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

YES 2.1590000000000003 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 c, Eq b) => Either c b -> [(Either c b,a)] -> Maybe a) :: (Eq b, Eq c) => Either c b -> [(Either c 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, Eq b) => Either a b -> [(Either a b,c)] -> Maybe c) :: (Eq b, Eq a) => Either a b -> [(Either a b,c)] -> Maybe c)

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

The following Function with conditions

lookup k [] = Nothing

lookup k ((x,y) : xys)

| k == x

= Just y

| otherwise

= lookup k xys

is transformed to

lookup k [] = lookup3 k []

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

lookup0 k x y xys True = lookup k xys

lookup1 k x y xys True = Just y

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

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

lookup3 k [] = Nothing

lookup3 xy xz = lookup2 xy xz

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

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

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookup\n  Eq a  Eq b",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookup yu3\n  Eq a  Eq b",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookup yu3 yu4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];758[label="yu4/yu40 : yu41",fontsize=10,color="white",style="solid",shape="box"];4 -> 758[label="",style="solid", color="burlywood", weight=9];
758 -> 5[label="",style="solid", color="burlywood", weight=3];
759[label="yu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 759[label="",style="solid", color="burlywood", weight=9];
759 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookup yu3 (yu40 : yu41)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];760[label="yu40/(yu400,yu401)",fontsize=10,color="white",style="solid",shape="box"];5 -> 760[label="",style="solid", color="burlywood", weight=9];
760 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup yu3 []\n  Eq a  Eq b",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  Eq b",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 yu3 []\n  Eq a  Eq b",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  Eq b",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  Eq b",fontsize=16,color="burlywood",shape="box"];761[label="yu3/Left yu30",fontsize=10,color="white",style="solid",shape="box"];11 -> 761[label="",style="solid", color="burlywood", weight=9];
761 -> 12[label="",style="solid", color="burlywood", weight=3];
762[label="yu3/Right yu30",fontsize=10,color="white",style="solid",shape="box"];11 -> 762[label="",style="solid", color="burlywood", weight=9];
762 -> 13[label="",style="solid", color="burlywood", weight=3];
12[label="lookup1 (Left yu30) yu400 yu401 yu41 (Left yu30 == yu400)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];763[label="yu400/Left yu4000",fontsize=10,color="white",style="solid",shape="box"];12 -> 763[label="",style="solid", color="burlywood", weight=9];
763 -> 14[label="",style="solid", color="burlywood", weight=3];
764[label="yu400/Right yu4000",fontsize=10,color="white",style="solid",shape="box"];12 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 15[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 (Right yu30) yu400 yu401 yu41 (Right yu30 == yu400)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];765[label="yu400/Left yu4000",fontsize=10,color="white",style="solid",shape="box"];13 -> 765[label="",style="solid", color="burlywood", weight=9];
765 -> 16[label="",style="solid", color="burlywood", weight=3];
766[label="yu400/Right yu4000",fontsize=10,color="white",style="solid",shape="box"];13 -> 766[label="",style="solid", color="burlywood", weight=9];
766 -> 17[label="",style="solid", color="burlywood", weight=3];
14[label="lookup1 (Left yu30) (Left yu4000) yu401 yu41 (Left yu30 == Left yu4000)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="lookup1 (Left yu30) (Right yu4000) yu401 yu41 (Left yu30 == Right yu4000)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="lookup1 (Right yu30) (Left yu4000) yu401 yu41 (Right yu30 == Left yu4000)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="lookup1 (Right yu30) (Right yu4000) yu401 yu41 (Right yu30 == Right yu4000)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18 -> 22[label="",style="dashed", color="red", weight=0];
18[label="lookup1 (Left yu30) (Left yu4000) yu401 yu41 (yu30 == yu4000)\n  Eq a  Eq b",fontsize=16,color="magenta"];18 -> 23[label="",style="dashed", color="magenta", weight=3];
18 -> 24[label="",style="dashed", color="magenta", weight=3];
18 -> 25[label="",style="dashed", color="magenta", weight=3];
18 -> 26[label="",style="dashed", color="magenta", weight=3];
18 -> 27[label="",style="dashed", color="magenta", weight=3];
19[label="lookup1 (Left yu30) (Right yu4000) yu401 yu41 False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
20[label="lookup1 (Right yu30) (Left yu4000) yu401 yu41 False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
21 -> 30[label="",style="dashed", color="red", weight=0];
21[label="lookup1 (Right yu30) (Right yu4000) yu401 yu41 (yu30 == yu4000)\n  Eq a  Eq b",fontsize=16,color="magenta"];21 -> 31[label="",style="dashed", color="magenta", weight=3];
21 -> 32[label="",style="dashed", color="magenta", weight=3];
21 -> 33[label="",style="dashed", color="magenta", weight=3];
21 -> 34[label="",style="dashed", color="magenta", weight=3];
21 -> 35[label="",style="dashed", color="magenta", weight=3];
23[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];24[label="yu401",fontsize=16,color="green",shape="box"];25[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];26[label="yu30 == yu4000\n  Eq a",fontsize=16,color="blue",shape="box"];769[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 769[label="",style="solid", color="blue", weight=9];
769 -> 36[label="",style="solid", color="blue", weight=3];
770[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 770[label="",style="solid", color="blue", weight=9];
770 -> 37[label="",style="solid", color="blue", weight=3];
771[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 771[label="",style="solid", color="blue", weight=9];
771 -> 38[label="",style="solid", color="blue", weight=3];
772[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 772[label="",style="solid", color="blue", weight=9];
772 -> 39[label="",style="solid", color="blue", weight=3];
773[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 773[label="",style="solid", color="blue", weight=9];
773 -> 40[label="",style="solid", color="blue", weight=3];
774[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 774[label="",style="solid", color="blue", weight=9];
774 -> 41[label="",style="solid", color="blue", weight=3];
775[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 775[label="",style="solid", color="blue", weight=9];
775 -> 42[label="",style="solid", color="blue", weight=3];
776[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 776[label="",style="solid", color="blue", weight=9];
776 -> 43[label="",style="solid", color="blue", weight=3];
777[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 777[label="",style="solid", color="blue", weight=9];
777 -> 44[label="",style="solid", color="blue", weight=3];
778[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 778[label="",style="solid", color="blue", weight=9];
778 -> 45[label="",style="solid", color="blue", weight=3];
779[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 779[label="",style="solid", color="blue", weight=9];
779 -> 46[label="",style="solid", color="blue", weight=3];
780[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 780[label="",style="solid", color="blue", weight=9];
780 -> 47[label="",style="solid", color="blue", weight=3];
781[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 781[label="",style="solid", color="blue", weight=9];
781 -> 48[label="",style="solid", color="blue", weight=3];
782[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];26 -> 782[label="",style="solid", color="blue", weight=9];
782 -> 49[label="",style="solid", color="blue", weight=3];
27[label="yu41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];22[label="lookup1 (Left yu11) (Left yu12) yu13 yu14 yu15\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];783[label="yu15/False",fontsize=10,color="white",style="solid",shape="box"];22 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 50[label="",style="solid", color="burlywood", weight=3];
784[label="yu15/True",fontsize=10,color="white",style="solid",shape="box"];22 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 51[label="",style="solid", color="burlywood", weight=3];
28[label="lookup0 (Left yu30) (Right yu4000) yu401 yu41 otherwise\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];28 -> 52[label="",style="solid", color="black", weight=3];
29[label="lookup0 (Right yu30) (Left yu4000) yu401 yu41 otherwise\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];29 -> 53[label="",style="solid", color="black", weight=3];
31[label="yu401",fontsize=16,color="green",shape="box"];32[label="yu30 == yu4000\n  Eq a",fontsize=16,color="blue",shape="box"];785[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 785[label="",style="solid", color="blue", weight=9];
785 -> 54[label="",style="solid", color="blue", weight=3];
786[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 786[label="",style="solid", color="blue", weight=9];
786 -> 55[label="",style="solid", color="blue", weight=3];
787[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 787[label="",style="solid", color="blue", weight=9];
787 -> 56[label="",style="solid", color="blue", weight=3];
788[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 788[label="",style="solid", color="blue", weight=9];
788 -> 57[label="",style="solid", color="blue", weight=3];
789[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 789[label="",style="solid", color="blue", weight=9];
789 -> 58[label="",style="solid", color="blue", weight=3];
790[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 790[label="",style="solid", color="blue", weight=9];
790 -> 59[label="",style="solid", color="blue", weight=3];
791[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 791[label="",style="solid", color="blue", weight=9];
791 -> 60[label="",style="solid", color="blue", weight=3];
792[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 792[label="",style="solid", color="blue", weight=9];
792 -> 61[label="",style="solid", color="blue", weight=3];
793[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 793[label="",style="solid", color="blue", weight=9];
793 -> 62[label="",style="solid", color="blue", weight=3];
794[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 794[label="",style="solid", color="blue", weight=9];
794 -> 63[label="",style="solid", color="blue", weight=3];
795[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 795[label="",style="solid", color="blue", weight=9];
795 -> 64[label="",style="solid", color="blue", weight=3];
796[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 796[label="",style="solid", color="blue", weight=9];
796 -> 65[label="",style="solid", color="blue", weight=3];
797[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 797[label="",style="solid", color="blue", weight=9];
797 -> 66[label="",style="solid", color="blue", weight=3];
798[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];32 -> 798[label="",style="solid", color="blue", weight=9];
798 -> 67[label="",style="solid", color="blue", weight=3];
33[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];34[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];35[label="yu41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];30[label="lookup1 (Right yu22) (Right yu23) yu24 yu25 yu26\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];799[label="yu26/False",fontsize=10,color="white",style="solid",shape="box"];30 -> 799[label="",style="solid", color="burlywood", weight=9];
799 -> 68[label="",style="solid", color="burlywood", weight=3];
800[label="yu26/True",fontsize=10,color="white",style="solid",shape="box"];30 -> 800[label="",style="solid", color="burlywood", weight=9];
800 -> 69[label="",style="solid", color="burlywood", weight=3];
36[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];36 -> 70[label="",style="solid", color="black", weight=3];
37[label="yu30 == yu4000\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];801[label="yu30/yu300 :% yu301",fontsize=10,color="white",style="solid",shape="box"];37 -> 801[label="",style="solid", color="burlywood", weight=9];
801 -> 71[label="",style="solid", color="burlywood", weight=3];
38[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];802[label="yu30/LT",fontsize=10,color="white",style="solid",shape="box"];38 -> 802[label="",style="solid", color="burlywood", weight=9];
802 -> 72[label="",style="solid", color="burlywood", weight=3];
803[label="yu30/EQ",fontsize=10,color="white",style="solid",shape="box"];38 -> 803[label="",style="solid", color="burlywood", weight=9];
803 -> 73[label="",style="solid", color="burlywood", weight=3];
804[label="yu30/GT",fontsize=10,color="white",style="solid",shape="box"];38 -> 804[label="",style="solid", color="burlywood", weight=9];
804 -> 74[label="",style="solid", color="burlywood", weight=3];
39[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];805[label="yu30/Integer yu300",fontsize=10,color="white",style="solid",shape="box"];39 -> 805[label="",style="solid", color="burlywood", weight=9];
805 -> 75[label="",style="solid", color="burlywood", weight=3];
40[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];806[label="yu30/Left yu300",fontsize=10,color="white",style="solid",shape="box"];40 -> 806[label="",style="solid", color="burlywood", weight=9];
806 -> 76[label="",style="solid", color="burlywood", weight=3];
807[label="yu30/Right yu300",fontsize=10,color="white",style="solid",shape="box"];40 -> 807[label="",style="solid", color="burlywood", weight=9];
807 -> 77[label="",style="solid", color="burlywood", weight=3];
41[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];41 -> 78[label="",style="solid", color="black", weight=3];
42[label="yu30 == yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];808[label="yu30/(yu300,yu301,yu302)",fontsize=10,color="white",style="solid",shape="box"];42 -> 808[label="",style="solid", color="burlywood", weight=9];
808 -> 79[label="",style="solid", color="burlywood", weight=3];
43[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];43 -> 80[label="",style="solid", color="black", weight=3];
44[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];44 -> 81[label="",style="solid", color="black", weight=3];
45[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];809[label="yu30/()",fontsize=10,color="white",style="solid",shape="box"];45 -> 809[label="",style="solid", color="burlywood", weight=9];
809 -> 82[label="",style="solid", color="burlywood", weight=3];
46[label="yu30 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];810[label="yu30/yu300 : yu301",fontsize=10,color="white",style="solid",shape="box"];46 -> 810[label="",style="solid", color="burlywood", weight=9];
810 -> 83[label="",style="solid", color="burlywood", weight=3];
811[label="yu30/[]",fontsize=10,color="white",style="solid",shape="box"];46 -> 811[label="",style="solid", color="burlywood", weight=9];
811 -> 84[label="",style="solid", color="burlywood", weight=3];
47[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];812[label="yu30/False",fontsize=10,color="white",style="solid",shape="box"];47 -> 812[label="",style="solid", color="burlywood", weight=9];
812 -> 85[label="",style="solid", color="burlywood", weight=3];
813[label="yu30/True",fontsize=10,color="white",style="solid",shape="box"];47 -> 813[label="",style="solid", color="burlywood", weight=9];
813 -> 86[label="",style="solid", color="burlywood", weight=3];
48[label="yu30 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];814[label="yu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];48 -> 814[label="",style="solid", color="burlywood", weight=9];
814 -> 87[label="",style="solid", color="burlywood", weight=3];
815[label="yu30/Just yu300",fontsize=10,color="white",style="solid",shape="box"];48 -> 815[label="",style="solid", color="burlywood", weight=9];
815 -> 88[label="",style="solid", color="burlywood", weight=3];
49[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];816[label="yu30/(yu300,yu301)",fontsize=10,color="white",style="solid",shape="box"];49 -> 816[label="",style="solid", color="burlywood", weight=9];
816 -> 89[label="",style="solid", color="burlywood", weight=3];
50[label="lookup1 (Left yu11) (Left yu12) yu13 yu14 False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];50 -> 90[label="",style="solid", color="black", weight=3];
51[label="lookup1 (Left yu11) (Left yu12) yu13 yu14 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];51 -> 91[label="",style="solid", color="black", weight=3];
52[label="lookup0 (Left yu30) (Right yu4000) yu401 yu41 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];52 -> 92[label="",style="solid", color="black", weight=3];
53[label="lookup0 (Right yu30) (Left yu4000) yu401 yu41 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];53 -> 93[label="",style="solid", color="black", weight=3];
54 -> 36[label="",style="dashed", color="red", weight=0];
54[label="yu30 == yu4000",fontsize=16,color="magenta"];54 -> 94[label="",style="dashed", color="magenta", weight=3];
54 -> 95[label="",style="dashed", color="magenta", weight=3];
55 -> 37[label="",style="dashed", color="red", weight=0];
55[label="yu30 == yu4000\n  Integral a",fontsize=16,color="magenta"];55 -> 96[label="",style="dashed", color="magenta", weight=3];
55 -> 97[label="",style="dashed", color="magenta", weight=3];
56 -> 38[label="",style="dashed", color="red", weight=0];
56[label="yu30 == yu4000",fontsize=16,color="magenta"];56 -> 98[label="",style="dashed", color="magenta", weight=3];
56 -> 99[label="",style="dashed", color="magenta", weight=3];
57 -> 39[label="",style="dashed", color="red", weight=0];
57[label="yu30 == yu4000",fontsize=16,color="magenta"];57 -> 100[label="",style="dashed", color="magenta", weight=3];
57 -> 101[label="",style="dashed", color="magenta", weight=3];
58 -> 40[label="",style="dashed", color="red", weight=0];
58[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="magenta"];58 -> 102[label="",style="dashed", color="magenta", weight=3];
58 -> 103[label="",style="dashed", color="magenta", weight=3];
59 -> 41[label="",style="dashed", color="red", weight=0];
59[label="yu30 == yu4000",fontsize=16,color="magenta"];59 -> 104[label="",style="dashed", color="magenta", weight=3];
59 -> 105[label="",style="dashed", color="magenta", weight=3];
60 -> 42[label="",style="dashed", color="red", weight=0];
60[label="yu30 == yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];60 -> 106[label="",style="dashed", color="magenta", weight=3];
60 -> 107[label="",style="dashed", color="magenta", weight=3];
61 -> 43[label="",style="dashed", color="red", weight=0];
61[label="yu30 == yu4000",fontsize=16,color="magenta"];61 -> 108[label="",style="dashed", color="magenta", weight=3];
61 -> 109[label="",style="dashed", color="magenta", weight=3];
62 -> 44[label="",style="dashed", color="red", weight=0];
62[label="yu30 == yu4000",fontsize=16,color="magenta"];62 -> 110[label="",style="dashed", color="magenta", weight=3];
62 -> 111[label="",style="dashed", color="magenta", weight=3];
63 -> 45[label="",style="dashed", color="red", weight=0];
63[label="yu30 == yu4000",fontsize=16,color="magenta"];63 -> 112[label="",style="dashed", color="magenta", weight=3];
63 -> 113[label="",style="dashed", color="magenta", weight=3];
64 -> 46[label="",style="dashed", color="red", weight=0];
64[label="yu30 == yu4000\n  Eq a",fontsize=16,color="magenta"];64 -> 114[label="",style="dashed", color="magenta", weight=3];
64 -> 115[label="",style="dashed", color="magenta", weight=3];
65 -> 47[label="",style="dashed", color="red", weight=0];
65[label="yu30 == yu4000",fontsize=16,color="magenta"];65 -> 116[label="",style="dashed", color="magenta", weight=3];
65 -> 117[label="",style="dashed", color="magenta", weight=3];
66 -> 48[label="",style="dashed", color="red", weight=0];
66[label="yu30 == yu4000\n  Eq a",fontsize=16,color="magenta"];66 -> 118[label="",style="dashed", color="magenta", weight=3];
66 -> 119[label="",style="dashed", color="magenta", weight=3];
67 -> 49[label="",style="dashed", color="red", weight=0];
67[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="magenta"];67 -> 120[label="",style="dashed", color="magenta", weight=3];
67 -> 121[label="",style="dashed", color="magenta", weight=3];
68[label="lookup1 (Right yu22) (Right yu23) yu24 yu25 False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];68 -> 122[label="",style="solid", color="black", weight=3];
69[label="lookup1 (Right yu22) (Right yu23) yu24 yu25 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];69 -> 123[label="",style="solid", color="black", weight=3];
70[label="primEqChar yu30 yu4000",fontsize=16,color="burlywood",shape="box"];831[label="yu30/Char yu300",fontsize=10,color="white",style="solid",shape="box"];70 -> 831[label="",style="solid", color="burlywood", weight=9];
831 -> 124[label="",style="solid", color="burlywood", weight=3];
71[label="yu300 :% yu301 == yu4000\n  Integral a",fontsize=16,color="burlywood",shape="box"];832[label="yu4000/yu40000 :% yu40001",fontsize=10,color="white",style="solid",shape="box"];71 -> 832[label="",style="solid", color="burlywood", weight=9];
832 -> 125[label="",style="solid", color="burlywood", weight=3];
72[label="LT == yu4000",fontsize=16,color="burlywood",shape="box"];833[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];72 -> 833[label="",style="solid", color="burlywood", weight=9];
833 -> 126[label="",style="solid", color="burlywood", weight=3];
834[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];72 -> 834[label="",style="solid", color="burlywood", weight=9];
834 -> 127[label="",style="solid", color="burlywood", weight=3];
835[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];72 -> 835[label="",style="solid", color="burlywood", weight=9];
835 -> 128[label="",style="solid", color="burlywood", weight=3];
73[label="EQ == yu4000",fontsize=16,color="burlywood",shape="box"];836[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];73 -> 836[label="",style="solid", color="burlywood", weight=9];
836 -> 129[label="",style="solid", color="burlywood", weight=3];
837[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];73 -> 837[label="",style="solid", color="burlywood", weight=9];
837 -> 130[label="",style="solid", color="burlywood", weight=3];
838[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];73 -> 838[label="",style="solid", color="burlywood", weight=9];
838 -> 131[label="",style="solid", color="burlywood", weight=3];
74[label="GT == yu4000",fontsize=16,color="burlywood",shape="box"];839[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];74 -> 839[label="",style="solid", color="burlywood", weight=9];
839 -> 132[label="",style="solid", color="burlywood", weight=3];
840[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];74 -> 840[label="",style="solid", color="burlywood", weight=9];
840 -> 133[label="",style="solid", color="burlywood", weight=3];
841[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];74 -> 841[label="",style="solid", color="burlywood", weight=9];
841 -> 134[label="",style="solid", color="burlywood", weight=3];
75[label="Integer yu300 == yu4000",fontsize=16,color="burlywood",shape="box"];842[label="yu4000/Integer yu40000",fontsize=10,color="white",style="solid",shape="box"];75 -> 842[label="",style="solid", color="burlywood", weight=9];
842 -> 135[label="",style="solid", color="burlywood", weight=3];
76[label="Left yu300 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];843[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];76 -> 843[label="",style="solid", color="burlywood", weight=9];
843 -> 136[label="",style="solid", color="burlywood", weight=3];
844[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];76 -> 844[label="",style="solid", color="burlywood", weight=9];
844 -> 137[label="",style="solid", color="burlywood", weight=3];
77[label="Right yu300 == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];845[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];77 -> 845[label="",style="solid", color="burlywood", weight=9];
845 -> 138[label="",style="solid", color="burlywood", weight=3];
846[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];77 -> 846[label="",style="solid", color="burlywood", weight=9];
846 -> 139[label="",style="solid", color="burlywood", weight=3];
78[label="primEqInt yu30 yu4000",fontsize=16,color="burlywood",shape="triangle"];847[label="yu30/Pos yu300",fontsize=10,color="white",style="solid",shape="box"];78 -> 847[label="",style="solid", color="burlywood", weight=9];
847 -> 140[label="",style="solid", color="burlywood", weight=3];
848[label="yu30/Neg yu300",fontsize=10,color="white",style="solid",shape="box"];78 -> 848[label="",style="solid", color="burlywood", weight=9];
848 -> 141[label="",style="solid", color="burlywood", weight=3];
79[label="(yu300,yu301,yu302) == yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];849[label="yu4000/(yu40000,yu40001,yu40002)",fontsize=10,color="white",style="solid",shape="box"];79 -> 849[label="",style="solid", color="burlywood", weight=9];
849 -> 142[label="",style="solid", color="burlywood", weight=3];
80[label="primEqDouble yu30 yu4000",fontsize=16,color="burlywood",shape="box"];850[label="yu30/Double yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];80 -> 850[label="",style="solid", color="burlywood", weight=9];
850 -> 143[label="",style="solid", color="burlywood", weight=3];
81[label="primEqFloat yu30 yu4000",fontsize=16,color="burlywood",shape="box"];851[label="yu30/Float yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];81 -> 851[label="",style="solid", color="burlywood", weight=9];
851 -> 144[label="",style="solid", color="burlywood", weight=3];
82[label="() == yu4000",fontsize=16,color="burlywood",shape="box"];852[label="yu4000/()",fontsize=10,color="white",style="solid",shape="box"];82 -> 852[label="",style="solid", color="burlywood", weight=9];
852 -> 145[label="",style="solid", color="burlywood", weight=3];
83[label="yu300 : yu301 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];853[label="yu4000/yu40000 : yu40001",fontsize=10,color="white",style="solid",shape="box"];83 -> 853[label="",style="solid", color="burlywood", weight=9];
853 -> 146[label="",style="solid", color="burlywood", weight=3];
854[label="yu4000/[]",fontsize=10,color="white",style="solid",shape="box"];83 -> 854[label="",style="solid", color="burlywood", weight=9];
854 -> 147[label="",style="solid", color="burlywood", weight=3];
84[label="[] == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];855[label="yu4000/yu40000 : yu40001",fontsize=10,color="white",style="solid",shape="box"];84 -> 855[label="",style="solid", color="burlywood", weight=9];
855 -> 148[label="",style="solid", color="burlywood", weight=3];
856[label="yu4000/[]",fontsize=10,color="white",style="solid",shape="box"];84 -> 856[label="",style="solid", color="burlywood", weight=9];
856 -> 149[label="",style="solid", color="burlywood", weight=3];
85[label="False == yu4000",fontsize=16,color="burlywood",shape="box"];857[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];85 -> 857[label="",style="solid", color="burlywood", weight=9];
857 -> 150[label="",style="solid", color="burlywood", weight=3];
858[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];85 -> 858[label="",style="solid", color="burlywood", weight=9];
858 -> 151[label="",style="solid", color="burlywood", weight=3];
86[label="True == yu4000",fontsize=16,color="burlywood",shape="box"];859[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];86 -> 859[label="",style="solid", color="burlywood", weight=9];
859 -> 152[label="",style="solid", color="burlywood", weight=3];
860[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];86 -> 860[label="",style="solid", color="burlywood", weight=9];
860 -> 153[label="",style="solid", color="burlywood", weight=3];
87[label="Nothing == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];861[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];87 -> 861[label="",style="solid", color="burlywood", weight=9];
861 -> 154[label="",style="solid", color="burlywood", weight=3];
862[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];87 -> 862[label="",style="solid", color="burlywood", weight=9];
862 -> 155[label="",style="solid", color="burlywood", weight=3];
88[label="Just yu300 == yu4000\n  Eq a",fontsize=16,color="burlywood",shape="box"];863[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];88 -> 863[label="",style="solid", color="burlywood", weight=9];
863 -> 156[label="",style="solid", color="burlywood", weight=3];
864[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];88 -> 864[label="",style="solid", color="burlywood", weight=9];
864 -> 157[label="",style="solid", color="burlywood", weight=3];
89[label="(yu300,yu301) == yu4000\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];865[label="yu4000/(yu40000,yu40001)",fontsize=10,color="white",style="solid",shape="box"];89 -> 865[label="",style="solid", color="burlywood", weight=9];
865 -> 158[label="",style="solid", color="burlywood", weight=3];
90[label="lookup0 (Left yu11) (Left yu12) yu13 yu14 otherwise\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];90 -> 159[label="",style="solid", color="black", weight=3];
91[label="Just yu13",fontsize=16,color="green",shape="box"];92 -> 4[label="",style="dashed", color="red", weight=0];
92[label="lookup (Left yu30) yu41\n  Eq a  Eq b",fontsize=16,color="magenta"];92 -> 160[label="",style="dashed", color="magenta", weight=3];
92 -> 161[label="",style="dashed", color="magenta", weight=3];
93 -> 4[label="",style="dashed", color="red", weight=0];
93[label="lookup (Right yu30) yu41\n  Eq a  Eq b",fontsize=16,color="magenta"];93 -> 162[label="",style="dashed", color="magenta", weight=3];
93 -> 163[label="",style="dashed", color="magenta", weight=3];
94[label="yu4000",fontsize=16,color="green",shape="box"];95[label="yu30",fontsize=16,color="green",shape="box"];96[label="yu4000\n  Integral a",fontsize=16,color="green",shape="box"];97[label="yu30\n  Integral a",fontsize=16,color="green",shape="box"];98[label="yu4000",fontsize=16,color="green",shape="box"];99[label="yu30",fontsize=16,color="green",shape="box"];100[label="yu4000",fontsize=16,color="green",shape="box"];101[label="yu30",fontsize=16,color="green",shape="box"];102[label="yu4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];103[label="yu30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];104[label="yu4000",fontsize=16,color="green",shape="box"];105[label="yu30",fontsize=16,color="green",shape="box"];106[label="yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];107[label="yu30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];108[label="yu4000",fontsize=16,color="green",shape="box"];109[label="yu30",fontsize=16,color="green",shape="box"];110[label="yu4000",fontsize=16,color="green",shape="box"];111[label="yu30",fontsize=16,color="green",shape="box"];112[label="yu4000",fontsize=16,color="green",shape="box"];113[label="yu30",fontsize=16,color="green",shape="box"];114[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];115[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];116[label="yu4000",fontsize=16,color="green",shape="box"];117[label="yu30",fontsize=16,color="green",shape="box"];118[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];119[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];120[label="yu4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];121[label="yu30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];122[label="lookup0 (Right yu22) (Right yu23) yu24 yu25 otherwise\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];122 -> 164[label="",style="solid", color="black", weight=3];
123[label="Just yu24",fontsize=16,color="green",shape="box"];124[label="primEqChar (Char yu300) yu4000",fontsize=16,color="burlywood",shape="box"];868[label="yu4000/Char yu40000",fontsize=10,color="white",style="solid",shape="box"];124 -> 868[label="",style="solid", color="burlywood", weight=9];
868 -> 165[label="",style="solid", color="burlywood", weight=3];
125[label="yu300 :% yu301 == yu40000 :% yu40001\n  Integral a",fontsize=16,color="black",shape="box"];125 -> 166[label="",style="solid", color="black", weight=3];
126[label="LT == LT",fontsize=16,color="black",shape="box"];126 -> 167[label="",style="solid", color="black", weight=3];
127[label="LT == EQ",fontsize=16,color="black",shape="box"];127 -> 168[label="",style="solid", color="black", weight=3];
128[label="LT == GT",fontsize=16,color="black",shape="box"];128 -> 169[label="",style="solid", color="black", weight=3];
129[label="EQ == LT",fontsize=16,color="black",shape="box"];129 -> 170[label="",style="solid", color="black", weight=3];
130[label="EQ == EQ",fontsize=16,color="black",shape="box"];130 -> 171[label="",style="solid", color="black", weight=3];
131[label="EQ == GT",fontsize=16,color="black",shape="box"];131 -> 172[label="",style="solid", color="black", weight=3];
132[label="GT == LT",fontsize=16,color="black",shape="box"];132 -> 173[label="",style="solid", color="black", weight=3];
133[label="GT == EQ",fontsize=16,color="black",shape="box"];133 -> 174[label="",style="solid", color="black", weight=3];
134[label="GT == GT",fontsize=16,color="black",shape="box"];134 -> 175[label="",style="solid", color="black", weight=3];
135[label="Integer yu300 == Integer yu40000",fontsize=16,color="black",shape="box"];135 -> 176[label="",style="solid", color="black", weight=3];
136[label="Left yu300 == Left yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];136 -> 177[label="",style="solid", color="black", weight=3];
137[label="Left yu300 == Right yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];137 -> 178[label="",style="solid", color="black", weight=3];
138[label="Right yu300 == Left yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];138 -> 179[label="",style="solid", color="black", weight=3];
139[label="Right yu300 == Right yu40000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];139 -> 180[label="",style="solid", color="black", weight=3];
140[label="primEqInt (Pos yu300) yu4000",fontsize=16,color="burlywood",shape="box"];869[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];140 -> 869[label="",style="solid", color="burlywood", weight=9];
869 -> 181[label="",style="solid", color="burlywood", weight=3];
870[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];140 -> 870[label="",style="solid", color="burlywood", weight=9];
870 -> 182[label="",style="solid", color="burlywood", weight=3];
141[label="primEqInt (Neg yu300) yu4000",fontsize=16,color="burlywood",shape="box"];871[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];141 -> 871[label="",style="solid", color="burlywood", weight=9];
871 -> 183[label="",style="solid", color="burlywood", weight=3];
872[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 872[label="",style="solid", color="burlywood", weight=9];
872 -> 184[label="",style="solid", color="burlywood", weight=3];
142[label="(yu300,yu301,yu302) == (yu40000,yu40001,yu40002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];142 -> 185[label="",style="solid", color="black", weight=3];
143[label="primEqDouble (Double yu300 yu301) yu4000",fontsize=16,color="burlywood",shape="box"];873[label="yu4000/Double yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];143 -> 873[label="",style="solid", color="burlywood", weight=9];
873 -> 186[label="",style="solid", color="burlywood", weight=3];
144[label="primEqFloat (Float yu300 yu301) yu4000",fontsize=16,color="burlywood",shape="box"];874[label="yu4000/Float yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];144 -> 874[label="",style="solid", color="burlywood", weight=9];
874 -> 187[label="",style="solid", color="burlywood", weight=3];
145[label="() == ()",fontsize=16,color="black",shape="box"];145 -> 188[label="",style="solid", color="black", weight=3];
146[label="yu300 : yu301 == yu40000 : yu40001\n  Eq a",fontsize=16,color="black",shape="box"];146 -> 189[label="",style="solid", color="black", weight=3];
147[label="yu300 : yu301 == []\n  Eq a",fontsize=16,color="black",shape="box"];147 -> 190[label="",style="solid", color="black", weight=3];
148[label="[] == yu40000 : yu40001\n  Eq a",fontsize=16,color="black",shape="box"];148 -> 191[label="",style="solid", color="black", weight=3];
149[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];149 -> 192[label="",style="solid", color="black", weight=3];
150[label="False == False",fontsize=16,color="black",shape="box"];150 -> 193[label="",style="solid", color="black", weight=3];
151[label="False == True",fontsize=16,color="black",shape="box"];151 -> 194[label="",style="solid", color="black", weight=3];
152[label="True == False",fontsize=16,color="black",shape="box"];152 -> 195[label="",style="solid", color="black", weight=3];
153[label="True == True",fontsize=16,color="black",shape="box"];153 -> 196[label="",style="solid", color="black", weight=3];
154[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];154 -> 197[label="",style="solid", color="black", weight=3];
155[label="Nothing == Just yu40000\n  Eq a",fontsize=16,color="black",shape="box"];155 -> 198[label="",style="solid", color="black", weight=3];
156[label="Just yu300 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];156 -> 199[label="",style="solid", color="black", weight=3];
157[label="Just yu300 == Just yu40000\n  Eq a",fontsize=16,color="black",shape="box"];157 -> 200[label="",style="solid", color="black", weight=3];
158[label="(yu300,yu301) == (yu40000,yu40001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];158 -> 201[label="",style="solid", color="black", weight=3];
159[label="lookup0 (Left yu11) (Left yu12) yu13 yu14 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];159 -> 202[label="",style="solid", color="black", weight=3];
160[label="Left yu30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];161[label="yu41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];162[label="Right yu30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];163[label="yu41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];164[label="lookup0 (Right yu22) (Right yu23) yu24 yu25 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];164 -> 203[label="",style="solid", color="black", weight=3];
165[label="primEqChar (Char yu300) (Char yu40000)",fontsize=16,color="black",shape="box"];165 -> 204[label="",style="solid", color="black", weight=3];
166 -> 288[label="",style="dashed", color="red", weight=0];
166[label="yu300 == yu40000 && yu301 == yu40001\n  Integral a",fontsize=16,color="magenta"];166 -> 289[label="",style="dashed", color="magenta", weight=3];
166 -> 290[label="",style="dashed", color="magenta", weight=3];
167[label="True",fontsize=16,color="green",shape="box"];168[label="False",fontsize=16,color="green",shape="box"];169[label="False",fontsize=16,color="green",shape="box"];170[label="False",fontsize=16,color="green",shape="box"];171[label="True",fontsize=16,color="green",shape="box"];172[label="False",fontsize=16,color="green",shape="box"];173[label="False",fontsize=16,color="green",shape="box"];174[label="False",fontsize=16,color="green",shape="box"];175[label="True",fontsize=16,color="green",shape="box"];176 -> 78[label="",style="dashed", color="red", weight=0];
176[label="primEqInt yu300 yu40000",fontsize=16,color="magenta"];176 -> 215[label="",style="dashed", color="magenta", weight=3];
176 -> 216[label="",style="dashed", color="magenta", weight=3];
177[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];877[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 877[label="",style="solid", color="blue", weight=9];
877 -> 217[label="",style="solid", color="blue", weight=3];
878[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 878[label="",style="solid", color="blue", weight=9];
878 -> 218[label="",style="solid", color="blue", weight=3];
879[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 879[label="",style="solid", color="blue", weight=9];
879 -> 219[label="",style="solid", color="blue", weight=3];
880[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 880[label="",style="solid", color="blue", weight=9];
880 -> 220[label="",style="solid", color="blue", weight=3];
881[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 881[label="",style="solid", color="blue", weight=9];
881 -> 221[label="",style="solid", color="blue", weight=3];
882[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 882[label="",style="solid", color="blue", weight=9];
882 -> 222[label="",style="solid", color="blue", weight=3];
883[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 883[label="",style="solid", color="blue", weight=9];
883 -> 223[label="",style="solid", color="blue", weight=3];
884[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 884[label="",style="solid", color="blue", weight=9];
884 -> 224[label="",style="solid", color="blue", weight=3];
885[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 885[label="",style="solid", color="blue", weight=9];
885 -> 225[label="",style="solid", color="blue", weight=3];
886[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 886[label="",style="solid", color="blue", weight=9];
886 -> 226[label="",style="solid", color="blue", weight=3];
887[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 887[label="",style="solid", color="blue", weight=9];
887 -> 227[label="",style="solid", color="blue", weight=3];
888[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 888[label="",style="solid", color="blue", weight=9];
888 -> 228[label="",style="solid", color="blue", weight=3];
889[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 889[label="",style="solid", color="blue", weight=9];
889 -> 229[label="",style="solid", color="blue", weight=3];
890[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];177 -> 890[label="",style="solid", color="blue", weight=9];
890 -> 230[label="",style="solid", color="blue", weight=3];
178[label="False",fontsize=16,color="green",shape="box"];179[label="False",fontsize=16,color="green",shape="box"];180[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];891[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 891[label="",style="solid", color="blue", weight=9];
891 -> 231[label="",style="solid", color="blue", weight=3];
892[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 892[label="",style="solid", color="blue", weight=9];
892 -> 232[label="",style="solid", color="blue", weight=3];
893[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 893[label="",style="solid", color="blue", weight=9];
893 -> 233[label="",style="solid", color="blue", weight=3];
894[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 894[label="",style="solid", color="blue", weight=9];
894 -> 234[label="",style="solid", color="blue", weight=3];
895[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 895[label="",style="solid", color="blue", weight=9];
895 -> 235[label="",style="solid", color="blue", weight=3];
896[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 896[label="",style="solid", color="blue", weight=9];
896 -> 236[label="",style="solid", color="blue", weight=3];
897[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 897[label="",style="solid", color="blue", weight=9];
897 -> 237[label="",style="solid", color="blue", weight=3];
898[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 898[label="",style="solid", color="blue", weight=9];
898 -> 238[label="",style="solid", color="blue", weight=3];
899[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 899[label="",style="solid", color="blue", weight=9];
899 -> 239[label="",style="solid", color="blue", weight=3];
900[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 900[label="",style="solid", color="blue", weight=9];
900 -> 240[label="",style="solid", color="blue", weight=3];
901[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 901[label="",style="solid", color="blue", weight=9];
901 -> 241[label="",style="solid", color="blue", weight=3];
902[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 902[label="",style="solid", color="blue", weight=9];
902 -> 242[label="",style="solid", color="blue", weight=3];
903[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 903[label="",style="solid", color="blue", weight=9];
903 -> 243[label="",style="solid", color="blue", weight=3];
904[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];180 -> 904[label="",style="solid", color="blue", weight=9];
904 -> 244[label="",style="solid", color="blue", weight=3];
181[label="primEqInt (Pos (Succ yu3000)) yu4000",fontsize=16,color="burlywood",shape="box"];905[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];181 -> 905[label="",style="solid", color="burlywood", weight=9];
905 -> 245[label="",style="solid", color="burlywood", weight=3];
906[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];181 -> 906[label="",style="solid", color="burlywood", weight=9];
906 -> 246[label="",style="solid", color="burlywood", weight=3];
182[label="primEqInt (Pos Zero) yu4000",fontsize=16,color="burlywood",shape="box"];907[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];182 -> 907[label="",style="solid", color="burlywood", weight=9];
907 -> 247[label="",style="solid", color="burlywood", weight=3];
908[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];182 -> 908[label="",style="solid", color="burlywood", weight=9];
908 -> 248[label="",style="solid", color="burlywood", weight=3];
183[label="primEqInt (Neg (Succ yu3000)) yu4000",fontsize=16,color="burlywood",shape="box"];909[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];183 -> 909[label="",style="solid", color="burlywood", weight=9];
909 -> 249[label="",style="solid", color="burlywood", weight=3];
910[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];183 -> 910[label="",style="solid", color="burlywood", weight=9];
910 -> 250[label="",style="solid", color="burlywood", weight=3];
184[label="primEqInt (Neg Zero) yu4000",fontsize=16,color="burlywood",shape="box"];911[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];184 -> 911[label="",style="solid", color="burlywood", weight=9];
911 -> 251[label="",style="solid", color="burlywood", weight=3];
912[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];184 -> 912[label="",style="solid", color="burlywood", weight=9];
912 -> 252[label="",style="solid", color="burlywood", weight=3];
185 -> 288[label="",style="dashed", color="red", weight=0];
185[label="yu300 == yu40000 && yu301 == yu40001 && yu302 == yu40002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];185 -> 291[label="",style="dashed", color="magenta", weight=3];
185 -> 292[label="",style="dashed", color="magenta", weight=3];
186[label="primEqDouble (Double yu300 yu301) (Double yu40000 yu40001)",fontsize=16,color="black",shape="box"];186 -> 264[label="",style="solid", color="black", weight=3];
187[label="primEqFloat (Float yu300 yu301) (Float yu40000 yu40001)",fontsize=16,color="black",shape="box"];187 -> 265[label="",style="solid", color="black", weight=3];
188[label="True",fontsize=16,color="green",shape="box"];189 -> 288[label="",style="dashed", color="red", weight=0];
189[label="yu300 == yu40000 && yu301 == yu40001\n  Eq a",fontsize=16,color="magenta"];189 -> 293[label="",style="dashed", color="magenta", weight=3];
189 -> 294[label="",style="dashed", color="magenta", weight=3];
190[label="False",fontsize=16,color="green",shape="box"];191[label="False",fontsize=16,color="green",shape="box"];192[label="True",fontsize=16,color="green",shape="box"];193[label="True",fontsize=16,color="green",shape="box"];194[label="False",fontsize=16,color="green",shape="box"];195[label="False",fontsize=16,color="green",shape="box"];196[label="True",fontsize=16,color="green",shape="box"];197[label="True",fontsize=16,color="green",shape="box"];198[label="False",fontsize=16,color="green",shape="box"];199[label="False",fontsize=16,color="green",shape="box"];200[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];915[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 915[label="",style="solid", color="blue", weight=9];
915 -> 266[label="",style="solid", color="blue", weight=3];
916[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 916[label="",style="solid", color="blue", weight=9];
916 -> 267[label="",style="solid", color="blue", weight=3];
917[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 917[label="",style="solid", color="blue", weight=9];
917 -> 268[label="",style="solid", color="blue", weight=3];
918[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 918[label="",style="solid", color="blue", weight=9];
918 -> 269[label="",style="solid", color="blue", weight=3];
919[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 919[label="",style="solid", color="blue", weight=9];
919 -> 270[label="",style="solid", color="blue", weight=3];
920[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 920[label="",style="solid", color="blue", weight=9];
920 -> 271[label="",style="solid", color="blue", weight=3];
921[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 921[label="",style="solid", color="blue", weight=9];
921 -> 272[label="",style="solid", color="blue", weight=3];
922[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 922[label="",style="solid", color="blue", weight=9];
922 -> 273[label="",style="solid", color="blue", weight=3];
923[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 923[label="",style="solid", color="blue", weight=9];
923 -> 274[label="",style="solid", color="blue", weight=3];
924[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 924[label="",style="solid", color="blue", weight=9];
924 -> 275[label="",style="solid", color="blue", weight=3];
925[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 925[label="",style="solid", color="blue", weight=9];
925 -> 276[label="",style="solid", color="blue", weight=3];
926[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 926[label="",style="solid", color="blue", weight=9];
926 -> 277[label="",style="solid", color="blue", weight=3];
927[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 927[label="",style="solid", color="blue", weight=9];
927 -> 278[label="",style="solid", color="blue", weight=3];
928[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];200 -> 928[label="",style="solid", color="blue", weight=9];
928 -> 279[label="",style="solid", color="blue", weight=3];
201 -> 288[label="",style="dashed", color="red", weight=0];
201[label="yu300 == yu40000 && yu301 == yu40001\n  Eq a  Eq b",fontsize=16,color="magenta"];201 -> 295[label="",style="dashed", color="magenta", weight=3];
201 -> 296[label="",style="dashed", color="magenta", weight=3];
202 -> 4[label="",style="dashed", color="red", weight=0];
202[label="lookup (Left yu11) yu14\n  Eq a  Eq b",fontsize=16,color="magenta"];202 -> 280[label="",style="dashed", color="magenta", weight=3];
202 -> 281[label="",style="dashed", color="magenta", weight=3];
203 -> 4[label="",style="dashed", color="red", weight=0];
203[label="lookup (Right yu22) yu25\n  Eq a  Eq b",fontsize=16,color="magenta"];203 -> 282[label="",style="dashed", color="magenta", weight=3];
203 -> 283[label="",style="dashed", color="magenta", weight=3];
204[label="primEqNat yu300 yu40000",fontsize=16,color="burlywood",shape="triangle"];932[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];204 -> 932[label="",style="solid", color="burlywood", weight=9];
932 -> 284[label="",style="solid", color="burlywood", weight=3];
933[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];204 -> 933[label="",style="solid", color="burlywood", weight=9];
933 -> 285[label="",style="solid", color="burlywood", weight=3];
289[label="yu300 == yu40000\n  Integral a",fontsize=16,color="blue",shape="box"];934[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];289 -> 934[label="",style="solid", color="blue", weight=9];
934 -> 301[label="",style="solid", color="blue", weight=3];
935[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];289 -> 935[label="",style="solid", color="blue", weight=9];
935 -> 302[label="",style="solid", color="blue", weight=3];
290[label="yu301 == yu40001\n  Integral a",fontsize=16,color="blue",shape="box"];936[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];290 -> 936[label="",style="solid", color="blue", weight=9];
936 -> 303[label="",style="solid", color="blue", weight=3];
937[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];290 -> 937[label="",style="solid", color="blue", weight=9];
937 -> 304[label="",style="solid", color="blue", weight=3];
288[label="yu38 && yu39",fontsize=16,color="burlywood",shape="triangle"];938[label="yu38/False",fontsize=10,color="white",style="solid",shape="box"];288 -> 938[label="",style="solid", color="burlywood", weight=9];
938 -> 305[label="",style="solid", color="burlywood", weight=3];
939[label="yu38/True",fontsize=10,color="white",style="solid",shape="box"];288 -> 939[label="",style="solid", color="burlywood", weight=9];
939 -> 306[label="",style="solid", color="burlywood", weight=3];
215[label="yu40000",fontsize=16,color="green",shape="box"];216[label="yu300",fontsize=16,color="green",shape="box"];217 -> 36[label="",style="dashed", color="red", weight=0];
217[label="yu300 == yu40000",fontsize=16,color="magenta"];217 -> 307[label="",style="dashed", color="magenta", weight=3];
217 -> 308[label="",style="dashed", color="magenta", weight=3];
218 -> 37[label="",style="dashed", color="red", weight=0];
218[label="yu300 == yu40000\n  Integral a",fontsize=16,color="magenta"];218 -> 309[label="",style="dashed", color="magenta", weight=3];
218 -> 310[label="",style="dashed", color="magenta", weight=3];
219 -> 38[label="",style="dashed", color="red", weight=0];
219[label="yu300 == yu40000",fontsize=16,color="magenta"];219 -> 311[label="",style="dashed", color="magenta", weight=3];
219 -> 312[label="",style="dashed", color="magenta", weight=3];
220 -> 39[label="",style="dashed", color="red", weight=0];
220[label="yu300 == yu40000",fontsize=16,color="magenta"];220 -> 313[label="",style="dashed", color="magenta", weight=3];
220 -> 314[label="",style="dashed", color="magenta", weight=3];
221 -> 40[label="",style="dashed", color="red", weight=0];
221[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];221 -> 315[label="",style="dashed", color="magenta", weight=3];
221 -> 316[label="",style="dashed", color="magenta", weight=3];
222 -> 41[label="",style="dashed", color="red", weight=0];
222[label="yu300 == yu40000",fontsize=16,color="magenta"];222 -> 317[label="",style="dashed", color="magenta", weight=3];
222 -> 318[label="",style="dashed", color="magenta", weight=3];
223 -> 42[label="",style="dashed", color="red", weight=0];
223[label="yu300 == yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];223 -> 319[label="",style="dashed", color="magenta", weight=3];
223 -> 320[label="",style="dashed", color="magenta", weight=3];
224 -> 43[label="",style="dashed", color="red", weight=0];
224[label="yu300 == yu40000",fontsize=16,color="magenta"];224 -> 321[label="",style="dashed", color="magenta", weight=3];
224 -> 322[label="",style="dashed", color="magenta", weight=3];
225 -> 44[label="",style="dashed", color="red", weight=0];
225[label="yu300 == yu40000",fontsize=16,color="magenta"];225 -> 323[label="",style="dashed", color="magenta", weight=3];
225 -> 324[label="",style="dashed", color="magenta", weight=3];
226 -> 45[label="",style="dashed", color="red", weight=0];
226[label="yu300 == yu40000",fontsize=16,color="magenta"];226 -> 325[label="",style="dashed", color="magenta", weight=3];
226 -> 326[label="",style="dashed", color="magenta", weight=3];
227 -> 46[label="",style="dashed", color="red", weight=0];
227[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];227 -> 327[label="",style="dashed", color="magenta", weight=3];
227 -> 328[label="",style="dashed", color="magenta", weight=3];
228 -> 47[label="",style="dashed", color="red", weight=0];
228[label="yu300 == yu40000",fontsize=16,color="magenta"];228 -> 329[label="",style="dashed", color="magenta", weight=3];
228 -> 330[label="",style="dashed", color="magenta", weight=3];
229 -> 48[label="",style="dashed", color="red", weight=0];
229[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];229 -> 331[label="",style="dashed", color="magenta", weight=3];
229 -> 332[label="",style="dashed", color="magenta", weight=3];
230 -> 49[label="",style="dashed", color="red", weight=0];
230[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];230 -> 333[label="",style="dashed", color="magenta", weight=3];
230 -> 334[label="",style="dashed", color="magenta", weight=3];
231 -> 36[label="",style="dashed", color="red", weight=0];
231[label="yu300 == yu40000",fontsize=16,color="magenta"];231 -> 335[label="",style="dashed", color="magenta", weight=3];
231 -> 336[label="",style="dashed", color="magenta", weight=3];
232 -> 37[label="",style="dashed", color="red", weight=0];
232[label="yu300 == yu40000\n  Integral a",fontsize=16,color="magenta"];232 -> 337[label="",style="dashed", color="magenta", weight=3];
232 -> 338[label="",style="dashed", color="magenta", weight=3];
233 -> 38[label="",style="dashed", color="red", weight=0];
233[label="yu300 == yu40000",fontsize=16,color="magenta"];233 -> 339[label="",style="dashed", color="magenta", weight=3];
233 -> 340[label="",style="dashed", color="magenta", weight=3];
234 -> 39[label="",style="dashed", color="red", weight=0];
234[label="yu300 == yu40000",fontsize=16,color="magenta"];234 -> 341[label="",style="dashed", color="magenta", weight=3];
234 -> 342[label="",style="dashed", color="magenta", weight=3];
235 -> 40[label="",style="dashed", color="red", weight=0];
235[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];235 -> 343[label="",style="dashed", color="magenta", weight=3];
235 -> 344[label="",style="dashed", color="magenta", weight=3];
236 -> 41[label="",style="dashed", color="red", weight=0];
236[label="yu300 == yu40000",fontsize=16,color="magenta"];236 -> 345[label="",style="dashed", color="magenta", weight=3];
236 -> 346[label="",style="dashed", color="magenta", weight=3];
237 -> 42[label="",style="dashed", color="red", weight=0];
237[label="yu300 == yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];237 -> 347[label="",style="dashed", color="magenta", weight=3];
237 -> 348[label="",style="dashed", color="magenta", weight=3];
238 -> 43[label="",style="dashed", color="red", weight=0];
238[label="yu300 == yu40000",fontsize=16,color="magenta"];238 -> 349[label="",style="dashed", color="magenta", weight=3];
238 -> 350[label="",style="dashed", color="magenta", weight=3];
239 -> 44[label="",style="dashed", color="red", weight=0];
239[label="yu300 == yu40000",fontsize=16,color="magenta"];239 -> 351[label="",style="dashed", color="magenta", weight=3];
239 -> 352[label="",style="dashed", color="magenta", weight=3];
240 -> 45[label="",style="dashed", color="red", weight=0];
240[label="yu300 == yu40000",fontsize=16,color="magenta"];240 -> 353[label="",style="dashed", color="magenta", weight=3];
240 -> 354[label="",style="dashed", color="magenta", weight=3];
241 -> 46[label="",style="dashed", color="red", weight=0];
241[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];241 -> 355[label="",style="dashed", color="magenta", weight=3];
241 -> 356[label="",style="dashed", color="magenta", weight=3];
242 -> 47[label="",style="dashed", color="red", weight=0];
242[label="yu300 == yu40000",fontsize=16,color="magenta"];242 -> 357[label="",style="dashed", color="magenta", weight=3];
242 -> 358[label="",style="dashed", color="magenta", weight=3];
243 -> 48[label="",style="dashed", color="red", weight=0];
243[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];243 -> 359[label="",style="dashed", color="magenta", weight=3];
243 -> 360[label="",style="dashed", color="magenta", weight=3];
244 -> 49[label="",style="dashed", color="red", weight=0];
244[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];244 -> 361[label="",style="dashed", color="magenta", weight=3];
244 -> 362[label="",style="dashed", color="magenta", weight=3];
245[label="primEqInt (Pos (Succ yu3000)) (Pos yu40000)",fontsize=16,color="burlywood",shape="box"];968[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];245 -> 968[label="",style="solid", color="burlywood", weight=9];
968 -> 363[label="",style="solid", color="burlywood", weight=3];
969[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];245 -> 969[label="",style="solid", color="burlywood", weight=9];
969 -> 364[label="",style="solid", color="burlywood", weight=3];
246[label="primEqInt (Pos (Succ yu3000)) (Neg yu40000)",fontsize=16,color="black",shape="box"];246 -> 365[label="",style="solid", color="black", weight=3];
247[label="primEqInt (Pos Zero) (Pos yu40000)",fontsize=16,color="burlywood",shape="box"];970[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];247 -> 970[label="",style="solid", color="burlywood", weight=9];
970 -> 366[label="",style="solid", color="burlywood", weight=3];
971[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];247 -> 971[label="",style="solid", color="burlywood", weight=9];
971 -> 367[label="",style="solid", color="burlywood", weight=3];
248[label="primEqInt (Pos Zero) (Neg yu40000)",fontsize=16,color="burlywood",shape="box"];972[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];248 -> 972[label="",style="solid", color="burlywood", weight=9];
972 -> 368[label="",style="solid", color="burlywood", weight=3];
973[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];248 -> 973[label="",style="solid", color="burlywood", weight=9];
973 -> 369[label="",style="solid", color="burlywood", weight=3];
249[label="primEqInt (Neg (Succ yu3000)) (Pos yu40000)",fontsize=16,color="black",shape="box"];249 -> 370[label="",style="solid", color="black", weight=3];
250[label="primEqInt (Neg (Succ yu3000)) (Neg yu40000)",fontsize=16,color="burlywood",shape="box"];974[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];250 -> 974[label="",style="solid", color="burlywood", weight=9];
974 -> 371[label="",style="solid", color="burlywood", weight=3];
975[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];250 -> 975[label="",style="solid", color="burlywood", weight=9];
975 -> 372[label="",style="solid", color="burlywood", weight=3];
251[label="primEqInt (Neg Zero) (Pos yu40000)",fontsize=16,color="burlywood",shape="box"];976[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];251 -> 976[label="",style="solid", color="burlywood", weight=9];
976 -> 373[label="",style="solid", color="burlywood", weight=3];
977[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];251 -> 977[label="",style="solid", color="burlywood", weight=9];
977 -> 374[label="",style="solid", color="burlywood", weight=3];
252[label="primEqInt (Neg Zero) (Neg yu40000)",fontsize=16,color="burlywood",shape="box"];978[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];252 -> 978[label="",style="solid", color="burlywood", weight=9];
978 -> 375[label="",style="solid", color="burlywood", weight=3];
979[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];252 -> 979[label="",style="solid", color="burlywood", weight=9];
979 -> 376[label="",style="solid", color="burlywood", weight=3];
291[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];980[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 980[label="",style="solid", color="blue", weight=9];
980 -> 377[label="",style="solid", color="blue", weight=3];
981[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 981[label="",style="solid", color="blue", weight=9];
981 -> 378[label="",style="solid", color="blue", weight=3];
982[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 982[label="",style="solid", color="blue", weight=9];
982 -> 379[label="",style="solid", color="blue", weight=3];
983[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 983[label="",style="solid", color="blue", weight=9];
983 -> 380[label="",style="solid", color="blue", weight=3];
984[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 984[label="",style="solid", color="blue", weight=9];
984 -> 381[label="",style="solid", color="blue", weight=3];
985[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 985[label="",style="solid", color="blue", weight=9];
985 -> 382[label="",style="solid", color="blue", weight=3];
986[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 986[label="",style="solid", color="blue", weight=9];
986 -> 383[label="",style="solid", color="blue", weight=3];
987[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 987[label="",style="solid", color="blue", weight=9];
987 -> 384[label="",style="solid", color="blue", weight=3];
988[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 988[label="",style="solid", color="blue", weight=9];
988 -> 385[label="",style="solid", color="blue", weight=3];
989[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 989[label="",style="solid", color="blue", weight=9];
989 -> 386[label="",style="solid", color="blue", weight=3];
990[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 990[label="",style="solid", color="blue", weight=9];
990 -> 387[label="",style="solid", color="blue", weight=3];
991[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 991[label="",style="solid", color="blue", weight=9];
991 -> 388[label="",style="solid", color="blue", weight=3];
992[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 992[label="",style="solid", color="blue", weight=9];
992 -> 389[label="",style="solid", color="blue", weight=3];
993[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];291 -> 993[label="",style="solid", color="blue", weight=9];
993 -> 390[label="",style="solid", color="blue", weight=3];
292 -> 288[label="",style="dashed", color="red", weight=0];
292[label="yu301 == yu40001 && yu302 == yu40002\n  Eq a  Eq b",fontsize=16,color="magenta"];292 -> 391[label="",style="dashed", color="magenta", weight=3];
292 -> 392[label="",style="dashed", color="magenta", weight=3];
264 -> 41[label="",style="dashed", color="red", weight=0];
264[label="yu300 * yu40000 == yu301 * yu40001",fontsize=16,color="magenta"];264 -> 393[label="",style="dashed", color="magenta", weight=3];
264 -> 394[label="",style="dashed", color="magenta", weight=3];
265 -> 41[label="",style="dashed", color="red", weight=0];
265[label="yu300 * yu40000 == yu301 * yu40001",fontsize=16,color="magenta"];265 -> 395[label="",style="dashed", color="magenta", weight=3];
265 -> 396[label="",style="dashed", color="magenta", weight=3];
293[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];997[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 997[label="",style="solid", color="blue", weight=9];
997 -> 397[label="",style="solid", color="blue", weight=3];
998[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 998[label="",style="solid", color="blue", weight=9];
998 -> 398[label="",style="solid", color="blue", weight=3];
999[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 999[label="",style="solid", color="blue", weight=9];
999 -> 399[label="",style="solid", color="blue", weight=3];
1000[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1000[label="",style="solid", color="blue", weight=9];
1000 -> 400[label="",style="solid", color="blue", weight=3];
1001[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1001[label="",style="solid", color="blue", weight=9];
1001 -> 401[label="",style="solid", color="blue", weight=3];
1002[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1002[label="",style="solid", color="blue", weight=9];
1002 -> 402[label="",style="solid", color="blue", weight=3];
1003[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1003[label="",style="solid", color="blue", weight=9];
1003 -> 403[label="",style="solid", color="blue", weight=3];
1004[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1004[label="",style="solid", color="blue", weight=9];
1004 -> 404[label="",style="solid", color="blue", weight=3];
1005[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1005[label="",style="solid", color="blue", weight=9];
1005 -> 405[label="",style="solid", color="blue", weight=3];
1006[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1006[label="",style="solid", color="blue", weight=9];
1006 -> 406[label="",style="solid", color="blue", weight=3];
1007[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1007[label="",style="solid", color="blue", weight=9];
1007 -> 407[label="",style="solid", color="blue", weight=3];
1008[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1008[label="",style="solid", color="blue", weight=9];
1008 -> 408[label="",style="solid", color="blue", weight=3];
1009[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1009[label="",style="solid", color="blue", weight=9];
1009 -> 409[label="",style="solid", color="blue", weight=3];
1010[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];293 -> 1010[label="",style="solid", color="blue", weight=9];
1010 -> 410[label="",style="solid", color="blue", weight=3];
294 -> 46[label="",style="dashed", color="red", weight=0];
294[label="yu301 == yu40001\n  Eq a",fontsize=16,color="magenta"];294 -> 411[label="",style="dashed", color="magenta", weight=3];
294 -> 412[label="",style="dashed", color="magenta", weight=3];
266 -> 36[label="",style="dashed", color="red", weight=0];
266[label="yu300 == yu40000",fontsize=16,color="magenta"];266 -> 413[label="",style="dashed", color="magenta", weight=3];
266 -> 414[label="",style="dashed", color="magenta", weight=3];
267 -> 37[label="",style="dashed", color="red", weight=0];
267[label="yu300 == yu40000\n  Integral a",fontsize=16,color="magenta"];267 -> 415[label="",style="dashed", color="magenta", weight=3];
267 -> 416[label="",style="dashed", color="magenta", weight=3];
268 -> 38[label="",style="dashed", color="red", weight=0];
268[label="yu300 == yu40000",fontsize=16,color="magenta"];268 -> 417[label="",style="dashed", color="magenta", weight=3];
268 -> 418[label="",style="dashed", color="magenta", weight=3];
269 -> 39[label="",style="dashed", color="red", weight=0];
269[label="yu300 == yu40000",fontsize=16,color="magenta"];269 -> 419[label="",style="dashed", color="magenta", weight=3];
269 -> 420[label="",style="dashed", color="magenta", weight=3];
270 -> 40[label="",style="dashed", color="red", weight=0];
270[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];270 -> 421[label="",style="dashed", color="magenta", weight=3];
270 -> 422[label="",style="dashed", color="magenta", weight=3];
271 -> 41[label="",style="dashed", color="red", weight=0];
271[label="yu300 == yu40000",fontsize=16,color="magenta"];271 -> 423[label="",style="dashed", color="magenta", weight=3];
271 -> 424[label="",style="dashed", color="magenta", weight=3];
272 -> 42[label="",style="dashed", color="red", weight=0];
272[label="yu300 == yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];272 -> 425[label="",style="dashed", color="magenta", weight=3];
272 -> 426[label="",style="dashed", color="magenta", weight=3];
273 -> 43[label="",style="dashed", color="red", weight=0];
273[label="yu300 == yu40000",fontsize=16,color="magenta"];273 -> 427[label="",style="dashed", color="magenta", weight=3];
273 -> 428[label="",style="dashed", color="magenta", weight=3];
274 -> 44[label="",style="dashed", color="red", weight=0];
274[label="yu300 == yu40000",fontsize=16,color="magenta"];274 -> 429[label="",style="dashed", color="magenta", weight=3];
274 -> 430[label="",style="dashed", color="magenta", weight=3];
275 -> 45[label="",style="dashed", color="red", weight=0];
275[label="yu300 == yu40000",fontsize=16,color="magenta"];275 -> 431[label="",style="dashed", color="magenta", weight=3];
275 -> 432[label="",style="dashed", color="magenta", weight=3];
276 -> 46[label="",style="dashed", color="red", weight=0];
276[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];276 -> 433[label="",style="dashed", color="magenta", weight=3];
276 -> 434[label="",style="dashed", color="magenta", weight=3];
277 -> 47[label="",style="dashed", color="red", weight=0];
277[label="yu300 == yu40000",fontsize=16,color="magenta"];277 -> 435[label="",style="dashed", color="magenta", weight=3];
277 -> 436[label="",style="dashed", color="magenta", weight=3];
278 -> 48[label="",style="dashed", color="red", weight=0];
278[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];278 -> 437[label="",style="dashed", color="magenta", weight=3];
278 -> 438[label="",style="dashed", color="magenta", weight=3];
279 -> 49[label="",style="dashed", color="red", weight=0];
279[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];279 -> 439[label="",style="dashed", color="magenta", weight=3];
279 -> 440[label="",style="dashed", color="magenta", weight=3];
295[label="yu300 == yu40000\n  Eq a",fontsize=16,color="blue",shape="box"];1026[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1026[label="",style="solid", color="blue", weight=9];
1026 -> 441[label="",style="solid", color="blue", weight=3];
1027[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1027[label="",style="solid", color="blue", weight=9];
1027 -> 442[label="",style="solid", color="blue", weight=3];
1028[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1028[label="",style="solid", color="blue", weight=9];
1028 -> 443[label="",style="solid", color="blue", weight=3];
1029[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1029[label="",style="solid", color="blue", weight=9];
1029 -> 444[label="",style="solid", color="blue", weight=3];
1030[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1030[label="",style="solid", color="blue", weight=9];
1030 -> 445[label="",style="solid", color="blue", weight=3];
1031[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1031[label="",style="solid", color="blue", weight=9];
1031 -> 446[label="",style="solid", color="blue", weight=3];
1032[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1032[label="",style="solid", color="blue", weight=9];
1032 -> 447[label="",style="solid", color="blue", weight=3];
1033[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1033[label="",style="solid", color="blue", weight=9];
1033 -> 448[label="",style="solid", color="blue", weight=3];
1034[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1034[label="",style="solid", color="blue", weight=9];
1034 -> 449[label="",style="solid", color="blue", weight=3];
1035[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1035[label="",style="solid", color="blue", weight=9];
1035 -> 450[label="",style="solid", color="blue", weight=3];
1036[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1036[label="",style="solid", color="blue", weight=9];
1036 -> 451[label="",style="solid", color="blue", weight=3];
1037[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1037[label="",style="solid", color="blue", weight=9];
1037 -> 452[label="",style="solid", color="blue", weight=3];
1038[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1038[label="",style="solid", color="blue", weight=9];
1038 -> 453[label="",style="solid", color="blue", weight=3];
1039[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];295 -> 1039[label="",style="solid", color="blue", weight=9];
1039 -> 454[label="",style="solid", color="blue", weight=3];
296[label="yu301 == yu40001\n  Eq a",fontsize=16,color="blue",shape="box"];1040[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1040[label="",style="solid", color="blue", weight=9];
1040 -> 455[label="",style="solid", color="blue", weight=3];
1041[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1041[label="",style="solid", color="blue", weight=9];
1041 -> 456[label="",style="solid", color="blue", weight=3];
1042[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1042[label="",style="solid", color="blue", weight=9];
1042 -> 457[label="",style="solid", color="blue", weight=3];
1043[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1043[label="",style="solid", color="blue", weight=9];
1043 -> 458[label="",style="solid", color="blue", weight=3];
1044[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1044[label="",style="solid", color="blue", weight=9];
1044 -> 459[label="",style="solid", color="blue", weight=3];
1045[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1045[label="",style="solid", color="blue", weight=9];
1045 -> 460[label="",style="solid", color="blue", weight=3];
1046[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1046[label="",style="solid", color="blue", weight=9];
1046 -> 461[label="",style="solid", color="blue", weight=3];
1047[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1047[label="",style="solid", color="blue", weight=9];
1047 -> 462[label="",style="solid", color="blue", weight=3];
1048[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1048[label="",style="solid", color="blue", weight=9];
1048 -> 463[label="",style="solid", color="blue", weight=3];
1049[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1049[label="",style="solid", color="blue", weight=9];
1049 -> 464[label="",style="solid", color="blue", weight=3];
1050[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1050[label="",style="solid", color="blue", weight=9];
1050 -> 465[label="",style="solid", color="blue", weight=3];
1051[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1051[label="",style="solid", color="blue", weight=9];
1051 -> 466[label="",style="solid", color="blue", weight=3];
1052[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1052[label="",style="solid", color="blue", weight=9];
1052 -> 467[label="",style="solid", color="blue", weight=3];
1053[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];296 -> 1053[label="",style="solid", color="blue", weight=9];
1053 -> 468[label="",style="solid", color="blue", weight=3];
280[label="Left yu11\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];281[label="yu14\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];282[label="Right yu22\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];283[label="yu25\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];284[label="primEqNat (Succ yu3000) yu40000",fontsize=16,color="burlywood",shape="box"];1054[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];284 -> 1054[label="",style="solid", color="burlywood", weight=9];
1054 -> 469[label="",style="solid", color="burlywood", weight=3];
1055[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];284 -> 1055[label="",style="solid", color="burlywood", weight=9];
1055 -> 470[label="",style="solid", color="burlywood", weight=3];
285[label="primEqNat Zero yu40000",fontsize=16,color="burlywood",shape="box"];1056[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];285 -> 1056[label="",style="solid", color="burlywood", weight=9];
1056 -> 471[label="",style="solid", color="burlywood", weight=3];
1057[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];285 -> 1057[label="",style="solid", color="burlywood", weight=9];
1057 -> 472[label="",style="solid", color="burlywood", weight=3];
301 -> 39[label="",style="dashed", color="red", weight=0];
301[label="yu300 == yu40000",fontsize=16,color="magenta"];301 -> 473[label="",style="dashed", color="magenta", weight=3];
301 -> 474[label="",style="dashed", color="magenta", weight=3];
302 -> 41[label="",style="dashed", color="red", weight=0];
302[label="yu300 == yu40000",fontsize=16,color="magenta"];302 -> 475[label="",style="dashed", color="magenta", weight=3];
302 -> 476[label="",style="dashed", color="magenta", weight=3];
303 -> 39[label="",style="dashed", color="red", weight=0];
303[label="yu301 == yu40001",fontsize=16,color="magenta"];303 -> 477[label="",style="dashed", color="magenta", weight=3];
303 -> 478[label="",style="dashed", color="magenta", weight=3];
304 -> 41[label="",style="dashed", color="red", weight=0];
304[label="yu301 == yu40001",fontsize=16,color="magenta"];304 -> 479[label="",style="dashed", color="magenta", weight=3];
304 -> 480[label="",style="dashed", color="magenta", weight=3];
305[label="False && yu39",fontsize=16,color="black",shape="box"];305 -> 481[label="",style="solid", color="black", weight=3];
306[label="True && yu39",fontsize=16,color="black",shape="box"];306 -> 482[label="",style="solid", color="black", weight=3];
307[label="yu40000",fontsize=16,color="green",shape="box"];308[label="yu300",fontsize=16,color="green",shape="box"];309[label="yu40000\n  Integral a",fontsize=16,color="green",shape="box"];310[label="yu300\n  Integral a",fontsize=16,color="green",shape="box"];311[label="yu40000",fontsize=16,color="green",shape="box"];312[label="yu300",fontsize=16,color="green",shape="box"];313[label="yu40000",fontsize=16,color="green",shape="box"];314[label="yu300",fontsize=16,color="green",shape="box"];315[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];316[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];317[label="yu40000",fontsize=16,color="green",shape="box"];318[label="yu300",fontsize=16,color="green",shape="box"];319[label="yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];320[label="yu300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];321[label="yu40000",fontsize=16,color="green",shape="box"];322[label="yu300",fontsize=16,color="green",shape="box"];323[label="yu40000",fontsize=16,color="green",shape="box"];324[label="yu300",fontsize=16,color="green",shape="box"];325[label="yu40000",fontsize=16,color="green",shape="box"];326[label="yu300",fontsize=16,color="green",shape="box"];327[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];328[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];329[label="yu40000",fontsize=16,color="green",shape="box"];330[label="yu300",fontsize=16,color="green",shape="box"];331[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];332[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];333[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];334[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];335[label="yu40000",fontsize=16,color="green",shape="box"];336[label="yu300",fontsize=16,color="green",shape="box"];337[label="yu40000\n  Integral a",fontsize=16,color="green",shape="box"];338[label="yu300\n  Integral a",fontsize=16,color="green",shape="box"];339[label="yu40000",fontsize=16,color="green",shape="box"];340[label="yu300",fontsize=16,color="green",shape="box"];341[label="yu40000",fontsize=16,color="green",shape="box"];342[label="yu300",fontsize=16,color="green",shape="box"];343[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];344[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];345[label="yu40000",fontsize=16,color="green",shape="box"];346[label="yu300",fontsize=16,color="green",shape="box"];347[label="yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];348[label="yu300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];349[label="yu40000",fontsize=16,color="green",shape="box"];350[label="yu300",fontsize=16,color="green",shape="box"];351[label="yu40000",fontsize=16,color="green",shape="box"];352[label="yu300",fontsize=16,color="green",shape="box"];353[label="yu40000",fontsize=16,color="green",shape="box"];354[label="yu300",fontsize=16,color="green",shape="box"];355[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];356[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];357[label="yu40000",fontsize=16,color="green",shape="box"];358[label="yu300",fontsize=16,color="green",shape="box"];359[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];360[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];361[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];362[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];363[label="primEqInt (Pos (Succ yu3000)) (Pos (Succ yu400000))",fontsize=16,color="black",shape="box"];363 -> 483[label="",style="solid", color="black", weight=3];
364[label="primEqInt (Pos (Succ yu3000)) (Pos Zero)",fontsize=16,color="black",shape="box"];364 -> 484[label="",style="solid", color="black", weight=3];
365[label="False",fontsize=16,color="green",shape="box"];366[label="primEqInt (Pos Zero) (Pos (Succ yu400000))",fontsize=16,color="black",shape="box"];366 -> 485[label="",style="solid", color="black", weight=3];
367[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];367 -> 486[label="",style="solid", color="black", weight=3];
368[label="primEqInt (Pos Zero) (Neg (Succ yu400000))",fontsize=16,color="black",shape="box"];368 -> 487[label="",style="solid", color="black", weight=3];
369[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];369 -> 488[label="",style="solid", color="black", weight=3];
370[label="False",fontsize=16,color="green",shape="box"];371[label="primEqInt (Neg (Succ yu3000)) (Neg (Succ yu400000))",fontsize=16,color="black",shape="box"];371 -> 489[label="",style="solid", color="black", weight=3];
372[label="primEqInt (Neg (Succ yu3000)) (Neg Zero)",fontsize=16,color="black",shape="box"];372 -> 490[label="",style="solid", color="black", weight=3];
373[label="primEqInt (Neg Zero) (Pos (Succ yu400000))",fontsize=16,color="black",shape="box"];373 -> 491[label="",style="solid", color="black", weight=3];
374[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];374 -> 492[label="",style="solid", color="black", weight=3];
375[label="primEqInt (Neg Zero) (Neg (Succ yu400000))",fontsize=16,color="black",shape="box"];375 -> 493[label="",style="solid", color="black", weight=3];
376[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];376 -> 494[label="",style="solid", color="black", weight=3];
377 -> 36[label="",style="dashed", color="red", weight=0];
377[label="yu300 == yu40000",fontsize=16,color="magenta"];377 -> 495[label="",style="dashed", color="magenta", weight=3];
377 -> 496[label="",style="dashed", color="magenta", weight=3];
378 -> 37[label="",style="dashed", color="red", weight=0];
378[label="yu300 == yu40000\n  Integral a",fontsize=16,color="magenta"];378 -> 497[label="",style="dashed", color="magenta", weight=3];
378 -> 498[label="",style="dashed", color="magenta", weight=3];
379 -> 38[label="",style="dashed", color="red", weight=0];
379[label="yu300 == yu40000",fontsize=16,color="magenta"];379 -> 499[label="",style="dashed", color="magenta", weight=3];
379 -> 500[label="",style="dashed", color="magenta", weight=3];
380 -> 39[label="",style="dashed", color="red", weight=0];
380[label="yu300 == yu40000",fontsize=16,color="magenta"];380 -> 501[label="",style="dashed", color="magenta", weight=3];
380 -> 502[label="",style="dashed", color="magenta", weight=3];
381 -> 40[label="",style="dashed", color="red", weight=0];
381[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];381 -> 503[label="",style="dashed", color="magenta", weight=3];
381 -> 504[label="",style="dashed", color="magenta", weight=3];
382 -> 41[label="",style="dashed", color="red", weight=0];
382[label="yu300 == yu40000",fontsize=16,color="magenta"];382 -> 505[label="",style="dashed", color="magenta", weight=3];
382 -> 506[label="",style="dashed", color="magenta", weight=3];
383 -> 42[label="",style="dashed", color="red", weight=0];
383[label="yu300 == yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];383 -> 507[label="",style="dashed", color="magenta", weight=3];
383 -> 508[label="",style="dashed", color="magenta", weight=3];
384 -> 43[label="",style="dashed", color="red", weight=0];
384[label="yu300 == yu40000",fontsize=16,color="magenta"];384 -> 509[label="",style="dashed", color="magenta", weight=3];
384 -> 510[label="",style="dashed", color="magenta", weight=3];
385 -> 44[label="",style="dashed", color="red", weight=0];
385[label="yu300 == yu40000",fontsize=16,color="magenta"];385 -> 511[label="",style="dashed", color="magenta", weight=3];
385 -> 512[label="",style="dashed", color="magenta", weight=3];
386 -> 45[label="",style="dashed", color="red", weight=0];
386[label="yu300 == yu40000",fontsize=16,color="magenta"];386 -> 513[label="",style="dashed", color="magenta", weight=3];
386 -> 514[label="",style="dashed", color="magenta", weight=3];
387 -> 46[label="",style="dashed", color="red", weight=0];
387[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];387 -> 515[label="",style="dashed", color="magenta", weight=3];
387 -> 516[label="",style="dashed", color="magenta", weight=3];
388 -> 47[label="",style="dashed", color="red", weight=0];
388[label="yu300 == yu40000",fontsize=16,color="magenta"];388 -> 517[label="",style="dashed", color="magenta", weight=3];
388 -> 518[label="",style="dashed", color="magenta", weight=3];
389 -> 48[label="",style="dashed", color="red", weight=0];
389[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];389 -> 519[label="",style="dashed", color="magenta", weight=3];
389 -> 520[label="",style="dashed", color="magenta", weight=3];
390 -> 49[label="",style="dashed", color="red", weight=0];
390[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];390 -> 521[label="",style="dashed", color="magenta", weight=3];
390 -> 522[label="",style="dashed", color="magenta", weight=3];
391[label="yu301 == yu40001\n  Eq a",fontsize=16,color="blue",shape="box"];1076[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1076[label="",style="solid", color="blue", weight=9];
1076 -> 523[label="",style="solid", color="blue", weight=3];
1077[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1077[label="",style="solid", color="blue", weight=9];
1077 -> 524[label="",style="solid", color="blue", weight=3];
1078[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1078[label="",style="solid", color="blue", weight=9];
1078 -> 525[label="",style="solid", color="blue", weight=3];
1079[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1079[label="",style="solid", color="blue", weight=9];
1079 -> 526[label="",style="solid", color="blue", weight=3];
1080[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1080[label="",style="solid", color="blue", weight=9];
1080 -> 527[label="",style="solid", color="blue", weight=3];
1081[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1081[label="",style="solid", color="blue", weight=9];
1081 -> 528[label="",style="solid", color="blue", weight=3];
1082[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1082[label="",style="solid", color="blue", weight=9];
1082 -> 529[label="",style="solid", color="blue", weight=3];
1083[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1083[label="",style="solid", color="blue", weight=9];
1083 -> 530[label="",style="solid", color="blue", weight=3];
1084[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1084[label="",style="solid", color="blue", weight=9];
1084 -> 531[label="",style="solid", color="blue", weight=3];
1085[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1085[label="",style="solid", color="blue", weight=9];
1085 -> 532[label="",style="solid", color="blue", weight=3];
1086[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1086[label="",style="solid", color="blue", weight=9];
1086 -> 533[label="",style="solid", color="blue", weight=3];
1087[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1087[label="",style="solid", color="blue", weight=9];
1087 -> 534[label="",style="solid", color="blue", weight=3];
1088[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1088[label="",style="solid", color="blue", weight=9];
1088 -> 535[label="",style="solid", color="blue", weight=3];
1089[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];391 -> 1089[label="",style="solid", color="blue", weight=9];
1089 -> 536[label="",style="solid", color="blue", weight=3];
392[label="yu302 == yu40002\n  Eq a",fontsize=16,color="blue",shape="box"];1090[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1090[label="",style="solid", color="blue", weight=9];
1090 -> 537[label="",style="solid", color="blue", weight=3];
1091[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1091[label="",style="solid", color="blue", weight=9];
1091 -> 538[label="",style="solid", color="blue", weight=3];
1092[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1092[label="",style="solid", color="blue", weight=9];
1092 -> 539[label="",style="solid", color="blue", weight=3];
1093[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1093[label="",style="solid", color="blue", weight=9];
1093 -> 540[label="",style="solid", color="blue", weight=3];
1094[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1094[label="",style="solid", color="blue", weight=9];
1094 -> 541[label="",style="solid", color="blue", weight=3];
1095[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1095[label="",style="solid", color="blue", weight=9];
1095 -> 542[label="",style="solid", color="blue", weight=3];
1096[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1096[label="",style="solid", color="blue", weight=9];
1096 -> 543[label="",style="solid", color="blue", weight=3];
1097[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1097[label="",style="solid", color="blue", weight=9];
1097 -> 544[label="",style="solid", color="blue", weight=3];
1098[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1098[label="",style="solid", color="blue", weight=9];
1098 -> 545[label="",style="solid", color="blue", weight=3];
1099[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1099[label="",style="solid", color="blue", weight=9];
1099 -> 546[label="",style="solid", color="blue", weight=3];
1100[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1100[label="",style="solid", color="blue", weight=9];
1100 -> 547[label="",style="solid", color="blue", weight=3];
1101[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1101[label="",style="solid", color="blue", weight=9];
1101 -> 548[label="",style="solid", color="blue", weight=3];
1102[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1102[label="",style="solid", color="blue", weight=9];
1102 -> 549[label="",style="solid", color="blue", weight=3];
1103[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];392 -> 1103[label="",style="solid", color="blue", weight=9];
1103 -> 550[label="",style="solid", color="blue", weight=3];
393[label="yu301 * yu40001",fontsize=16,color="black",shape="triangle"];393 -> 551[label="",style="solid", color="black", weight=3];
394 -> 393[label="",style="dashed", color="red", weight=0];
394[label="yu300 * yu40000",fontsize=16,color="magenta"];394 -> 552[label="",style="dashed", color="magenta", weight=3];
394 -> 553[label="",style="dashed", color="magenta", weight=3];
395 -> 393[label="",style="dashed", color="red", weight=0];
395[label="yu301 * yu40001",fontsize=16,color="magenta"];395 -> 554[label="",style="dashed", color="magenta", weight=3];
395 -> 555[label="",style="dashed", color="magenta", weight=3];
396 -> 393[label="",style="dashed", color="red", weight=0];
396[label="yu300 * yu40000",fontsize=16,color="magenta"];396 -> 556[label="",style="dashed", color="magenta", weight=3];
396 -> 557[label="",style="dashed", color="magenta", weight=3];
397 -> 36[label="",style="dashed", color="red", weight=0];
397[label="yu300 == yu40000",fontsize=16,color="magenta"];397 -> 558[label="",style="dashed", color="magenta", weight=3];
397 -> 559[label="",style="dashed", color="magenta", weight=3];
398 -> 37[label="",style="dashed", color="red", weight=0];
398[label="yu300 == yu40000\n  Integral a",fontsize=16,color="magenta"];398 -> 560[label="",style="dashed", color="magenta", weight=3];
398 -> 561[label="",style="dashed", color="magenta", weight=3];
399 -> 38[label="",style="dashed", color="red", weight=0];
399[label="yu300 == yu40000",fontsize=16,color="magenta"];399 -> 562[label="",style="dashed", color="magenta", weight=3];
399 -> 563[label="",style="dashed", color="magenta", weight=3];
400 -> 39[label="",style="dashed", color="red", weight=0];
400[label="yu300 == yu40000",fontsize=16,color="magenta"];400 -> 564[label="",style="dashed", color="magenta", weight=3];
400 -> 565[label="",style="dashed", color="magenta", weight=3];
401 -> 40[label="",style="dashed", color="red", weight=0];
401[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];401 -> 566[label="",style="dashed", color="magenta", weight=3];
401 -> 567[label="",style="dashed", color="magenta", weight=3];
402 -> 41[label="",style="dashed", color="red", weight=0];
402[label="yu300 == yu40000",fontsize=16,color="magenta"];402 -> 568[label="",style="dashed", color="magenta", weight=3];
402 -> 569[label="",style="dashed", color="magenta", weight=3];
403 -> 42[label="",style="dashed", color="red", weight=0];
403[label="yu300 == yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];403 -> 570[label="",style="dashed", color="magenta", weight=3];
403 -> 571[label="",style="dashed", color="magenta", weight=3];
404 -> 43[label="",style="dashed", color="red", weight=0];
404[label="yu300 == yu40000",fontsize=16,color="magenta"];404 -> 572[label="",style="dashed", color="magenta", weight=3];
404 -> 573[label="",style="dashed", color="magenta", weight=3];
405 -> 44[label="",style="dashed", color="red", weight=0];
405[label="yu300 == yu40000",fontsize=16,color="magenta"];405 -> 574[label="",style="dashed", color="magenta", weight=3];
405 -> 575[label="",style="dashed", color="magenta", weight=3];
406 -> 45[label="",style="dashed", color="red", weight=0];
406[label="yu300 == yu40000",fontsize=16,color="magenta"];406 -> 576[label="",style="dashed", color="magenta", weight=3];
406 -> 577[label="",style="dashed", color="magenta", weight=3];
407 -> 46[label="",style="dashed", color="red", weight=0];
407[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];407 -> 578[label="",style="dashed", color="magenta", weight=3];
407 -> 579[label="",style="dashed", color="magenta", weight=3];
408 -> 47[label="",style="dashed", color="red", weight=0];
408[label="yu300 == yu40000",fontsize=16,color="magenta"];408 -> 580[label="",style="dashed", color="magenta", weight=3];
408 -> 581[label="",style="dashed", color="magenta", weight=3];
409 -> 48[label="",style="dashed", color="red", weight=0];
409[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];409 -> 582[label="",style="dashed", color="magenta", weight=3];
409 -> 583[label="",style="dashed", color="magenta", weight=3];
410 -> 49[label="",style="dashed", color="red", weight=0];
410[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];410 -> 584[label="",style="dashed", color="magenta", weight=3];
410 -> 585[label="",style="dashed", color="magenta", weight=3];
411[label="yu40001\n  Eq a",fontsize=16,color="green",shape="box"];412[label="yu301\n  Eq a",fontsize=16,color="green",shape="box"];413[label="yu40000",fontsize=16,color="green",shape="box"];414[label="yu300",fontsize=16,color="green",shape="box"];415[label="yu40000\n  Integral a",fontsize=16,color="green",shape="box"];416[label="yu300\n  Integral a",fontsize=16,color="green",shape="box"];417[label="yu40000",fontsize=16,color="green",shape="box"];418[label="yu300",fontsize=16,color="green",shape="box"];419[label="yu40000",fontsize=16,color="green",shape="box"];420[label="yu300",fontsize=16,color="green",shape="box"];421[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];422[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];423[label="yu40000",fontsize=16,color="green",shape="box"];424[label="yu300",fontsize=16,color="green",shape="box"];425[label="yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];426[label="yu300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];427[label="yu40000",fontsize=16,color="green",shape="box"];428[label="yu300",fontsize=16,color="green",shape="box"];429[label="yu40000",fontsize=16,color="green",shape="box"];430[label="yu300",fontsize=16,color="green",shape="box"];431[label="yu40000",fontsize=16,color="green",shape="box"];432[label="yu300",fontsize=16,color="green",shape="box"];433[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];434[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];435[label="yu40000",fontsize=16,color="green",shape="box"];436[label="yu300",fontsize=16,color="green",shape="box"];437[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];438[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];439[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];440[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];441 -> 36[label="",style="dashed", color="red", weight=0];
441[label="yu300 == yu40000",fontsize=16,color="magenta"];441 -> 586[label="",style="dashed", color="magenta", weight=3];
441 -> 587[label="",style="dashed", color="magenta", weight=3];
442 -> 37[label="",style="dashed", color="red", weight=0];
442[label="yu300 == yu40000\n  Integral a",fontsize=16,color="magenta"];442 -> 588[label="",style="dashed", color="magenta", weight=3];
442 -> 589[label="",style="dashed", color="magenta", weight=3];
443 -> 38[label="",style="dashed", color="red", weight=0];
443[label="yu300 == yu40000",fontsize=16,color="magenta"];443 -> 590[label="",style="dashed", color="magenta", weight=3];
443 -> 591[label="",style="dashed", color="magenta", weight=3];
444 -> 39[label="",style="dashed", color="red", weight=0];
444[label="yu300 == yu40000",fontsize=16,color="magenta"];444 -> 592[label="",style="dashed", color="magenta", weight=3];
444 -> 593[label="",style="dashed", color="magenta", weight=3];
445 -> 40[label="",style="dashed", color="red", weight=0];
445[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];445 -> 594[label="",style="dashed", color="magenta", weight=3];
445 -> 595[label="",style="dashed", color="magenta", weight=3];
446 -> 41[label="",style="dashed", color="red", weight=0];
446[label="yu300 == yu40000",fontsize=16,color="magenta"];446 -> 596[label="",style="dashed", color="magenta", weight=3];
446 -> 597[label="",style="dashed", color="magenta", weight=3];
447 -> 42[label="",style="dashed", color="red", weight=0];
447[label="yu300 == yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];447 -> 598[label="",style="dashed", color="magenta", weight=3];
447 -> 599[label="",style="dashed", color="magenta", weight=3];
448 -> 43[label="",style="dashed", color="red", weight=0];
448[label="yu300 == yu40000",fontsize=16,color="magenta"];448 -> 600[label="",style="dashed", color="magenta", weight=3];
448 -> 601[label="",style="dashed", color="magenta", weight=3];
449 -> 44[label="",style="dashed", color="red", weight=0];
449[label="yu300 == yu40000",fontsize=16,color="magenta"];449 -> 602[label="",style="dashed", color="magenta", weight=3];
449 -> 603[label="",style="dashed", color="magenta", weight=3];
450 -> 45[label="",style="dashed", color="red", weight=0];
450[label="yu300 == yu40000",fontsize=16,color="magenta"];450 -> 604[label="",style="dashed", color="magenta", weight=3];
450 -> 605[label="",style="dashed", color="magenta", weight=3];
451 -> 46[label="",style="dashed", color="red", weight=0];
451[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];451 -> 606[label="",style="dashed", color="magenta", weight=3];
451 -> 607[label="",style="dashed", color="magenta", weight=3];
452 -> 47[label="",style="dashed", color="red", weight=0];
452[label="yu300 == yu40000",fontsize=16,color="magenta"];452 -> 608[label="",style="dashed", color="magenta", weight=3];
452 -> 609[label="",style="dashed", color="magenta", weight=3];
453 -> 48[label="",style="dashed", color="red", weight=0];
453[label="yu300 == yu40000\n  Eq a",fontsize=16,color="magenta"];453 -> 610[label="",style="dashed", color="magenta", weight=3];
453 -> 611[label="",style="dashed", color="magenta", weight=3];
454 -> 49[label="",style="dashed", color="red", weight=0];
454[label="yu300 == yu40000\n  Eq a  Eq b",fontsize=16,color="magenta"];454 -> 612[label="",style="dashed", color="magenta", weight=3];
454 -> 613[label="",style="dashed", color="magenta", weight=3];
455 -> 36[label="",style="dashed", color="red", weight=0];
455[label="yu301 == yu40001",fontsize=16,color="magenta"];455 -> 614[label="",style="dashed", color="magenta", weight=3];
455 -> 615[label="",style="dashed", color="magenta", weight=3];
456 -> 37[label="",style="dashed", color="red", weight=0];
456[label="yu301 == yu40001\n  Integral a",fontsize=16,color="magenta"];456 -> 616[label="",style="dashed", color="magenta", weight=3];
456 -> 617[label="",style="dashed", color="magenta", weight=3];
457 -> 38[label="",style="dashed", color="red", weight=0];
457[label="yu301 == yu40001",fontsize=16,color="magenta"];457 -> 618[label="",style="dashed", color="magenta", weight=3];
457 -> 619[label="",style="dashed", color="magenta", weight=3];
458 -> 39[label="",style="dashed", color="red", weight=0];
458[label="yu301 == yu40001",fontsize=16,color="magenta"];458 -> 620[label="",style="dashed", color="magenta", weight=3];
458 -> 621[label="",style="dashed", color="magenta", weight=3];
459 -> 40[label="",style="dashed", color="red", weight=0];
459[label="yu301 == yu40001\n  Eq a  Eq b",fontsize=16,color="magenta"];459 -> 622[label="",style="dashed", color="magenta", weight=3];
459 -> 623[label="",style="dashed", color="magenta", weight=3];
460 -> 41[label="",style="dashed", color="red", weight=0];
460[label="yu301 == yu40001",fontsize=16,color="magenta"];460 -> 624[label="",style="dashed", color="magenta", weight=3];
460 -> 625[label="",style="dashed", color="magenta", weight=3];
461 -> 42[label="",style="dashed", color="red", weight=0];
461[label="yu301 == yu40001\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];461 -> 626[label="",style="dashed", color="magenta", weight=3];
461 -> 627[label="",style="dashed", color="magenta", weight=3];
462 -> 43[label="",style="dashed", color="red", weight=0];
462[label="yu301 == yu40001",fontsize=16,color="magenta"];462 -> 628[label="",style="dashed", color="magenta", weight=3];
462 -> 629[label="",style="dashed", color="magenta", weight=3];
463 -> 44[label="",style="dashed", color="red", weight=0];
463[label="yu301 == yu40001",fontsize=16,color="magenta"];463 -> 630[label="",style="dashed", color="magenta", weight=3];
463 -> 631[label="",style="dashed", color="magenta", weight=3];
464 -> 45[label="",style="dashed", color="red", weight=0];
464[label="yu301 == yu40001",fontsize=16,color="magenta"];464 -> 632[label="",style="dashed", color="magenta", weight=3];
464 -> 633[label="",style="dashed", color="magenta", weight=3];
465 -> 46[label="",style="dashed", color="red", weight=0];
465[label="yu301 == yu40001\n  Eq a",fontsize=16,color="magenta"];465 -> 634[label="",style="dashed", color="magenta", weight=3];
465 -> 635[label="",style="dashed", color="magenta", weight=3];
466 -> 47[label="",style="dashed", color="red", weight=0];
466[label="yu301 == yu40001",fontsize=16,color="magenta"];466 -> 636[label="",style="dashed", color="magenta", weight=3];
466 -> 637[label="",style="dashed", color="magenta", weight=3];
467 -> 48[label="",style="dashed", color="red", weight=0];
467[label="yu301 == yu40001\n  Eq a",fontsize=16,color="magenta"];467 -> 638[label="",style="dashed", color="magenta", weight=3];
467 -> 639[label="",style="dashed", color="magenta", weight=3];
468 -> 49[label="",style="dashed", color="red", weight=0];
468[label="yu301 == yu40001\n  Eq a  Eq b",fontsize=16,color="magenta"];468 -> 640[label="",style="dashed", color="magenta", weight=3];
468 -> 641[label="",style="dashed", color="magenta", weight=3];
469[label="primEqNat (Succ yu3000) (Succ yu400000)",fontsize=16,color="black",shape="box"];469 -> 642[label="",style="solid", color="black", weight=3];
470[label="primEqNat (Succ yu3000) Zero",fontsize=16,color="black",shape="box"];470 -> 643[label="",style="solid", color="black", weight=3];
471[label="primEqNat Zero (Succ yu400000)",fontsize=16,color="black",shape="box"];471 -> 644[label="",style="solid", color="black", weight=3];
472[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];472 -> 645[label="",style="solid", color="black", weight=3];
473[label="yu40000",fontsize=16,color="green",shape="box"];474[label="yu300",fontsize=16,color="green",shape="box"];475[label="yu40000",fontsize=16,color="green",shape="box"];476[label="yu300",fontsize=16,color="green",shape="box"];477[label="yu40001",fontsize=16,color="green",shape="box"];478[label="yu301",fontsize=16,color="green",shape="box"];479[label="yu40001",fontsize=16,color="green",shape="box"];480[label="yu301",fontsize=16,color="green",shape="box"];481[label="False",fontsize=16,color="green",shape="box"];482[label="yu39",fontsize=16,color="green",shape="box"];483 -> 204[label="",style="dashed", color="red", weight=0];
483[label="primEqNat yu3000 yu400000",fontsize=16,color="magenta"];483 -> 646[label="",style="dashed", color="magenta", weight=3];
483 -> 647[label="",style="dashed", color="magenta", weight=3];
484[label="False",fontsize=16,color="green",shape="box"];485[label="False",fontsize=16,color="green",shape="box"];486[label="True",fontsize=16,color="green",shape="box"];487[label="False",fontsize=16,color="green",shape="box"];488[label="True",fontsize=16,color="green",shape="box"];489 -> 204[label="",style="dashed", color="red", weight=0];
489[label="primEqNat yu3000 yu400000",fontsize=16,color="magenta"];489 -> 648[label="",style="dashed", color="magenta", weight=3];
489 -> 649[label="",style="dashed", color="magenta", weight=3];
490[label="False",fontsize=16,color="green",shape="box"];491[label="False",fontsize=16,color="green",shape="box"];492[label="True",fontsize=16,color="green",shape="box"];493[label="False",fontsize=16,color="green",shape="box"];494[label="True",fontsize=16,color="green",shape="box"];495[label="yu40000",fontsize=16,color="green",shape="box"];496[label="yu300",fontsize=16,color="green",shape="box"];497[label="yu40000\n  Integral a",fontsize=16,color="green",shape="box"];498[label="yu300\n  Integral a",fontsize=16,color="green",shape="box"];499[label="yu40000",fontsize=16,color="green",shape="box"];500[label="yu300",fontsize=16,color="green",shape="box"];501[label="yu40000",fontsize=16,color="green",shape="box"];502[label="yu300",fontsize=16,color="green",shape="box"];503[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];504[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];505[label="yu40000",fontsize=16,color="green",shape="box"];506[label="yu300",fontsize=16,color="green",shape="box"];507[label="yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];508[label="yu300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];509[label="yu40000",fontsize=16,color="green",shape="box"];510[label="yu300",fontsize=16,color="green",shape="box"];511[label="yu40000",fontsize=16,color="green",shape="box"];512[label="yu300",fontsize=16,color="green",shape="box"];513[label="yu40000",fontsize=16,color="green",shape="box"];514[label="yu300",fontsize=16,color="green",shape="box"];515[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];516[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];517[label="yu40000",fontsize=16,color="green",shape="box"];518[label="yu300",fontsize=16,color="green",shape="box"];519[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];520[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];521[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];522[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];523 -> 36[label="",style="dashed", color="red", weight=0];
523[label="yu301 == yu40001",fontsize=16,color="magenta"];523 -> 650[label="",style="dashed", color="magenta", weight=3];
523 -> 651[label="",style="dashed", color="magenta", weight=3];
524 -> 37[label="",style="dashed", color="red", weight=0];
524[label="yu301 == yu40001\n  Integral a",fontsize=16,color="magenta"];524 -> 652[label="",style="dashed", color="magenta", weight=3];
524 -> 653[label="",style="dashed", color="magenta", weight=3];
525 -> 38[label="",style="dashed", color="red", weight=0];
525[label="yu301 == yu40001",fontsize=16,color="magenta"];525 -> 654[label="",style="dashed", color="magenta", weight=3];
525 -> 655[label="",style="dashed", color="magenta", weight=3];
526 -> 39[label="",style="dashed", color="red", weight=0];
526[label="yu301 == yu40001",fontsize=16,color="magenta"];526 -> 656[label="",style="dashed", color="magenta", weight=3];
526 -> 657[label="",style="dashed", color="magenta", weight=3];
527 -> 40[label="",style="dashed", color="red", weight=0];
527[label="yu301 == yu40001\n  Eq a  Eq b",fontsize=16,color="magenta"];527 -> 658[label="",style="dashed", color="magenta", weight=3];
527 -> 659[label="",style="dashed", color="magenta", weight=3];
528 -> 41[label="",style="dashed", color="red", weight=0];
528[label="yu301 == yu40001",fontsize=16,color="magenta"];528 -> 660[label="",style="dashed", color="magenta", weight=3];
528 -> 661[label="",style="dashed", color="magenta", weight=3];
529 -> 42[label="",style="dashed", color="red", weight=0];
529[label="yu301 == yu40001\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];529 -> 662[label="",style="dashed", color="magenta", weight=3];
529 -> 663[label="",style="dashed", color="magenta", weight=3];
530 -> 43[label="",style="dashed", color="red", weight=0];
530[label="yu301 == yu40001",fontsize=16,color="magenta"];530 -> 664[label="",style="dashed", color="magenta", weight=3];
530 -> 665[label="",style="dashed", color="magenta", weight=3];
531 -> 44[label="",style="dashed", color="red", weight=0];
531[label="yu301 == yu40001",fontsize=16,color="magenta"];531 -> 666[label="",style="dashed", color="magenta", weight=3];
531 -> 667[label="",style="dashed", color="magenta", weight=3];
532 -> 45[label="",style="dashed", color="red", weight=0];
532[label="yu301 == yu40001",fontsize=16,color="magenta"];532 -> 668[label="",style="dashed", color="magenta", weight=3];
532 -> 669[label="",style="dashed", color="magenta", weight=3];
533 -> 46[label="",style="dashed", color="red", weight=0];
533[label="yu301 == yu40001\n  Eq a",fontsize=16,color="magenta"];533 -> 670[label="",style="dashed", color="magenta", weight=3];
533 -> 671[label="",style="dashed", color="magenta", weight=3];
534 -> 47[label="",style="dashed", color="red", weight=0];
534[label="yu301 == yu40001",fontsize=16,color="magenta"];534 -> 672[label="",style="dashed", color="magenta", weight=3];
534 -> 673[label="",style="dashed", color="magenta", weight=3];
535 -> 48[label="",style="dashed", color="red", weight=0];
535[label="yu301 == yu40001\n  Eq a",fontsize=16,color="magenta"];535 -> 674[label="",style="dashed", color="magenta", weight=3];
535 -> 675[label="",style="dashed", color="magenta", weight=3];
536 -> 49[label="",style="dashed", color="red", weight=0];
536[label="yu301 == yu40001\n  Eq a  Eq b",fontsize=16,color="magenta"];536 -> 676[label="",style="dashed", color="magenta", weight=3];
536 -> 677[label="",style="dashed", color="magenta", weight=3];
537 -> 36[label="",style="dashed", color="red", weight=0];
537[label="yu302 == yu40002",fontsize=16,color="magenta"];537 -> 678[label="",style="dashed", color="magenta", weight=3];
537 -> 679[label="",style="dashed", color="magenta", weight=3];
538 -> 37[label="",style="dashed", color="red", weight=0];
538[label="yu302 == yu40002\n  Integral a",fontsize=16,color="magenta"];538 -> 680[label="",style="dashed", color="magenta", weight=3];
538 -> 681[label="",style="dashed", color="magenta", weight=3];
539 -> 38[label="",style="dashed", color="red", weight=0];
539[label="yu302 == yu40002",fontsize=16,color="magenta"];539 -> 682[label="",style="dashed", color="magenta", weight=3];
539 -> 683[label="",style="dashed", color="magenta", weight=3];
540 -> 39[label="",style="dashed", color="red", weight=0];
540[label="yu302 == yu40002",fontsize=16,color="magenta"];540 -> 684[label="",style="dashed", color="magenta", weight=3];
540 -> 685[label="",style="dashed", color="magenta", weight=3];
541 -> 40[label="",style="dashed", color="red", weight=0];
541[label="yu302 == yu40002\n  Eq a  Eq b",fontsize=16,color="magenta"];541 -> 686[label="",style="dashed", color="magenta", weight=3];
541 -> 687[label="",style="dashed", color="magenta", weight=3];
542 -> 41[label="",style="dashed", color="red", weight=0];
542[label="yu302 == yu40002",fontsize=16,color="magenta"];542 -> 688[label="",style="dashed", color="magenta", weight=3];
542 -> 689[label="",style="dashed", color="magenta", weight=3];
543 -> 42[label="",style="dashed", color="red", weight=0];
543[label="yu302 == yu40002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];543 -> 690[label="",style="dashed", color="magenta", weight=3];
543 -> 691[label="",style="dashed", color="magenta", weight=3];
544 -> 43[label="",style="dashed", color="red", weight=0];
544[label="yu302 == yu40002",fontsize=16,color="magenta"];544 -> 692[label="",style="dashed", color="magenta", weight=3];
544 -> 693[label="",style="dashed", color="magenta", weight=3];
545 -> 44[label="",style="dashed", color="red", weight=0];
545[label="yu302 == yu40002",fontsize=16,color="magenta"];545 -> 694[label="",style="dashed", color="magenta", weight=3];
545 -> 695[label="",style="dashed", color="magenta", weight=3];
546 -> 45[label="",style="dashed", color="red", weight=0];
546[label="yu302 == yu40002",fontsize=16,color="magenta"];546 -> 696[label="",style="dashed", color="magenta", weight=3];
546 -> 697[label="",style="dashed", color="magenta", weight=3];
547 -> 46[label="",style="dashed", color="red", weight=0];
547[label="yu302 == yu40002\n  Eq a",fontsize=16,color="magenta"];547 -> 698[label="",style="dashed", color="magenta", weight=3];
547 -> 699[label="",style="dashed", color="magenta", weight=3];
548 -> 47[label="",style="dashed", color="red", weight=0];
548[label="yu302 == yu40002",fontsize=16,color="magenta"];548 -> 700[label="",style="dashed", color="magenta", weight=3];
548 -> 701[label="",style="dashed", color="magenta", weight=3];
549 -> 48[label="",style="dashed", color="red", weight=0];
549[label="yu302 == yu40002\n  Eq a",fontsize=16,color="magenta"];549 -> 702[label="",style="dashed", color="magenta", weight=3];
549 -> 703[label="",style="dashed", color="magenta", weight=3];
550 -> 49[label="",style="dashed", color="red", weight=0];
550[label="yu302 == yu40002\n  Eq a  Eq b",fontsize=16,color="magenta"];550 -> 704[label="",style="dashed", color="magenta", weight=3];
550 -> 705[label="",style="dashed", color="magenta", weight=3];
551[label="primMulInt yu301 yu40001",fontsize=16,color="burlywood",shape="box"];1179[label="yu301/Pos yu3010",fontsize=10,color="white",style="solid",shape="box"];551 -> 1179[label="",style="solid", color="burlywood", weight=9];
1179 -> 706[label="",style="solid", color="burlywood", weight=3];
1180[label="yu301/Neg yu3010",fontsize=10,color="white",style="solid",shape="box"];551 -> 1180[label="",style="solid", color="burlywood", weight=9];
1180 -> 707[label="",style="solid", color="burlywood", weight=3];
552[label="yu300",fontsize=16,color="green",shape="box"];553[label="yu40000",fontsize=16,color="green",shape="box"];554[label="yu301",fontsize=16,color="green",shape="box"];555[label="yu40001",fontsize=16,color="green",shape="box"];556[label="yu300",fontsize=16,color="green",shape="box"];557[label="yu40000",fontsize=16,color="green",shape="box"];558[label="yu40000",fontsize=16,color="green",shape="box"];559[label="yu300",fontsize=16,color="green",shape="box"];560[label="yu40000\n  Integral a",fontsize=16,color="green",shape="box"];561[label="yu300\n  Integral a",fontsize=16,color="green",shape="box"];562[label="yu40000",fontsize=16,color="green",shape="box"];563[label="yu300",fontsize=16,color="green",shape="box"];564[label="yu40000",fontsize=16,color="green",shape="box"];565[label="yu300",fontsize=16,color="green",shape="box"];566[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];567[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];568[label="yu40000",fontsize=16,color="green",shape="box"];569[label="yu300",fontsize=16,color="green",shape="box"];570[label="yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];571[label="yu300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];572[label="yu40000",fontsize=16,color="green",shape="box"];573[label="yu300",fontsize=16,color="green",shape="box"];574[label="yu40000",fontsize=16,color="green",shape="box"];575[label="yu300",fontsize=16,color="green",shape="box"];576[label="yu40000",fontsize=16,color="green",shape="box"];577[label="yu300",fontsize=16,color="green",shape="box"];578[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];579[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];580[label="yu40000",fontsize=16,color="green",shape="box"];581[label="yu300",fontsize=16,color="green",shape="box"];582[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];583[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];584[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];585[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];586[label="yu40000",fontsize=16,color="green",shape="box"];587[label="yu300",fontsize=16,color="green",shape="box"];588[label="yu40000\n  Integral a",fontsize=16,color="green",shape="box"];589[label="yu300\n  Integral a",fontsize=16,color="green",shape="box"];590[label="yu40000",fontsize=16,color="green",shape="box"];591[label="yu300",fontsize=16,color="green",shape="box"];592[label="yu40000",fontsize=16,color="green",shape="box"];593[label="yu300",fontsize=16,color="green",shape="box"];594[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];595[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];596[label="yu40000",fontsize=16,color="green",shape="box"];597[label="yu300",fontsize=16,color="green",shape="box"];598[label="yu40000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];599[label="yu300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];600[label="yu40000",fontsize=16,color="green",shape="box"];601[label="yu300",fontsize=16,color="green",shape="box"];602[label="yu40000",fontsize=16,color="green",shape="box"];603[label="yu300",fontsize=16,color="green",shape="box"];604[label="yu40000",fontsize=16,color="green",shape="box"];605[label="yu300",fontsize=16,color="green",shape="box"];606[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];607[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];608[label="yu40000",fontsize=16,color="green",shape="box"];609[label="yu300",fontsize=16,color="green",shape="box"];610[label="yu40000\n  Eq a",fontsize=16,color="green",shape="box"];611[label="yu300\n  Eq a",fontsize=16,color="green",shape="box"];612[label="yu40000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];613[label="yu300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];614[label="yu40001",fontsize=16,color="green",shape="box"];615[label="yu301",fontsize=16,color="green",shape="box"];616[label="yu40001\n  Integral a",fontsize=16,color="green",shape="box"];617[label="yu301\n  Integral a",fontsize=16,color="green",shape="box"];618[label="yu40001",fontsize=16,color="green",shape="box"];619[label="yu301",fontsize=16,color="green",shape="box"];620[label="yu40001",fontsize=16,color="green",shape="box"];621[label="yu301",fontsize=16,color="green",shape="box"];622[label="yu40001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];623[label="yu301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];624[label="yu40001",fontsize=16,color="green",shape="box"];625[label="yu301",fontsize=16,color="green",shape="box"];626[label="yu40001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];627[label="yu301\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];628[label="yu40001",fontsize=16,color="green",shape="box"];629[label="yu301",fontsize=16,color="green",shape="box"];630[label="yu40001",fontsize=16,color="green",shape="box"];631[label="yu301",fontsize=16,color="green",shape="box"];632[label="yu40001",fontsize=16,color="green",shape="box"];633[label="yu301",fontsize=16,color="green",shape="box"];634[label="yu40001\n  Eq a",fontsize=16,color="green",shape="box"];635[label="yu301\n  Eq a",fontsize=16,color="green",shape="box"];636[label="yu40001",fontsize=16,color="green",shape="box"];637[label="yu301",fontsize=16,color="green",shape="box"];638[label="yu40001\n  Eq a",fontsize=16,color="green",shape="box"];639[label="yu301\n  Eq a",fontsize=16,color="green",shape="box"];640[label="yu40001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];641[label="yu301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];642 -> 204[label="",style="dashed", color="red", weight=0];
642[label="primEqNat yu3000 yu400000",fontsize=16,color="magenta"];642 -> 708[label="",style="dashed", color="magenta", weight=3];
642 -> 709[label="",style="dashed", color="magenta", weight=3];
643[label="False",fontsize=16,color="green",shape="box"];644[label="False",fontsize=16,color="green",shape="box"];645[label="True",fontsize=16,color="green",shape="box"];646[label="yu3000",fontsize=16,color="green",shape="box"];647[label="yu400000",fontsize=16,color="green",shape="box"];648[label="yu3000",fontsize=16,color="green",shape="box"];649[label="yu400000",fontsize=16,color="green",shape="box"];650[label="yu40001",fontsize=16,color="green",shape="box"];651[label="yu301",fontsize=16,color="green",shape="box"];652[label="yu40001\n  Integral a",fontsize=16,color="green",shape="box"];653[label="yu301\n  Integral a",fontsize=16,color="green",shape="box"];654[label="yu40001",fontsize=16,color="green",shape="box"];655[label="yu301",fontsize=16,color="green",shape="box"];656[label="yu40001",fontsize=16,color="green",shape="box"];657[label="yu301",fontsize=16,color="green",shape="box"];658[label="yu40001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];659[label="yu301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];660[label="yu40001",fontsize=16,color="green",shape="box"];661[label="yu301",fontsize=16,color="green",shape="box"];662[label="yu40001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];663[label="yu301\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];664[label="yu40001",fontsize=16,color="green",shape="box"];665[label="yu301",fontsize=16,color="green",shape="box"];666[label="yu40001",fontsize=16,color="green",shape="box"];667[label="yu301",fontsize=16,color="green",shape="box"];668[label="yu40001",fontsize=16,color="green",shape="box"];669[label="yu301",fontsize=16,color="green",shape="box"];670[label="yu40001\n  Eq a",fontsize=16,color="green",shape="box"];671[label="yu301\n  Eq a",fontsize=16,color="green",shape="box"];672[label="yu40001",fontsize=16,color="green",shape="box"];673[label="yu301",fontsize=16,color="green",shape="box"];674[label="yu40001\n  Eq a",fontsize=16,color="green",shape="box"];675[label="yu301\n  Eq a",fontsize=16,color="green",shape="box"];676[label="yu40001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];677[label="yu301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];678[label="yu40002",fontsize=16,color="green",shape="box"];679[label="yu302",fontsize=16,color="green",shape="box"];680[label="yu40002\n  Integral a",fontsize=16,color="green",shape="box"];681[label="yu302\n  Integral a",fontsize=16,color="green",shape="box"];682[label="yu40002",fontsize=16,color="green",shape="box"];683[label="yu302",fontsize=16,color="green",shape="box"];684[label="yu40002",fontsize=16,color="green",shape="box"];685[label="yu302",fontsize=16,color="green",shape="box"];686[label="yu40002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];687[label="yu302\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];688[label="yu40002",fontsize=16,color="green",shape="box"];689[label="yu302",fontsize=16,color="green",shape="box"];690[label="yu40002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];691[label="yu302\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];692[label="yu40002",fontsize=16,color="green",shape="box"];693[label="yu302",fontsize=16,color="green",shape="box"];694[label="yu40002",fontsize=16,color="green",shape="box"];695[label="yu302",fontsize=16,color="green",shape="box"];696[label="yu40002",fontsize=16,color="green",shape="box"];697[label="yu302",fontsize=16,color="green",shape="box"];698[label="yu40002\n  Eq a",fontsize=16,color="green",shape="box"];699[label="yu302\n  Eq a",fontsize=16,color="green",shape="box"];700[label="yu40002",fontsize=16,color="green",shape="box"];701[label="yu302",fontsize=16,color="green",shape="box"];702[label="yu40002\n  Eq a",fontsize=16,color="green",shape="box"];703[label="yu302\n  Eq a",fontsize=16,color="green",shape="box"];704[label="yu40002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];705[label="yu302\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];706[label="primMulInt (Pos yu3010) yu40001",fontsize=16,color="burlywood",shape="box"];1182[label="yu40001/Pos yu400010",fontsize=10,color="white",style="solid",shape="box"];706 -> 1182[label="",style="solid", color="burlywood", weight=9];
1182 -> 710[label="",style="solid", color="burlywood", weight=3];
1183[label="yu40001/Neg yu400010",fontsize=10,color="white",style="solid",shape="box"];706 -> 1183[label="",style="solid", color="burlywood", weight=9];
1183 -> 711[label="",style="solid", color="burlywood", weight=3];
707[label="primMulInt (Neg yu3010) yu40001",fontsize=16,color="burlywood",shape="box"];1184[label="yu40001/Pos yu400010",fontsize=10,color="white",style="solid",shape="box"];707 -> 1184[label="",style="solid", color="burlywood", weight=9];
1184 -> 712[label="",style="solid", color="burlywood", weight=3];
1185[label="yu40001/Neg yu400010",fontsize=10,color="white",style="solid",shape="box"];707 -> 1185[label="",style="solid", color="burlywood", weight=9];
1185 -> 713[label="",style="solid", color="burlywood", weight=3];
708[label="yu3000",fontsize=16,color="green",shape="box"];709[label="yu400000",fontsize=16,color="green",shape="box"];710[label="primMulInt (Pos yu3010) (Pos yu400010)",fontsize=16,color="black",shape="box"];710 -> 714[label="",style="solid", color="black", weight=3];
711[label="primMulInt (Pos yu3010) (Neg yu400010)",fontsize=16,color="black",shape="box"];711 -> 715[label="",style="solid", color="black", weight=3];
712[label="primMulInt (Neg yu3010) (Pos yu400010)",fontsize=16,color="black",shape="box"];712 -> 716[label="",style="solid", color="black", weight=3];
713[label="primMulInt (Neg yu3010) (Neg yu400010)",fontsize=16,color="black",shape="box"];713 -> 717[label="",style="solid", color="black", weight=3];
714[label="Pos (primMulNat yu3010 yu400010)",fontsize=16,color="green",shape="box"];714 -> 718[label="",style="dashed", color="green", weight=3];
715[label="Neg (primMulNat yu3010 yu400010)",fontsize=16,color="green",shape="box"];715 -> 719[label="",style="dashed", color="green", weight=3];
716[label="Neg (primMulNat yu3010 yu400010)",fontsize=16,color="green",shape="box"];716 -> 720[label="",style="dashed", color="green", weight=3];
717[label="Pos (primMulNat yu3010 yu400010)",fontsize=16,color="green",shape="box"];717 -> 721[label="",style="dashed", color="green", weight=3];
718[label="primMulNat yu3010 yu400010",fontsize=16,color="burlywood",shape="triangle"];1186[label="yu3010/Succ yu30100",fontsize=10,color="white",style="solid",shape="box"];718 -> 1186[label="",style="solid", color="burlywood", weight=9];
1186 -> 722[label="",style="solid", color="burlywood", weight=3];
1187[label="yu3010/Zero",fontsize=10,color="white",style="solid",shape="box"];718 -> 1187[label="",style="solid", color="burlywood", weight=9];
1187 -> 723[label="",style="solid", color="burlywood", weight=3];
719 -> 718[label="",style="dashed", color="red", weight=0];
719[label="primMulNat yu3010 yu400010",fontsize=16,color="magenta"];719 -> 724[label="",style="dashed", color="magenta", weight=3];
720 -> 718[label="",style="dashed", color="red", weight=0];
720[label="primMulNat yu3010 yu400010",fontsize=16,color="magenta"];720 -> 725[label="",style="dashed", color="magenta", weight=3];
721 -> 718[label="",style="dashed", color="red", weight=0];
721[label="primMulNat yu3010 yu400010",fontsize=16,color="magenta"];721 -> 726[label="",style="dashed", color="magenta", weight=3];
721 -> 727[label="",style="dashed", color="magenta", weight=3];
722[label="primMulNat (Succ yu30100) yu400010",fontsize=16,color="burlywood",shape="box"];1191[label="yu400010/Succ yu4000100",fontsize=10,color="white",style="solid",shape="box"];722 -> 1191[label="",style="solid", color="burlywood", weight=9];
1191 -> 728[label="",style="solid", color="burlywood", weight=3];
1192[label="yu400010/Zero",fontsize=10,color="white",style="solid",shape="box"];722 -> 1192[label="",style="solid", color="burlywood", weight=9];
1192 -> 729[label="",style="solid", color="burlywood", weight=3];
723[label="primMulNat Zero yu400010",fontsize=16,color="burlywood",shape="box"];1193[label="yu400010/Succ yu4000100",fontsize=10,color="white",style="solid",shape="box"];723 -> 1193[label="",style="solid", color="burlywood", weight=9];
1193 -> 730[label="",style="solid", color="burlywood", weight=3];
1194[label="yu400010/Zero",fontsize=10,color="white",style="solid",shape="box"];723 -> 1194[label="",style="solid", color="burlywood", weight=9];
1194 -> 731[label="",style="solid", color="burlywood", weight=3];
724[label="yu400010",fontsize=16,color="green",shape="box"];725[label="yu3010",fontsize=16,color="green",shape="box"];726[label="yu400010",fontsize=16,color="green",shape="box"];727[label="yu3010",fontsize=16,color="green",shape="box"];728[label="primMulNat (Succ yu30100) (Succ yu4000100)",fontsize=16,color="black",shape="box"];728 -> 732[label="",style="solid", color="black", weight=3];
729[label="primMulNat (Succ yu30100) Zero",fontsize=16,color="black",shape="box"];729 -> 733[label="",style="solid", color="black", weight=3];
730[label="primMulNat Zero (Succ yu4000100)",fontsize=16,color="black",shape="box"];730 -> 734[label="",style="solid", color="black", weight=3];
731[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];731 -> 735[label="",style="solid", color="black", weight=3];
732 -> 736[label="",style="dashed", color="red", weight=0];
732[label="primPlusNat (primMulNat yu30100 (Succ yu4000100)) (Succ yu4000100)",fontsize=16,color="magenta"];732 -> 737[label="",style="dashed", color="magenta", weight=3];
733[label="Zero",fontsize=16,color="green",shape="box"];734[label="Zero",fontsize=16,color="green",shape="box"];735[label="Zero",fontsize=16,color="green",shape="box"];737 -> 718[label="",style="dashed", color="red", weight=0];
737[label="primMulNat yu30100 (Succ yu4000100)",fontsize=16,color="magenta"];737 -> 738[label="",style="dashed", color="magenta", weight=3];
737 -> 739[label="",style="dashed", color="magenta", weight=3];
736[label="primPlusNat yu40 (Succ yu4000100)",fontsize=16,color="burlywood",shape="triangle"];1197[label="yu40/Succ yu400",fontsize=10,color="white",style="solid",shape="box"];736 -> 1197[label="",style="solid", color="burlywood", weight=9];
1197 -> 740[label="",style="solid", color="burlywood", weight=3];
1198[label="yu40/Zero",fontsize=10,color="white",style="solid",shape="box"];736 -> 1198[label="",style="solid", color="burlywood", weight=9];
1198 -> 741[label="",style="solid", color="burlywood", weight=3];
738[label="Succ yu4000100",fontsize=16,color="green",shape="box"];739[label="yu30100",fontsize=16,color="green",shape="box"];740[label="primPlusNat (Succ yu400) (Succ yu4000100)",fontsize=16,color="black",shape="box"];740 -> 742[label="",style="solid", color="black", weight=3];
741[label="primPlusNat Zero (Succ yu4000100)",fontsize=16,color="black",shape="box"];741 -> 743[label="",style="solid", color="black", weight=3];
742[label="Succ (Succ (primPlusNat yu400 yu4000100))",fontsize=16,color="green",shape="box"];742 -> 744[label="",style="dashed", color="green", weight=3];
743[label="Succ yu4000100",fontsize=16,color="green",shape="box"];744[label="primPlusNat yu400 yu4000100",fontsize=16,color="burlywood",shape="triangle"];1199[label="yu400/Succ yu4000",fontsize=10,color="white",style="solid",shape="box"];744 -> 1199[label="",style="solid", color="burlywood", weight=9];
1199 -> 745[label="",style="solid", color="burlywood", weight=3];
1200[label="yu400/Zero",fontsize=10,color="white",style="solid",shape="box"];744 -> 1200[label="",style="solid", color="burlywood", weight=9];
1200 -> 746[label="",style="solid", color="burlywood", weight=3];
745[label="primPlusNat (Succ yu4000) yu4000100",fontsize=16,color="burlywood",shape="box"];1201[label="yu4000100/Succ yu40001000",fontsize=10,color="white",style="solid",shape="box"];745 -> 1201[label="",style="solid", color="burlywood", weight=9];
1201 -> 747[label="",style="solid", color="burlywood", weight=3];
1202[label="yu4000100/Zero",fontsize=10,color="white",style="solid",shape="box"];745 -> 1202[label="",style="solid", color="burlywood", weight=9];
1202 -> 748[label="",style="solid", color="burlywood", weight=3];
746[label="primPlusNat Zero yu4000100",fontsize=16,color="burlywood",shape="box"];1203[label="yu4000100/Succ yu40001000",fontsize=10,color="white",style="solid",shape="box"];746 -> 1203[label="",style="solid", color="burlywood", weight=9];
1203 -> 749[label="",style="solid", color="burlywood", weight=3];
1204[label="yu4000100/Zero",fontsize=10,color="white",style="solid",shape="box"];746 -> 1204[label="",style="solid", color="burlywood", weight=9];
1204 -> 750[label="",style="solid", color="burlywood", weight=3];
747[label="primPlusNat (Succ yu4000) (Succ yu40001000)",fontsize=16,color="black",shape="box"];747 -> 751[label="",style="solid", color="black", weight=3];
748[label="primPlusNat (Succ yu4000) Zero",fontsize=16,color="black",shape="box"];748 -> 752[label="",style="solid", color="black", weight=3];
749[label="primPlusNat Zero (Succ yu40001000)",fontsize=16,color="black",shape="box"];749 -> 753[label="",style="solid", color="black", weight=3];
750[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];750 -> 754[label="",style="solid", color="black", weight=3];
751[label="Succ (Succ (primPlusNat yu4000 yu40001000))",fontsize=16,color="green",shape="box"];751 -> 755[label="",style="dashed", color="green", weight=3];
752[label="Succ yu4000",fontsize=16,color="green",shape="box"];753[label="Succ yu40001000",fontsize=16,color="green",shape="box"];754[label="Zero",fontsize=16,color="green",shape="box"];755 -> 744[label="",style="dashed", color="red", weight=0];
755[label="primPlusNat yu4000 yu40001000",fontsize=16,color="magenta"];755 -> 756[label="",style="dashed", color="magenta", weight=3];
755 -> 757[label="",style="dashed", color="magenta", weight=3];
756[label="yu40001000",fontsize=16,color="green",shape="box"];757[label="yu4000",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(yu4000), Succ(yu40001000)) → new_primPlusNat(yu4000, 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(yu4000), Succ(yu40001000)) → new_primPlusNat(yu4000, 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_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(app(ty_@2, hc), hd)) → new_esEs3(yu302, yu40002, hc, hd)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, df), dg), dh, ea) → new_esEs(yu300, yu40000, df, dg)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(ty_Maybe, bea)) → new_esEs2(yu301, yu40001, bea)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], ee), dh, ea) → new_esEs1(yu300, yu40000, ee)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(ty_Maybe, hb)) → new_esEs2(yu302, yu40002, hb)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, ef), dh, ea) → new_esEs2(yu300, yu40000, ef)
new_esEs2(Just(yu300), Just(yu40000), app(app(ty_Either, bag), bah)) → new_esEs(yu300, yu40000, bag, bah)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(app(ty_Either, gd), ge)) → new_esEs(yu302, yu40002, gd, ge)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(ty_[], fh), ea) → new_esEs1(yu301, yu40001, fh)
new_esEs(Right(yu300), Right(yu40000), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(yu300, yu40000, cf, cg, da)
new_esEs(Right(yu300), Right(yu40000), cc, app(ty_[], db)) → new_esEs1(yu300, yu40000, db)
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), baf) → new_esEs1(yu301, yu40001, baf)
new_esEs(Right(yu300), Right(yu40000), cc, app(app(ty_@2, dd), de)) → new_esEs3(yu300, yu40000, dd, de)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, bcc), bcd), bce), bcb) → new_esEs0(yu300, yu40000, bcc, bcd, bce)
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(ty_[], bab)) → new_esEs1(yu300, yu40000, bab)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(ty_[], bdh)) → new_esEs1(yu301, yu40001, bdh)
new_esEs2(Just(yu300), Just(yu40000), app(ty_[], bbd)) → new_esEs1(yu300, yu40000, bbd)
new_esEs2(Just(yu300), Just(yu40000), app(ty_Maybe, bbe)) → new_esEs2(yu300, yu40000, bbe)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(yu301, yu40001, fd, ff, fg)
new_esEs(Left(yu300), Left(yu40000), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(yu300, yu40000, bd, be, bf)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], bcf), bcb) → new_esEs1(yu300, yu40000, bcf)
new_esEs(Left(yu300), Left(yu40000), app(ty_Maybe, bh), bc) → new_esEs2(yu300, yu40000, bh)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(app(ty_@2, gb), gc), ea) → new_esEs3(yu301, yu40001, gb, gc)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(ty_[], ha)) → new_esEs1(yu302, yu40002, ha)
new_esEs2(Just(yu300), Just(yu40000), app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs0(yu300, yu40000, bba, bbb, bbc)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(app(ty_@2, beb), bec)) → new_esEs3(yu301, yu40001, beb, bec)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, eg), eh), dh, ea) → new_esEs3(yu300, yu40000, eg, eh)
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_@2, bad), bae)) → new_esEs3(yu300, yu40000, bad, bae)
new_esEs(Right(yu300), Right(yu40000), cc, app(app(ty_Either, cd), ce)) → new_esEs(yu300, yu40000, cd, ce)
new_esEs(Left(yu300), Left(yu40000), app(app(ty_@2, ca), cb), bc) → new_esEs3(yu300, yu40000, ca, cb)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, bcg), bcb) → new_esEs2(yu300, yu40000, bcg)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(yu302, yu40002, gf, gg, gh)
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(ty_Maybe, bac)) → new_esEs2(yu300, yu40000, bac)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, bch), bda), bcb) → new_esEs3(yu300, yu40000, bch, bda)
new_esEs(Right(yu300), Right(yu40000), cc, app(ty_Maybe, dc)) → new_esEs2(yu300, yu40000, dc)
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(app(app(ty_@3, hg), hh), baa)) → new_esEs0(yu300, yu40000, hg, hh, baa)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(app(ty_Either, bdc), bdd)) → new_esEs(yu301, yu40001, bdc, bdd)
new_esEs2(Just(yu300), Just(yu40000), app(app(ty_@2, bbf), bbg)) → new_esEs3(yu300, yu40000, bbf, bbg)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, bbh), bca), bcb) → new_esEs(yu300, yu40000, bbh, bca)
new_esEs(Left(yu300), Left(yu40000), app(ty_[], bg), bc) → new_esEs1(yu300, yu40000, bg)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(app(ty_Either, fb), fc), ea) → new_esEs(yu301, yu40001, fb, fc)
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(yu301, yu40001, bde, bdf, bdg)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(ty_Maybe, ga), ea) → new_esEs2(yu301, yu40001, ga)
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_Either, he), hf)) → new_esEs(yu300, yu40000, he, hf)
new_esEs(Left(yu300), Left(yu40000), app(app(ty_Either, ba), bb), bc) → new_esEs(yu300, yu40000, ba, bb)
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(yu300, yu40000, eb, ec, ed)

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

new_esEs2(Just(yu300), Just(yu40000), app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs0(yu300, yu40000, bba, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Just(yu300), Just(yu40000), app(app(ty_@2, bbf), bbg)) → new_esEs3(yu300, yu40000, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(app(app(ty_@3, hg), hh), baa)) → new_esEs0(yu300, yu40000, hg, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_@2, bad), bae)) → new_esEs3(yu300, yu40000, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(yu300), Just(yu40000), app(ty_Maybe, bbe)) → new_esEs2(yu300, yu40000, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(ty_Maybe, bac)) → new_esEs2(yu300, yu40000, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Just(yu300), Just(yu40000), app(app(ty_Either, bag), bah)) → new_esEs(yu300, yu40000, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(yu300), Just(yu40000), app(ty_[], bbd)) → new_esEs1(yu300, yu40000, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_Either, he), hf)) → new_esEs(yu300, yu40000, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, bcc), bcd), bce), bcb) → new_esEs0(yu300, yu40000, bcc, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(yu301, yu40001, bde, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(app(ty_@2, beb), bec)) → new_esEs3(yu301, yu40001, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, bch), bda), bcb) → new_esEs3(yu300, yu40000, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(ty_Maybe, bea)) → new_esEs2(yu301, yu40001, bea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, bcg), bcb) → new_esEs2(yu300, yu40000, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(app(ty_Either, bdc), bdd)) → new_esEs(yu301, yu40001, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, bbh), bca), bcb) → new_esEs(yu300, yu40000, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), bdb, app(ty_[], bdh)) → new_esEs1(yu301, yu40001, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], bcf), bcb) → new_esEs1(yu300, yu40000, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Right(yu300), Right(yu40000), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(yu300, yu40000, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(Left(yu300), Left(yu40000), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(yu300, yu40000, bd, be, bf)
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), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(yu301, yu40001, fd, ff, fg)
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), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(yu302, yu40002, gf, gg, gh)
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, eb), ec), ed), dh, ea) → new_esEs0(yu300, yu40000, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(Right(yu300), Right(yu40000), cc, app(app(ty_@2, dd), de)) → new_esEs3(yu300, yu40000, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Left(yu300), Left(yu40000), app(app(ty_@2, ca), cb), bc) → new_esEs3(yu300, yu40000, ca, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(app(ty_@2, hc), hd)) → new_esEs3(yu302, yu40002, hc, hd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(app(ty_@2, gb), gc), ea) → new_esEs3(yu301, yu40001, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, eg), eh), dh, ea) → new_esEs3(yu300, yu40000, eg, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Left(yu300), Left(yu40000), app(ty_Maybe, bh), bc) → new_esEs2(yu300, yu40000, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Right(yu300), Right(yu40000), cc, app(ty_Maybe, dc)) → new_esEs2(yu300, yu40000, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Right(yu300), Right(yu40000), cc, app(app(ty_Either, cd), ce)) → new_esEs(yu300, yu40000, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Left(yu300), Left(yu40000), app(app(ty_Either, ba), bb), bc) → new_esEs(yu300, yu40000, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Right(yu300), Right(yu40000), cc, app(ty_[], db)) → new_esEs1(yu300, yu40000, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Left(yu300), Left(yu40000), app(ty_[], bg), bc) → new_esEs1(yu300, yu40000, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), baf) → new_esEs1(yu301, yu40001, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs1(:(yu300, yu301), :(yu40000, yu40001), app(ty_[], bab)) → new_esEs1(yu300, yu40000, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, ef), dh, ea) → new_esEs2(yu300, yu40000, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(ty_Maybe, hb)) → new_esEs2(yu302, yu40002, hb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(ty_Maybe, ga), ea) → new_esEs2(yu301, yu40001, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, df), dg), dh, ea) → new_esEs(yu300, yu40000, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(app(ty_Either, gd), ge)) → new_esEs(yu302, yu40002, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(app(ty_Either, fb), fc), ea) → new_esEs(yu301, yu40001, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], ee), dh, ea) → new_esEs1(yu300, yu40000, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, app(ty_[], fh), ea) → new_esEs1(yu301, yu40001, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), fa, dh, app(ty_[], ha)) → new_esEs1(yu302, yu40002, ha)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 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(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Left(yu30), yu41, bd, be, bf)
new_lookup10(yu22, yu23, yu24, yu25, False, bg, bh, ca) → new_lookup(Right(yu22), yu25, bg, bh, ca)
new_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, bf), bd, be, bf)
new_lookup1(yu11, yu12, yu13, yu14, False, ba, bb, bc) → new_lookup(Left(yu11), yu14, ba, bb, bc)
new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Right(yu30), yu41, bd, be, bf)
new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, be), bd, be, bf)

The TRS R consists of the following rules:

new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_esEs4(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_esEs5(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_esEs4(yu30, yu4000, app(app(app(ty_@3, df), dg), dh)) → new_esEs13(yu30, yu4000, df, dg, dh)
new_esEs5(yu30, yu4000, app(ty_Ratio, bbc)) → new_esEs8(yu30, yu4000, bbc)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs4(yu30, yu4000, app(app(ty_Either, bcf), bcg)) → new_esEs11(yu30, yu4000, bcf, bcg)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs4(yu30, yu4000, app(ty_[], hh)) → new_esEs17(yu30, yu4000, hh)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Maybe, cb)) → new_esEs6(yu30, yu4000, cb)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs9(GT, GT) → True
new_esEs4(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs5(yu30, yu4000, app(ty_Maybe, bcb)) → new_esEs6(yu30, yu4000, bcb)
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs5(yu30, yu4000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs13(yu30, yu4000, bbf, bbg, bbh)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs5(yu30, yu4000, app(app(ty_@2, bcc), bcd)) → new_esEs19(yu30, yu4000, bcc, bcd)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_asAs(False, yu39) → False
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_esEs5(yu30, yu4000, app(app(ty_Either, bbd), bbe)) → new_esEs11(yu30, yu4000, bbd, bbe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs18(True, True) → True
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs16(@0, @0) → True
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs4(yu30, yu4000, app(ty_Ratio, bce)) → new_esEs8(yu30, yu4000, bce)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs9(EQ, EQ) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs5(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs4(yu30, yu4000, app(app(ty_@2, bch), bda)) → new_esEs19(yu30, yu4000, bch, bda)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_asAs(True, yu39) → yu39
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_esEs6(Nothing, Nothing, cb) → True
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs5(yu30, yu4000, app(ty_[], bca)) → new_esEs17(yu30, yu4000, bca)
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs9(LT, LT) → True
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs18(False, False) → True
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs4(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs4(x0, x1, ty_Double)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_@0)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs4(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_esEs5(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

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_lookup10(yu22, yu23, yu24, yu25, False, bg, bh, ca) → new_lookup(Right(yu22), yu25, bg, bh, ca)
new_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, bf), bd, be, bf)
new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Right(yu30), yu41, bd, be, bf)

The TRS R consists of the following rules:

new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_esEs4(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_esEs5(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_esEs4(yu30, yu4000, app(app(app(ty_@3, df), dg), dh)) → new_esEs13(yu30, yu4000, df, dg, dh)
new_esEs5(yu30, yu4000, app(ty_Ratio, bbc)) → new_esEs8(yu30, yu4000, bbc)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs4(yu30, yu4000, app(app(ty_Either, bcf), bcg)) → new_esEs11(yu30, yu4000, bcf, bcg)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs4(yu30, yu4000, app(ty_[], hh)) → new_esEs17(yu30, yu4000, hh)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Maybe, cb)) → new_esEs6(yu30, yu4000, cb)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs9(GT, GT) → True
new_esEs4(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs5(yu30, yu4000, app(ty_Maybe, bcb)) → new_esEs6(yu30, yu4000, bcb)
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs5(yu30, yu4000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs13(yu30, yu4000, bbf, bbg, bbh)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs5(yu30, yu4000, app(app(ty_@2, bcc), bcd)) → new_esEs19(yu30, yu4000, bcc, bcd)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_asAs(False, yu39) → False
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_esEs5(yu30, yu4000, app(app(ty_Either, bbd), bbe)) → new_esEs11(yu30, yu4000, bbd, bbe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs18(True, True) → True
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs16(@0, @0) → True
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs4(yu30, yu4000, app(ty_Ratio, bce)) → new_esEs8(yu30, yu4000, bce)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs9(EQ, EQ) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs5(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs4(yu30, yu4000, app(app(ty_@2, bch), bda)) → new_esEs19(yu30, yu4000, bch, bda)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_asAs(True, yu39) → yu39
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_esEs6(Nothing, Nothing, cb) → True
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs5(yu30, yu4000, app(ty_[], bca)) → new_esEs17(yu30, yu4000, bca)
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs9(LT, LT) → True
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs18(False, False) → True
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs4(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs4(x0, x1, ty_Double)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_@0)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs4(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_esEs5(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

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_lookup10(yu22, yu23, yu24, yu25, False, bg, bh, ca) → new_lookup(Right(yu22), yu25, bg, bh, ca)
new_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, bf), bd, be, bf)
new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Right(yu30), yu41, bd, be, bf)

The TRS R consists of the following rules:

new_esEs5(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs5(yu30, yu4000, app(ty_Ratio, bbc)) → new_esEs8(yu30, yu4000, bbc)
new_esEs5(yu30, yu4000, app(ty_Maybe, bcb)) → new_esEs6(yu30, yu4000, bcb)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs5(yu30, yu4000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs13(yu30, yu4000, bbf, bbg, bbh)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs5(yu30, yu4000, app(app(ty_@2, bcc), bcd)) → new_esEs19(yu30, yu4000, bcc, bcd)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs5(yu30, yu4000, app(app(ty_Either, bbd), bbe)) → new_esEs11(yu30, yu4000, bbd, bbe)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs5(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs5(yu30, yu4000, app(ty_[], bca)) → new_esEs17(yu30, yu4000, bca)
new_esEs5(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_asAs(False, yu39) → False
new_asAs(True, yu39) → yu39
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Nothing, Nothing, cb) → True
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs9(GT, GT) → True
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_esEs16(@0, @0) → True

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs4(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs4(x0, x1, ty_Double)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_@0)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs4(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_esEs5(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

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_esEs4(x0, x1, ty_Bool)
new_esEs4(x0, x1, ty_Integer)
new_esEs4(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Ordering)
new_esEs4(x0, x1, ty_Float)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))

↳ 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_lookup10(yu22, yu23, yu24, yu25, False, bg, bh, ca) → new_lookup(Right(yu22), yu25, bg, bh, ca)
new_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, bf), bd, be, bf)
new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Right(yu30), yu41, bd, be, bf)

The TRS R consists of the following rules:

new_esEs5(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs5(yu30, yu4000, app(ty_Ratio, bbc)) → new_esEs8(yu30, yu4000, bbc)
new_esEs5(yu30, yu4000, app(ty_Maybe, bcb)) → new_esEs6(yu30, yu4000, bcb)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs5(yu30, yu4000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs13(yu30, yu4000, bbf, bbg, bbh)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs5(yu30, yu4000, app(app(ty_@2, bcc), bcd)) → new_esEs19(yu30, yu4000, bcc, bcd)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs5(yu30, yu4000, app(app(ty_Either, bbd), bbe)) → new_esEs11(yu30, yu4000, bbd, bbe)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs5(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs5(yu30, yu4000, app(ty_[], bca)) → new_esEs17(yu30, yu4000, bca)
new_esEs5(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_asAs(False, yu39) → False
new_asAs(True, yu39) → yu39
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Nothing, Nothing, cb) → True
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs9(GT, GT) → True
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_esEs16(@0, @0) → True

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs5(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_@0)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_esEs5(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

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(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, bf), bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 3 >= 6, 4 >= 7, 5 >= 8
new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Right(yu30), yu41, bd, be, bf)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
new_lookup10(yu22, yu23, yu24, yu25, False, bg, bh, ca) → new_lookup(Right(yu22), yu25, bg, bh, ca)
The graph contains the following edges 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                    ↳ QDP

                      ↳ UsableRulesProof

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

new_lookup(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Left(yu30), yu41, bd, be, bf)
new_lookup1(yu11, yu12, yu13, yu14, False, ba, bb, bc) → new_lookup(Left(yu11), yu14, ba, bb, bc)
new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, be), bd, be, bf)

The TRS R consists of the following rules:

new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_esEs4(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_esEs5(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_esEs4(yu30, yu4000, app(app(app(ty_@3, df), dg), dh)) → new_esEs13(yu30, yu4000, df, dg, dh)
new_esEs5(yu30, yu4000, app(ty_Ratio, bbc)) → new_esEs8(yu30, yu4000, bbc)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs4(yu30, yu4000, app(app(ty_Either, bcf), bcg)) → new_esEs11(yu30, yu4000, bcf, bcg)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs4(yu30, yu4000, app(ty_[], hh)) → new_esEs17(yu30, yu4000, hh)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Maybe, cb)) → new_esEs6(yu30, yu4000, cb)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs9(GT, GT) → True
new_esEs4(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs5(yu30, yu4000, app(ty_Maybe, bcb)) → new_esEs6(yu30, yu4000, bcb)
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs5(yu30, yu4000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs13(yu30, yu4000, bbf, bbg, bbh)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs5(yu30, yu4000, app(app(ty_@2, bcc), bcd)) → new_esEs19(yu30, yu4000, bcc, bcd)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_asAs(False, yu39) → False
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_primEqNat0(Zero, Zero) → True
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_esEs5(yu30, yu4000, app(app(ty_Either, bbd), bbe)) → new_esEs11(yu30, yu4000, bbd, bbe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs18(True, True) → True
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs16(@0, @0) → True
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs4(yu30, yu4000, app(ty_Ratio, bce)) → new_esEs8(yu30, yu4000, bce)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs9(EQ, EQ) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs5(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs4(yu30, yu4000, app(app(ty_@2, bch), bda)) → new_esEs19(yu30, yu4000, bch, bda)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_asAs(True, yu39) → yu39
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_esEs6(Nothing, Nothing, cb) → True
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs5(yu30, yu4000, app(ty_[], bca)) → new_esEs17(yu30, yu4000, bca)
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs9(LT, LT) → True
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs18(False, False) → True
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs4(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs4(x0, x1, ty_Double)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_@0)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs4(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_esEs5(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                    ↳ QDP

                      ↳ UsableRulesProof

                        ↳ QDP

                          ↳ QReductionProof

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

new_lookup(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Left(yu30), yu41, bd, be, bf)
new_lookup1(yu11, yu12, yu13, yu14, False, ba, bb, bc) → new_lookup(Left(yu11), yu14, ba, bb, bc)
new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, be), bd, be, bf)

The TRS R consists of the following rules:

new_esEs4(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs4(yu30, yu4000, app(app(app(ty_@3, df), dg), dh)) → new_esEs13(yu30, yu4000, df, dg, dh)
new_esEs4(yu30, yu4000, app(app(ty_Either, bcf), bcg)) → new_esEs11(yu30, yu4000, bcf, bcg)
new_esEs4(yu30, yu4000, app(ty_[], hh)) → new_esEs17(yu30, yu4000, hh)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Maybe, cb)) → new_esEs6(yu30, yu4000, cb)
new_esEs4(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Ratio, bce)) → new_esEs8(yu30, yu4000, bce)
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs4(yu30, yu4000, app(app(ty_@2, bch), bda)) → new_esEs19(yu30, yu4000, bch, bda)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs9(GT, GT) → True
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_asAs(False, yu39) → False
new_asAs(True, yu39) → yu39
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Nothing, Nothing, cb) → True
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs16(@0, @0) → True

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Char)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs4(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs4(x0, x1, ty_Double)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_@0)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs4(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_esEs5(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

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_esEs5(x0, x1, ty_Char)
new_esEs5(x0, x1, ty_Float)
new_esEs5(x0, x1, ty_Bool)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_Int)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ DependencyGraphProof

                  ↳ AND

                    ↳ QDP

                    ↳ QDP

                      ↳ UsableRulesProof

                        ↳ QDP

                          ↳ QReductionProof

                            ↳ QDP

                              ↳ QDPSizeChangeProof

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

new_lookup(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Left(yu30), yu41, bd, be, bf)
new_lookup1(yu11, yu12, yu13, yu14, False, ba, bb, bc) → new_lookup(Left(yu11), yu14, ba, bb, bc)
new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, be), bd, be, bf)

The TRS R consists of the following rules:

new_esEs4(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs4(yu30, yu4000, app(app(app(ty_@3, df), dg), dh)) → new_esEs13(yu30, yu4000, df, dg, dh)
new_esEs4(yu30, yu4000, app(app(ty_Either, bcf), bcg)) → new_esEs11(yu30, yu4000, bcf, bcg)
new_esEs4(yu30, yu4000, app(ty_[], hh)) → new_esEs17(yu30, yu4000, hh)
new_esEs4(yu30, yu4000, ty_Int) → new_esEs12(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Maybe, cb)) → new_esEs6(yu30, yu4000, cb)
new_esEs4(yu30, yu4000, ty_Float) → new_esEs15(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs4(yu30, yu4000, app(ty_Ratio, bce)) → new_esEs8(yu30, yu4000, bce)
new_esEs4(yu30, yu4000, ty_Bool) → new_esEs18(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Integer) → new_esEs10(yu30, yu4000)
new_esEs4(yu30, yu4000, ty_Char) → new_esEs7(yu30, yu4000)
new_esEs4(yu30, yu4000, app(app(ty_@2, bch), bda)) → new_esEs19(yu30, yu4000, bch, bda)
new_esEs4(yu30, yu4000, ty_Ordering) → new_esEs9(yu30, yu4000)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs9(GT, GT) → True
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_esEs19(@2(yu300, yu301), @2(yu40000, yu40001), bch, bda) → new_asAs(new_esEs24(yu300, yu40000, bch), new_esEs25(yu301, yu40001, bda))
new_esEs24(yu300, yu40000, app(ty_[], bdh)) → new_esEs17(yu300, yu40000, bdh)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Ratio, bdb)) → new_esEs8(yu300, yu40000, bdb)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs13(yu300, yu40000, bde, bdf, bdg)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, app(ty_Maybe, bea)) → new_esEs6(yu300, yu40000, bea)
new_esEs24(yu300, yu40000, app(app(ty_Either, bdc), bdd)) → new_esEs11(yu300, yu40000, bdc, bdd)
new_esEs24(yu300, yu40000, app(app(ty_@2, beb), bec)) → new_esEs19(yu300, yu40000, beb, bec)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Maybe, bfc)) → new_esEs6(yu301, yu40001, bfc)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_Ratio, bed)) → new_esEs8(yu301, yu40001, bed)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs25(yu301, yu40001, app(ty_[], bfb)) → new_esEs17(yu301, yu40001, bfb)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, beg), beh), bfa)) → new_esEs13(yu301, yu40001, beg, beh, bfa)
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs25(yu301, yu40001, app(app(ty_Either, bee), bef)) → new_esEs11(yu301, yu40001, bee, bef)
new_esEs25(yu301, yu40001, app(app(ty_@2, bfd), bfe)) → new_esEs19(yu301, yu40001, bfd, bfe)
new_asAs(False, yu39) → False
new_asAs(True, yu39) → yu39
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_[], bhf)) → new_esEs17(yu300, yu40000, bhf)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Maybe, dc)) → new_esEs6(yu300, yu40000, dc)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, bfg), bfh), bcg) → new_esEs11(yu300, yu40000, bfg, bfh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_Either, bha), bhb)) → new_esEs11(yu300, yu40000, bha, bhb)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Maybe, bhg)) → new_esEs6(yu300, yu40000, bhg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, bge), bcg) → new_esEs6(yu300, yu40000, bge)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_Either, cd), ce)) → new_esEs11(yu300, yu40000, cd, ce)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, bcg) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(ty_Ratio, bgh)) → new_esEs8(yu300, yu40000, bgh)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(ty_@2, bhh), caa)) → new_esEs19(yu300, yu40000, bhh, caa)
new_esEs11(Right(yu300), Right(yu40000), bcf, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs13(yu300, yu40000, bhc, bhd, bhe)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, bcg) → new_esEs15(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, bcg) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], bgd), bcg) → new_esEs17(yu300, yu40000, bgd)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, bcg) → new_esEs10(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, bgf), bgg), bcg) → new_esEs19(yu300, yu40000, bgf, bgg)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, bcg) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, bff), bcg) → new_esEs8(yu300, yu40000, bff)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, bcg) → new_esEs16(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, bcg) → new_esEs9(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, bga), bgb), bgc), bcg) → new_esEs13(yu300, yu40000, bga, bgb, bgc)
new_esEs11(Right(yu300), Right(yu40000), bcf, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_Int, bcg) → new_esEs12(yu300, yu40000)
new_esEs11(Left(yu300), Right(yu40000), bcf, bcg) → False
new_esEs11(Right(yu300), Left(yu40000), bcf, bcg) → False
new_esEs12(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Succ(yu400000)) → False
new_primEqNat0(Succ(yu3000), Zero) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(yu3000), Succ(yu400000)) → new_primEqNat0(yu3000, yu400000)
new_esEs13(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), df, dg, dh) → new_asAs(new_esEs20(yu300, yu40000, df), new_asAs(new_esEs21(yu301, yu40001, dg), new_esEs22(yu302, yu40002, dh)))
new_esEs20(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(ty_Either, eb), ec)) → new_esEs11(yu300, yu40000, eb, ec)
new_esEs20(yu300, yu40000, app(app(ty_@2, fa), fb)) → new_esEs19(yu300, yu40000, fa, fb)
new_esEs20(yu300, yu40000, app(ty_[], eg)) → new_esEs17(yu300, yu40000, eg)
new_esEs20(yu300, yu40000, app(ty_Maybe, eh)) → new_esEs6(yu300, yu40000, eh)
new_esEs20(yu300, yu40000, app(ty_Ratio, ea)) → new_esEs8(yu300, yu40000, ea)
new_esEs20(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs20(yu300, yu40000, app(app(app(ty_@3, ed), ee), ef)) → new_esEs13(yu300, yu40000, ed, ee, ef)
new_esEs20(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs20(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs21(yu301, yu40001, ty_Float) → new_esEs15(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(ty_Either, fd), ff)) → new_esEs11(yu301, yu40001, fd, ff)
new_esEs21(yu301, yu40001, app(app(ty_@2, gd), ge)) → new_esEs19(yu301, yu40001, gd, ge)
new_esEs21(yu301, yu40001, app(ty_[], gb)) → new_esEs17(yu301, yu40001, gb)
new_esEs21(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs21(yu301, yu40001, app(app(app(ty_@3, fg), fh), ga)) → new_esEs13(yu301, yu40001, fg, fh, ga)
new_esEs21(yu301, yu40001, ty_Bool) → new_esEs18(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Ordering) → new_esEs9(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Ratio, fc)) → new_esEs8(yu301, yu40001, fc)
new_esEs21(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs21(yu301, yu40001, ty_Double) → new_esEs14(yu301, yu40001)
new_esEs21(yu301, yu40001, app(ty_Maybe, gc)) → new_esEs6(yu301, yu40001, gc)
new_esEs21(yu301, yu40001, ty_Char) → new_esEs7(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs18(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs9(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs7(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_Ratio, gf)) → new_esEs8(yu302, yu40002, gf)
new_esEs22(yu302, yu40002, app(ty_Maybe, he)) → new_esEs6(yu302, yu40002, he)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs10(yu302, yu40002)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs14(yu302, yu40002)
new_esEs22(yu302, yu40002, app(ty_[], hd)) → new_esEs17(yu302, yu40002, hd)
new_esEs22(yu302, yu40002, app(app(ty_@2, hf), hg)) → new_esEs19(yu302, yu40002, hf, hg)
new_esEs22(yu302, yu40002, ty_Float) → new_esEs15(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, ha), hb), hc)) → new_esEs13(yu302, yu40002, ha, hb, hc)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs12(yu302, yu40002)
new_esEs22(yu302, yu40002, app(app(ty_Either, gg), gh)) → new_esEs11(yu302, yu40002, gg, gh)
new_esEs15(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_sr(Pos(yu3010), Neg(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Pos(yu400010)) → Neg(new_primMulNat0(yu3010, yu400010))
new_sr(Neg(yu3010), Neg(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_sr(Pos(yu3010), Pos(yu400010)) → Pos(new_primMulNat0(yu3010, yu400010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(yu30100), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000100)) → Zero
new_primMulNat0(Succ(yu30100), Succ(yu4000100)) → new_primPlusNat0(new_primMulNat0(yu30100, Succ(yu4000100)), yu4000100)
new_primPlusNat0(Zero, yu4000100) → Succ(yu4000100)
new_primPlusNat0(Succ(yu400), yu4000100) → Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) → Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
new_primPlusNat1(Succ(yu4000), Zero) → Succ(yu4000)
new_primPlusNat1(Zero, Succ(yu40001000)) → Succ(yu40001000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs17(:(yu300, yu301), :(yu40000, yu40001), hh) → new_asAs(new_esEs23(yu300, yu40000, hh), new_esEs17(yu301, yu40001, hh))
new_esEs17([], [], hh) → True
new_esEs17(:(yu300, yu301), [], hh) → False
new_esEs17([], :(yu40000, yu40001), hh) → False
new_esEs23(yu300, yu40000, app(ty_[], bag)) → new_esEs17(yu300, yu40000, bag)
new_esEs23(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Ratio, baa)) → new_esEs8(yu300, yu40000, baa)
new_esEs23(yu300, yu40000, ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_Either, bab), bac)) → new_esEs11(yu300, yu40000, bab, bac)
new_esEs23(yu300, yu40000, ty_Char) → new_esEs7(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Double) → new_esEs14(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(app(ty_@3, bad), bae), baf)) → new_esEs13(yu300, yu40000, bad, bae, baf)
new_esEs23(yu300, yu40000, ty_Float) → new_esEs15(yu300, yu40000)
new_esEs23(yu300, yu40000, app(ty_Maybe, bah)) → new_esEs6(yu300, yu40000, bah)
new_esEs23(yu300, yu40000, ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs23(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs23(yu300, yu40000, app(app(ty_@2, bba), bbb)) → new_esEs19(yu300, yu40000, bba, bbb)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs6(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs9(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Float) → new_esEs15(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(app(ty_@2, dd), de)) → new_esEs19(yu300, yu40000, dd, de)
new_esEs6(Just(yu300), Just(yu40000), app(ty_Ratio, cc)) → new_esEs8(yu300, yu40000, cc)
new_esEs6(Just(yu300), Just(yu40000), ty_Int) → new_esEs12(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), app(ty_[], db)) → new_esEs17(yu300, yu40000, db)
new_esEs6(Just(yu300), Just(yu40000), app(app(app(ty_@3, cf), cg), da)) → new_esEs13(yu300, yu40000, cf, cg, da)
new_esEs6(Just(yu300), Just(yu40000), ty_Bool) → new_esEs18(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Double) → new_esEs14(yu300, yu40000)
new_esEs6(Nothing, Nothing, cb) → True
new_esEs6(Just(yu300), Nothing, cb) → False
new_esEs6(Nothing, Just(yu40000), cb) → False
new_esEs6(Just(yu300), Just(yu40000), ty_Char) → new_esEs7(yu300, yu40000)
new_esEs6(Just(yu300), Just(yu40000), ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs10(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs7(Char(yu300), Char(yu40000)) → new_primEqNat0(yu300, yu40000)
new_esEs14(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs12(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs8(:%(yu300, yu301), :%(yu40000, yu40001), bce) → new_asAs(new_esEs26(yu300, yu40000, bce), new_esEs27(yu301, yu40001, bce))
new_esEs26(yu300, yu40000, ty_Int) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs10(yu300, yu40000)
new_esEs27(yu301, yu40001, ty_Integer) → new_esEs10(yu301, yu40001)
new_esEs27(yu301, yu40001, ty_Int) → new_esEs12(yu301, yu40001)
new_esEs16(@0, @0) → True

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_esEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs10(Integer(x0), Integer(x1))
new_esEs6(Nothing, Just(x0), x1)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(False, True)
new_esEs18(True, False)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs9(EQ, EQ)
new_esEs25(x0, x1, ty_Bool)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs24(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs6(Just(x0), Nothing, x1)
new_esEs4(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Neg(x0), Neg(x1))
new_esEs22(x0, x1, ty_Int)
new_esEs17([], :(x0, x1), x2)
new_esEs4(x0, x1, ty_Double)
new_esEs18(True, True)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Char(x0), Char(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_primPlusNat0(Zero, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs16(@0, @0)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_esEs4(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs17(:(x0, x1), [], x2)
new_primPlusNat1(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs24(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs22(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs13(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sr(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Double)
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs9(LT, EQ)
new_esEs9(EQ, LT)
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Double)
new_esEs17([], [], x0)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs27(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs21(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs24(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs9(LT, LT)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_sr(Neg(x0), Pos(x1))
new_sr(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))

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(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bd, be, bf) → new_lookup(Left(yu30), yu41, bd, be, bf)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5
new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, be), bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 3 >= 6, 4 >= 7, 5 >= 8
new_lookup1(yu11, yu12, yu13, yu14, False, ba, bb, bc) → new_lookup(Left(yu11), yu14, ba, bb, bc)
The graph contains the following edges 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5

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