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

YES 1.924 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ IFR

mainModule List

((delete :: Eq a => a -> [a] -> [a]) :: Eq a => a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

delete :: Eq a => a -> [a] -> [a]

delete

deleteBy (==)

deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]

deleteBy	_ _ []	=	[]
deleteBy	eq x (y : ys)	=	if x `eq` y then ys else y : deleteBy eq x ys

module Maybe where

import qualified List
import qualified Prelude

If Reductions:
The following If expression

if eq x y then ys else y : deleteBy eq x ys

is transformed to

deleteBy0 ys y eq x True = ys

deleteBy0 ys y eq x False = y : deleteBy eq x ys

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

mainModule List

((delete :: Eq a => a -> [a] -> [a]) :: Eq a => a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

delete :: Eq a => a -> [a] -> [a]

delete

deleteBy (==)

deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]

deleteBy	_ _ []	=	[]
deleteBy	eq x (y : ys)	=	deleteBy0 ys y eq x (x `eq` y)

deleteBy0	ys y eq x True	=	ys
deleteBy0	ys y eq x False	=	y : deleteBy eq x ys

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule List

((delete :: Eq a => a -> [a] -> [a]) :: Eq a => a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

delete :: Eq a => a -> [a] -> [a]

delete

deleteBy (==)

deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]

deleteBy	vw vx []	=	[]
deleteBy	eq x (y : ys)	=	deleteBy0 ys y eq x (x `eq` y)

deleteBy0	ys y eq x True	=	ys
deleteBy0	ys y eq x False	=	y : deleteBy eq x ys

module Maybe where

import qualified List
import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

mainModule List

(delete :: Eq a => a -> [a] -> [a])

module List where

import qualified Maybe
import qualified Prelude

delete :: Eq a => a -> [a] -> [a]

delete

deleteBy (==)

deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]

deleteBy	vw vx []	=	[]
deleteBy	eq x (y : ys)	=	deleteBy0 ys y eq x (x `eq` y)

deleteBy0	ys y eq x True	=	ys
deleteBy0	ys y eq x False	=	y : deleteBy eq x ys

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="delete\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="delete xy3\n  Eq a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="delete xy3 xy4\n  Eq a",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="deleteBy (==) xy3 xy4\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];678[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 678[label="",style="solid", color="burlywood", weight=9];
678 -> 6[label="",style="solid", color="burlywood", weight=3];
679[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 679[label="",style="solid", color="burlywood", weight=9];
679 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="deleteBy (==) xy3 (xy40 : xy41)\n  Eq a",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="deleteBy (==) xy3 []\n  Eq a",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8 -> 10[label="",style="dashed", color="red", weight=0];
8[label="deleteBy0 xy41 xy40 (==) xy3 ((==) xy3 xy40)\n  Eq a",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3];
8 -> 12[label="",style="dashed", color="magenta", weight=3];
8 -> 13[label="",style="dashed", color="magenta", weight=3];
8 -> 14[label="",style="dashed", color="magenta", weight=3];
9[label="[]\n  Eq a",fontsize=16,color="green",shape="box"];11[label="xy40\n  Eq a",fontsize=16,color="green",shape="box"];12[label="(==) xy3 xy40\n  Eq a",fontsize=16,color="blue",shape="box"];681[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 681[label="",style="solid", color="blue", weight=9];
681 -> 15[label="",style="solid", color="blue", weight=3];
682[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 682[label="",style="solid", color="blue", weight=9];
682 -> 16[label="",style="solid", color="blue", weight=3];
683[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 683[label="",style="solid", color="blue", weight=9];
683 -> 17[label="",style="solid", color="blue", weight=3];
684[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 684[label="",style="solid", color="blue", weight=9];
684 -> 18[label="",style="solid", color="blue", weight=3];
685[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 685[label="",style="solid", color="blue", weight=9];
685 -> 19[label="",style="solid", color="blue", weight=3];
686[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 686[label="",style="solid", color="blue", weight=9];
686 -> 20[label="",style="solid", color="blue", weight=3];
687[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 687[label="",style="solid", color="blue", weight=9];
687 -> 21[label="",style="solid", color="blue", weight=3];
688[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 688[label="",style="solid", color="blue", weight=9];
688 -> 22[label="",style="solid", color="blue", weight=3];
689[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 689[label="",style="solid", color="blue", weight=9];
689 -> 23[label="",style="solid", color="blue", weight=3];
690[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 690[label="",style="solid", color="blue", weight=9];
690 -> 24[label="",style="solid", color="blue", weight=3];
691[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 691[label="",style="solid", color="blue", weight=9];
691 -> 25[label="",style="solid", color="blue", weight=3];
692[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 692[label="",style="solid", color="blue", weight=9];
692 -> 26[label="",style="solid", color="blue", weight=3];
693[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 693[label="",style="solid", color="blue", weight=9];
693 -> 27[label="",style="solid", color="blue", weight=3];
694[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12 -> 694[label="",style="solid", color="blue", weight=9];
694 -> 28[label="",style="solid", color="blue", weight=3];
13[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];14[label="xy3\n  Eq a",fontsize=16,color="green",shape="box"];10[label="deleteBy0 xy10 xy11 (==) xy12 xy13\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];695[label="xy13/False",fontsize=10,color="white",style="solid",shape="box"];10 -> 695[label="",style="solid", color="burlywood", weight=9];
695 -> 29[label="",style="solid", color="burlywood", weight=3];
696[label="xy13/True",fontsize=10,color="white",style="solid",shape="box"];10 -> 696[label="",style="solid", color="burlywood", weight=9];
696 -> 30[label="",style="solid", color="burlywood", weight=3];
15[label="(==) xy3 xy40",fontsize=16,color="burlywood",shape="triangle"];697[label="xy3/()",fontsize=10,color="white",style="solid",shape="box"];15 -> 697[label="",style="solid", color="burlywood", weight=9];
697 -> 31[label="",style="solid", color="burlywood", weight=3];
16[label="(==) xy3 xy40",fontsize=16,color="black",shape="triangle"];16 -> 32[label="",style="solid", color="black", weight=3];
17[label="(==) xy3 xy40\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];698[label="xy3/xy30 :% xy31",fontsize=10,color="white",style="solid",shape="box"];17 -> 698[label="",style="solid", color="burlywood", weight=9];
698 -> 33[label="",style="solid", color="burlywood", weight=3];
18[label="(==) xy3 xy40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];699[label="xy3/(xy30,xy31)",fontsize=10,color="white",style="solid",shape="box"];18 -> 699[label="",style="solid", color="burlywood", weight=9];
699 -> 34[label="",style="solid", color="burlywood", weight=3];
19[label="(==) xy3 xy40\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];700[label="xy3/(xy30,xy31,xy32)",fontsize=10,color="white",style="solid",shape="box"];19 -> 700[label="",style="solid", color="burlywood", weight=9];
700 -> 35[label="",style="solid", color="burlywood", weight=3];
20[label="(==) xy3 xy40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];701[label="xy3/Left xy30",fontsize=10,color="white",style="solid",shape="box"];20 -> 701[label="",style="solid", color="burlywood", weight=9];
701 -> 36[label="",style="solid", color="burlywood", weight=3];
702[label="xy3/Right xy30",fontsize=10,color="white",style="solid",shape="box"];20 -> 702[label="",style="solid", color="burlywood", weight=9];
702 -> 37[label="",style="solid", color="burlywood", weight=3];
21[label="(==) xy3 xy40",fontsize=16,color="black",shape="triangle"];21 -> 38[label="",style="solid", color="black", weight=3];
22[label="(==) xy3 xy40",fontsize=16,color="burlywood",shape="triangle"];703[label="xy3/Integer xy30",fontsize=10,color="white",style="solid",shape="box"];22 -> 703[label="",style="solid", color="burlywood", weight=9];
703 -> 39[label="",style="solid", color="burlywood", weight=3];
23[label="(==) xy3 xy40",fontsize=16,color="burlywood",shape="triangle"];704[label="xy3/False",fontsize=10,color="white",style="solid",shape="box"];23 -> 704[label="",style="solid", color="burlywood", weight=9];
704 -> 40[label="",style="solid", color="burlywood", weight=3];
705[label="xy3/True",fontsize=10,color="white",style="solid",shape="box"];23 -> 705[label="",style="solid", color="burlywood", weight=9];
705 -> 41[label="",style="solid", color="burlywood", weight=3];
24[label="(==) xy3 xy40",fontsize=16,color="black",shape="triangle"];24 -> 42[label="",style="solid", color="black", weight=3];
25[label="(==) xy3 xy40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];706[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];25 -> 706[label="",style="solid", color="burlywood", weight=9];
706 -> 43[label="",style="solid", color="burlywood", weight=3];
707[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];25 -> 707[label="",style="solid", color="burlywood", weight=9];
707 -> 44[label="",style="solid", color="burlywood", weight=3];
26[label="(==) xy3 xy40",fontsize=16,color="burlywood",shape="triangle"];708[label="xy3/LT",fontsize=10,color="white",style="solid",shape="box"];26 -> 708[label="",style="solid", color="burlywood", weight=9];
708 -> 45[label="",style="solid", color="burlywood", weight=3];
709[label="xy3/EQ",fontsize=10,color="white",style="solid",shape="box"];26 -> 709[label="",style="solid", color="burlywood", weight=9];
709 -> 46[label="",style="solid", color="burlywood", weight=3];
710[label="xy3/GT",fontsize=10,color="white",style="solid",shape="box"];26 -> 710[label="",style="solid", color="burlywood", weight=9];
710 -> 47[label="",style="solid", color="burlywood", weight=3];
27[label="(==) xy3 xy40",fontsize=16,color="black",shape="triangle"];27 -> 48[label="",style="solid", color="black", weight=3];
28[label="(==) xy3 xy40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];711[label="xy3/Nothing",fontsize=10,color="white",style="solid",shape="box"];28 -> 711[label="",style="solid", color="burlywood", weight=9];
711 -> 49[label="",style="solid", color="burlywood", weight=3];
712[label="xy3/Just xy30",fontsize=10,color="white",style="solid",shape="box"];28 -> 712[label="",style="solid", color="burlywood", weight=9];
712 -> 50[label="",style="solid", color="burlywood", weight=3];
29[label="deleteBy0 xy10 xy11 (==) xy12 False\n  Eq a",fontsize=16,color="black",shape="box"];29 -> 51[label="",style="solid", color="black", weight=3];
30[label="deleteBy0 xy10 xy11 (==) xy12 True\n  Eq a",fontsize=16,color="black",shape="box"];30 -> 52[label="",style="solid", color="black", weight=3];
31[label="(==) () xy40",fontsize=16,color="burlywood",shape="box"];713[label="xy40/()",fontsize=10,color="white",style="solid",shape="box"];31 -> 713[label="",style="solid", color="burlywood", weight=9];
713 -> 53[label="",style="solid", color="burlywood", weight=3];
32[label="primEqChar xy3 xy40",fontsize=16,color="burlywood",shape="box"];714[label="xy3/Char xy30",fontsize=10,color="white",style="solid",shape="box"];32 -> 714[label="",style="solid", color="burlywood", weight=9];
714 -> 54[label="",style="solid", color="burlywood", weight=3];
33[label="(==) xy30 :% xy31 xy40\n  Integral a",fontsize=16,color="burlywood",shape="box"];715[label="xy40/xy400 :% xy401",fontsize=10,color="white",style="solid",shape="box"];33 -> 715[label="",style="solid", color="burlywood", weight=9];
715 -> 55[label="",style="solid", color="burlywood", weight=3];
34[label="(==) (xy30,xy31) xy40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];716[label="xy40/(xy400,xy401)",fontsize=10,color="white",style="solid",shape="box"];34 -> 716[label="",style="solid", color="burlywood", weight=9];
716 -> 56[label="",style="solid", color="burlywood", weight=3];
35[label="(==) (xy30,xy31,xy32) xy40\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];717[label="xy40/(xy400,xy401,xy402)",fontsize=10,color="white",style="solid",shape="box"];35 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 57[label="",style="solid", color="burlywood", weight=3];
36[label="(==) Left xy30 xy40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];718[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];36 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 58[label="",style="solid", color="burlywood", weight=3];
719[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];36 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 59[label="",style="solid", color="burlywood", weight=3];
37[label="(==) Right xy30 xy40\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];720[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];37 -> 720[label="",style="solid", color="burlywood", weight=9];
720 -> 60[label="",style="solid", color="burlywood", weight=3];
721[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];37 -> 721[label="",style="solid", color="burlywood", weight=9];
721 -> 61[label="",style="solid", color="burlywood", weight=3];
38[label="primEqDouble xy3 xy40",fontsize=16,color="burlywood",shape="box"];722[label="xy3/Double xy30 xy31",fontsize=10,color="white",style="solid",shape="box"];38 -> 722[label="",style="solid", color="burlywood", weight=9];
722 -> 62[label="",style="solid", color="burlywood", weight=3];
39[label="(==) Integer xy30 xy40",fontsize=16,color="burlywood",shape="box"];723[label="xy40/Integer xy400",fontsize=10,color="white",style="solid",shape="box"];39 -> 723[label="",style="solid", color="burlywood", weight=9];
723 -> 63[label="",style="solid", color="burlywood", weight=3];
40[label="(==) False xy40",fontsize=16,color="burlywood",shape="box"];724[label="xy40/False",fontsize=10,color="white",style="solid",shape="box"];40 -> 724[label="",style="solid", color="burlywood", weight=9];
724 -> 64[label="",style="solid", color="burlywood", weight=3];
725[label="xy40/True",fontsize=10,color="white",style="solid",shape="box"];40 -> 725[label="",style="solid", color="burlywood", weight=9];
725 -> 65[label="",style="solid", color="burlywood", weight=3];
41[label="(==) True xy40",fontsize=16,color="burlywood",shape="box"];726[label="xy40/False",fontsize=10,color="white",style="solid",shape="box"];41 -> 726[label="",style="solid", color="burlywood", weight=9];
726 -> 66[label="",style="solid", color="burlywood", weight=3];
727[label="xy40/True",fontsize=10,color="white",style="solid",shape="box"];41 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 67[label="",style="solid", color="burlywood", weight=3];
42[label="primEqFloat xy3 xy40",fontsize=16,color="burlywood",shape="box"];728[label="xy3/Float xy30 xy31",fontsize=10,color="white",style="solid",shape="box"];42 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 68[label="",style="solid", color="burlywood", weight=3];
43[label="(==) xy30 : xy31 xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];729[label="xy40/xy400 : xy401",fontsize=10,color="white",style="solid",shape="box"];43 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 69[label="",style="solid", color="burlywood", weight=3];
730[label="xy40/[]",fontsize=10,color="white",style="solid",shape="box"];43 -> 730[label="",style="solid", color="burlywood", weight=9];
730 -> 70[label="",style="solid", color="burlywood", weight=3];
44[label="(==) [] xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];731[label="xy40/xy400 : xy401",fontsize=10,color="white",style="solid",shape="box"];44 -> 731[label="",style="solid", color="burlywood", weight=9];
731 -> 71[label="",style="solid", color="burlywood", weight=3];
732[label="xy40/[]",fontsize=10,color="white",style="solid",shape="box"];44 -> 732[label="",style="solid", color="burlywood", weight=9];
732 -> 72[label="",style="solid", color="burlywood", weight=3];
45[label="(==) LT xy40",fontsize=16,color="burlywood",shape="box"];733[label="xy40/LT",fontsize=10,color="white",style="solid",shape="box"];45 -> 733[label="",style="solid", color="burlywood", weight=9];
733 -> 73[label="",style="solid", color="burlywood", weight=3];
734[label="xy40/EQ",fontsize=10,color="white",style="solid",shape="box"];45 -> 734[label="",style="solid", color="burlywood", weight=9];
734 -> 74[label="",style="solid", color="burlywood", weight=3];
735[label="xy40/GT",fontsize=10,color="white",style="solid",shape="box"];45 -> 735[label="",style="solid", color="burlywood", weight=9];
735 -> 75[label="",style="solid", color="burlywood", weight=3];
46[label="(==) EQ xy40",fontsize=16,color="burlywood",shape="box"];736[label="xy40/LT",fontsize=10,color="white",style="solid",shape="box"];46 -> 736[label="",style="solid", color="burlywood", weight=9];
736 -> 76[label="",style="solid", color="burlywood", weight=3];
737[label="xy40/EQ",fontsize=10,color="white",style="solid",shape="box"];46 -> 737[label="",style="solid", color="burlywood", weight=9];
737 -> 77[label="",style="solid", color="burlywood", weight=3];
738[label="xy40/GT",fontsize=10,color="white",style="solid",shape="box"];46 -> 738[label="",style="solid", color="burlywood", weight=9];
738 -> 78[label="",style="solid", color="burlywood", weight=3];
47[label="(==) GT xy40",fontsize=16,color="burlywood",shape="box"];739[label="xy40/LT",fontsize=10,color="white",style="solid",shape="box"];47 -> 739[label="",style="solid", color="burlywood", weight=9];
739 -> 79[label="",style="solid", color="burlywood", weight=3];
740[label="xy40/EQ",fontsize=10,color="white",style="solid",shape="box"];47 -> 740[label="",style="solid", color="burlywood", weight=9];
740 -> 80[label="",style="solid", color="burlywood", weight=3];
741[label="xy40/GT",fontsize=10,color="white",style="solid",shape="box"];47 -> 741[label="",style="solid", color="burlywood", weight=9];
741 -> 81[label="",style="solid", color="burlywood", weight=3];
48[label="primEqInt xy3 xy40",fontsize=16,color="burlywood",shape="triangle"];742[label="xy3/Pos xy30",fontsize=10,color="white",style="solid",shape="box"];48 -> 742[label="",style="solid", color="burlywood", weight=9];
742 -> 82[label="",style="solid", color="burlywood", weight=3];
743[label="xy3/Neg xy30",fontsize=10,color="white",style="solid",shape="box"];48 -> 743[label="",style="solid", color="burlywood", weight=9];
743 -> 83[label="",style="solid", color="burlywood", weight=3];
49[label="(==) Nothing xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];744[label="xy40/Nothing",fontsize=10,color="white",style="solid",shape="box"];49 -> 744[label="",style="solid", color="burlywood", weight=9];
744 -> 84[label="",style="solid", color="burlywood", weight=3];
745[label="xy40/Just xy400",fontsize=10,color="white",style="solid",shape="box"];49 -> 745[label="",style="solid", color="burlywood", weight=9];
745 -> 85[label="",style="solid", color="burlywood", weight=3];
50[label="(==) Just xy30 xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];746[label="xy40/Nothing",fontsize=10,color="white",style="solid",shape="box"];50 -> 746[label="",style="solid", color="burlywood", weight=9];
746 -> 86[label="",style="solid", color="burlywood", weight=3];
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63[label="(==) Integer xy30 Integer xy400",fontsize=16,color="black",shape="box"];63 -> 99[label="",style="solid", color="black", weight=3];
64[label="(==) False False",fontsize=16,color="black",shape="box"];64 -> 100[label="",style="solid", color="black", weight=3];
65[label="(==) False True",fontsize=16,color="black",shape="box"];65 -> 101[label="",style="solid", color="black", weight=3];
66[label="(==) True False",fontsize=16,color="black",shape="box"];66 -> 102[label="",style="solid", color="black", weight=3];
67[label="(==) True True",fontsize=16,color="black",shape="box"];67 -> 103[label="",style="solid", color="black", weight=3];
68[label="primEqFloat (Float xy30 xy31) xy40",fontsize=16,color="burlywood",shape="box"];750[label="xy40/Float xy400 xy401",fontsize=10,color="white",style="solid",shape="box"];68 -> 750[label="",style="solid", color="burlywood", weight=9];
750 -> 104[label="",style="solid", color="burlywood", weight=3];
69[label="(==) xy30 : xy31 xy400 : xy401\n  Eq a",fontsize=16,color="black",shape="box"];69 -> 105[label="",style="solid", color="black", weight=3];
70[label="(==) xy30 : xy31 []\n  Eq a",fontsize=16,color="black",shape="box"];70 -> 106[label="",style="solid", color="black", weight=3];
71[label="(==) [] xy400 : xy401\n  Eq a",fontsize=16,color="black",shape="box"];71 -> 107[label="",style="solid", color="black", weight=3];
72[label="(==) [] []\n  Eq a",fontsize=16,color="black",shape="box"];72 -> 108[label="",style="solid", color="black", weight=3];
73[label="(==) LT LT",fontsize=16,color="black",shape="box"];73 -> 109[label="",style="solid", color="black", weight=3];
74[label="(==) LT EQ",fontsize=16,color="black",shape="box"];74 -> 110[label="",style="solid", color="black", weight=3];
75[label="(==) LT GT",fontsize=16,color="black",shape="box"];75 -> 111[label="",style="solid", color="black", weight=3];
76[label="(==) EQ LT",fontsize=16,color="black",shape="box"];76 -> 112[label="",style="solid", color="black", weight=3];
77[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];77 -> 113[label="",style="solid", color="black", weight=3];
78[label="(==) EQ GT",fontsize=16,color="black",shape="box"];78 -> 114[label="",style="solid", color="black", weight=3];
79[label="(==) GT LT",fontsize=16,color="black",shape="box"];79 -> 115[label="",style="solid", color="black", weight=3];
80[label="(==) GT EQ",fontsize=16,color="black",shape="box"];80 -> 116[label="",style="solid", color="black", weight=3];
81[label="(==) GT GT",fontsize=16,color="black",shape="box"];81 -> 117[label="",style="solid", color="black", weight=3];
82[label="primEqInt (Pos xy30) xy40",fontsize=16,color="burlywood",shape="box"];751[label="xy30/Succ xy300",fontsize=10,color="white",style="solid",shape="box"];82 -> 751[label="",style="solid", color="burlywood", weight=9];
751 -> 118[label="",style="solid", color="burlywood", weight=3];
752[label="xy30/Zero",fontsize=10,color="white",style="solid",shape="box"];82 -> 752[label="",style="solid", color="burlywood", weight=9];
752 -> 119[label="",style="solid", color="burlywood", weight=3];
83[label="primEqInt (Neg xy30) xy40",fontsize=16,color="burlywood",shape="box"];753[label="xy30/Succ xy300",fontsize=10,color="white",style="solid",shape="box"];83 -> 753[label="",style="solid", color="burlywood", weight=9];
753 -> 120[label="",style="solid", color="burlywood", weight=3];
754[label="xy30/Zero",fontsize=10,color="white",style="solid",shape="box"];83 -> 754[label="",style="solid", color="burlywood", weight=9];
754 -> 121[label="",style="solid", color="burlywood", weight=3];
84[label="(==) Nothing Nothing\n  Eq a",fontsize=16,color="black",shape="box"];84 -> 122[label="",style="solid", color="black", weight=3];
85[label="(==) Nothing Just xy400\n  Eq a",fontsize=16,color="black",shape="box"];85 -> 123[label="",style="solid", color="black", weight=3];
86[label="(==) Just xy30 Nothing\n  Eq a",fontsize=16,color="black",shape="box"];86 -> 124[label="",style="solid", color="black", weight=3];
87[label="(==) Just xy30 Just xy400\n  Eq a",fontsize=16,color="black",shape="box"];87 -> 125[label="",style="solid", color="black", weight=3];
88 -> 5[label="",style="dashed", color="red", weight=0];
88[label="deleteBy (==) xy12 xy10\n  Eq a",fontsize=16,color="magenta"];88 -> 126[label="",style="dashed", color="magenta", weight=3];
88 -> 127[label="",style="dashed", color="magenta", weight=3];
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91 -> 208[label="",style="dashed", color="red", weight=0];
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91 -> 210[label="",style="dashed", color="magenta", weight=3];
92 -> 208[label="",style="dashed", color="red", weight=0];
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92 -> 212[label="",style="dashed", color="magenta", weight=3];
93 -> 208[label="",style="dashed", color="red", weight=0];
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93 -> 214[label="",style="dashed", color="magenta", weight=3];
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759 -> 150[label="",style="solid", color="blue", weight=3];
760[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 760[label="",style="solid", color="blue", weight=9];
760 -> 151[label="",style="solid", color="blue", weight=3];
761[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 761[label="",style="solid", color="blue", weight=9];
761 -> 152[label="",style="solid", color="blue", weight=3];
762[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 762[label="",style="solid", color="blue", weight=9];
762 -> 153[label="",style="solid", color="blue", weight=3];
763[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 763[label="",style="solid", color="blue", weight=9];
763 -> 154[label="",style="solid", color="blue", weight=3];
764[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 764[label="",style="solid", color="blue", weight=9];
764 -> 155[label="",style="solid", color="blue", weight=3];
765[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 765[label="",style="solid", color="blue", weight=9];
765 -> 156[label="",style="solid", color="blue", weight=3];
766[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 766[label="",style="solid", color="blue", weight=9];
766 -> 157[label="",style="solid", color="blue", weight=3];
767[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 767[label="",style="solid", color="blue", weight=9];
767 -> 158[label="",style="solid", color="blue", weight=3];
768[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 768[label="",style="solid", color="blue", weight=9];
768 -> 159[label="",style="solid", color="blue", weight=3];
769[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 769[label="",style="solid", color="blue", weight=9];
769 -> 160[label="",style="solid", color="blue", weight=3];
770[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 770[label="",style="solid", color="blue", weight=9];
770 -> 161[label="",style="solid", color="blue", weight=3];
771[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 771[label="",style="solid", color="blue", weight=9];
771 -> 162[label="",style="solid", color="blue", weight=3];
772[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];94 -> 772[label="",style="solid", color="blue", weight=9];
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773 -> 164[label="",style="solid", color="blue", weight=3];
774[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 774[label="",style="solid", color="blue", weight=9];
774 -> 165[label="",style="solid", color="blue", weight=3];
775[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 775[label="",style="solid", color="blue", weight=9];
775 -> 166[label="",style="solid", color="blue", weight=3];
776[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 776[label="",style="solid", color="blue", weight=9];
776 -> 167[label="",style="solid", color="blue", weight=3];
777[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 777[label="",style="solid", color="blue", weight=9];
777 -> 168[label="",style="solid", color="blue", weight=3];
778[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 778[label="",style="solid", color="blue", weight=9];
778 -> 169[label="",style="solid", color="blue", weight=3];
779[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 779[label="",style="solid", color="blue", weight=9];
779 -> 170[label="",style="solid", color="blue", weight=3];
780[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 780[label="",style="solid", color="blue", weight=9];
780 -> 171[label="",style="solid", color="blue", weight=3];
781[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 781[label="",style="solid", color="blue", weight=9];
781 -> 172[label="",style="solid", color="blue", weight=3];
782[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 782[label="",style="solid", color="blue", weight=9];
782 -> 173[label="",style="solid", color="blue", weight=3];
783[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 783[label="",style="solid", color="blue", weight=9];
783 -> 174[label="",style="solid", color="blue", weight=3];
784[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 784[label="",style="solid", color="blue", weight=9];
784 -> 175[label="",style="solid", color="blue", weight=3];
785[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 785[label="",style="solid", color="blue", weight=9];
785 -> 176[label="",style="solid", color="blue", weight=3];
786[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];97 -> 786[label="",style="solid", color="blue", weight=9];
786 -> 177[label="",style="solid", color="blue", weight=3];
98[label="primEqDouble (Double xy30 xy31) (Double xy400 xy401)",fontsize=16,color="black",shape="box"];98 -> 178[label="",style="solid", color="black", weight=3];
99 -> 48[label="",style="dashed", color="red", weight=0];
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99 -> 180[label="",style="dashed", color="magenta", weight=3];
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105 -> 208[label="",style="dashed", color="red", weight=0];
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105 -> 216[label="",style="dashed", color="magenta", weight=3];
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789 -> 182[label="",style="solid", color="burlywood", weight=3];
790[label="xy40/Neg xy400",fontsize=10,color="white",style="solid",shape="box"];118 -> 790[label="",style="solid", color="burlywood", weight=9];
790 -> 183[label="",style="solid", color="burlywood", weight=3];
119[label="primEqInt (Pos Zero) xy40",fontsize=16,color="burlywood",shape="box"];791[label="xy40/Pos xy400",fontsize=10,color="white",style="solid",shape="box"];119 -> 791[label="",style="solid", color="burlywood", weight=9];
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792[label="xy40/Neg xy400",fontsize=10,color="white",style="solid",shape="box"];119 -> 792[label="",style="solid", color="burlywood", weight=9];
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120[label="primEqInt (Neg (Succ xy300)) xy40",fontsize=16,color="burlywood",shape="box"];793[label="xy40/Pos xy400",fontsize=10,color="white",style="solid",shape="box"];120 -> 793[label="",style="solid", color="burlywood", weight=9];
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794[label="xy40/Neg xy400",fontsize=10,color="white",style="solid",shape="box"];120 -> 794[label="",style="solid", color="burlywood", weight=9];
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796[label="xy40/Neg xy400",fontsize=10,color="white",style="solid",shape="box"];121 -> 796[label="",style="solid", color="burlywood", weight=9];
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798[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 798[label="",style="solid", color="blue", weight=9];
798 -> 191[label="",style="solid", color="blue", weight=3];
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800[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 800[label="",style="solid", color="blue", weight=9];
800 -> 193[label="",style="solid", color="blue", weight=3];
801[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 801[label="",style="solid", color="blue", weight=9];
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802[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 802[label="",style="solid", color="blue", weight=9];
802 -> 195[label="",style="solid", color="blue", weight=3];
803[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 803[label="",style="solid", color="blue", weight=9];
803 -> 196[label="",style="solid", color="blue", weight=3];
804[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 804[label="",style="solid", color="blue", weight=9];
804 -> 197[label="",style="solid", color="blue", weight=3];
805[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 805[label="",style="solid", color="blue", weight=9];
805 -> 198[label="",style="solid", color="blue", weight=3];
806[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 806[label="",style="solid", color="blue", weight=9];
806 -> 199[label="",style="solid", color="blue", weight=3];
807[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 807[label="",style="solid", color="blue", weight=9];
807 -> 200[label="",style="solid", color="blue", weight=3];
808[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 808[label="",style="solid", color="blue", weight=9];
808 -> 201[label="",style="solid", color="blue", weight=3];
809[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 809[label="",style="solid", color="blue", weight=9];
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810[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];125 -> 810[label="",style="solid", color="blue", weight=9];
810 -> 203[label="",style="solid", color="blue", weight=3];
126[label="xy10\n  Eq a",fontsize=16,color="green",shape="box"];127[label="xy12\n  Eq a",fontsize=16,color="green",shape="box"];128[label="primEqNat xy30 xy400",fontsize=16,color="burlywood",shape="triangle"];811[label="xy30/Succ xy300",fontsize=10,color="white",style="solid",shape="box"];128 -> 811[label="",style="solid", color="burlywood", weight=9];
811 -> 204[label="",style="solid", color="burlywood", weight=3];
812[label="xy30/Zero",fontsize=10,color="white",style="solid",shape="box"];128 -> 812[label="",style="solid", color="burlywood", weight=9];
812 -> 205[label="",style="solid", color="burlywood", weight=3];
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813 -> 221[label="",style="solid", color="blue", weight=3];
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910[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];184 -> 910[label="",style="solid", color="burlywood", weight=9];
910 -> 351[label="",style="solid", color="burlywood", weight=3];
185[label="primEqInt (Pos Zero) (Neg xy400)",fontsize=16,color="burlywood",shape="box"];911[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];185 -> 911[label="",style="solid", color="burlywood", weight=9];
911 -> 352[label="",style="solid", color="burlywood", weight=3];
912[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];185 -> 912[label="",style="solid", color="burlywood", weight=9];
912 -> 353[label="",style="solid", color="burlywood", weight=3];
186[label="primEqInt (Neg (Succ xy300)) (Pos xy400)",fontsize=16,color="black",shape="box"];186 -> 354[label="",style="solid", color="black", weight=3];
187[label="primEqInt (Neg (Succ xy300)) (Neg xy400)",fontsize=16,color="burlywood",shape="box"];913[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];187 -> 913[label="",style="solid", color="burlywood", weight=9];
913 -> 355[label="",style="solid", color="burlywood", weight=3];
914[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];187 -> 914[label="",style="solid", color="burlywood", weight=9];
914 -> 356[label="",style="solid", color="burlywood", weight=3];
188[label="primEqInt (Neg Zero) (Pos xy400)",fontsize=16,color="burlywood",shape="box"];915[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];188 -> 915[label="",style="solid", color="burlywood", weight=9];
915 -> 357[label="",style="solid", color="burlywood", weight=3];
916[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];188 -> 916[label="",style="solid", color="burlywood", weight=9];
916 -> 358[label="",style="solid", color="burlywood", weight=3];
189[label="primEqInt (Neg Zero) (Neg xy400)",fontsize=16,color="burlywood",shape="box"];917[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];189 -> 917[label="",style="solid", color="burlywood", weight=9];
917 -> 359[label="",style="solid", color="burlywood", weight=3];
918[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];189 -> 918[label="",style="solid", color="burlywood", weight=9];
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190 -> 15[label="",style="dashed", color="red", weight=0];
190[label="xy30 == xy400",fontsize=16,color="magenta"];190 -> 361[label="",style="dashed", color="magenta", weight=3];
190 -> 362[label="",style="dashed", color="magenta", weight=3];
191 -> 16[label="",style="dashed", color="red", weight=0];
191[label="xy30 == xy400",fontsize=16,color="magenta"];191 -> 363[label="",style="dashed", color="magenta", weight=3];
191 -> 364[label="",style="dashed", color="magenta", weight=3];
192 -> 17[label="",style="dashed", color="red", weight=0];
192[label="xy30 == xy400\n  Integral a",fontsize=16,color="magenta"];192 -> 365[label="",style="dashed", color="magenta", weight=3];
192 -> 366[label="",style="dashed", color="magenta", weight=3];
193 -> 18[label="",style="dashed", color="red", weight=0];
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194 -> 19[label="",style="dashed", color="red", weight=0];
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194 -> 370[label="",style="dashed", color="magenta", weight=3];
195 -> 20[label="",style="dashed", color="red", weight=0];
195[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="magenta"];195 -> 371[label="",style="dashed", color="magenta", weight=3];
195 -> 372[label="",style="dashed", color="magenta", weight=3];
196 -> 21[label="",style="dashed", color="red", weight=0];
196[label="xy30 == xy400",fontsize=16,color="magenta"];196 -> 373[label="",style="dashed", color="magenta", weight=3];
196 -> 374[label="",style="dashed", color="magenta", weight=3];
197 -> 22[label="",style="dashed", color="red", weight=0];
197[label="xy30 == xy400",fontsize=16,color="magenta"];197 -> 375[label="",style="dashed", color="magenta", weight=3];
197 -> 376[label="",style="dashed", color="magenta", weight=3];
198 -> 23[label="",style="dashed", color="red", weight=0];
198[label="xy30 == xy400",fontsize=16,color="magenta"];198 -> 377[label="",style="dashed", color="magenta", weight=3];
198 -> 378[label="",style="dashed", color="magenta", weight=3];
199 -> 24[label="",style="dashed", color="red", weight=0];
199[label="xy30 == xy400",fontsize=16,color="magenta"];199 -> 379[label="",style="dashed", color="magenta", weight=3];
199 -> 380[label="",style="dashed", color="magenta", weight=3];
200 -> 25[label="",style="dashed", color="red", weight=0];
200[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];200 -> 381[label="",style="dashed", color="magenta", weight=3];
200 -> 382[label="",style="dashed", color="magenta", weight=3];
201 -> 26[label="",style="dashed", color="red", weight=0];
201[label="xy30 == xy400",fontsize=16,color="magenta"];201 -> 383[label="",style="dashed", color="magenta", weight=3];
201 -> 384[label="",style="dashed", color="magenta", weight=3];
202 -> 27[label="",style="dashed", color="red", weight=0];
202[label="xy30 == xy400",fontsize=16,color="magenta"];202 -> 385[label="",style="dashed", color="magenta", weight=3];
202 -> 386[label="",style="dashed", color="magenta", weight=3];
203 -> 28[label="",style="dashed", color="red", weight=0];
203[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];203 -> 387[label="",style="dashed", color="magenta", weight=3];
203 -> 388[label="",style="dashed", color="magenta", weight=3];
204[label="primEqNat (Succ xy300) xy400",fontsize=16,color="burlywood",shape="box"];933[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];204 -> 933[label="",style="solid", color="burlywood", weight=9];
933 -> 389[label="",style="solid", color="burlywood", weight=3];
934[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];204 -> 934[label="",style="solid", color="burlywood", weight=9];
934 -> 390[label="",style="solid", color="burlywood", weight=3];
205[label="primEqNat Zero xy400",fontsize=16,color="burlywood",shape="box"];935[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];205 -> 935[label="",style="solid", color="burlywood", weight=9];
935 -> 391[label="",style="solid", color="burlywood", weight=3];
936[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];205 -> 936[label="",style="solid", color="burlywood", weight=9];
936 -> 392[label="",style="solid", color="burlywood", weight=3];
221 -> 22[label="",style="dashed", color="red", weight=0];
221[label="xy31 == xy401",fontsize=16,color="magenta"];221 -> 393[label="",style="dashed", color="magenta", weight=3];
221 -> 394[label="",style="dashed", color="magenta", weight=3];
222 -> 27[label="",style="dashed", color="red", weight=0];
222[label="xy31 == xy401",fontsize=16,color="magenta"];222 -> 395[label="",style="dashed", color="magenta", weight=3];
222 -> 396[label="",style="dashed", color="magenta", weight=3];
223 -> 22[label="",style="dashed", color="red", weight=0];
223[label="xy30 == xy400",fontsize=16,color="magenta"];223 -> 397[label="",style="dashed", color="magenta", weight=3];
223 -> 398[label="",style="dashed", color="magenta", weight=3];
224 -> 27[label="",style="dashed", color="red", weight=0];
224[label="xy30 == xy400",fontsize=16,color="magenta"];224 -> 399[label="",style="dashed", color="magenta", weight=3];
224 -> 400[label="",style="dashed", color="magenta", weight=3];
225[label="False && xy26",fontsize=16,color="black",shape="box"];225 -> 401[label="",style="solid", color="black", weight=3];
226[label="True && xy26",fontsize=16,color="black",shape="box"];226 -> 402[label="",style="solid", color="black", weight=3];
227 -> 15[label="",style="dashed", color="red", weight=0];
227[label="xy31 == xy401",fontsize=16,color="magenta"];227 -> 403[label="",style="dashed", color="magenta", weight=3];
227 -> 404[label="",style="dashed", color="magenta", weight=3];
228 -> 16[label="",style="dashed", color="red", weight=0];
228[label="xy31 == xy401",fontsize=16,color="magenta"];228 -> 405[label="",style="dashed", color="magenta", weight=3];
228 -> 406[label="",style="dashed", color="magenta", weight=3];
229 -> 17[label="",style="dashed", color="red", weight=0];
229[label="xy31 == xy401\n  Integral a",fontsize=16,color="magenta"];229 -> 407[label="",style="dashed", color="magenta", weight=3];
229 -> 408[label="",style="dashed", color="magenta", weight=3];
230 -> 18[label="",style="dashed", color="red", weight=0];
230[label="xy31 == xy401\n  Eq a  Eq b",fontsize=16,color="magenta"];230 -> 409[label="",style="dashed", color="magenta", weight=3];
230 -> 410[label="",style="dashed", color="magenta", weight=3];
231 -> 19[label="",style="dashed", color="red", weight=0];
231[label="xy31 == xy401\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];231 -> 411[label="",style="dashed", color="magenta", weight=3];
231 -> 412[label="",style="dashed", color="magenta", weight=3];
232 -> 20[label="",style="dashed", color="red", weight=0];
232[label="xy31 == xy401\n  Eq a  Eq b",fontsize=16,color="magenta"];232 -> 413[label="",style="dashed", color="magenta", weight=3];
232 -> 414[label="",style="dashed", color="magenta", weight=3];
233 -> 21[label="",style="dashed", color="red", weight=0];
233[label="xy31 == xy401",fontsize=16,color="magenta"];233 -> 415[label="",style="dashed", color="magenta", weight=3];
233 -> 416[label="",style="dashed", color="magenta", weight=3];
234 -> 22[label="",style="dashed", color="red", weight=0];
234[label="xy31 == xy401",fontsize=16,color="magenta"];234 -> 417[label="",style="dashed", color="magenta", weight=3];
234 -> 418[label="",style="dashed", color="magenta", weight=3];
235 -> 23[label="",style="dashed", color="red", weight=0];
235[label="xy31 == xy401",fontsize=16,color="magenta"];235 -> 419[label="",style="dashed", color="magenta", weight=3];
235 -> 420[label="",style="dashed", color="magenta", weight=3];
236 -> 24[label="",style="dashed", color="red", weight=0];
236[label="xy31 == xy401",fontsize=16,color="magenta"];236 -> 421[label="",style="dashed", color="magenta", weight=3];
236 -> 422[label="",style="dashed", color="magenta", weight=3];
237 -> 25[label="",style="dashed", color="red", weight=0];
237[label="xy31 == xy401\n  Eq a",fontsize=16,color="magenta"];237 -> 423[label="",style="dashed", color="magenta", weight=3];
237 -> 424[label="",style="dashed", color="magenta", weight=3];
238 -> 26[label="",style="dashed", color="red", weight=0];
238[label="xy31 == xy401",fontsize=16,color="magenta"];238 -> 425[label="",style="dashed", color="magenta", weight=3];
238 -> 426[label="",style="dashed", color="magenta", weight=3];
239 -> 27[label="",style="dashed", color="red", weight=0];
239[label="xy31 == xy401",fontsize=16,color="magenta"];239 -> 427[label="",style="dashed", color="magenta", weight=3];
239 -> 428[label="",style="dashed", color="magenta", weight=3];
240 -> 28[label="",style="dashed", color="red", weight=0];
240[label="xy31 == xy401\n  Eq a",fontsize=16,color="magenta"];240 -> 429[label="",style="dashed", color="magenta", weight=3];
240 -> 430[label="",style="dashed", color="magenta", weight=3];
241 -> 15[label="",style="dashed", color="red", weight=0];
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242 -> 16[label="",style="dashed", color="red", weight=0];
242[label="xy30 == xy400",fontsize=16,color="magenta"];242 -> 433[label="",style="dashed", color="magenta", weight=3];
242 -> 434[label="",style="dashed", color="magenta", weight=3];
243 -> 17[label="",style="dashed", color="red", weight=0];
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243 -> 436[label="",style="dashed", color="magenta", weight=3];
244 -> 18[label="",style="dashed", color="red", weight=0];
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246 -> 20[label="",style="dashed", color="red", weight=0];
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247 -> 21[label="",style="dashed", color="red", weight=0];
247[label="xy30 == xy400",fontsize=16,color="magenta"];247 -> 443[label="",style="dashed", color="magenta", weight=3];
247 -> 444[label="",style="dashed", color="magenta", weight=3];
248 -> 22[label="",style="dashed", color="red", weight=0];
248[label="xy30 == xy400",fontsize=16,color="magenta"];248 -> 445[label="",style="dashed", color="magenta", weight=3];
248 -> 446[label="",style="dashed", color="magenta", weight=3];
249 -> 23[label="",style="dashed", color="red", weight=0];
249[label="xy30 == xy400",fontsize=16,color="magenta"];249 -> 447[label="",style="dashed", color="magenta", weight=3];
249 -> 448[label="",style="dashed", color="magenta", weight=3];
250 -> 24[label="",style="dashed", color="red", weight=0];
250[label="xy30 == xy400",fontsize=16,color="magenta"];250 -> 449[label="",style="dashed", color="magenta", weight=3];
250 -> 450[label="",style="dashed", color="magenta", weight=3];
251 -> 25[label="",style="dashed", color="red", weight=0];
251[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];251 -> 451[label="",style="dashed", color="magenta", weight=3];
251 -> 452[label="",style="dashed", color="magenta", weight=3];
252 -> 26[label="",style="dashed", color="red", weight=0];
252[label="xy30 == xy400",fontsize=16,color="magenta"];252 -> 453[label="",style="dashed", color="magenta", weight=3];
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253 -> 27[label="",style="dashed", color="red", weight=0];
253[label="xy30 == xy400",fontsize=16,color="magenta"];253 -> 455[label="",style="dashed", color="magenta", weight=3];
253 -> 456[label="",style="dashed", color="magenta", weight=3];
254 -> 28[label="",style="dashed", color="red", weight=0];
254[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];254 -> 457[label="",style="dashed", color="magenta", weight=3];
254 -> 458[label="",style="dashed", color="magenta", weight=3];
255[label="xy32 == xy402\n  Eq a",fontsize=16,color="blue",shape="box"];969[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 969[label="",style="solid", color="blue", weight=9];
969 -> 459[label="",style="solid", color="blue", weight=3];
970[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 970[label="",style="solid", color="blue", weight=9];
970 -> 460[label="",style="solid", color="blue", weight=3];
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972[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 972[label="",style="solid", color="blue", weight=9];
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973[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 973[label="",style="solid", color="blue", weight=9];
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974[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 974[label="",style="solid", color="blue", weight=9];
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975[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 975[label="",style="solid", color="blue", weight=9];
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976[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 976[label="",style="solid", color="blue", weight=9];
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978[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 978[label="",style="solid", color="blue", weight=9];
978 -> 468[label="",style="solid", color="blue", weight=3];
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980[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 980[label="",style="solid", color="blue", weight=9];
980 -> 470[label="",style="solid", color="blue", weight=3];
981[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];255 -> 981[label="",style="solid", color="blue", weight=9];
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256[label="xy31 == xy401\n  Eq a",fontsize=16,color="blue",shape="box"];983[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 983[label="",style="solid", color="blue", weight=9];
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984[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 984[label="",style="solid", color="blue", weight=9];
984 -> 474[label="",style="solid", color="blue", weight=3];
985[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 985[label="",style="solid", color="blue", weight=9];
985 -> 475[label="",style="solid", color="blue", weight=3];
986[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 986[label="",style="solid", color="blue", weight=9];
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987[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 987[label="",style="solid", color="blue", weight=9];
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988[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 988[label="",style="solid", color="blue", weight=9];
988 -> 478[label="",style="solid", color="blue", weight=3];
989[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 989[label="",style="solid", color="blue", weight=9];
989 -> 479[label="",style="solid", color="blue", weight=3];
990[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 990[label="",style="solid", color="blue", weight=9];
990 -> 480[label="",style="solid", color="blue", weight=3];
991[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 991[label="",style="solid", color="blue", weight=9];
991 -> 481[label="",style="solid", color="blue", weight=3];
992[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 992[label="",style="solid", color="blue", weight=9];
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993[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 993[label="",style="solid", color="blue", weight=9];
993 -> 483[label="",style="solid", color="blue", weight=3];
994[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 994[label="",style="solid", color="blue", weight=9];
994 -> 484[label="",style="solid", color="blue", weight=3];
995[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 995[label="",style="solid", color="blue", weight=9];
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996[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];256 -> 996[label="",style="solid", color="blue", weight=9];
996 -> 486[label="",style="solid", color="blue", weight=3];
257 -> 15[label="",style="dashed", color="red", weight=0];
257[label="xy30 == xy400",fontsize=16,color="magenta"];257 -> 487[label="",style="dashed", color="magenta", weight=3];
257 -> 488[label="",style="dashed", color="magenta", weight=3];
258 -> 16[label="",style="dashed", color="red", weight=0];
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259 -> 17[label="",style="dashed", color="red", weight=0];
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1082 -> 669[label="",style="solid", color="burlywood", weight=3];
1083[label="xy40100/Zero",fontsize=10,color="white",style="solid",shape="box"];666 -> 1083[label="",style="solid", color="burlywood", weight=9];
1083 -> 670[label="",style="solid", color="burlywood", weight=3];
667[label="primPlusNat (Succ xy2700) (Succ xy401000)",fontsize=16,color="black",shape="box"];667 -> 671[label="",style="solid", color="black", weight=3];
668[label="primPlusNat (Succ xy2700) Zero",fontsize=16,color="black",shape="box"];668 -> 672[label="",style="solid", color="black", weight=3];
669[label="primPlusNat Zero (Succ xy401000)",fontsize=16,color="black",shape="box"];669 -> 673[label="",style="solid", color="black", weight=3];
670[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];670 -> 674[label="",style="solid", color="black", weight=3];
671[label="Succ (Succ (primPlusNat xy2700 xy401000))",fontsize=16,color="green",shape="box"];671 -> 675[label="",style="dashed", color="green", weight=3];
672[label="Succ xy2700",fontsize=16,color="green",shape="box"];673[label="Succ xy401000",fontsize=16,color="green",shape="box"];674[label="Zero",fontsize=16,color="green",shape="box"];675 -> 664[label="",style="dashed", color="red", weight=0];
675[label="primPlusNat xy2700 xy401000",fontsize=16,color="magenta"];675 -> 676[label="",style="dashed", color="magenta", weight=3];
675 -> 677[label="",style="dashed", color="magenta", weight=3];
676[label="xy2700",fontsize=16,color="green",shape="box"];677[label="xy401000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ IFR

    ↳ 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(xy2700), Succ(xy401000)) → new_primPlusNat(xy2700, xy401000)

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(xy2700), Succ(xy401000)) → new_primPlusNat(xy2700, xy401000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ 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(xy3100), Succ(xy40100)) → new_primMulNat(xy3100, Succ(xy40100))

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

new_primMulNat(Succ(xy3100), Succ(xy40100)) → new_primMulNat(xy3100, Succ(xy40100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ IFR

    ↳ 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(xy300), Succ(xy4000)) → new_primEqNat(xy300, xy4000)

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

new_primEqNat(Succ(xy300), Succ(xy4000)) → new_primEqNat(xy300, xy4000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ 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_esEs(@2(xy30, xy31), @2(xy400, xy401), app(app(ty_@2, cc), cd), ce) → new_esEs(xy30, xy400, cc, cd)
new_esEs1(Right(xy30), Right(xy400), bag, app(ty_Maybe, bbh)) → new_esEs3(xy30, xy400, bbh)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(app(app(ty_@3, bd), be), bf)) → new_esEs0(xy31, xy401, bd, be, bf)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(app(ty_Either, ee), ef)) → new_esEs1(xy32, xy402, ee, ef)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(ty_Maybe, hd), dg, fc) → new_esEs3(xy30, xy400, hd)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(ty_[], ca)) → new_esEs2(xy31, xy401, ca)
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(ty_Maybe, bdb)) → new_esEs3(xy30, xy400, bdb)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(app(ty_@2, dh), ea)) → new_esEs(xy32, xy402, dh, ea)
new_esEs1(Left(xy30), Left(xy400), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(xy30, xy400, hh, baa, bab)
new_esEs1(Left(xy30), Left(xy400), app(ty_[], bae), hg) → new_esEs2(xy30, xy400, bae)
new_esEs3(Just(xy30), Just(xy400), app(ty_[], beb)) → new_esEs2(xy30, xy400, beb)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(ty_Maybe, de), ce) → new_esEs3(xy30, xy400, de)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(app(ty_Either, ha), hb), dg, fc) → new_esEs1(xy30, xy400, ha, hb)
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs0(xy30, xy400, bcd, bce, bcf)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(ty_[], hc), dg, fc) → new_esEs2(xy30, xy400, hc)
new_esEs1(Right(xy30), Right(xy400), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(xy30, xy400, bbb, bbc, bbd)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(app(ty_@2, fa), fb), fc) → new_esEs(xy31, xy401, fa, fb)
new_esEs1(Left(xy30), Left(xy400), app(app(ty_Either, bac), bad), hg) → new_esEs1(xy30, xy400, bac, bad)
new_esEs1(Right(xy30), Right(xy400), bag, app(app(ty_Either, bbe), bbf)) → new_esEs1(xy30, xy400, bbe, bbf)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(app(app(ty_@3, fd), ff), fg), fc) → new_esEs0(xy31, xy401, fd, ff, fg)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(app(ty_Either, fh), ga), fc) → new_esEs1(xy31, xy401, fh, ga)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(ty_Maybe, cb)) → new_esEs3(xy31, xy401, cb)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(app(ty_@2, gd), ge), dg, fc) → new_esEs(xy30, xy400, gd, ge)
new_esEs3(Just(xy30), Just(xy400), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(xy30, xy400, bde, bdf, bdg)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(ty_Maybe, gc), fc) → new_esEs3(xy31, xy401, gc)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(ty_Maybe, eh)) → new_esEs3(xy32, xy402, eh)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(ty_[], gb), fc) → new_esEs2(xy31, xy401, gb)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(app(app(ty_@3, eb), ec), ed)) → new_esEs0(xy32, xy402, eb, ec, ed)
new_esEs1(Right(xy30), Right(xy400), bag, app(app(ty_@2, bah), bba)) → new_esEs(xy30, xy400, bah, bba)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(app(ty_Either, bg), bh)) → new_esEs1(xy31, xy401, bg, bh)
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(app(ty_Either, bcg), bch)) → new_esEs1(xy30, xy400, bcg, bch)
new_esEs2(:(xy30, xy31), :(xy400, xy401), bca) → new_esEs2(xy31, xy401, bca)
new_esEs3(Just(xy30), Just(xy400), app(ty_Maybe, bec)) → new_esEs3(xy30, xy400, bec)
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(app(ty_@2, bcb), bcc)) → new_esEs(xy30, xy400, bcb, bcc)
new_esEs3(Just(xy30), Just(xy400), app(app(ty_@2, bdc), bdd)) → new_esEs(xy30, xy400, bdc, bdd)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(ty_[], eg)) → new_esEs2(xy32, xy402, eg)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(app(ty_@2, bb), bc)) → new_esEs(xy31, xy401, bb, bc)
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(ty_[], bda)) → new_esEs2(xy30, xy400, bda)
new_esEs1(Left(xy30), Left(xy400), app(ty_Maybe, baf), hg) → new_esEs3(xy30, xy400, baf)
new_esEs1(Left(xy30), Left(xy400), app(app(ty_@2, he), hf), hg) → new_esEs(xy30, xy400, he, hf)
new_esEs1(Right(xy30), Right(xy400), bag, app(ty_[], bbg)) → new_esEs2(xy30, xy400, bbg)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(app(app(ty_@3, cf), cg), da), ce) → new_esEs0(xy30, xy400, cf, cg, da)
new_esEs3(Just(xy30), Just(xy400), app(app(ty_Either, bdh), bea)) → new_esEs1(xy30, xy400, bdh, bea)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(app(ty_Either, db), dc), ce) → new_esEs1(xy30, xy400, db, dc)
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(app(app(ty_@3, gf), gg), gh), dg, fc) → new_esEs0(xy30, xy400, gf, gg, gh)
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(ty_[], dd), ce) → new_esEs2(xy30, xy400, dd)

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

new_esEs3(Just(xy30), Just(xy400), app(app(ty_@2, bdc), bdd)) → new_esEs(xy30, xy400, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(xy30), Just(xy400), app(app(ty_Either, bdh), bea)) → new_esEs1(xy30, xy400, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(xy30), Just(xy400), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(xy30, xy400, bde, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(app(ty_@2, bcb), bcc)) → new_esEs(xy30, xy400, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(app(ty_Either, bcg), bch)) → new_esEs1(xy30, xy400, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs0(xy30, xy400, bcd, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(xy30), Just(xy400), app(ty_[], beb)) → new_esEs2(xy30, xy400, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xy30), Just(xy400), app(ty_Maybe, bec)) → new_esEs3(xy30, xy400, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(ty_Maybe, bdb)) → new_esEs3(xy30, xy400, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(app(ty_@2, cc), cd), ce) → new_esEs(xy30, xy400, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(app(ty_@2, bb), bc)) → new_esEs(xy31, xy401, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(app(ty_Either, bg), bh)) → new_esEs1(xy31, xy401, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(app(ty_Either, db), dc), ce) → new_esEs1(xy30, xy400, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(app(app(ty_@3, bd), be), bf)) → new_esEs0(xy31, xy401, bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(app(app(ty_@3, cf), cg), da), ce) → new_esEs0(xy30, xy400, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(ty_[], ca)) → new_esEs2(xy31, xy401, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(ty_[], dd), ce) → new_esEs2(xy30, xy400, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xy30, xy31), @2(xy400, xy401), app(ty_Maybe, de), ce) → new_esEs3(xy30, xy400, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xy30, xy31), @2(xy400, xy401), ba, app(ty_Maybe, cb)) → new_esEs3(xy31, xy401, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Right(xy30), Right(xy400), bag, app(app(ty_@2, bah), bba)) → new_esEs(xy30, xy400, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(Left(xy30), Left(xy400), app(app(ty_@2, he), hf), hg) → new_esEs(xy30, xy400, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(app(ty_@2, dh), ea)) → new_esEs(xy32, xy402, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(app(ty_@2, fa), fb), fc) → new_esEs(xy31, xy401, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(app(ty_@2, gd), ge), dg, fc) → new_esEs(xy30, xy400, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Left(xy30), Left(xy400), app(app(ty_Either, bac), bad), hg) → new_esEs1(xy30, xy400, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Right(xy30), Right(xy400), bag, app(app(ty_Either, bbe), bbf)) → new_esEs1(xy30, xy400, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(app(ty_Either, ee), ef)) → new_esEs1(xy32, xy402, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(app(ty_Either, ha), hb), dg, fc) → new_esEs1(xy30, xy400, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(app(ty_Either, fh), ga), fc) → new_esEs1(xy31, xy401, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(Left(xy30), Left(xy400), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(xy30, xy400, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(Right(xy30), Right(xy400), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(xy30, xy400, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(Left(xy30), Left(xy400), app(ty_[], bae), hg) → new_esEs2(xy30, xy400, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Right(xy30), Right(xy400), bag, app(ty_[], bbg)) → new_esEs2(xy30, xy400, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Right(xy30), Right(xy400), bag, app(ty_Maybe, bbh)) → new_esEs3(xy30, xy400, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Left(xy30), Left(xy400), app(ty_Maybe, baf), hg) → new_esEs3(xy30, xy400, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(app(app(ty_@3, fd), ff), fg), fc) → new_esEs0(xy31, xy401, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(app(app(ty_@3, eb), ec), ed)) → new_esEs0(xy32, xy402, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(app(app(ty_@3, gf), gg), gh), dg, fc) → new_esEs0(xy30, xy400, gf, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(ty_[], hc), dg, fc) → new_esEs2(xy30, xy400, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(ty_[], gb), fc) → new_esEs2(xy31, xy401, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(ty_[], eg)) → new_esEs2(xy32, xy402, eg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), app(ty_Maybe, hd), dg, fc) → new_esEs3(xy30, xy400, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, app(ty_Maybe, gc), fc) → new_esEs3(xy31, xy401, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), df, dg, app(ty_Maybe, eh)) → new_esEs3(xy32, xy402, eh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(:(xy30, xy31), :(xy400, xy401), bca) → new_esEs2(xy31, xy401, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs2(:(xy30, xy31), :(xy400, xy401), app(ty_[], bda)) → new_esEs2(xy30, xy400, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_deleteBy(xy3, :(xy40, xy41), bb) → new_deleteBy0(xy41, xy40, xy3, new_esEs4(xy3, xy40, bb), bb)
new_deleteBy0(xy10, xy11, xy12, False, ba) → new_deleteBy(xy12, xy10, ba)

The TRS R consists of the following rules:

new_esEs22(xy30, xy400, ty_Integer) → new_esEs14(xy30, xy400)
new_esEs25(xy31, xy401, ty_Ordering) → new_esEs17(xy31, xy401)
new_esEs21(xy31, xy401, ty_Double) → new_esEs13(xy31, xy401)
new_primPlusNat1(Succ(xy2700), Succ(xy401000)) → Succ(Succ(new_primPlusNat1(xy2700, xy401000)))
new_esEs22(xy30, xy400, app(ty_Ratio, bae)) → new_esEs9(xy30, xy400, bae)
new_primEqInt(Pos(Succ(xy300)), Neg(xy400)) → False
new_primEqInt(Neg(Succ(xy300)), Pos(xy400)) → False
new_esEs25(xy31, xy401, ty_Bool) → new_esEs15(xy31, xy401)
new_esEs6(xy30, xy400, app(app(ty_@2, be), bf)) → new_esEs10(xy30, xy400, be, bf)
new_esEs26(xy30, xy400, ty_Double) → new_esEs13(xy30, xy400)
new_esEs26(xy30, xy400, app(app(ty_Either, bfe), bff)) → new_esEs12(xy30, xy400, bfe, bff)
new_esEs25(xy31, xy401, ty_Char) → new_esEs8(xy31, xy401)
new_esEs12(Left(xy30), Left(xy400), ty_@0, cf) → new_esEs7(xy30, xy400)
new_primEqInt(Pos(Zero), Neg(Succ(xy4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xy4000))) → False
new_esEs4(xy3, xy40, ty_Int) → new_esEs18(xy3, xy40)
new_esEs9(:%(xy30, xy31), :%(xy400, xy401), bdb) → new_asAs(new_esEs24(xy30, xy400, bdb), new_esEs23(xy31, xy401, bdb))
new_esEs5([], [], bc) → True
new_esEs4(xy3, xy40, app(app(ty_@2, bdc), bdd)) → new_esEs10(xy3, xy40, bdc, bdd)
new_esEs6(xy30, xy400, ty_Integer) → new_esEs14(xy30, xy400)
new_esEs21(xy31, xy401, ty_Ordering) → new_esEs17(xy31, xy401)
new_esEs26(xy30, xy400, app(ty_Maybe, bfh)) → new_esEs19(xy30, xy400, bfh)
new_esEs23(xy31, xy401, ty_Int) → new_esEs18(xy31, xy401)
new_esEs12(Left(xy30), Left(xy400), ty_Bool, cf) → new_esEs15(xy30, xy400)
new_esEs21(xy31, xy401, app(ty_Maybe, bad)) → new_esEs19(xy31, xy401, bad)
new_esEs19(Just(xy30), Just(xy400), app(app(ty_Either, bcf), bcg)) → new_esEs12(xy30, xy400, bcf, bcg)
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(xy30, xy400, ty_Float) → new_esEs16(xy30, xy400)
new_esEs5(:(xy30, xy31), :(xy400, xy401), bc) → new_asAs(new_esEs6(xy30, xy400, bc), new_esEs5(xy31, xy401, bc))
new_esEs21(xy31, xy401, app(ty_[], bac)) → new_esEs5(xy31, xy401, bac)
new_esEs12(Right(xy30), Right(xy400), eb, ty_Int) → new_esEs18(xy30, xy400)
new_esEs20(xy32, xy402, ty_Double) → new_esEs13(xy32, xy402)
new_esEs21(xy31, xy401, ty_Integer) → new_esEs14(xy31, xy401)
new_esEs5([], :(xy400, xy401), bc) → False
new_esEs5(:(xy30, xy31), [], bc) → False
new_esEs20(xy32, xy402, app(app(ty_Either, gg), gh)) → new_esEs12(xy32, xy402, gg, gh)
new_esEs21(xy31, xy401, app(app(ty_Either, baa), bab)) → new_esEs12(xy31, xy401, baa, bab)
new_primPlusNat0(Zero, xy40100) → Succ(xy40100)
new_esEs25(xy31, xy401, ty_Double) → new_esEs13(xy31, xy401)
new_esEs4(xy3, xy40, app(app(app(ty_@3, ff), fg), fh)) → new_esEs11(xy3, xy40, ff, fg, fh)
new_esEs26(xy30, xy400, ty_Int) → new_esEs18(xy30, xy400)
new_esEs26(xy30, xy400, ty_@0) → new_esEs7(xy30, xy400)
new_sr(Neg(xy310), Pos(xy4010)) → Neg(new_primMulNat0(xy310, xy4010))
new_sr(Pos(xy310), Neg(xy4010)) → Neg(new_primMulNat0(xy310, xy4010))
new_esEs13(Double(xy30, xy31), Double(xy400, xy401)) → new_esEs18(new_sr(xy30, xy400), new_sr(xy31, xy401))
new_esEs20(xy32, xy402, ty_Ordering) → new_esEs17(xy32, xy402)
new_esEs6(xy30, xy400, ty_Int) → new_esEs18(xy30, xy400)
new_esEs20(xy32, xy402, ty_Int) → new_esEs18(xy32, xy402)
new_esEs12(Right(xy30), Right(xy400), eb, ty_Double) → new_esEs13(xy30, xy400)
new_esEs12(Right(xy30), Left(xy400), eb, cf) → False
new_esEs12(Left(xy30), Right(xy400), eb, cf) → False
new_esEs6(xy30, xy400, app(ty_Maybe, ce)) → new_esEs19(xy30, xy400, ce)
new_esEs19(Just(xy30), Nothing, bbg) → False
new_esEs19(Nothing, Just(xy400), bbg) → False
new_esEs25(xy31, xy401, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs11(xy31, xy401, bdh, bea, beb)
new_esEs20(xy32, xy402, app(app(app(ty_@3, gd), ge), gf)) → new_esEs11(xy32, xy402, gd, ge, gf)
new_esEs6(xy30, xy400, ty_@0) → new_esEs7(xy30, xy400)
new_esEs19(Just(xy30), Just(xy400), ty_Float) → new_esEs16(xy30, xy400)
new_esEs19(Nothing, Nothing, bbg) → True
new_esEs12(Right(xy30), Right(xy400), eb, ty_Float) → new_esEs16(xy30, xy400)
new_esEs20(xy32, xy402, app(app(ty_@2, gb), gc)) → new_esEs10(xy32, xy402, gb, gc)
new_esEs12(Right(xy30), Right(xy400), eb, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs10(@2(xy30, xy31), @2(xy400, xy401), bdc, bdd) → new_asAs(new_esEs26(xy30, xy400, bdc), new_esEs25(xy31, xy401, bdd))
new_esEs22(xy30, xy400, ty_Double) → new_esEs13(xy30, xy400)
new_esEs26(xy30, xy400, ty_Integer) → new_esEs14(xy30, xy400)
new_esEs6(xy30, xy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs11(xy30, xy400, bg, bh, ca)
new_esEs12(Left(xy30), Left(xy400), app(app(ty_Either, df), dg), cf) → new_esEs12(xy30, xy400, df, dg)
new_esEs6(xy30, xy400, app(ty_Ratio, bd)) → new_esEs9(xy30, xy400, bd)
new_esEs12(Right(xy30), Right(xy400), eb, ty_Integer) → new_esEs14(xy30, xy400)
new_esEs12(Left(xy30), Left(xy400), ty_Float, cf) → new_esEs16(xy30, xy400)
new_esEs12(Left(xy30), Left(xy400), app(ty_Maybe, ea), cf) → new_esEs19(xy30, xy400, ea)
new_primEqNat0(Zero, Succ(xy4000)) → False
new_primEqNat0(Succ(xy300), Zero) → False
new_esEs4(xy3, xy40, app(ty_[], bc)) → new_esEs5(xy3, xy40, bc)
new_esEs12(Left(xy30), Left(xy400), app(app(app(ty_@3, dc), dd), de), cf) → new_esEs11(xy30, xy400, dc, dd, de)
new_esEs20(xy32, xy402, ty_@0) → new_esEs7(xy32, xy402)
new_esEs12(Right(xy30), Right(xy400), eb, app(ty_[], fc)) → new_esEs5(xy30, xy400, fc)
new_esEs12(Right(xy30), Right(xy400), eb, app(ty_Maybe, fd)) → new_esEs19(xy30, xy400, fd)
new_esEs20(xy32, xy402, app(ty_[], ha)) → new_esEs5(xy32, xy402, ha)
new_esEs25(xy31, xy401, ty_@0) → new_esEs7(xy31, xy401)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs12(Left(xy30), Left(xy400), ty_Integer, cf) → new_esEs14(xy30, xy400)
new_esEs12(Left(xy30), Left(xy400), ty_Double, cf) → new_esEs13(xy30, xy400)
new_esEs15(True, False) → False
new_esEs15(False, True) → False
new_esEs16(Float(xy30, xy31), Float(xy400, xy401)) → new_esEs18(new_sr(xy30, xy400), new_sr(xy31, xy401))
new_esEs26(xy30, xy400, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs11(xy30, xy400, bfb, bfc, bfd)
new_esEs25(xy31, xy401, ty_Integer) → new_esEs14(xy31, xy401)
new_esEs21(xy31, xy401, ty_Int) → new_esEs18(xy31, xy401)
new_esEs26(xy30, xy400, ty_Char) → new_esEs8(xy30, xy400)
new_esEs18(xy3, xy40) → new_primEqInt(xy3, xy40)
new_esEs14(Integer(xy30), Integer(xy400)) → new_primEqInt(xy30, xy400)
new_esEs4(xy3, xy40, ty_Integer) → new_esEs14(xy3, xy40)
new_esEs12(Right(xy30), Right(xy400), eb, app(app(app(ty_@3, ef), eg), eh)) → new_esEs11(xy30, xy400, ef, eg, eh)
new_esEs17(LT, LT) → True
new_esEs22(xy30, xy400, app(ty_[], bbe)) → new_esEs5(xy30, xy400, bbe)
new_esEs22(xy30, xy400, ty_Char) → new_esEs8(xy30, xy400)
new_sr(Neg(xy310), Neg(xy4010)) → Pos(new_primMulNat0(xy310, xy4010))
new_esEs12(Right(xy30), Right(xy400), eb, app(app(ty_@2, ed), ee)) → new_esEs10(xy30, xy400, ed, ee)
new_esEs19(Just(xy30), Just(xy400), ty_Double) → new_esEs13(xy30, xy400)
new_esEs12(Left(xy30), Left(xy400), ty_Ordering, cf) → new_esEs17(xy30, xy400)
new_sr(Pos(xy310), Pos(xy4010)) → Pos(new_primMulNat0(xy310, xy4010))
new_asAs(False, xy26) → False
new_esEs25(xy31, xy401, app(ty_[], bee)) → new_esEs5(xy31, xy401, bee)
new_esEs25(xy31, xy401, app(ty_Ratio, bde)) → new_esEs9(xy31, xy401, bde)
new_esEs22(xy30, xy400, ty_Int) → new_esEs18(xy30, xy400)
new_primEqNat0(Zero, Zero) → True
new_esEs22(xy30, xy400, app(app(ty_Either, bbc), bbd)) → new_esEs12(xy30, xy400, bbc, bbd)
new_esEs6(xy30, xy400, ty_Double) → new_esEs13(xy30, xy400)
new_primMulNat0(Succ(xy3100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy40100)) → Zero
new_esEs19(Just(xy30), Just(xy400), app(ty_Ratio, bbh)) → new_esEs9(xy30, xy400, bbh)
new_esEs12(Left(xy30), Left(xy400), app(ty_Ratio, cg), cf) → new_esEs9(xy30, xy400, cg)
new_esEs19(Just(xy30), Just(xy400), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs11(xy30, xy400, bcc, bcd, bce)
new_esEs20(xy32, xy402, ty_Float) → new_esEs16(xy32, xy402)
new_esEs20(xy32, xy402, app(ty_Maybe, hb)) → new_esEs19(xy32, xy402, hb)
new_esEs26(xy30, xy400, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs26(xy30, xy400, app(ty_Ratio, beg)) → new_esEs9(xy30, xy400, beg)
new_esEs6(xy30, xy400, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs26(xy30, xy400, app(app(ty_@2, beh), bfa)) → new_esEs10(xy30, xy400, beh, bfa)
new_esEs21(xy31, xy401, ty_@0) → new_esEs7(xy31, xy401)
new_esEs19(Just(xy30), Just(xy400), ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs19(Just(xy30), Just(xy400), ty_@0) → new_esEs7(xy30, xy400)
new_esEs19(Just(xy30), Just(xy400), ty_Integer) → new_esEs14(xy30, xy400)
new_esEs22(xy30, xy400, ty_@0) → new_esEs7(xy30, xy400)
new_esEs6(xy30, xy400, ty_Float) → new_esEs16(xy30, xy400)
new_esEs26(xy30, xy400, app(ty_[], bfg)) → new_esEs5(xy30, xy400, bfg)
new_primPlusNat0(Succ(xy270), xy40100) → Succ(Succ(new_primPlusNat1(xy270, xy40100)))
new_esEs25(xy31, xy401, ty_Float) → new_esEs16(xy31, xy401)
new_esEs11(@3(xy30, xy31, xy32), @3(xy400, xy401, xy402), ff, fg, fh) → new_asAs(new_esEs22(xy30, xy400, ff), new_asAs(new_esEs21(xy31, xy401, fg), new_esEs20(xy32, xy402, fh)))
new_esEs17(EQ, LT) → False
new_esEs17(LT, EQ) → False
new_esEs20(xy32, xy402, ty_Integer) → new_esEs14(xy32, xy402)
new_esEs12(Left(xy30), Left(xy400), ty_Int, cf) → new_esEs18(xy30, xy400)
new_esEs12(Left(xy30), Left(xy400), app(ty_[], dh), cf) → new_esEs5(xy30, xy400, dh)
new_esEs24(xy30, xy400, ty_Integer) → new_esEs14(xy30, xy400)
new_esEs22(xy30, xy400, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs4(xy3, xy40, app(app(ty_Either, eb), cf)) → new_esEs12(xy3, xy40, eb, cf)
new_esEs22(xy30, xy400, ty_Float) → new_esEs16(xy30, xy400)
new_primEqInt(Neg(Succ(xy300)), Neg(Succ(xy4000))) → new_primEqNat0(xy300, xy4000)
new_esEs22(xy30, xy400, app(ty_Maybe, bbf)) → new_esEs19(xy30, xy400, bbf)
new_esEs15(True, True) → True
new_esEs4(xy3, xy40, ty_Double) → new_esEs13(xy3, xy40)
new_primPlusNat1(Zero, Succ(xy401000)) → Succ(xy401000)
new_primPlusNat1(Succ(xy2700), Zero) → Succ(xy2700)
new_esEs19(Just(xy30), Just(xy400), ty_Int) → new_esEs18(xy30, xy400)
new_esEs12(Right(xy30), Right(xy400), eb, ty_@0) → new_esEs7(xy30, xy400)
new_esEs21(xy31, xy401, app(ty_Ratio, hc)) → new_esEs9(xy31, xy401, hc)
new_esEs20(xy32, xy402, app(ty_Ratio, ga)) → new_esEs9(xy32, xy402, ga)
new_esEs4(xy3, xy40, ty_Bool) → new_esEs15(xy3, xy40)
new_esEs4(xy3, xy40, ty_Char) → new_esEs8(xy3, xy40)
new_esEs26(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs21(xy31, xy401, ty_Char) → new_esEs8(xy31, xy401)
new_esEs25(xy31, xy401, ty_Int) → new_esEs18(xy31, xy401)
new_esEs22(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(xy3, xy40, ty_Float) → new_esEs16(xy3, xy40)
new_esEs17(EQ, EQ) → True
new_esEs12(Right(xy30), Right(xy400), eb, app(app(ty_Either, fa), fb)) → new_esEs12(xy30, xy400, fa, fb)
new_esEs25(xy31, xy401, app(app(ty_Either, bec), bed)) → new_esEs12(xy31, xy401, bec, bed)
new_esEs19(Just(xy30), Just(xy400), app(app(ty_@2, bca), bcb)) → new_esEs10(xy30, xy400, bca, bcb)
new_primEqInt(Neg(Succ(xy300)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy4000))) → False
new_esEs20(xy32, xy402, ty_Bool) → new_esEs15(xy32, xy402)
new_esEs22(xy30, xy400, app(app(ty_@2, baf), bag)) → new_esEs10(xy30, xy400, baf, bag)
new_esEs12(Right(xy30), Right(xy400), eb, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs19(Just(xy30), Just(xy400), app(ty_Maybe, bda)) → new_esEs19(xy30, xy400, bda)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs25(xy31, xy401, app(app(ty_@2, bdf), bdg)) → new_esEs10(xy31, xy401, bdf, bdg)
new_esEs12(Left(xy30), Left(xy400), ty_Char, cf) → new_esEs8(xy30, xy400)
new_asAs(True, xy26) → xy26
new_esEs23(xy31, xy401, ty_Integer) → new_esEs14(xy31, xy401)
new_primMulNat0(Succ(xy3100), Succ(xy40100)) → new_primPlusNat0(new_primMulNat0(xy3100, Succ(xy40100)), xy40100)
new_esEs4(xy3, xy40, app(ty_Ratio, bdb)) → new_esEs9(xy3, xy40, bdb)
new_esEs4(xy3, xy40, ty_@0) → new_esEs7(xy3, xy40)
new_esEs17(GT, GT) → True
new_esEs6(xy30, xy400, app(app(ty_Either, cb), cc)) → new_esEs12(xy30, xy400, cb, cc)
new_primEqInt(Pos(Succ(xy300)), Pos(Succ(xy4000))) → new_primEqNat0(xy300, xy4000)
new_esEs4(xy3, xy40, app(ty_Maybe, bbg)) → new_esEs19(xy3, xy40, bbg)
new_esEs22(xy30, xy400, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs11(xy30, xy400, bah, bba, bbb)
new_esEs25(xy31, xy401, app(ty_Maybe, bef)) → new_esEs19(xy31, xy401, bef)
new_esEs17(GT, LT) → False
new_esEs17(LT, GT) → False
new_esEs24(xy30, xy400, ty_Int) → new_esEs18(xy30, xy400)
new_esEs8(Char(xy30), Char(xy400)) → new_primEqNat0(xy30, xy400)
new_esEs6(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_primEqNat0(Succ(xy300), Succ(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs17(GT, EQ) → False
new_esEs17(EQ, GT) → False
new_esEs6(xy30, xy400, app(ty_[], cd)) → new_esEs5(xy30, xy400, cd)
new_esEs19(Just(xy30), Just(xy400), ty_Bool) → new_esEs15(xy30, xy400)
new_esEs19(Just(xy30), Just(xy400), app(ty_[], bch)) → new_esEs5(xy30, xy400, bch)
new_esEs7(@0, @0) → True
new_esEs21(xy31, xy401, app(app(app(ty_@3, hf), hg), hh)) → new_esEs11(xy31, xy401, hf, hg, hh)
new_esEs12(Right(xy30), Right(xy400), eb, app(ty_Ratio, ec)) → new_esEs9(xy30, xy400, ec)
new_esEs20(xy32, xy402, ty_Char) → new_esEs8(xy32, xy402)
new_esEs19(Just(xy30), Just(xy400), ty_Char) → new_esEs8(xy30, xy400)
new_esEs6(xy30, xy400, ty_Char) → new_esEs8(xy30, xy400)
new_esEs21(xy31, xy401, ty_Float) → new_esEs16(xy31, xy401)
new_esEs12(Left(xy30), Left(xy400), app(app(ty_@2, da), db), cf) → new_esEs10(xy30, xy400, da, db)
new_esEs4(xy3, xy40, ty_Ordering) → new_esEs17(xy3, xy40)
new_esEs21(xy31, xy401, app(app(ty_@2, hd), he)) → new_esEs10(xy31, xy401, hd, he)
new_primEqInt(Pos(Succ(xy300)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy4000))) → False
new_esEs21(xy31, xy401, ty_Bool) → new_esEs15(xy31, xy401)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs15(False, False) → True
new_esEs12(Right(xy30), Right(xy400), eb, ty_Char) → new_esEs8(xy30, xy400)

The set Q consists of the following terms:

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

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_deleteBy0(xy10, xy11, xy12, False, ba) → new_deleteBy(xy12, xy10, ba)
The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
new_deleteBy(xy3, :(xy40, xy41), bb) → new_deleteBy0(xy41, xy40, xy3, new_esEs4(xy3, xy40, bb), bb)
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5

deleteBy0	ys y eq x True	= ys
deleteBy0	ys y eq x False	= y : deleteBy eq x ys