPlusNat yu290 yu4000100))",fontsize=16,color="green",shape="box"];687 -> 689[label="",style="dashed", color="green", weight=3];
688[label="Succ yu4000100",fontsize=16,color="green",shape="box"];689[label="primPlusNat yu290 yu4000100",fontsize=16,color="burlywood",shape="triangle"];1112[label="yu290/Succ yu2900",fontsize=10,color="white",style="solid",shape="box"];689 -> 1112[label="",style="solid", color="burlywood", weight=9];
1112 -> 690[label="",style="solid", color="burlywood", weight=3];
1113[label="yu290/Zero",fontsize=10,color="white",style="solid",shape="box"];689 -> 1113[label="",style="solid", color="burlywood", weight=9];
1113 -> 691[label="",style="solid", color="burlywood", weight=3];
690[label="primPlusNat (Succ yu2900) yu4000100",fontsize=16,color="burlywood",shape="box"];1114[label="yu4000100/Succ yu40001000",fontsize=10,color="white",style="solid",shape="box"];690 -> 1114[label="",style="solid", color="burlywood", weight=9];
1114 -> 692[label="",style="solid", color="burlywood", weight=3];
1115[label="yu4000100/Zero",fontsize=10,color="white",style="solid",shape="box"];690 -> 1115[label="",style="solid", color="burlywood", weight=9];
1115 -> 693[label="",style="solid", color="burlywood", weight=3];
691[label="primPlusNat Zero yu4000100",fontsize=16,color="burlywood",shape="box"];1116[label="yu4000100/Succ yu40001000",fontsize=10,color="white",style="solid",shape="box"];691 -> 1116[label="",style="solid", color="burlywood", weight=9];
1116 -> 694[label="",style="solid", color="burlywood", weight=3];
1117[label="yu4000100/Zero",fontsize=10,color="white",style="solid",shape="box"];691 -> 1117[label="",style="solid", color="burlywood", weight=9];
1117 -> 695[label="",style="solid", color="burlywood", weight=3];
692[label="primPlusNat (Succ yu2900) (Succ yu40001000)",fontsize=16,color="black",shape="box"];692 -> 696[label="",style="solid", color="black", weight=3];
693[label="primPlusNat (Succ yu2900) Zero",fontsize=16,color="black",shape="box"];693 -> 697[label="",style="solid", color="black", weight=3];
694[label="primPlusNat Zero (Succ yu40001000)",fontsize=16,color="black",shape="box"];694 -> 698[label="",style="solid", color="black", weight=3];
695[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];695 -> 699[label="",style="solid", color="black", weight=3];
696[label="Succ (Succ (primPlusNat yu2900 yu40001000))",fontsize=16,color="green",shape="box"];696 -> 700[label="",style="dashed", color="green", weight=3];
697[label="Succ yu2900",fontsize=16,color="green",shape="box"];698[label="Succ yu40001000",fontsize=16,color="green",shape="box"];699[label="Zero",fontsize=16,color="green",shape="box"];700 -> 689[label="",style="dashed", color="red", weight=0];
700[label="primPlusNat yu2900 yu40001000",fontsize=16,color="magenta"];700 -> 701[label="",style="dashed", color="magenta", weight=3];
700 -> 702[label="",style="dashed", color="magenta", weight=3];
701[label="yu40001000",fontsize=16,color="green",shape="box"];702[label="yu2900",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(yu2900), Succ(yu40001000)) → new_primPlusNat(yu2900, yu40001000)

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_primPlusNat(Succ(yu2900), Succ(yu40001000)) → new_primPlusNat(yu2900, yu40001000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(yu30100), Succ(yu4000100)) → new_primMulNat(yu30100, Succ(yu4000100))

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

new_primMulNat(Succ(yu30100), Succ(yu4000100)) → new_primMulNat(yu30100, Succ(yu4000100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(yu3000), Succ(yu400000)) → new_primEqNat(yu3000, yu400000)

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

new_primEqNat(Succ(yu3000), Succ(yu400000)) → new_primEqNat(yu3000, yu400000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, gd), ge), gf), gc) → new_esEs0(yu300, yu40000, gd, ge, gf)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(app(ty_@2, ec), ed), cd) → new_esEs1(yu301, yu40001, ec, ed)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, ha), hb), gc) → new_esEs2(yu300, yu40000, ha, hb)
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_[], beb)) → new_esEs3(yu300, yu40000, beb)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(ty_[], ga)) → new_esEs3(yu302, yu40002, ga)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, dc), dd), cc, cd) → new_esEs2(yu300, yu40000, dc, dd)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], hc), gc) → new_esEs3(yu300, yu40000, hc)
new_esEs(Just(yu300), Just(yu40000), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(yu300, yu40000, bb, bc, bd)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], de), cc, cd) → new_esEs3(yu300, yu40000, de)
new_esEs2(Right(yu300), Right(yu40000), bbh, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs0(yu300, yu40000, bcb, bcc, bcd)
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs0(yu300, yu40000, bdc, bdd, bde)
new_esEs(Just(yu300), Just(yu40000), app(app(ty_Either, bg), bh)) → new_esEs2(yu300, yu40000, bg, bh)
new_esEs(Just(yu300), Just(yu40000), app(ty_[], ca)) → new_esEs3(yu300, yu40000, ca)
new_esEs2(Right(yu300), Right(yu40000), bbh, app(app(ty_@2, bce), bcf)) → new_esEs1(yu300, yu40000, bce, bcf)
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_Either, bbe), bbf), bag) → new_esEs2(yu300, yu40000, bbe, bbf)
new_esEs(Just(yu300), Just(yu40000), app(ty_Maybe, ba)) → new_esEs(yu300, yu40000, ba)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(app(app(ty_@3, dh), ea), eb), cd) → new_esEs0(yu301, yu40001, dh, ea, eb)
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), bec) → new_esEs3(yu301, yu40001, bec)
new_esEs2(Left(yu300), Left(yu40000), app(ty_[], bbg), bag) → new_esEs3(yu300, yu40000, bbg)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(ty_[], eg), cd) → new_esEs3(yu301, yu40001, eg)
new_esEs2(Left(yu300), Left(yu40000), app(ty_Maybe, baf), bag) → new_esEs(yu300, yu40000, baf)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(app(ty_@2, baa), bab)) → new_esEs1(yu301, yu40001, baa, bab)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(app(ty_@2, fd), ff)) → new_esEs1(yu302, yu40002, fd, ff)
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_@2, bdf), bdg)) → new_esEs1(yu300, yu40000, bdf, bdg)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(app(app(ty_@3, fa), fb), fc)) → new_esEs0(yu302, yu40002, fa, fb, fc)
new_esEs2(Right(yu300), Right(yu40000), bbh, app(ty_Maybe, bca)) → new_esEs(yu300, yu40000, bca)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, gg), gh), gc) → new_esEs1(yu300, yu40000, gg, gh)
new_esEs2(Right(yu300), Right(yu40000), bbh, app(app(ty_Either, bcg), bch)) → new_esEs2(yu300, yu40000, bcg, bch)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(app(ty_Either, bac), bad)) → new_esEs2(yu301, yu40001, bac, bad)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(ty_[], bae)) → new_esEs3(yu301, yu40001, bae)
new_esEs2(Right(yu300), Right(yu40000), bbh, app(ty_[], bda)) → new_esEs3(yu300, yu40000, bda)
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_Either, bdh), bea)) → new_esEs2(yu300, yu40000, bdh, bea)
new_esEs(Just(yu300), Just(yu40000), app(app(ty_@2, be), bf)) → new_esEs1(yu300, yu40000, be, bf)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, da), db), cc, cd) → new_esEs1(yu300, yu40000, da, db)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(ty_Maybe, dg), cd) → new_esEs(yu301, yu40001, dg)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, gb), gc) → new_esEs(yu300, yu40000, gb)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(app(ty_Either, fg), fh)) → new_esEs2(yu302, yu40002, fg, fh)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(ty_Maybe, he)) → new_esEs(yu301, yu40001, he)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(app(ty_Either, ee), ef), cd) → new_esEs2(yu301, yu40001, ee, ef)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(ty_Maybe, eh)) → new_esEs(yu302, yu40002, eh)
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_Maybe, bdb)) → new_esEs(yu300, yu40000, bdb)
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_@2, bbc), bbd), bag) → new_esEs1(yu300, yu40000, bbc, bbd)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, cb), cc, cd) → new_esEs(yu300, yu40000, cb)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, ce), cf), cg), cc, cd) → new_esEs0(yu300, yu40000, ce, cf, cg)
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(app(app(ty_@3, hf), hg), hh)) → new_esEs0(yu301, yu40001, hf, hg, hh)
new_esEs2(Left(yu300), Left(yu40000), app(app(app(ty_@3, bah), bba), bbb), bag) → new_esEs0(yu300, yu40000, bah, bba, bbb)

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

new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs0(yu300, yu40000, bdc, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(Just(yu300), Just(yu40000), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(yu300, yu40000, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_@2, bdf), bdg)) → new_esEs1(yu300, yu40000, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Just(yu300), Just(yu40000), app(app(ty_@2, be), bf)) → new_esEs1(yu300, yu40000, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Just(yu300), Just(yu40000), app(ty_[], ca)) → new_esEs3(yu300, yu40000, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_Maybe, bdb)) → new_esEs(yu300, yu40000, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_Either, bdh), bea)) → new_esEs2(yu300, yu40000, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Just(yu300), Just(yu40000), app(ty_Maybe, ba)) → new_esEs(yu300, yu40000, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Just(yu300), Just(yu40000), app(app(ty_Either, bg), bh)) → new_esEs2(yu300, yu40000, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, gd), ge), gf), gc) → new_esEs0(yu300, yu40000, gd, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(app(app(ty_@3, hf), hg), hh)) → new_esEs0(yu301, yu40001, hf, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(app(ty_@2, baa), bab)) → new_esEs1(yu301, yu40001, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, gg), gh), gc) → new_esEs1(yu300, yu40000, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], hc), gc) → new_esEs3(yu300, yu40000, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(ty_[], bae)) → new_esEs3(yu301, yu40001, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, gb), gc) → new_esEs(yu300, yu40000, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(ty_Maybe, he)) → new_esEs(yu301, yu40001, he)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, ha), hb), gc) → new_esEs2(yu300, yu40000, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(yu300, yu301), @2(yu40000, yu40001), hd, app(app(ty_Either, bac), bad)) → new_esEs2(yu301, yu40001, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(app(app(ty_@3, dh), ea), eb), cd) → new_esEs0(yu301, yu40001, dh, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(app(app(ty_@3, fa), fb), fc)) → new_esEs0(yu302, yu40002, fa, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, ce), cf), cg), cc, cd) → new_esEs0(yu300, yu40000, ce, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Right(yu300), Right(yu40000), bbh, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs0(yu300, yu40000, bcb, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(Left(yu300), Left(yu40000), app(app(app(ty_@3, bah), bba), bbb), bag) → new_esEs0(yu300, yu40000, bah, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(app(ty_@2, ec), ed), cd) → new_esEs1(yu301, yu40001, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(app(ty_@2, fd), ff)) → new_esEs1(yu302, yu40002, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, da), db), cc, cd) → new_esEs1(yu300, yu40000, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(ty_[], ga)) → new_esEs3(yu302, yu40002, ga)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], de), cc, cd) → new_esEs3(yu300, yu40000, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(ty_[], eg), cd) → new_esEs3(yu301, yu40001, eg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(ty_Maybe, dg), cd) → new_esEs(yu301, yu40001, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(ty_Maybe, eh)) → new_esEs(yu302, yu40002, eh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, cb), cc, cd) → new_esEs(yu300, yu40000, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, dc), dd), cc, cd) → new_esEs2(yu300, yu40000, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, cc, app(app(ty_Either, fg), fh)) → new_esEs2(yu302, yu40002, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, app(app(ty_Either, ee), ef), cd) → new_esEs2(yu301, yu40001, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Right(yu300), Right(yu40000), bbh, app(app(ty_@2, bce), bcf)) → new_esEs1(yu300, yu40000, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_@2, bbc), bbd), bag) → new_esEs1(yu300, yu40000, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Left(yu300), Left(yu40000), app(ty_[], bbg), bag) → new_esEs3(yu300, yu40000, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(yu300), Right(yu40000), bbh, app(ty_[], bda)) → new_esEs3(yu300, yu40000, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(yu300), Left(yu40000), app(ty_Maybe, baf), bag) → new_esEs(yu300, yu40000, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(yu300), Right(yu40000), bbh, app(ty_Maybe, bca)) → new_esEs(yu300, yu40000, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_Either, bbe), bbf), bag) → new_esEs2(yu300, yu40000, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(yu300), Right(yu40000), bbh, app(app(ty_Either, bcg), bch)) → new_esEs2(yu300, yu40000, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_[], beb)) → new_esEs3(yu300, yu40000, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(yu300, yu301), :(yu40000, yu40001), bec) → new_esEs3(yu301, yu40001, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

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

new_lookup(Just(yu30), :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, bb), ba, bb)
new_lookup1(yu11, yu12, yu13, yu14, False, bc, bd) → new_lookup(Just(yu11), yu14, bc, bd)
new_lookup(Nothing, :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup(Nothing, yu41, ba, bb)
new_lookup(Just(yu30), :(@2(Nothing, yu401), yu41), ba, bb) → new_lookup(Just(yu30), yu41, ba, bb)

The TRS R consists of the following rules:

new_esEs21(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Float) → new_esEs5(yu302, yu40002)
new_primPlusNat1(Succ(yu2900), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu2900, yu40001000)))
new_esEs25(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_esEs21(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs6(yu30, yu4000)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_esEs16(Left(yu300), Left(yu40000), app(ty_[], fc), ce) → new_esEs18(yu300, yu40000, fc)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs18(:(yu300, yu301), :(yu40000, yu40001), cf) → new_asAs(new_esEs24(yu300, yu40000, cf), new_esEs18(yu301, yu40001, cf))
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_esEs24(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs23(yu302, yu40002, app(ty_Ratio, bbd)) → new_esEs10(yu302, yu40002, bbd)
new_esEs22(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(yu301, yu40001, app(ty_Ratio, bfb)) → new_esEs10(yu301, yu40001, bfb)
new_esEs26(yu301, yu40001, ty_Double) → new_esEs6(yu301, yu40001)
new_esEs21(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_esEs23(yu302, yu40002, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs11(yu302, yu40002, bbe, bbf, bbg)
new_esEs4(yu30, yu4000, app(app(app(ty_@3, bg), bh), ca)) → new_esEs11(yu30, yu4000, bg, bh, ca)
new_esEs22(yu301, yu40001, ty_Bool) → new_esEs17(yu301, yu40001)
new_esEs9(GT, GT) → True
new_esEs24(yu300, yu40000, app(app(ty_@2, bdb), bdc)) → new_esEs13(yu300, yu40000, bdb, bdc)
new_esEs25(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), ty_Double) → new_esEs6(yu300, yu40000)
new_esEs26(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs26(yu301, yu40001, ty_@0) → new_esEs7(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Char) → new_esEs15(yu302, yu40002)
new_esEs23(yu302, yu40002, app(ty_Maybe, bbc)) → new_esEs8(yu302, yu40002, bbc)
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_esEs16(Left(yu300), Left(yu40000), app(ty_Maybe, eb), ce) → new_esEs8(yu300, yu40000, eb)
new_esEs17(True, True) → True
new_esEs8(Just(yu300), Just(yu40000), app(app(ty_@2, de), df)) → new_esEs13(yu300, yu40000, de, df)
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(ty_Either, gd), ge)) → new_esEs16(yu300, yu40000, gd, ge)
new_esEs8(Just(yu300), Just(yu40000), app(app(app(ty_@3, db), dc), dd)) → new_esEs11(yu300, yu40000, db, dc, dd)
new_esEs23(yu302, yu40002, ty_Double) → new_esEs6(yu302, yu40002)
new_esEs25(yu300, yu40000, app(app(app(ty_@3, bea), beb), bec)) → new_esEs11(yu300, yu40000, bea, beb, bec)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_[], gf)) → new_esEs18(yu300, yu40000, gf)
new_esEs4(yu30, yu4000, app(app(ty_@2, cb), cc)) → new_esEs13(yu30, yu4000, cb, cc)
new_esEs23(yu302, yu40002, ty_Integer) → new_esEs12(yu302, yu40002)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_Maybe, fd)) → new_esEs8(yu300, yu40000, fd)
new_esEs12(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu301, yu40001, ty_Float) → new_esEs5(yu301, yu40001)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs16(Left(yu300), Left(yu40000), app(app(app(ty_@3, ed), ee), ef), ce) → new_esEs11(yu300, yu40000, ed, ee, ef)
new_esEs26(yu301, yu40001, app(app(ty_@2, bff), bfg)) → new_esEs13(yu301, yu40001, bff, bfg)
new_esEs21(yu300, yu40000, app(ty_Ratio, gh)) → new_esEs10(yu300, yu40000, gh)
new_esEs8(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_esEs11(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bg, bh, ca) → new_asAs(new_esEs21(yu300, yu40000, bg), new_asAs(new_esEs22(yu301, yu40001, bh), new_esEs23(yu302, yu40002, ca)))
new_esEs25(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs18([], :(yu40000, yu40001), cf) → False
new_esEs18(:(yu300, yu301), [], cf) → False
new_esEs23(yu302, yu40002, app(app(ty_@2, bbh), bca)) → new_esEs13(yu302, yu40002, bbh, bca)
new_esEs16(Left(yu300), Left(yu40000), app(app(ty_Either, fa), fb), ce) → new_esEs16(yu300, yu40000, fa, fb)
new_esEs16(Left(yu300), Left(yu40000), ty_Bool, ce) → new_esEs17(yu300, yu40000)
new_esEs22(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs16(Left(yu300), Right(yu40000), cd, ce) → False
new_esEs16(Right(yu300), Left(yu40000), cd, ce) → False
new_esEs26(yu301, yu40001, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs11(yu301, yu40001, bfc, bfd, bfe)
new_esEs23(yu302, yu40002, ty_Bool) → new_esEs17(yu302, yu40002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs14(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs25(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(app(ty_Either, dg), dh)) → new_esEs16(yu300, yu40000, dg, dh)
new_esEs8(Nothing, Nothing, be) → True
new_esEs4(yu30, yu4000, app(ty_Maybe, be)) → new_esEs8(yu30, yu4000, be)
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs4(yu30, yu4000, app(ty_Ratio, bf)) → new_esEs10(yu30, yu4000, bf)
new_esEs21(yu300, yu40000, app(app(ty_@2, hd), he)) → new_esEs13(yu300, yu40000, hd, he)
new_esEs8(Just(yu300), Just(yu40000), ty_Int) → new_esEs14(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Double, ce) → new_esEs6(yu300, yu40000)
new_esEs26(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs19(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Ordering, ce) → new_esEs9(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Int) → new_esEs14(yu302, yu40002)
new_asAs(False, yu28) → False
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs8(Just(yu300), Just(yu40000), ty_@0) → new_esEs7(yu300, yu40000)
new_primEqNat0(Zero, Zero) → True
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs22(yu301, yu40001, app(ty_Maybe, baa)) → new_esEs8(yu301, yu40001, baa)
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_esEs18([], [], cf) → True
new_esEs25(yu300, yu40000, app(ty_[], beh)) → new_esEs18(yu300, yu40000, beh)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_[], bdf)) → new_esEs18(yu300, yu40000, bdf)
new_esEs22(yu301, yu40001, app(app(ty_Either, bah), bba)) → new_esEs16(yu301, yu40001, bah, bba)
new_esEs17(False, False) → True
new_esEs8(Just(yu300), Just(yu40000), ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, app(ty_[], cf)) → new_esEs18(yu30, yu4000, cf)
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs12(yu30, yu4000)
new_esEs21(yu300, yu40000, app(app(ty_Either, hf), hg)) → new_esEs16(yu300, yu40000, hf, hg)
new_esEs21(yu300, yu40000, app(ty_Maybe, gg)) → new_esEs8(yu300, yu40000, gg)
new_esEs15(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Integer, ce) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs26(yu301, yu40001, app(app(ty_Either, bfh), bga)) → new_esEs16(yu301, yu40001, bfh, bga)
new_esEs23(yu302, yu40002, ty_@0) → new_esEs7(yu302, yu40002)
new_esEs21(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), app(app(ty_@2, eg), eh), ce) → new_esEs13(yu300, yu40000, eg, eh)
new_esEs13(@2(yu300, yu301), @2(yu40000, yu40001), cb, cc) → new_asAs(new_esEs25(yu300, yu40000, cb), new_esEs26(yu301, yu40001, cc))
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(ty_@2, gb), gc)) → new_esEs13(yu300, yu40000, gb, gc)
new_esEs8(Just(yu300), Just(yu40000), ty_Char) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bcf)) → new_esEs10(yu300, yu40000, bcf)
new_esEs23(yu302, yu40002, app(app(ty_Either, bcb), bcc)) → new_esEs16(yu302, yu40002, bcb, bcc)
new_esEs22(yu301, yu40001, ty_@0) → new_esEs7(yu301, yu40001)
new_primPlusNat0(Succ(yu290), yu4000100) → Succ(Succ(new_primPlusNat1(yu290, yu4000100)))
new_esEs20(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs16(Left(yu300), Left(yu40000), ty_Int, ce) → new_esEs14(yu300, yu40000)
new_esEs22(yu301, yu40001, app(ty_[], bbb)) → new_esEs18(yu301, yu40001, bbb)
new_esEs22(yu301, yu40001, app(ty_Ratio, bab)) → new_esEs10(yu301, yu40001, bab)
new_esEs21(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_Ratio, da)) → new_esEs10(yu300, yu40000, da)
new_esEs26(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs8(Nothing, Just(yu40000), be) → False
new_esEs8(Just(yu300), Nothing, be) → False
new_esEs9(EQ, EQ) → True
new_esEs14(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs22(yu301, yu40001, app(app(ty_@2, baf), bag)) → new_esEs13(yu301, yu40001, baf, bag)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs26(yu301, yu40001, app(ty_Maybe, bfa)) → new_esEs8(yu301, yu40001, bfa)
new_primPlusNat1(Succ(yu2900), Zero) → Succ(yu2900)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_esEs25(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs25(yu300, yu40000, app(ty_Ratio, bdh)) → new_esEs10(yu300, yu40000, bdh)
new_esEs21(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bce)) → new_esEs8(yu300, yu40000, bce)
new_esEs26(yu301, yu40001, ty_Bool) → new_esEs17(yu301, yu40001)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs21(yu300, yu40000, app(ty_[], hh)) → new_esEs18(yu300, yu40000, hh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(yu30, yu4000, app(app(ty_Either, cd), ce)) → new_esEs16(yu30, yu4000, cd, ce)
new_esEs25(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs15(yu30, yu4000)
new_esEs19(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_esEs25(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), app(ty_Ratio, ec), ce) → new_esEs10(yu300, yu40000, ec)
new_esEs22(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs26(yu301, yu40001, app(ty_[], bgb)) → new_esEs18(yu301, yu40001, bgb)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_asAs(True, yu28) → yu28
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_esEs22(yu301, yu40001, ty_Double) → new_esEs6(yu301, yu40001)
new_esEs4(yu30, yu4000, ty_@0) → new_esEs7(yu30, yu4000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_Maybe, cg)) → new_esEs8(yu300, yu40000, cg)
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs22(yu301, yu40001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs11(yu301, yu40001, bac, bad, bae)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs14(yu30, yu4000)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_Ratio, ff)) → new_esEs10(yu300, yu40000, ff)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs11(yu300, yu40000, bcg, bch, bda)
new_esEs26(yu301, yu40001, ty_Float) → new_esEs5(yu301, yu40001)
new_esEs8(Just(yu300), Just(yu40000), ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Char, ce) → new_esEs15(yu300, yu40000)
new_esEs21(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdd), bde)) → new_esEs16(yu300, yu40000, bdd, bde)
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_[], ea)) → new_esEs18(yu300, yu40000, ea)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs6(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs14(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs25(yu300, yu40000, app(app(ty_@2, bed), bee)) → new_esEs13(yu300, yu40000, bed, bee)
new_esEs10(:%(yu300, yu301), :%(yu40000, yu40001), bf) → new_asAs(new_esEs19(yu300, yu40000, bf), new_esEs20(yu301, yu40001, bf))
new_esEs25(yu300, yu40000, app(app(ty_Either, bef), beg)) → new_esEs16(yu300, yu40000, bef, beg)
new_esEs7(@0, @0) → True
new_esEs23(yu302, yu40002, app(ty_[], bcd)) → new_esEs18(yu302, yu40002, bcd)
new_esEs21(yu300, yu40000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs11(yu300, yu40000, ha, hb, hc)
new_esEs9(LT, LT) → True
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs17(yu30, yu4000)
new_esEs25(yu300, yu40000, app(ty_Maybe, bdg)) → new_esEs8(yu300, yu40000, bdg)
new_esEs22(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs16(Left(yu300), Left(yu40000), ty_Float, ce) → new_esEs5(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(app(ty_@3, fg), fh), ga)) → new_esEs11(yu300, yu40000, fg, fh, ga)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs4(yu30, yu4000, ty_Float) → new_esEs5(yu30, yu4000)
new_esEs16(Left(yu300), Left(yu40000), ty_@0, ce) → new_esEs7(yu300, yu40000)

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), x1)
new_esEs8(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Nothing, x1)
new_esEs9(GT, GT)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs7(@0, @0)
new_esEs4(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Nothing, Just(x0), x1)
new_esEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs16(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(EQ, EQ)
new_esEs16(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs14(x0, x1)
new_esEs18([], [], x0)
new_esEs19(x0, x1, ty_Int)
new_esEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Right(x1), x2, x3)
new_esEs16(Right(x0), Left(x1), x2, x3)
new_esEs4(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs21(x0, x1, ty_Double)
new_esEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Float)
new_esEs17(False, False)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_Char)
new_esEs5(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Float)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Zero)
new_esEs22(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr(Pos(x0), Pos(x1))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Char)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs17(True, False)
new_esEs17(False, True)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(True, x0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, LT)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Left(x1), ty_Integer, x2)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                      ↳ UsableRulesProof

                    ↳ QDP

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

new_lookup(Nothing, :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup(Nothing, yu41, ba, bb)

The TRS R consists of the following rules:

new_esEs21(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Float) → new_esEs5(yu302, yu40002)
new_primPlusNat1(Succ(yu2900), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu2900, yu40001000)))
new_esEs25(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_esEs21(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs6(yu30, yu4000)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_esEs16(Left(yu300), Left(yu40000), app(ty_[], fc), ce) → new_esEs18(yu300, yu40000, fc)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs18(:(yu300, yu301), :(yu40000, yu40001), cf) → new_asAs(new_esEs24(yu300, yu40000, cf), new_esEs18(yu301, yu40001, cf))
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_esEs24(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs23(yu302, yu40002, app(ty_Ratio, bbd)) → new_esEs10(yu302, yu40002, bbd)
new_esEs22(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(yu301, yu40001, app(ty_Ratio, bfb)) → new_esEs10(yu301, yu40001, bfb)
new_esEs26(yu301, yu40001, ty_Double) → new_esEs6(yu301, yu40001)
new_esEs21(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_esEs23(yu302, yu40002, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs11(yu302, yu40002, bbe, bbf, bbg)
new_esEs4(yu30, yu4000, app(app(app(ty_@3, bg), bh), ca)) → new_esEs11(yu30, yu4000, bg, bh, ca)
new_esEs22(yu301, yu40001, ty_Bool) → new_esEs17(yu301, yu40001)
new_esEs9(GT, GT) → True
new_esEs24(yu300, yu40000, app(app(ty_@2, bdb), bdc)) → new_esEs13(yu300, yu40000, bdb, bdc)
new_esEs25(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), ty_Double) → new_esEs6(yu300, yu40000)
new_esEs26(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs26(yu301, yu40001, ty_@0) → new_esEs7(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Char) → new_esEs15(yu302, yu40002)
new_esEs23(yu302, yu40002, app(ty_Maybe, bbc)) → new_esEs8(yu302, yu40002, bbc)
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_esEs16(Left(yu300), Left(yu40000), app(ty_Maybe, eb), ce) → new_esEs8(yu300, yu40000, eb)
new_esEs17(True, True) → True
new_esEs8(Just(yu300), Just(yu40000), app(app(ty_@2, de), df)) → new_esEs13(yu300, yu40000, de, df)
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(ty_Either, gd), ge)) → new_esEs16(yu300, yu40000, gd, ge)
new_esEs8(Just(yu300), Just(yu40000), app(app(app(ty_@3, db), dc), dd)) → new_esEs11(yu300, yu40000, db, dc, dd)
new_esEs23(yu302, yu40002, ty_Double) → new_esEs6(yu302, yu40002)
new_esEs25(yu300, yu40000, app(app(app(ty_@3, bea), beb), bec)) → new_esEs11(yu300, yu40000, bea, beb, bec)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_[], gf)) → new_esEs18(yu300, yu40000, gf)
new_esEs4(yu30, yu4000, app(app(ty_@2, cb), cc)) → new_esEs13(yu30, yu4000, cb, cc)
new_esEs23(yu302, yu40002, ty_Integer) → new_esEs12(yu302, yu40002)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_Maybe, fd)) → new_esEs8(yu300, yu40000, fd)
new_esEs12(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu301, yu40001, ty_Float) → new_esEs5(yu301, yu40001)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs16(Left(yu300), Left(yu40000), app(app(app(ty_@3, ed), ee), ef), ce) → new_esEs11(yu300, yu40000, ed, ee, ef)
new_esEs26(yu301, yu40001, app(app(ty_@2, bff), bfg)) → new_esEs13(yu301, yu40001, bff, bfg)
new_esEs21(yu300, yu40000, app(ty_Ratio, gh)) → new_esEs10(yu300, yu40000, gh)
new_esEs8(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_esEs11(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bg, bh, ca) → new_asAs(new_esEs21(yu300, yu40000, bg), new_asAs(new_esEs22(yu301, yu40001, bh), new_esEs23(yu302, yu40002, ca)))
new_esEs25(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs18([], :(yu40000, yu40001), cf) → False
new_esEs18(:(yu300, yu301), [], cf) → False
new_esEs23(yu302, yu40002, app(app(ty_@2, bbh), bca)) → new_esEs13(yu302, yu40002, bbh, bca)
new_esEs16(Left(yu300), Left(yu40000), app(app(ty_Either, fa), fb), ce) → new_esEs16(yu300, yu40000, fa, fb)
new_esEs16(Left(yu300), Left(yu40000), ty_Bool, ce) → new_esEs17(yu300, yu40000)
new_esEs22(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs16(Left(yu300), Right(yu40000), cd, ce) → False
new_esEs16(Right(yu300), Left(yu40000), cd, ce) → False
new_esEs26(yu301, yu40001, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs11(yu301, yu40001, bfc, bfd, bfe)
new_esEs23(yu302, yu40002, ty_Bool) → new_esEs17(yu302, yu40002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs14(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs25(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(app(ty_Either, dg), dh)) → new_esEs16(yu300, yu40000, dg, dh)
new_esEs8(Nothing, Nothing, be) → True
new_esEs4(yu30, yu4000, app(ty_Maybe, be)) → new_esEs8(yu30, yu4000, be)
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs4(yu30, yu4000, app(ty_Ratio, bf)) → new_esEs10(yu30, yu4000, bf)
new_esEs21(yu300, yu40000, app(app(ty_@2, hd), he)) → new_esEs13(yu300, yu40000, hd, he)
new_esEs8(Just(yu300), Just(yu40000), ty_Int) → new_esEs14(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Double, ce) → new_esEs6(yu300, yu40000)
new_esEs26(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs19(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Ordering, ce) → new_esEs9(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Int) → new_esEs14(yu302, yu40002)
new_asAs(False, yu28) → False
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs8(Just(yu300), Just(yu40000), ty_@0) → new_esEs7(yu300, yu40000)
new_primEqNat0(Zero, Zero) → True
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs22(yu301, yu40001, app(ty_Maybe, baa)) → new_esEs8(yu301, yu40001, baa)
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_esEs18([], [], cf) → True
new_esEs25(yu300, yu40000, app(ty_[], beh)) → new_esEs18(yu300, yu40000, beh)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_[], bdf)) → new_esEs18(yu300, yu40000, bdf)
new_esEs22(yu301, yu40001, app(app(ty_Either, bah), bba)) → new_esEs16(yu301, yu40001, bah, bba)
new_esEs17(False, False) → True
new_esEs8(Just(yu300), Just(yu40000), ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, app(ty_[], cf)) → new_esEs18(yu30, yu4000, cf)
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs12(yu30, yu4000)
new_esEs21(yu300, yu40000, app(app(ty_Either, hf), hg)) → new_esEs16(yu300, yu40000, hf, hg)
new_esEs21(yu300, yu40000, app(ty_Maybe, gg)) → new_esEs8(yu300, yu40000, gg)
new_esEs15(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Integer, ce) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs26(yu301, yu40001, app(app(ty_Either, bfh), bga)) → new_esEs16(yu301, yu40001, bfh, bga)
new_esEs23(yu302, yu40002, ty_@0) → new_esEs7(yu302, yu40002)
new_esEs21(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), app(app(ty_@2, eg), eh), ce) → new_esEs13(yu300, yu40000, eg, eh)
new_esEs13(@2(yu300, yu301), @2(yu40000, yu40001), cb, cc) → new_asAs(new_esEs25(yu300, yu40000, cb), new_esEs26(yu301, yu40001, cc))
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(ty_@2, gb), gc)) → new_esEs13(yu300, yu40000, gb, gc)
new_esEs8(Just(yu300), Just(yu40000), ty_Char) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bcf)) → new_esEs10(yu300, yu40000, bcf)
new_esEs23(yu302, yu40002, app(app(ty_Either, bcb), bcc)) → new_esEs16(yu302, yu40002, bcb, bcc)
new_esEs22(yu301, yu40001, ty_@0) → new_esEs7(yu301, yu40001)
new_primPlusNat0(Succ(yu290), yu4000100) → Succ(Succ(new_primPlusNat1(yu290, yu4000100)))
new_esEs20(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs16(Left(yu300), Left(yu40000), ty_Int, ce) → new_esEs14(yu300, yu40000)
new_esEs22(yu301, yu40001, app(ty_[], bbb)) → new_esEs18(yu301, yu40001, bbb)
new_esEs22(yu301, yu40001, app(ty_Ratio, bab)) → new_esEs10(yu301, yu40001, bab)
new_esEs21(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_Ratio, da)) → new_esEs10(yu300, yu40000, da)
new_esEs26(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs8(Nothing, Just(yu40000), be) → False
new_esEs8(Just(yu300), Nothing, be) → False
new_esEs9(EQ, EQ) → True
new_esEs14(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs22(yu301, yu40001, app(app(ty_@2, baf), bag)) → new_esEs13(yu301, yu40001, baf, bag)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs26(yu301, yu40001, app(ty_Maybe, bfa)) → new_esEs8(yu301, yu40001, bfa)
new_primPlusNat1(Succ(yu2900), Zero) → Succ(yu2900)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_esEs25(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs25(yu300, yu40000, app(ty_Ratio, bdh)) → new_esEs10(yu300, yu40000, bdh)
new_esEs21(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bce)) → new_esEs8(yu300, yu40000, bce)
new_esEs26(yu301, yu40001, ty_Bool) → new_esEs17(yu301, yu40001)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs21(yu300, yu40000, app(ty_[], hh)) → new_esEs18(yu300, yu40000, hh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(yu30, yu4000, app(app(ty_Either, cd), ce)) → new_esEs16(yu30, yu4000, cd, ce)
new_esEs25(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs15(yu30, yu4000)
new_esEs19(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_esEs25(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), app(ty_Ratio, ec), ce) → new_esEs10(yu300, yu40000, ec)
new_esEs22(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs26(yu301, yu40001, app(ty_[], bgb)) → new_esEs18(yu301, yu40001, bgb)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_asAs(True, yu28) → yu28
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_esEs22(yu301, yu40001, ty_Double) → new_esEs6(yu301, yu40001)
new_esEs4(yu30, yu4000, ty_@0) → new_esEs7(yu30, yu4000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_Maybe, cg)) → new_esEs8(yu300, yu40000, cg)
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs22(yu301, yu40001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs11(yu301, yu40001, bac, bad, bae)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs14(yu30, yu4000)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_Ratio, ff)) → new_esEs10(yu300, yu40000, ff)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs11(yu300, yu40000, bcg, bch, bda)
new_esEs26(yu301, yu40001, ty_Float) → new_esEs5(yu301, yu40001)
new_esEs8(Just(yu300), Just(yu40000), ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Char, ce) → new_esEs15(yu300, yu40000)
new_esEs21(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdd), bde)) → new_esEs16(yu300, yu40000, bdd, bde)
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_[], ea)) → new_esEs18(yu300, yu40000, ea)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs6(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs14(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs25(yu300, yu40000, app(app(ty_@2, bed), bee)) → new_esEs13(yu300, yu40000, bed, bee)
new_esEs10(:%(yu300, yu301), :%(yu40000, yu40001), bf) → new_asAs(new_esEs19(yu300, yu40000, bf), new_esEs20(yu301, yu40001, bf))
new_esEs25(yu300, yu40000, app(app(ty_Either, bef), beg)) → new_esEs16(yu300, yu40000, bef, beg)
new_esEs7(@0, @0) → True
new_esEs23(yu302, yu40002, app(ty_[], bcd)) → new_esEs18(yu302, yu40002, bcd)
new_esEs21(yu300, yu40000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs11(yu300, yu40000, ha, hb, hc)
new_esEs9(LT, LT) → True
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs17(yu30, yu4000)
new_esEs25(yu300, yu40000, app(ty_Maybe, bdg)) → new_esEs8(yu300, yu40000, bdg)
new_esEs22(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs16(Left(yu300), Left(yu40000), ty_Float, ce) → new_esEs5(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(app(ty_@3, fg), fh), ga)) → new_esEs11(yu300, yu40000, fg, fh, ga)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs4(yu30, yu4000, ty_Float) → new_esEs5(yu30, yu4000)
new_esEs16(Left(yu300), Left(yu40000), ty_@0, ce) → new_esEs7(yu300, yu40000)

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), x1)
new_esEs8(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Nothing, x1)
new_esEs9(GT, GT)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs7(@0, @0)
new_esEs4(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Nothing, Just(x0), x1)
new_esEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs16(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(EQ, EQ)
new_esEs16(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs14(x0, x1)
new_esEs18([], [], x0)
new_esEs19(x0, x1, ty_Int)
new_esEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Right(x1), x2, x3)
new_esEs16(Right(x0), Left(x1), x2, x3)
new_esEs4(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs21(x0, x1, ty_Double)
new_esEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Float)
new_esEs17(False, False)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_Char)
new_esEs5(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Float)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Zero)
new_esEs22(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr(Pos(x0), Pos(x1))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Char)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs17(True, False)
new_esEs17(False, True)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(True, x0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, LT)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Left(x1), ty_Integer, x2)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                      ↳ UsableRulesProof

                        ↳ QDP

                          ↳ QReductionProof

                    ↳ QDP

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

new_lookup(Nothing, :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup(Nothing, yu41, ba, bb)

R is empty.
The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), x1)
new_esEs8(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Nothing, x1)
new_esEs9(GT, GT)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs7(@0, @0)
new_esEs4(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Nothing, Just(x0), x1)
new_esEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs16(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(EQ, EQ)
new_esEs16(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs14(x0, x1)
new_esEs18([], [], x0)
new_esEs19(x0, x1, ty_Int)
new_esEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Right(x1), x2, x3)
new_esEs16(Right(x0), Left(x1), x2, x3)
new_esEs4(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs21(x0, x1, ty_Double)
new_esEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Float)
new_esEs17(False, False)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_Char)
new_esEs5(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Float)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Zero)
new_esEs22(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr(Pos(x0), Pos(x1))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Char)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs17(True, False)
new_esEs17(False, True)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(True, x0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, LT)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Left(x1), ty_Integer, x2)

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat0(Succ(x0), x1)
new_esEs8(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Nothing, x1)
new_esEs9(GT, GT)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs7(@0, @0)
new_esEs4(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Nothing, Just(x0), x1)
new_esEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs16(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(EQ, EQ)
new_esEs16(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs14(x0, x1)
new_esEs18([], [], x0)
new_esEs19(x0, x1, ty_Int)
new_esEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Right(x1), x2, x3)
new_esEs16(Right(x0), Left(x1), x2, x3)
new_esEs4(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs21(x0, x1, ty_Double)
new_esEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Float)
new_esEs17(False, False)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_Char)
new_esEs5(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Float)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Zero)
new_esEs22(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr(Pos(x0), Pos(x1))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Char)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs17(True, False)
new_esEs17(False, True)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(True, x0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, LT)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Left(x1), ty_Integer, x2)

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                      ↳ UsableRulesProof

                        ↳ QDP

                          ↳ QReductionProof

                            ↳ QDP

                              ↳ QDPSizeChangeProof

                    ↳ QDP

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

new_lookup(Nothing, :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup(Nothing, yu41, ba, bb)

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

new_lookup(Nothing, :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup(Nothing, yu41, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                    ↳ QDP

                      ↳ QDPSizeChangeProof

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

new_lookup(Just(yu30), :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, bb), ba, bb)
new_lookup1(yu11, yu12, yu13, yu14, False, bc, bd) → new_lookup(Just(yu11), yu14, bc, bd)
new_lookup(Just(yu30), :(@2(Nothing, yu401), yu41), ba, bb) → new_lookup(Just(yu30), yu41, ba, bb)

The TRS R consists of the following rules:

new_esEs21(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Float) → new_esEs5(yu302, yu40002)
new_primPlusNat1(Succ(yu2900), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu2900, yu40001000)))
new_esEs25(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_esEs21(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs6(yu30, yu4000)
new_esEs9(LT, GT) → False
new_esEs9(GT, LT) → False
new_esEs16(Left(yu300), Left(yu40000), app(ty_[], fc), ce) → new_esEs18(yu300, yu40000, fc)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs18(:(yu300, yu301), :(yu40000, yu40001), cf) → new_asAs(new_esEs24(yu300, yu40000, cf), new_esEs18(yu301, yu40001, cf))
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_esEs24(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs23(yu302, yu40002, app(ty_Ratio, bbd)) → new_esEs10(yu302, yu40002, bbd)
new_esEs22(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(yu301, yu40001, app(ty_Ratio, bfb)) → new_esEs10(yu301, yu40001, bfb)
new_esEs26(yu301, yu40001, ty_Double) → new_esEs6(yu301, yu40001)
new_esEs21(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_esEs23(yu302, yu40002, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs11(yu302, yu40002, bbe, bbf, bbg)
new_esEs4(yu30, yu4000, app(app(app(ty_@3, bg), bh), ca)) → new_esEs11(yu30, yu4000, bg, bh, ca)
new_esEs22(yu301, yu40001, ty_Bool) → new_esEs17(yu301, yu40001)
new_esEs9(GT, GT) → True
new_esEs24(yu300, yu40000, app(app(ty_@2, bdb), bdc)) → new_esEs13(yu300, yu40000, bdb, bdc)
new_esEs25(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), ty_Double) → new_esEs6(yu300, yu40000)
new_esEs26(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs26(yu301, yu40001, ty_@0) → new_esEs7(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Char) → new_esEs15(yu302, yu40002)
new_esEs23(yu302, yu40002, app(ty_Maybe, bbc)) → new_esEs8(yu302, yu40002, bbc)
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_esEs16(Left(yu300), Left(yu40000), app(ty_Maybe, eb), ce) → new_esEs8(yu300, yu40000, eb)
new_esEs17(True, True) → True
new_esEs8(Just(yu300), Just(yu40000), app(app(ty_@2, de), df)) → new_esEs13(yu300, yu40000, de, df)
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(ty_Either, gd), ge)) → new_esEs16(yu300, yu40000, gd, ge)
new_esEs8(Just(yu300), Just(yu40000), app(app(app(ty_@3, db), dc), dd)) → new_esEs11(yu300, yu40000, db, dc, dd)
new_esEs23(yu302, yu40002, ty_Double) → new_esEs6(yu302, yu40002)
new_esEs25(yu300, yu40000, app(app(app(ty_@3, bea), beb), bec)) → new_esEs11(yu300, yu40000, bea, beb, bec)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_[], gf)) → new_esEs18(yu300, yu40000, gf)
new_esEs4(yu30, yu4000, app(app(ty_@2, cb), cc)) → new_esEs13(yu30, yu4000, cb, cc)
new_esEs23(yu302, yu40002, ty_Integer) → new_esEs12(yu302, yu40002)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_Maybe, fd)) → new_esEs8(yu300, yu40000, fd)
new_esEs12(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu301, yu40001, ty_Float) → new_esEs5(yu301, yu40001)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs16(Left(yu300), Left(yu40000), app(app(app(ty_@3, ed), ee), ef), ce) → new_esEs11(yu300, yu40000, ed, ee, ef)
new_esEs26(yu301, yu40001, app(app(ty_@2, bff), bfg)) → new_esEs13(yu301, yu40001, bff, bfg)
new_esEs21(yu300, yu40000, app(ty_Ratio, gh)) → new_esEs10(yu300, yu40000, gh)
new_esEs8(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_esEs11(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bg, bh, ca) → new_asAs(new_esEs21(yu300, yu40000, bg), new_asAs(new_esEs22(yu301, yu40001, bh), new_esEs23(yu302, yu40002, ca)))
new_esEs25(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs18([], :(yu40000, yu40001), cf) → False
new_esEs18(:(yu300, yu301), [], cf) → False
new_esEs23(yu302, yu40002, app(app(ty_@2, bbh), bca)) → new_esEs13(yu302, yu40002, bbh, bca)
new_esEs16(Left(yu300), Left(yu40000), app(app(ty_Either, fa), fb), ce) → new_esEs16(yu300, yu40000, fa, fb)
new_esEs16(Left(yu300), Left(yu40000), ty_Bool, ce) → new_esEs17(yu300, yu40000)
new_esEs22(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs16(Left(yu300), Right(yu40000), cd, ce) → False
new_esEs16(Right(yu300), Left(yu40000), cd, ce) → False
new_esEs26(yu301, yu40001, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs11(yu301, yu40001, bfc, bfd, bfe)
new_esEs23(yu302, yu40002, ty_Bool) → new_esEs17(yu302, yu40002)
new_esEs9(EQ, GT) → False
new_esEs9(GT, EQ) → False
new_esEs5(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs14(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs25(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(app(ty_Either, dg), dh)) → new_esEs16(yu300, yu40000, dg, dh)
new_esEs8(Nothing, Nothing, be) → True
new_esEs4(yu30, yu4000, app(ty_Maybe, be)) → new_esEs8(yu30, yu4000, be)
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs4(yu30, yu4000, app(ty_Ratio, bf)) → new_esEs10(yu30, yu4000, bf)
new_esEs21(yu300, yu40000, app(app(ty_@2, hd), he)) → new_esEs13(yu300, yu40000, hd, he)
new_esEs8(Just(yu300), Just(yu40000), ty_Int) → new_esEs14(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Double, ce) → new_esEs6(yu300, yu40000)
new_esEs26(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs19(yu300, yu40000, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Ordering, ce) → new_esEs9(yu300, yu40000)
new_esEs23(yu302, yu40002, ty_Int) → new_esEs14(yu302, yu40002)
new_asAs(False, yu28) → False
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs8(Just(yu300), Just(yu40000), ty_@0) → new_esEs7(yu300, yu40000)
new_primEqNat0(Zero, Zero) → True
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Int) → new_esEs14(yu300, yu40000)
new_esEs22(yu301, yu40001, app(ty_Maybe, baa)) → new_esEs8(yu301, yu40001, baa)
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_esEs18([], [], cf) → True
new_esEs25(yu300, yu40000, app(ty_[], beh)) → new_esEs18(yu300, yu40000, beh)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_[], bdf)) → new_esEs18(yu300, yu40000, bdf)
new_esEs22(yu301, yu40001, app(app(ty_Either, bah), bba)) → new_esEs16(yu301, yu40001, bah, bba)
new_esEs17(False, False) → True
new_esEs8(Just(yu300), Just(yu40000), ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, app(ty_[], cf)) → new_esEs18(yu30, yu4000, cf)
new_esEs17(False, True) → False
new_esEs17(True, False) → False
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs12(yu30, yu4000)
new_esEs21(yu300, yu40000, app(app(ty_Either, hf), hg)) → new_esEs16(yu300, yu40000, hf, hg)
new_esEs21(yu300, yu40000, app(ty_Maybe, gg)) → new_esEs8(yu300, yu40000, gg)
new_esEs15(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Integer, ce) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs17(yu300, yu40000)
new_esEs26(yu301, yu40001, app(app(ty_Either, bfh), bga)) → new_esEs16(yu301, yu40001, bfh, bga)
new_esEs23(yu302, yu40002, ty_@0) → new_esEs7(yu302, yu40002)
new_esEs21(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), app(app(ty_@2, eg), eh), ce) → new_esEs13(yu300, yu40000, eg, eh)
new_esEs13(@2(yu300, yu301), @2(yu40000, yu40001), cb, cc) → new_asAs(new_esEs25(yu300, yu40000, cb), new_esEs26(yu301, yu40001, cc))
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(ty_@2, gb), gc)) → new_esEs13(yu300, yu40000, gb, gc)
new_esEs8(Just(yu300), Just(yu40000), ty_Char) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bcf)) → new_esEs10(yu300, yu40000, bcf)
new_esEs23(yu302, yu40002, app(app(ty_Either, bcb), bcc)) → new_esEs16(yu302, yu40002, bcb, bcc)
new_esEs22(yu301, yu40001, ty_@0) → new_esEs7(yu301, yu40001)
new_primPlusNat0(Succ(yu290), yu4000100) → Succ(Succ(new_primPlusNat1(yu290, yu4000100)))
new_esEs20(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs16(Left(yu300), Left(yu40000), ty_Int, ce) → new_esEs14(yu300, yu40000)
new_esEs22(yu301, yu40001, app(ty_[], bbb)) → new_esEs18(yu301, yu40001, bbb)
new_esEs22(yu301, yu40001, app(ty_Ratio, bab)) → new_esEs10(yu301, yu40001, bab)
new_esEs21(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_Ratio, da)) → new_esEs10(yu300, yu40000, da)
new_esEs26(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs8(Nothing, Just(yu40000), be) → False
new_esEs8(Just(yu300), Nothing, be) → False
new_esEs9(EQ, EQ) → True
new_esEs14(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_esEs22(yu301, yu40001, app(app(ty_@2, baf), bag)) → new_esEs13(yu301, yu40001, baf, bag)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs26(yu301, yu40001, app(ty_Maybe, bfa)) → new_esEs8(yu301, yu40001, bfa)
new_primPlusNat1(Succ(yu2900), Zero) → Succ(yu2900)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_esEs25(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs25(yu300, yu40000, app(ty_Ratio, bdh)) → new_esEs10(yu300, yu40000, bdh)
new_esEs21(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bce)) → new_esEs8(yu300, yu40000, bce)
new_esEs26(yu301, yu40001, ty_Bool) → new_esEs17(yu301, yu40001)
new_esEs9(LT, EQ) → False
new_esEs9(EQ, LT) → False
new_esEs20(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs21(yu300, yu40000, app(ty_[], hh)) → new_esEs18(yu300, yu40000, hh)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(yu30, yu4000, app(app(ty_Either, cd), ce)) → new_esEs16(yu30, yu4000, cd, ce)
new_esEs25(yu300, yu40000, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs15(yu30, yu4000)
new_esEs19(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_esEs25(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), app(ty_Ratio, ec), ce) → new_esEs10(yu300, yu40000, ec)
new_esEs22(yu301, yu40001, ty_Int) → new_esEs14(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs26(yu301, yu40001, app(ty_[], bgb)) → new_esEs18(yu301, yu40001, bgb)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu300, yu40000, ty_Double) → new_esEs6(yu300, yu40000)
new_asAs(True, yu28) → yu28
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_esEs22(yu301, yu40001, ty_Double) → new_esEs6(yu301, yu40001)
new_esEs4(yu30, yu4000, ty_@0) → new_esEs7(yu30, yu4000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs7(yu300, yu40000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_Maybe, cg)) → new_esEs8(yu300, yu40000, cg)
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Float) → new_esEs5(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs22(yu301, yu40001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs11(yu301, yu40001, bac, bad, bae)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs14(yu30, yu4000)
new_esEs16(Right(yu300), Right(yu40000), cd, app(ty_Ratio, ff)) → new_esEs10(yu300, yu40000, ff)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs11(yu300, yu40000, bcg, bch, bda)
new_esEs26(yu301, yu40001, ty_Float) → new_esEs5(yu301, yu40001)
new_esEs8(Just(yu300), Just(yu40000), ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs16(Left(yu300), Left(yu40000), ty_Char, ce) → new_esEs15(yu300, yu40000)
new_esEs21(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdd), bde)) → new_esEs16(yu300, yu40000, bdd, bde)
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs8(Just(yu300), Just(yu40000), app(ty_[], ea)) → new_esEs18(yu300, yu40000, ea)
new_esEs16(Right(yu300), Right(yu40000), cd, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs6(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs14(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs25(yu300, yu40000, app(app(ty_@2, bed), bee)) → new_esEs13(yu300, yu40000, bed, bee)
new_esEs10(:%(yu300, yu301), :%(yu40000, yu40001), bf) → new_asAs(new_esEs19(yu300, yu40000, bf), new_esEs20(yu301, yu40001, bf))
new_esEs25(yu300, yu40000, app(app(ty_Either, bef), beg)) → new_esEs16(yu300, yu40000, bef, beg)
new_esEs7(@0, @0) → True
new_esEs23(yu302, yu40002, app(ty_[], bcd)) → new_esEs18(yu302, yu40002, bcd)
new_esEs21(yu300, yu40000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs11(yu300, yu40000, ha, hb, hc)
new_esEs9(LT, LT) → True
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs17(yu30, yu4000)
new_esEs25(yu300, yu40000, app(ty_Maybe, bdg)) → new_esEs8(yu300, yu40000, bdg)
new_esEs22(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs16(Left(yu300), Left(yu40000), ty_Float, ce) → new_esEs5(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_esEs16(Right(yu300), Right(yu40000), cd, app(app(app(ty_@3, fg), fh), ga)) → new_esEs11(yu300, yu40000, fg, fh, ga)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs4(yu30, yu4000, ty_Float) → new_esEs5(yu30, yu4000)
new_esEs16(Left(yu300), Left(yu40000), ty_@0, ce) → new_esEs7(yu300, yu40000)

The set Q consists of the following terms:

new_primPlusNat0(Succ(x0), x1)
new_esEs8(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Ordering)
new_esEs8(Just(x0), Nothing, x1)
new_esEs9(GT, GT)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs7(@0, @0)
new_esEs4(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(Nothing, Just(x0), x1)
new_esEs16(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Right(x0), Right(x1), x2, ty_Int)
new_esEs25(x0, x1, ty_@0)
new_esEs16(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, ty_Double)
new_esEs9(EQ, EQ)
new_esEs16(Right(x0), Right(x1), x2, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs16(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs16(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs14(x0, x1)
new_esEs18([], [], x0)
new_esEs19(x0, x1, ty_Int)
new_esEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Right(x1), x2, x3)
new_esEs16(Right(x0), Left(x1), x2, x3)
new_esEs4(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, LT)
new_esEs9(LT, GT)
new_esEs21(x0, x1, ty_Double)
new_esEs16(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Float)
new_esEs17(False, False)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_esEs16(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_esEs16(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs8(Just(x0), Just(x1), ty_@0)
new_esEs16(Left(x0), Left(x1), ty_@0, x2)
new_esEs16(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Int)
new_esEs10(:%(x0, x1), :%(x2, x3), x4)
new_esEs24(x0, x1, ty_Char)
new_esEs5(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Float)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs21(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs25(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), ty_Char, x2)
new_primEqNat0(Zero, Zero)
new_esEs22(x0, x1, ty_Integer)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs16(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_@0)
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, ty_Double)
new_primMulNat0(Zero, Zero)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs23(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Ordering)
new_esEs16(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Bool)
new_esEs16(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_sr(Pos(x0), Pos(x1))
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, ty_Char)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primEqNat0(Succ(x0), Succ(x1))
new_asAs(False, x0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Left(x0), Left(x1), ty_Float, x2)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs17(True, False)
new_esEs17(False, True)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs18(:(x0, x1), [], x2)
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs16(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs16(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs17(True, True)
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs16(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Char(x0), Char(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs12(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs16(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_asAs(True, x0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, LT)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs16(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Left(x0), Left(x1), ty_Integer, x2)

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(Just(yu30), :(@2(Just(yu4000), yu401), yu41), ba, bb) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, bb), ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 3 >= 6, 4 >= 7
new_lookup(Just(yu30), :(@2(Nothing, yu401), yu41), ba, bb) → new_lookup(Just(yu30), yu41, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
new_lookup1(yu11, yu12, yu13, yu14, False, bc, bd) → new_lookup(Just(yu11), yu14, bc, bd)
The graph contains the following edges 4 >= 2, 6 >= 3, 7 >= 4

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