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

YES 2.437 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, Eq b) => Either b a -> [Either b a] -> [Either b a]) :: (Eq b, Eq a) => Either b a -> [Either b a] -> [Either b 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 b, Eq a) => Either a b -> [Either a b] -> [Either a b]) :: (Eq a, Eq b) => Either a b -> [Either a b] -> [Either a b])

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

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, Eq b) => Either b a -> [Either b a] -> [Either b 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  Eq b",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="delete xy3\n  Eq a  Eq b",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="delete xy3 xy4\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="deleteBy (==) xy3 xy4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];740[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 740[label="",style="solid", color="burlywood", weight=9];
740 -> 6[label="",style="solid", color="burlywood", weight=3];
741[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 741[label="",style="solid", color="burlywood", weight=9];
741 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="deleteBy (==) xy3 (xy40 : xy41)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="deleteBy (==) xy3 []\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="deleteBy0 xy41 xy40 (==) xy3 ((==) xy3 xy40)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];742[label="xy3/Left xy30",fontsize=10,color="white",style="solid",shape="box"];8 -> 742[label="",style="solid", color="burlywood", weight=9];
742 -> 10[label="",style="solid", color="burlywood", weight=3];
743[label="xy3/Right xy30",fontsize=10,color="white",style="solid",shape="box"];8 -> 743[label="",style="solid", color="burlywood", weight=9];
743 -> 11[label="",style="solid", color="burlywood", weight=3];
9[label="[]\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];10[label="deleteBy0 xy41 xy40 (==) (Left xy30) ((==) Left xy30 xy40)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];744[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];10 -> 744[label="",style="solid", color="burlywood", weight=9];
744 -> 12[label="",style="solid", color="burlywood", weight=3];
745[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];10 -> 745[label="",style="solid", color="burlywood", weight=9];
745 -> 13[label="",style="solid", color="burlywood", weight=3];
11[label="deleteBy0 xy41 xy40 (==) (Right xy30) ((==) Right xy30 xy40)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];746[label="xy40/Left xy400",fontsize=10,color="white",style="solid",shape="box"];11 -> 746[label="",style="solid", color="burlywood", weight=9];
746 -> 14[label="",style="solid", color="burlywood", weight=3];
747[label="xy40/Right xy400",fontsize=10,color="white",style="solid",shape="box"];11 -> 747[label="",style="solid", color="burlywood", weight=9];
747 -> 15[label="",style="solid", color="burlywood", weight=3];
12[label="deleteBy0 xy41 (Left xy400) (==) (Left xy30) ((==) Left xy30 Left xy400)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="deleteBy0 xy41 (Right xy400) (==) (Left xy30) ((==) Left xy30 Right xy400)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="deleteBy0 xy41 (Left xy400) (==) (Right xy30) ((==) Right xy30 Left xy400)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="deleteBy0 xy41 (Right xy400) (==) (Right xy30) ((==) Right xy30 Right xy400)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16 -> 20[label="",style="dashed", color="red", weight=0];
16[label="deleteBy0 xy41 (Left xy400) (==) (Left xy30) (xy30 == xy400)\n  Eq a  Eq b",fontsize=16,color="magenta"];16 -> 21[label="",style="dashed", color="magenta", weight=3];
16 -> 22[label="",style="dashed", color="magenta", weight=3];
16 -> 23[label="",style="dashed", color="magenta", weight=3];
16 -> 24[label="",style="dashed", color="magenta", weight=3];
17[label="deleteBy0 xy41 (Right xy400) (==) (Left xy30) False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];17 -> 25[label="",style="solid", color="black", weight=3];
18[label="deleteBy0 xy41 (Left xy400) (==) (Right xy30) False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];18 -> 26[label="",style="solid", color="black", weight=3];
19 -> 27[label="",style="dashed", color="red", weight=0];
19[label="deleteBy0 xy41 (Right xy400) (==) (Right xy30) (xy30 == xy400)\n  Eq a  Eq b",fontsize=16,color="magenta"];19 -> 28[label="",style="dashed", color="magenta", weight=3];
19 -> 29[label="",style="dashed", color="magenta", weight=3];
19 -> 30[label="",style="dashed", color="magenta", weight=3];
19 -> 31[label="",style="dashed", color="magenta", weight=3];
21[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];22[label="xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];23[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];24[label="xy30 == xy400\n  Eq a",fontsize=16,color="blue",shape="box"];750[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 750[label="",style="solid", color="blue", weight=9];
750 -> 32[label="",style="solid", color="blue", weight=3];
751[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 751[label="",style="solid", color="blue", weight=9];
751 -> 33[label="",style="solid", color="blue", weight=3];
752[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 752[label="",style="solid", color="blue", weight=9];
752 -> 34[label="",style="solid", color="blue", weight=3];
753[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 753[label="",style="solid", color="blue", weight=9];
753 -> 35[label="",style="solid", color="blue", weight=3];
754[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 754[label="",style="solid", color="blue", weight=9];
754 -> 36[label="",style="solid", color="blue", weight=3];
755[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 755[label="",style="solid", color="blue", weight=9];
755 -> 37[label="",style="solid", color="blue", weight=3];
756[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 756[label="",style="solid", color="blue", weight=9];
756 -> 38[label="",style="solid", color="blue", weight=3];
757[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 757[label="",style="solid", color="blue", weight=9];
757 -> 39[label="",style="solid", color="blue", weight=3];
758[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 758[label="",style="solid", color="blue", weight=9];
758 -> 40[label="",style="solid", color="blue", weight=3];
759[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 759[label="",style="solid", color="blue", weight=9];
759 -> 41[label="",style="solid", color="blue", weight=3];
760[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 760[label="",style="solid", color="blue", weight=9];
760 -> 42[label="",style="solid", color="blue", weight=3];
761[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 761[label="",style="solid", color="blue", weight=9];
761 -> 43[label="",style="solid", color="blue", weight=3];
762[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 762[label="",style="solid", color="blue", weight=9];
762 -> 44[label="",style="solid", color="blue", weight=3];
763[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];24 -> 763[label="",style="solid", color="blue", weight=9];
763 -> 45[label="",style="solid", color="blue", weight=3];
20[label="deleteBy0 xy10 (Left xy11) (==) (Left xy12) xy13\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];764[label="xy13/False",fontsize=10,color="white",style="solid",shape="box"];20 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 46[label="",style="solid", color="burlywood", weight=3];
765[label="xy13/True",fontsize=10,color="white",style="solid",shape="box"];20 -> 765[label="",style="solid", color="burlywood", weight=9];
765 -> 47[label="",style="solid", color="burlywood", weight=3];
25[label="Right xy400 : deleteBy (==) (Left xy30) xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];25 -> 48[label="",style="dashed", color="green", weight=3];
26[label="Left xy400 : deleteBy (==) (Right xy30) xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];26 -> 49[label="",style="dashed", color="green", weight=3];
28[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];29[label="xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];30[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];31[label="xy30 == xy400\n  Eq a",fontsize=16,color="blue",shape="box"];766[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 766[label="",style="solid", color="blue", weight=9];
766 -> 50[label="",style="solid", color="blue", weight=3];
767[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 767[label="",style="solid", color="blue", weight=9];
767 -> 51[label="",style="solid", color="blue", weight=3];
768[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 768[label="",style="solid", color="blue", weight=9];
768 -> 52[label="",style="solid", color="blue", weight=3];
769[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 769[label="",style="solid", color="blue", weight=9];
769 -> 53[label="",style="solid", color="blue", weight=3];
770[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 770[label="",style="solid", color="blue", weight=9];
770 -> 54[label="",style="solid", color="blue", weight=3];
771[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 771[label="",style="solid", color="blue", weight=9];
771 -> 55[label="",style="solid", color="blue", weight=3];
772[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 772[label="",style="solid", color="blue", weight=9];
772 -> 56[label="",style="solid", color="blue", weight=3];
773[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 773[label="",style="solid", color="blue", weight=9];
773 -> 57[label="",style="solid", color="blue", weight=3];
774[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 774[label="",style="solid", color="blue", weight=9];
774 -> 58[label="",style="solid", color="blue", weight=3];
775[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 775[label="",style="solid", color="blue", weight=9];
775 -> 59[label="",style="solid", color="blue", weight=3];
776[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 776[label="",style="solid", color="blue", weight=9];
776 -> 60[label="",style="solid", color="blue", weight=3];
777[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 777[label="",style="solid", color="blue", weight=9];
777 -> 61[label="",style="solid", color="blue", weight=3];
778[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 778[label="",style="solid", color="blue", weight=9];
778 -> 62[label="",style="solid", color="blue", weight=3];
779[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];31 -> 779[label="",style="solid", color="blue", weight=9];
779 -> 63[label="",style="solid", color="blue", weight=3];
27[label="deleteBy0 xy19 (Right xy20) (==) (Right xy21) xy22\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];780[label="xy22/False",fontsize=10,color="white",style="solid",shape="box"];27 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 64[label="",style="solid", color="burlywood", weight=3];
781[label="xy22/True",fontsize=10,color="white",style="solid",shape="box"];27 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 65[label="",style="solid", color="burlywood", weight=3];
32[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];782[label="xy30/Integer xy300",fontsize=10,color="white",style="solid",shape="box"];32 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 66[label="",style="solid", color="burlywood", weight=3];
33[label="xy30 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];783[label="xy30/xy300 : xy301",fontsize=10,color="white",style="solid",shape="box"];33 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 67[label="",style="solid", color="burlywood", weight=3];
784[label="xy30/[]",fontsize=10,color="white",style="solid",shape="box"];33 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 68[label="",style="solid", color="burlywood", weight=3];
34[label="xy30 == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];785[label="xy30/(xy300,xy301,xy302)",fontsize=10,color="white",style="solid",shape="box"];34 -> 785[label="",style="solid", color="burlywood", weight=9];
785 -> 69[label="",style="solid", color="burlywood", weight=3];
35[label="xy30 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];786[label="xy30/xy300 :% xy301",fontsize=10,color="white",style="solid",shape="box"];35 -> 786[label="",style="solid", color="burlywood", weight=9];
786 -> 70[label="",style="solid", color="burlywood", weight=3];
36[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];787[label="xy30/(xy300,xy301)",fontsize=10,color="white",style="solid",shape="box"];36 -> 787[label="",style="solid", color="burlywood", weight=9];
787 -> 71[label="",style="solid", color="burlywood", weight=3];
37[label="xy30 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];788[label="xy30/Nothing",fontsize=10,color="white",style="solid",shape="box"];37 -> 788[label="",style="solid", color="burlywood", weight=9];
788 -> 72[label="",style="solid", color="burlywood", weight=3];
789[label="xy30/Just xy300",fontsize=10,color="white",style="solid",shape="box"];37 -> 789[label="",style="solid", color="burlywood", weight=9];
789 -> 73[label="",style="solid", color="burlywood", weight=3];
38[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];790[label="xy30/LT",fontsize=10,color="white",style="solid",shape="box"];38 -> 790[label="",style="solid", color="burlywood", weight=9];
790 -> 74[label="",style="solid", color="burlywood", weight=3];
791[label="xy30/EQ",fontsize=10,color="white",style="solid",shape="box"];38 -> 791[label="",style="solid", color="burlywood", weight=9];
791 -> 75[label="",style="solid", color="burlywood", weight=3];
792[label="xy30/GT",fontsize=10,color="white",style="solid",shape="box"];38 -> 792[label="",style="solid", color="burlywood", weight=9];
792 -> 76[label="",style="solid", color="burlywood", weight=3];
39[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];793[label="xy30/False",fontsize=10,color="white",style="solid",shape="box"];39 -> 793[label="",style="solid", color="burlywood", weight=9];
793 -> 77[label="",style="solid", color="burlywood", weight=3];
794[label="xy30/True",fontsize=10,color="white",style="solid",shape="box"];39 -> 794[label="",style="solid", color="burlywood", weight=9];
794 -> 78[label="",style="solid", color="burlywood", weight=3];
40[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];40 -> 79[label="",style="solid", color="black", weight=3];
41[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];795[label="xy30/()",fontsize=10,color="white",style="solid",shape="box"];41 -> 795[label="",style="solid", color="burlywood", weight=9];
795 -> 80[label="",style="solid", color="burlywood", weight=3];
42[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];42 -> 81[label="",style="solid", color="black", weight=3];
43[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];43 -> 82[label="",style="solid", color="black", weight=3];
44[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];796[label="xy30/Left xy300",fontsize=10,color="white",style="solid",shape="box"];44 -> 796[label="",style="solid", color="burlywood", weight=9];
796 -> 83[label="",style="solid", color="burlywood", weight=3];
797[label="xy30/Right xy300",fontsize=10,color="white",style="solid",shape="box"];44 -> 797[label="",style="solid", color="burlywood", weight=9];
797 -> 84[label="",style="solid", color="burlywood", weight=3];
45[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];45 -> 85[label="",style="solid", color="black", weight=3];
46[label="deleteBy0 xy10 (Left xy11) (==) (Left xy12) False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];46 -> 86[label="",style="solid", color="black", weight=3];
47[label="deleteBy0 xy10 (Left xy11) (==) (Left xy12) True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];47 -> 87[label="",style="solid", color="black", weight=3];
48 -> 5[label="",style="dashed", color="red", weight=0];
48[label="deleteBy (==) (Left xy30) xy41\n  Eq a  Eq b",fontsize=16,color="magenta"];48 -> 88[label="",style="dashed", color="magenta", weight=3];
48 -> 89[label="",style="dashed", color="magenta", weight=3];
49 -> 5[label="",style="dashed", color="red", weight=0];
49[label="deleteBy (==) (Right xy30) xy41\n  Eq a  Eq b",fontsize=16,color="magenta"];49 -> 90[label="",style="dashed", color="magenta", weight=3];
49 -> 91[label="",style="dashed", color="magenta", weight=3];
50 -> 32[label="",style="dashed", color="red", weight=0];
50[label="xy30 == xy400",fontsize=16,color="magenta"];50 -> 92[label="",style="dashed", color="magenta", weight=3];
50 -> 93[label="",style="dashed", color="magenta", weight=3];
51 -> 33[label="",style="dashed", color="red", weight=0];
51[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];51 -> 94[label="",style="dashed", color="magenta", weight=3];
51 -> 95[label="",style="dashed", color="magenta", weight=3];
52 -> 34[label="",style="dashed", color="red", weight=0];
52[label="xy30 == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];52 -> 96[label="",style="dashed", color="magenta", weight=3];
52 -> 97[label="",style="dashed", color="magenta", weight=3];
53 -> 35[label="",style="dashed", color="red", weight=0];
53[label="xy30 == xy400\n  Integral a",fontsize=16,color="magenta"];53 -> 98[label="",style="dashed", color="magenta", weight=3];
53 -> 99[label="",style="dashed", color="magenta", weight=3];
54 -> 36[label="",style="dashed", color="red", weight=0];
54[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="magenta"];54 -> 100[label="",style="dashed", color="magenta", weight=3];
54 -> 101[label="",style="dashed", color="magenta", weight=3];
55 -> 37[label="",style="dashed", color="red", weight=0];
55[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];55 -> 102[label="",style="dashed", color="magenta", weight=3];
55 -> 103[label="",style="dashed", color="magenta", weight=3];
56 -> 38[label="",style="dashed", color="red", weight=0];
56[label="xy30 == xy400",fontsize=16,color="magenta"];56 -> 104[label="",style="dashed", color="magenta", weight=3];
56 -> 105[label="",style="dashed", color="magenta", weight=3];
57 -> 39[label="",style="dashed", color="red", weight=0];
57[label="xy30 == xy400",fontsize=16,color="magenta"];57 -> 106[label="",style="dashed", color="magenta", weight=3];
57 -> 107[label="",style="dashed", color="magenta", weight=3];
58 -> 40[label="",style="dashed", color="red", weight=0];
58[label="xy30 == xy400",fontsize=16,color="magenta"];58 -> 108[label="",style="dashed", color="magenta", weight=3];
58 -> 109[label="",style="dashed", color="magenta", weight=3];
59 -> 41[label="",style="dashed", color="red", weight=0];
59[label="xy30 == xy400",fontsize=16,color="magenta"];59 -> 110[label="",style="dashed", color="magenta", weight=3];
59 -> 111[label="",style="dashed", color="magenta", weight=3];
60 -> 42[label="",style="dashed", color="red", weight=0];
60[label="xy30 == xy400",fontsize=16,color="magenta"];60 -> 112[label="",style="dashed", color="magenta", weight=3];
60 -> 113[label="",style="dashed", color="magenta", weight=3];
61 -> 43[label="",style="dashed", color="red", weight=0];
61[label="xy30 == xy400",fontsize=16,color="magenta"];61 -> 114[label="",style="dashed", color="magenta", weight=3];
61 -> 115[label="",style="dashed", color="magenta", weight=3];
62 -> 44[label="",style="dashed", color="red", weight=0];
62[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="magenta"];62 -> 116[label="",style="dashed", color="magenta", weight=3];
62 -> 117[label="",style="dashed", color="magenta", weight=3];
63 -> 45[label="",style="dashed", color="red", weight=0];
63[label="xy30 == xy400",fontsize=16,color="magenta"];63 -> 118[label="",style="dashed", color="magenta", weight=3];
63 -> 119[label="",style="dashed", color="magenta", weight=3];
64[label="deleteBy0 xy19 (Right xy20) (==) (Right xy21) False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];64 -> 120[label="",style="solid", color="black", weight=3];
65[label="deleteBy0 xy19 (Right xy20) (==) (Right xy21) True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];65 -> 121[label="",style="solid", color="black", weight=3];
66[label="Integer xy300 == xy400",fontsize=16,color="burlywood",shape="box"];814[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];66 -> 814[label="",style="solid", color="burlywood", weight=9];
814 -> 122[label="",style="solid", color="burlywood", weight=3];
67[label="xy300 : xy301 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];815[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];67 -> 815[label="",style="solid", color="burlywood", weight=9];
815 -> 123[label="",style="solid", color="burlywood", weight=3];
816[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];67 -> 816[label="",style="solid", color="burlywood", weight=9];
816 -> 124[label="",style="solid", color="burlywood", weight=3];
68[label="[] == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];817[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];68 -> 817[label="",style="solid", color="burlywood", weight=9];
817 -> 125[label="",style="solid", color="burlywood", weight=3];
818[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];68 -> 818[label="",style="solid", color="burlywood", weight=9];
818 -> 126[label="",style="solid", color="burlywood", weight=3];
69[label="(xy300,xy301,xy302) == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];819[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];69 -> 819[label="",style="solid", color="burlywood", weight=9];
819 -> 127[label="",style="solid", color="burlywood", weight=3];
70[label="xy300 :% xy301 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="box"];820[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];70 -> 820[label="",style="solid", color="burlywood", weight=9];
820 -> 128[label="",style="solid", color="burlywood", weight=3];
71[label="(xy300,xy301) == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];821[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];71 -> 821[label="",style="solid", color="burlywood", weight=9];
821 -> 129[label="",style="solid", color="burlywood", weight=3];
72[label="Nothing == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];822[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];72 -> 822[label="",style="solid", color="burlywood", weight=9];
822 -> 130[label="",style="solid", color="burlywood", weight=3];
823[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];72 -> 823[label="",style="solid", color="burlywood", weight=9];
823 -> 131[label="",style="solid", color="burlywood", weight=3];
73[label="Just xy300 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];824[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];73 -> 824[label="",style="solid", color="burlywood", weight=9];
824 -> 132[label="",style="solid", color="burlywood", weight=3];
825[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];73 -> 825[label="",style="solid", color="burlywood", weight=9];
825 -> 133[label="",style="solid", color="burlywood", weight=3];
74[label="LT == xy400",fontsize=16,color="burlywood",shape="box"];826[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];74 -> 826[label="",style="solid", color="burlywood", weight=9];
826 -> 134[label="",style="solid", color="burlywood", weight=3];
827[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];74 -> 827[label="",style="solid", color="burlywood", weight=9];
827 -> 135[label="",style="solid", color="burlywood", weight=3];
828[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];74 -> 828[label="",style="solid", color="burlywood", weight=9];
828 -> 136[label="",style="solid", color="burlywood", weight=3];
75[label="EQ == xy400",fontsize=16,color="burlywood",shape="box"];829[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];75 -> 829[label="",style="solid", color="burlywood", weight=9];
829 -> 137[label="",style="solid", color="burlywood", weight=3];
830[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];75 -> 830[label="",style="solid", color="burlywood", weight=9];
830 -> 138[label="",style="solid", color="burlywood", weight=3];
831[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];75 -> 831[label="",style="solid", color="burlywood", weight=9];
831 -> 139[label="",style="solid", color="burlywood", weight=3];
76[label="GT == xy400",fontsize=16,color="burlywood",shape="box"];832[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];76 -> 832[label="",style="solid", color="burlywood", weight=9];
832 -> 140[label="",style="solid", color="burlywood", weight=3];
833[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];76 -> 833[label="",style="solid", color="burlywood", weight=9];
833 -> 141[label="",style="solid", color="burlywood", weight=3];
834[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];76 -> 834[label="",style="solid", color="burlywood", weight=9];
834 -> 142[label="",style="solid", color="burlywood", weight=3];
77[label="False == xy400",fontsize=16,color="burlywood",shape="box"];835[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];77 -> 835[label="",style="solid", color="burlywood", weight=9];
835 -> 143[label="",style="solid", color="burlywood", weight=3];
836[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];77 -> 836[label="",style="solid", color="burlywood", weight=9];
836 -> 144[label="",style="solid", color="burlywood", weight=3];
78[label="True == xy400",fontsize=16,color="burlywood",shape="box"];837[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];78 -> 837[label="",style="solid", color="burlywood", weight=9];
837 -> 145[label="",style="solid", color="burlywood", weight=3];
838[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];78 -> 838[label="",style="solid", color="burlywood", weight=9];
838 -> 146[label="",style="solid", color="burlywood", weight=3];
79[label="primEqDouble xy30 xy400",fontsize=16,color="burlywood",shape="box"];839[label="xy30/Double xy300 xy301",fontsize=10,color="white",style="solid",shape="box"];79 -> 839[label="",style="solid", color="burlywood", weight=9];
839 -> 147[label="",style="solid", color="burlywood", weight=3];
80[label="() == xy400",fontsize=16,color="burlywood",shape="box"];840[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];80 -> 840[label="",style="solid", color="burlywood", weight=9];
840 -> 148[label="",style="solid", color="burlywood", weight=3];
81[label="primEqChar xy30 xy400",fontsize=16,color="burlywood",shape="box"];841[label="xy30/Char xy300",fontsize=10,color="white",style="solid",shape="box"];81 -> 841[label="",style="solid", color="burlywood", weight=9];
841 -> 149[label="",style="solid", color="burlywood", weight=3];
82[label="primEqInt xy30 xy400",fontsize=16,color="burlywood",shape="triangle"];842[label="xy30/Pos xy300",fontsize=10,color="white",style="solid",shape="box"];82 -> 842[label="",style="solid", color="burlywood", weight=9];
842 -> 150[label="",style="solid", color="burlywood", weight=3];
843[label="xy30/Neg xy300",fontsize=10,color="white",style="solid",shape="box"];82 -> 843[label="",style="solid", color="burlywood", weight=9];
843 -> 151[label="",style="solid", color="burlywood", weight=3];
83[label="Left xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];844[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];83 -> 844[label="",style="solid", color="burlywood", weight=9];
844 -> 152[label="",style="solid", color="burlywood", weight=3];
845[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];83 -> 845[label="",style="solid", color="burlywood", weight=9];
845 -> 153[label="",style="solid", color="burlywood", weight=3];
84[label="Right xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];846[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];84 -> 846[label="",style="solid", color="burlywood", weight=9];
846 -> 154[label="",style="solid", color="burlywood", weight=3];
847[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];84 -> 847[label="",style="solid", color="burlywood", weight=9];
847 -> 155[label="",style="solid", color="burlywood", weight=3];
85[label="primEqFloat xy30 xy400",fontsize=16,color="burlywood",shape="box"];848[label="xy30/Float xy300 xy301",fontsize=10,color="white",style="solid",shape="box"];85 -> 848[label="",style="solid", color="burlywood", weight=9];
848 -> 156[label="",style="solid", color="burlywood", weight=3];
86[label="Left xy11 : deleteBy (==) (Left xy12) xy10\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];86 -> 157[label="",style="dashed", color="green", weight=3];
87[label="xy10\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];88[label="xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];89[label="Left xy30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];90[label="xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];91[label="Right xy30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];92[label="xy400",fontsize=16,color="green",shape="box"];93[label="xy30",fontsize=16,color="green",shape="box"];94[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];95[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];96[label="xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];97[label="xy30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];98[label="xy400\n  Integral a",fontsize=16,color="green",shape="box"];99[label="xy30\n  Integral a",fontsize=16,color="green",shape="box"];100[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];101[label="xy30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];102[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];103[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];104[label="xy400",fontsize=16,color="green",shape="box"];105[label="xy30",fontsize=16,color="green",shape="box"];106[label="xy400",fontsize=16,color="green",shape="box"];107[label="xy30",fontsize=16,color="green",shape="box"];108[label="xy400",fontsize=16,color="green",shape="box"];109[label="xy30",fontsize=16,color="green",shape="box"];110[label="xy400",fontsize=16,color="green",shape="box"];111[label="xy30",fontsize=16,color="green",shape="box"];112[label="xy400",fontsize=16,color="green",shape="box"];113[label="xy30",fontsize=16,color="green",shape="box"];114[label="xy400",fontsize=16,color="green",shape="box"];115[label="xy30",fontsize=16,color="green",shape="box"];116[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];117[label="xy30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];118[label="xy400",fontsize=16,color="green",shape="box"];119[label="xy30",fontsize=16,color="green",shape="box"];120[label="Right xy20 : deleteBy (==) (Right xy21) xy19\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];120 -> 158[label="",style="dashed", color="green", weight=3];
121[label="xy19\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];122[label="Integer xy300 == Integer xy4000",fontsize=16,color="black",shape="box"];122 -> 159[label="",style="solid", color="black", weight=3];
123[label="xy300 : xy301 == xy4000 : xy4001\n  Eq a",fontsize=16,color="black",shape="box"];123 -> 160[label="",style="solid", color="black", weight=3];
124[label="xy300 : xy301 == []\n  Eq a",fontsize=16,color="black",shape="box"];124 -> 161[label="",style="solid", color="black", weight=3];
125[label="[] == xy4000 : xy4001\n  Eq a",fontsize=16,color="black",shape="box"];125 -> 162[label="",style="solid", color="black", weight=3];
126[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];126 -> 163[label="",style="solid", color="black", weight=3];
127[label="(xy300,xy301,xy302) == (xy4000,xy4001,xy4002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];127 -> 164[label="",style="solid", color="black", weight=3];
128[label="xy300 :% xy301 == xy4000 :% xy4001\n  Integral a",fontsize=16,color="black",shape="box"];128 -> 165[label="",style="solid", color="black", weight=3];
129[label="(xy300,xy301) == (xy4000,xy4001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];129 -> 166[label="",style="solid", color="black", weight=3];
130[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];130 -> 167[label="",style="solid", color="black", weight=3];
131[label="Nothing == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];131 -> 168[label="",style="solid", color="black", weight=3];
132[label="Just xy300 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];132 -> 169[label="",style="solid", color="black", weight=3];
133[label="Just xy300 == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];133 -> 170[label="",style="solid", color="black", weight=3];
134[label="LT == LT",fontsize=16,color="black",shape="box"];134 -> 171[label="",style="solid", color="black", weight=3];
135[label="LT == EQ",fontsize=16,color="black",shape="box"];135 -> 172[label="",style="solid", color="black", weight=3];
136[label="LT == GT",fontsize=16,color="black",shape="box"];136 -> 173[label="",style="solid", color="black", weight=3];
137[label="EQ == LT",fontsize=16,color="black",shape="box"];137 -> 174[label="",style="solid", color="black", weight=3];
138[label="EQ == EQ",fontsize=16,color="black",shape="box"];138 -> 175[label="",style="solid", color="black", weight=3];
139[label="EQ == GT",fontsize=16,color="black",shape="box"];139 -> 176[label="",style="solid", color="black", weight=3];
140[label="GT == LT",fontsize=16,color="black",shape="box"];140 -> 177[label="",style="solid", color="black", weight=3];
141[label="GT == EQ",fontsize=16,color="black",shape="box"];141 -> 178[label="",style="solid", color="black", weight=3];
142[label="GT == GT",fontsize=16,color="black",shape="box"];142 -> 179[label="",style="solid", color="black", weight=3];
143[label="False == False",fontsize=16,color="black",shape="box"];143 -> 180[label="",style="solid", color="black", weight=3];
144[label="False == True",fontsize=16,color="black",shape="box"];144 -> 181[label="",style="solid", color="black", weight=3];
145[label="True == False",fontsize=16,color="black",shape="box"];145 -> 182[label="",style="solid", color="black", weight=3];
146[label="True == True",fontsize=16,color="black",shape="box"];146 -> 183[label="",style="solid", color="black", weight=3];
147[label="primEqDouble (Double xy300 xy301) xy400",fontsize=16,color="burlywood",shape="box"];849[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];147 -> 849[label="",style="solid", color="burlywood", weight=9];
849 -> 184[label="",style="solid", color="burlywood", weight=3];
148[label="() == ()",fontsize=16,color="black",shape="box"];148 -> 185[label="",style="solid", color="black", weight=3];
149[label="primEqChar (Char xy300) xy400",fontsize=16,color="burlywood",shape="box"];850[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];149 -> 850[label="",style="solid", color="burlywood", weight=9];
850 -> 186[label="",style="solid", color="burlywood", weight=3];
150[label="primEqInt (Pos xy300) xy400",fontsize=16,color="burlywood",shape="box"];851[label="xy300/Succ xy3000",fontsize=10,color="white",style="solid",shape="box"];150 -> 851[label="",style="solid", color="burlywood", weight=9];
851 -> 187[label="",style="solid", color="burlywood", weight=3];
852[label="xy300/Zero",fontsize=10,color="white",style="solid",shape="box"];150 -> 852[label="",style="solid", color="burlywood", weight=9];
852 -> 188[label="",style="solid", color="burlywood", weight=3];
151[label="primEqInt (Neg xy300) xy400",fontsize=16,color="burlywood",shape="box"];853[label="xy300/Succ xy3000",fontsize=10,color="white",style="solid",shape="box"];151 -> 853[label="",style="solid", color="burlywood", weight=9];
853 -> 189[label="",style="solid", color="burlywood", weight=3];
854[label="xy300/Zero",fontsize=10,color="white",style="solid",shape="box"];151 -> 854[label="",style="solid", color="burlywood", weight=9];
854 -> 190[label="",style="solid", color="burlywood", weight=3];
152[label="Left xy300 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];152 -> 191[label="",style="solid", color="black", weight=3];
153[label="Left xy300 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];153 -> 192[label="",style="solid", color="black", weight=3];
154[label="Right xy300 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];154 -> 193[label="",style="solid", color="black", weight=3];
155[label="Right xy300 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];155 -> 194[label="",style="solid", color="black", weight=3];
156[label="primEqFloat (Float xy300 xy301) xy400",fontsize=16,color="burlywood",shape="box"];855[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];156 -> 855[label="",style="solid", color="burlywood", weight=9];
855 -> 195[label="",style="solid", color="burlywood", weight=3];
157 -> 5[label="",style="dashed", color="red", weight=0];
157[label="deleteBy (==) (Left xy12) xy10\n  Eq a  Eq b",fontsize=16,color="magenta"];157 -> 196[label="",style="dashed", color="magenta", weight=3];
157 -> 197[label="",style="dashed", color="magenta", weight=3];
158 -> 5[label="",style="dashed", color="red", weight=0];
158[label="deleteBy (==) (Right xy21) xy19\n  Eq a  Eq b",fontsize=16,color="magenta"];158 -> 198[label="",style="dashed", color="magenta", weight=3];
158 -> 199[label="",style="dashed", color="magenta", weight=3];
159 -> 82[label="",style="dashed", color="red", weight=0];
159[label="primEqInt xy300 xy4000",fontsize=16,color="magenta"];159 -> 200[label="",style="dashed", color="magenta", weight=3];
159 -> 201[label="",style="dashed", color="magenta", weight=3];
160 -> 268[label="",style="dashed", color="red", weight=0];
160[label="xy300 == xy4000 && xy301 == xy4001\n  Eq a",fontsize=16,color="magenta"];160 -> 269[label="",style="dashed", color="magenta", weight=3];
160 -> 270[label="",style="dashed", color="magenta", weight=3];
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164 -> 272[label="",style="dashed", color="magenta", weight=3];
165 -> 268[label="",style="dashed", color="red", weight=0];
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165 -> 274[label="",style="dashed", color="magenta", weight=3];
166 -> 268[label="",style="dashed", color="red", weight=0];
166[label="xy300 == xy4000 && xy301 == xy4001\n  Eq a  Eq b",fontsize=16,color="magenta"];166 -> 275[label="",style="dashed", color="magenta", weight=3];
166 -> 276[label="",style="dashed", color="magenta", weight=3];
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863 -> 213[label="",style="solid", color="blue", weight=3];
864[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 864[label="",style="solid", color="blue", weight=9];
864 -> 214[label="",style="solid", color="blue", weight=3];
865[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 865[label="",style="solid", color="blue", weight=9];
865 -> 215[label="",style="solid", color="blue", weight=3];
866[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 866[label="",style="solid", color="blue", weight=9];
866 -> 216[label="",style="solid", color="blue", weight=3];
867[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 867[label="",style="solid", color="blue", weight=9];
867 -> 217[label="",style="solid", color="blue", weight=3];
868[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 868[label="",style="solid", color="blue", weight=9];
868 -> 218[label="",style="solid", color="blue", weight=3];
869[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 869[label="",style="solid", color="blue", weight=9];
869 -> 219[label="",style="solid", color="blue", weight=3];
870[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 870[label="",style="solid", color="blue", weight=9];
870 -> 220[label="",style="solid", color="blue", weight=3];
871[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 871[label="",style="solid", color="blue", weight=9];
871 -> 221[label="",style="solid", color="blue", weight=3];
872[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 872[label="",style="solid", color="blue", weight=9];
872 -> 222[label="",style="solid", color="blue", weight=3];
873[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 873[label="",style="solid", color="blue", weight=9];
873 -> 223[label="",style="solid", color="blue", weight=3];
874[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 874[label="",style="solid", color="blue", weight=9];
874 -> 224[label="",style="solid", color="blue", weight=3];
875[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 875[label="",style="solid", color="blue", weight=9];
875 -> 225[label="",style="solid", color="blue", weight=3];
876[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];170 -> 876[label="",style="solid", color="blue", weight=9];
876 -> 226[label="",style="solid", color="blue", weight=3];
171[label="True",fontsize=16,color="green",shape="box"];172[label="False",fontsize=16,color="green",shape="box"];173[label="False",fontsize=16,color="green",shape="box"];174[label="False",fontsize=16,color="green",shape="box"];175[label="True",fontsize=16,color="green",shape="box"];176[label="False",fontsize=16,color="green",shape="box"];177[label="False",fontsize=16,color="green",shape="box"];178[label="False",fontsize=16,color="green",shape="box"];179[label="True",fontsize=16,color="green",shape="box"];180[label="True",fontsize=16,color="green",shape="box"];181[label="False",fontsize=16,color="green",shape="box"];182[label="False",fontsize=16,color="green",shape="box"];183[label="True",fontsize=16,color="green",shape="box"];184[label="primEqDouble (Double xy300 xy301) (Double xy4000 xy4001)",fontsize=16,color="black",shape="box"];184 -> 227[label="",style="solid", color="black", weight=3];
185[label="True",fontsize=16,color="green",shape="box"];186[label="primEqChar (Char xy300) (Char xy4000)",fontsize=16,color="black",shape="box"];186 -> 228[label="",style="solid", color="black", weight=3];
187[label="primEqInt (Pos (Succ xy3000)) xy400",fontsize=16,color="burlywood",shape="box"];877[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];187 -> 877[label="",style="solid", color="burlywood", weight=9];
877 -> 229[label="",style="solid", color="burlywood", weight=3];
878[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];187 -> 878[label="",style="solid", color="burlywood", weight=9];
878 -> 230[label="",style="solid", color="burlywood", weight=3];
188[label="primEqInt (Pos Zero) xy400",fontsize=16,color="burlywood",shape="box"];879[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];188 -> 879[label="",style="solid", color="burlywood", weight=9];
879 -> 231[label="",style="solid", color="burlywood", weight=3];
880[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];188 -> 880[label="",style="solid", color="burlywood", weight=9];
880 -> 232[label="",style="solid", color="burlywood", weight=3];
189[label="primEqInt (Neg (Succ xy3000)) xy400",fontsize=16,color="burlywood",shape="box"];881[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];189 -> 881[label="",style="solid", color="burlywood", weight=9];
881 -> 233[label="",style="solid", color="burlywood", weight=3];
882[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];189 -> 882[label="",style="solid", color="burlywood", weight=9];
882 -> 234[label="",style="solid", color="burlywood", weight=3];
190[label="primEqInt (Neg Zero) xy400",fontsize=16,color="burlywood",shape="box"];883[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];190 -> 883[label="",style="solid", color="burlywood", weight=9];
883 -> 235[label="",style="solid", color="burlywood", weight=3];
884[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];190 -> 884[label="",style="solid", color="burlywood", weight=9];
884 -> 236[label="",style="solid", color="burlywood", weight=3];
191[label="xy300 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];885[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 885[label="",style="solid", color="blue", weight=9];
885 -> 237[label="",style="solid", color="blue", weight=3];
886[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 886[label="",style="solid", color="blue", weight=9];
886 -> 238[label="",style="solid", color="blue", weight=3];
887[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 887[label="",style="solid", color="blue", weight=9];
887 -> 239[label="",style="solid", color="blue", weight=3];
888[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 888[label="",style="solid", color="blue", weight=9];
888 -> 240[label="",style="solid", color="blue", weight=3];
889[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 889[label="",style="solid", color="blue", weight=9];
889 -> 241[label="",style="solid", color="blue", weight=3];
890[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 890[label="",style="solid", color="blue", weight=9];
890 -> 242[label="",style="solid", color="blue", weight=3];
891[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 891[label="",style="solid", color="blue", weight=9];
891 -> 243[label="",style="solid", color="blue", weight=3];
892[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 892[label="",style="solid", color="blue", weight=9];
892 -> 244[label="",style="solid", color="blue", weight=3];
893[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 893[label="",style="solid", color="blue", weight=9];
893 -> 245[label="",style="solid", color="blue", weight=3];
894[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 894[label="",style="solid", color="blue", weight=9];
894 -> 246[label="",style="solid", color="blue", weight=3];
895[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 895[label="",style="solid", color="blue", weight=9];
895 -> 247[label="",style="solid", color="blue", weight=3];
896[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 896[label="",style="solid", color="blue", weight=9];
896 -> 248[label="",style="solid", color="blue", weight=3];
897[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 897[label="",style="solid", color="blue", weight=9];
897 -> 249[label="",style="solid", color="blue", weight=3];
898[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 898[label="",style="solid", color="blue", weight=9];
898 -> 250[label="",style="solid", color="blue", weight=3];
192[label="False",fontsize=16,color="green",shape="box"];193[label="False",fontsize=16,color="green",shape="box"];194[label="xy300 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];899[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 899[label="",style="solid", color="blue", weight=9];
899 -> 251[label="",style="solid", color="blue", weight=3];
900[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 900[label="",style="solid", color="blue", weight=9];
900 -> 252[label="",style="solid", color="blue", weight=3];
901[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 901[label="",style="solid", color="blue", weight=9];
901 -> 253[label="",style="solid", color="blue", weight=3];
902[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 902[label="",style="solid", color="blue", weight=9];
902 -> 254[label="",style="solid", color="blue", weight=3];
903[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 903[label="",style="solid", color="blue", weight=9];
903 -> 255[label="",style="solid", color="blue", weight=3];
904[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 904[label="",style="solid", color="blue", weight=9];
904 -> 256[label="",style="solid", color="blue", weight=3];
905[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 905[label="",style="solid", color="blue", weight=9];
905 -> 257[label="",style="solid", color="blue", weight=3];
906[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 906[label="",style="solid", color="blue", weight=9];
906 -> 258[label="",style="solid", color="blue", weight=3];
907[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 907[label="",style="solid", color="blue", weight=9];
907 -> 259[label="",style="solid", color="blue", weight=3];
908[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 908[label="",style="solid", color="blue", weight=9];
908 -> 260[label="",style="solid", color="blue", weight=3];
909[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 909[label="",style="solid", color="blue", weight=9];
909 -> 261[label="",style="solid", color="blue", weight=3];
910[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 910[label="",style="solid", color="blue", weight=9];
910 -> 262[label="",style="solid", color="blue", weight=3];
911[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 911[label="",style="solid", color="blue", weight=9];
911 -> 263[label="",style="solid", color="blue", weight=3];
912[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];194 -> 912[label="",style="solid", color="blue", weight=9];
912 -> 264[label="",style="solid", color="blue", weight=3];
195[label="primEqFloat (Float xy300 xy301) (Float xy4000 xy4001)",fontsize=16,color="black",shape="box"];195 -> 265[label="",style="solid", color="black", weight=3];
196[label="xy10\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];197[label="Left xy12\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];198[label="xy19\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];199[label="Right xy21\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];200[label="xy4000",fontsize=16,color="green",shape="box"];201[label="xy300",fontsize=16,color="green",shape="box"];269 -> 33[label="",style="dashed", color="red", weight=0];
269[label="xy301 == xy4001\n  Eq a",fontsize=16,color="magenta"];269 -> 281[label="",style="dashed", color="magenta", weight=3];
269 -> 282[label="",style="dashed", color="magenta", weight=3];
270[label="xy300 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];914[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 914[label="",style="solid", color="blue", weight=9];
914 -> 283[label="",style="solid", color="blue", weight=3];
915[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 915[label="",style="solid", color="blue", weight=9];
915 -> 284[label="",style="solid", color="blue", weight=3];
916[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 916[label="",style="solid", color="blue", weight=9];
916 -> 285[label="",style="solid", color="blue", weight=3];
917[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 917[label="",style="solid", color="blue", weight=9];
917 -> 286[label="",style="solid", color="blue", weight=3];
918[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 918[label="",style="solid", color="blue", weight=9];
918 -> 287[label="",style="solid", color="blue", weight=3];
919[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 919[label="",style="solid", color="blue", weight=9];
919 -> 288[label="",style="solid", color="blue", weight=3];
920[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 920[label="",style="solid", color="blue", weight=9];
920 -> 289[label="",style="solid", color="blue", weight=3];
921[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 921[label="",style="solid", color="blue", weight=9];
921 -> 290[label="",style="solid", color="blue", weight=3];
922[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 922[label="",style="solid", color="blue", weight=9];
922 -> 291[label="",style="solid", color="blue", weight=3];
923[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 923[label="",style="solid", color="blue", weight=9];
923 -> 292[label="",style="solid", color="blue", weight=3];
924[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 924[label="",style="solid", color="blue", weight=9];
924 -> 293[label="",style="solid", color="blue", weight=3];
925[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 925[label="",style="solid", color="blue", weight=9];
925 -> 294[label="",style="solid", color="blue", weight=3];
926[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 926[label="",style="solid", color="blue", weight=9];
926 -> 295[label="",style="solid", color="blue", weight=3];
927[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];270 -> 927[label="",style="solid", color="blue", weight=9];
927 -> 296[label="",style="solid", color="blue", weight=3];
268[label="xy27 && xy28",fontsize=16,color="burlywood",shape="triangle"];928[label="xy27/False",fontsize=10,color="white",style="solid",shape="box"];268 -> 928[label="",style="solid", color="burlywood", weight=9];
928 -> 297[label="",style="solid", color="burlywood", weight=3];
929[label="xy27/True",fontsize=10,color="white",style="solid",shape="box"];268 -> 929[label="",style="solid", color="burlywood", weight=9];
929 -> 298[label="",style="solid", color="burlywood", weight=3];
271 -> 268[label="",style="dashed", color="red", weight=0];
271[label="xy301 == xy4001 && xy302 == xy4002\n  Eq a  Eq b",fontsize=16,color="magenta"];271 -> 299[label="",style="dashed", color="magenta", weight=3];
271 -> 300[label="",style="dashed", color="magenta", weight=3];
272[label="xy300 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];931[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 931[label="",style="solid", color="blue", weight=9];
931 -> 301[label="",style="solid", color="blue", weight=3];
932[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 932[label="",style="solid", color="blue", weight=9];
932 -> 302[label="",style="solid", color="blue", weight=3];
933[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 933[label="",style="solid", color="blue", weight=9];
933 -> 303[label="",style="solid", color="blue", weight=3];
934[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 934[label="",style="solid", color="blue", weight=9];
934 -> 304[label="",style="solid", color="blue", weight=3];
935[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 935[label="",style="solid", color="blue", weight=9];
935 -> 305[label="",style="solid", color="blue", weight=3];
936[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 936[label="",style="solid", color="blue", weight=9];
936 -> 306[label="",style="solid", color="blue", weight=3];
937[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 937[label="",style="solid", color="blue", weight=9];
937 -> 307[label="",style="solid", color="blue", weight=3];
938[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 938[label="",style="solid", color="blue", weight=9];
938 -> 308[label="",style="solid", color="blue", weight=3];
939[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 939[label="",style="solid", color="blue", weight=9];
939 -> 309[label="",style="solid", color="blue", weight=3];
940[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 940[label="",style="solid", color="blue", weight=9];
940 -> 310[label="",style="solid", color="blue", weight=3];
941[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 941[label="",style="solid", color="blue", weight=9];
941 -> 311[label="",style="solid", color="blue", weight=3];
942[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 942[label="",style="solid", color="blue", weight=9];
942 -> 312[label="",style="solid", color="blue", weight=3];
943[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 943[label="",style="solid", color="blue", weight=9];
943 -> 313[label="",style="solid", color="blue", weight=3];
944[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];272 -> 944[label="",style="solid", color="blue", weight=9];
944 -> 314[label="",style="solid", color="blue", weight=3];
273[label="xy301 == xy4001\n  Integral a",fontsize=16,color="blue",shape="box"];945[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];273 -> 945[label="",style="solid", color="blue", weight=9];
945 -> 315[label="",style="solid", color="blue", weight=3];
946[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];273 -> 946[label="",style="solid", color="blue", weight=9];
946 -> 316[label="",style="solid", color="blue", weight=3];
274[label="xy300 == xy4000\n  Integral a",fontsize=16,color="blue",shape="box"];947[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];274 -> 947[label="",style="solid", color="blue", weight=9];
947 -> 317[label="",style="solid", color="blue", weight=3];
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347[label="xy4000",fontsize=16,color="green",shape="box"];348[label="xy300",fontsize=16,color="green",shape="box"];349[label="xy4000\n  Eq a",fontsize=16,color="green",shape="box"];350[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];351[label="xy4000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];352[label="xy300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];353[label="xy4000\n  Integral a",fontsize=16,color="green",shape="box"];354[label="xy300\n  Integral a",fontsize=16,color="green",shape="box"];355[label="xy4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];356[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];357[label="xy4000\n  Eq a",fontsize=16,color="green",shape="box"];358[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];359[label="xy4000",fontsize=16,color="green",shape="box"];360[label="xy300",fontsize=16,color="green",shape="box"];361[label="xy4000",fontsize=16,color="green",shape="box"];362[label="xy300",fontsize=16,color="green",shape="box"];363[label="xy4000",fontsize=16,color="green",shape="box"];364[label="xy300",fontsize=16,color="green",shape="box"];365[label="xy4000",fontsize=16,color="green",shape="box"];366[label="xy300",fontsize=16,color="green",shape="box"];367[label="xy4000",fontsize=16,color="green",shape="box"];368[label="xy300",fontsize=16,color="green",shape="box"];369[label="xy4000",fontsize=16,color="green",shape="box"];370[label="xy300",fontsize=16,color="green",shape="box"];371[label="xy4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];372[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];373[label="xy4000",fontsize=16,color="green",shape="box"];374[label="xy300",fontsize=16,color="green",shape="box"];375[label="xy301 * xy4001",fontsize=16,color="black",shape="triangle"];375 -> 601[label="",style="solid", color="black", weight=3];
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376[label="xy300 * xy4000",fontsize=16,color="magenta"];376 -> 602[label="",style="dashed", color="magenta", weight=3];
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482 -> 33[label="",style="dashed", color="red", weight=0];
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483 -> 34[label="",style="dashed", color="red", weight=0];
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484 -> 35[label="",style="dashed", color="red", weight=0];
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485 -> 36[label="",style="dashed", color="red", weight=0];
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496 -> 33[label="",style="dashed", color="red", weight=0];
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496 -> 655[label="",style="dashed", color="magenta", weight=3];
497 -> 34[label="",style="dashed", color="red", weight=0];
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c",fontsize=16,color="green",shape="box"];551[label="xy4001\n  Integral a",fontsize=16,color="green",shape="box"];552[label="xy301\n  Integral a",fontsize=16,color="green",shape="box"];553[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];554[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];555[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];556[label="xy301\n  Eq a",fontsize=16,color="green",shape="box"];557[label="xy4001",fontsize=16,color="green",shape="box"];558[label="xy301",fontsize=16,color="green",shape="box"];559[label="xy4001",fontsize=16,color="green",shape="box"];560[label="xy301",fontsize=16,color="green",shape="box"];561[label="xy4001",fontsize=16,color="green",shape="box"];562[label="xy301",fontsize=16,color="green",shape="box"];563[label="xy4001",fontsize=16,color="green",shape="box"];564[label="xy301",fontsize=16,color="green",shape="box"];565[label="xy4001",fontsize=16,color="green",shape="box"];566[label="xy301",fontsize=16,color="green",shape="box"];567[label="xy4001",fontsize=16,color="green",shape="box"];568[label="xy301",fontsize=16,color="green",shape="box"];569[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];570[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];571[label="xy4001",fontsize=16,color="green",shape="box"];572[label="xy301",fontsize=16,color="green",shape="box"];573[label="xy4000",fontsize=16,color="green",shape="box"];574[label="xy300",fontsize=16,color="green",shape="box"];575[label="xy4000\n  Eq a",fontsize=16,color="green",shape="box"];576[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];577[label="xy4000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];578[label="xy300\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];579[label="xy4000\n  Integral a",fontsize=16,color="green",shape="box"];580[label="xy300\n  Integral a",fontsize=16,color="green",shape="box"];581[label="xy4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];582[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];583[label="xy4000\n  Eq a",fontsize=16,color="green",shape="box"];584[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];585[label="xy4000",fontsize=16,color="green",shape="box"];586[label="xy300",fontsize=16,color="green",shape="box"];587[label="xy4000",fontsize=16,color="green",shape="box"];588[label="xy300",fontsize=16,color="green",shape="box"];589[label="xy4000",fontsize=16,color="green",shape="box"];590[label="xy300",fontsize=16,color="green",shape="box"];591[label="xy4000",fontsize=16,color="green",shape="box"];592[label="xy300",fontsize=16,color="green",shape="box"];593[label="xy4000",fontsize=16,color="green",shape="box"];594[label="xy300",fontsize=16,color="green",shape="box"];595[label="xy4000",fontsize=16,color="green",shape="box"];596[label="xy300",fontsize=16,color="green",shape="box"];597[label="xy4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];598[label="xy300\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];599[label="xy4000",fontsize=16,color="green",shape="box"];600[label="xy300",fontsize=16,color="green",shape="box"];601[label="primMulInt xy301 xy4001",fontsize=16,color="burlywood",shape="box"];1158[label="xy301/Pos xy3010",fontsize=10,color="white",style="solid",shape="box"];601 -> 1158[label="",style="solid", color="burlywood", weight=9];
1158 -> 680[label="",style="solid", color="burlywood", weight=3];
1159[label="xy301/Neg xy3010",fontsize=10,color="white",style="solid",shape="box"];601 -> 1159[label="",style="solid", color="burlywood", weight=9];
1159 -> 681[label="",style="solid", color="burlywood", weight=3];
602[label="xy4000",fontsize=16,color="green",shape="box"];603[label="xy300",fontsize=16,color="green",shape="box"];604[label="primEqNat (Succ xy3000) (Succ xy40000)",fontsize=16,color="black",shape="box"];604 -> 682[label="",style="solid", color="black", weight=3];
605[label="primEqNat (Succ xy3000) Zero",fontsize=16,color="black",shape="box"];605 -> 683[label="",style="solid", color="black", weight=3];
606[label="primEqNat Zero (Succ xy40000)",fontsize=16,color="black",shape="box"];606 -> 684[label="",style="solid", color="black", weight=3];
607[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];607 -> 685[label="",style="solid", color="black", weight=3];
608 -> 228[label="",style="dashed", color="red", weight=0];
608[label="primEqNat xy3000 xy40000",fontsize=16,color="magenta"];608 -> 686[label="",style="dashed", color="magenta", weight=3];
608 -> 687[label="",style="dashed", color="magenta", weight=3];
609[label="False",fontsize=16,color="green",shape="box"];610[label="False",fontsize=16,color="green",shape="box"];611[label="True",fontsize=16,color="green",shape="box"];612[label="False",fontsize=16,color="green",shape="box"];613[label="True",fontsize=16,color="green",shape="box"];614 -> 228[label="",style="dashed", color="red", weight=0];
614[label="primEqNat xy3000 xy40000",fontsize=16,color="magenta"];614 -> 688[label="",style="dashed", color="magenta", weight=3];
614 -> 689[label="",style="dashed", color="magenta", weight=3];
615[label="False",fontsize=16,color="green",shape="box"];616[label="False",fontsize=16,color="green",shape="box"];617[label="True",fontsize=16,color="green",shape="box"];618[label="False",fontsize=16,color="green",shape="box"];619[label="True",fontsize=16,color="green",shape="box"];620[label="xy4001",fontsize=16,color="green",shape="box"];621[label="xy301",fontsize=16,color="green",shape="box"];622[label="xy4000",fontsize=16,color="green",shape="box"];623[label="xy300",fontsize=16,color="green",shape="box"];624[label="xy4002",fontsize=16,color="green",shape="box"];625[label="xy302",fontsize=16,color="green",shape="box"];626[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];627[label="xy302\n  Eq a",fontsize=16,color="green",shape="box"];628[label="xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];629[label="xy302\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];630[label="xy4002\n  Integral a",fontsize=16,color="green",shape="box"];631[label="xy302\n  Integral a",fontsize=16,color="green",shape="box"];632[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];633[label="xy302\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];634[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];635[label="xy302\n  Eq a",fontsize=16,color="green",shape="box"];636[label="xy4002",fontsize=16,color="green",shape="box"];637[label="xy302",fontsize=16,color="green",shape="box"];638[label="xy4002",fontsize=16,color="green",shape="box"];639[label="xy302",fontsize=16,color="green",shape="box"];640[label="xy4002",fontsize=16,color="green",shape="box"];641[label="xy302",fontsize=16,color="green",shape="box"];642[label="xy4002",fontsize=16,color="green",shape="box"];643[label="xy302",fontsize=16,color="green",shape="box"];644[label="xy4002",fontsize=16,color="green",shape="box"];645[label="xy302",fontsize=16,color="green",shape="box"];646[label="xy4002",fontsize=16,color="green",shape="box"];647[label="xy302",fontsize=16,color="green",shape="box"];648[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];649[label="xy302\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];650[label="xy4002",fontsize=16,color="green",shape="box"];651[label="xy302",fontsize=16,color="green",shape="box"];652[label="xy4001",fontsize=16,color="green",shape="box"];653[label="xy301",fontsize=16,color="green",shape="box"];654[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];655[label="xy301\n  Eq a",fontsize=16,color="green",shape="box"];656[label="xy4001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];657[label="xy301\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];658[label="xy4001\n  Integral a",fontsize=16,color="green",shape="box"];659[label="xy301\n  Integral a",fontsize=16,color="green",shape="box"];660[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];661[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];662[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];663[label="xy301\n  Eq a",fontsize=16,color="green",shape="box"];664[label="xy4001",fontsize=16,color="green",shape="box"];665[label="xy301",fontsize=16,color="green",shape="box"];666[label="xy4001",fontsize=16,color="green",shape="box"];667[label="xy301",fontsize=16,color="green",shape="box"];668[label="xy4001",fontsize=16,color="green",shape="box"];669[label="xy301",fontsize=16,color="green",shape="box"];670[label="xy4001",fontsize=16,color="green",shape="box"];671[label="xy301",fontsize=16,color="green",shape="box"];672[label="xy4001",fontsize=16,color="green",shape="box"];673[label="xy301",fontsize=16,color="green",shape="box"];674[label="xy4001",fontsize=16,color="green",shape="box"];675[label="xy301",fontsize=16,color="green",shape="box"];676[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];677[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];678[label="xy4001",fontsize=16,color="green",shape="box"];679[label="xy301",fontsize=16,color="green",shape="box"];680[label="primMulInt (Pos xy3010) xy4001",fontsize=16,color="burlywood",shape="box"];1162[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];680 -> 1162[label="",style="solid", color="burlywood", weight=9];
1162 -> 690[label="",style="solid", color="burlywood", weight=3];
1163[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];680 -> 1163[label="",style="solid", color="burlywood", weight=9];
1163 -> 691[label="",style="solid", color="burlywood", weight=3];
681[label="primMulInt (Neg xy3010) xy4001",fontsize=16,color="burlywood",shape="box"];1164[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];681 -> 1164[label="",style="solid", color="burlywood", weight=9];
1164 -> 692[label="",style="solid", color="burlywood", weight=3];
1165[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];681 -> 1165[label="",style="solid", color="burlywood", weight=9];
1165 -> 693[label="",style="solid", color="burlywood", weight=3];
682 -> 228[label="",style="dashed", color="red", weight=0];
682[label="primEqNat xy3000 xy40000",fontsize=16,color="magenta"];682 -> 694[label="",style="dashed", color="magenta", weight=3];
682 -> 695[label="",style="dashed", color="magenta", weight=3];
683[label="False",fontsize=16,color="green",shape="box"];684[label="False",fontsize=16,color="green",shape="box"];685[label="True",fontsize=16,color="green",shape="box"];686[label="xy3000",fontsize=16,color="green",shape="box"];687[label="xy40000",fontsize=16,color="green",shape="box"];688[label="xy3000",fontsize=16,color="green",shape="box"];689[label="xy40000",fontsize=16,color="green",shape="box"];690[label="primMulInt (Pos xy3010) (Pos xy40010)",fontsize=16,color="black",shape="box"];690 -> 696[label="",style="solid", color="black", weight=3];
691[label="primMulInt (Pos xy3010) (Neg xy40010)",fontsize=16,color="black",shape="box"];691 -> 697[label="",style="solid", color="black", weight=3];
692[label="primMulInt (Neg xy3010) (Pos xy40010)",fontsize=16,color="black",shape="box"];692 -> 698[label="",style="solid", color="black", weight=3];
693[label="primMulInt (Neg xy3010) (Neg xy40010)",fontsize=16,color="black",shape="box"];693 -> 699[label="",style="solid", color="black", weight=3];
694[label="xy3000",fontsize=16,color="green",shape="box"];695[label="xy40000",fontsize=16,color="green",shape="box"];696[label="Pos (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];696 -> 700[label="",style="dashed", color="green", weight=3];
697[label="Neg (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];697 -> 701[label="",style="dashed", color="green", weight=3];
698[label="Neg (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];698 -> 702[label="",style="dashed", color="green", weight=3];
699[label="Pos (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];699 -> 703[label="",style="dashed", color="green", weight=3];
700[label="primMulNat xy3010 xy40010",fontsize=16,color="burlywood",shape="triangle"];1167[label="xy3010/Succ xy30100",fontsize=10,color="white",style="solid",shape="box"];700 -> 1167[label="",style="solid", color="burlywood", weight=9];
1167 -> 704[label="",style="solid", color="burlywood", weight=3];
1168[label="xy3010/Zero",fontsize=10,color="white",style="solid",shape="box"];700 -> 1168[label="",style="solid", color="burlywood", weight=9];
1168 -> 705[label="",style="solid", color="burlywood", weight=3];
701 -> 700[label="",style="dashed", color="red", weight=0];
701[label="primMulNat xy3010 xy40010",fontsize=16,color="magenta"];701 -> 706[label="",style="dashed", color="magenta", weight=3];
702 -> 700[label="",style="dashed", color="red", weight=0];
702[label="primMulNat xy3010 xy40010",fontsize=16,color="magenta"];702 -> 707[label="",style="dashed", color="magenta", weight=3];
703 -> 700[label="",style="dashed", color="red", weight=0];
703[label="primMulNat xy3010 xy40010",fontsize=16,color="magenta"];703 -> 708[label="",style="dashed", color="magenta", weight=3];
703 -> 709[label="",style="dashed", color="magenta", weight=3];
704[label="primMulNat (Succ xy30100) xy40010",fontsize=16,color="burlywood",shape="box"];1172[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];704 -> 1172[label="",style="solid", color="burlywood", weight=9];
1172 -> 710[label="",style="solid", color="burlywood", weight=3];
1173[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];704 -> 1173[label="",style="solid", color="burlywood", weight=9];
1173 -> 711[label="",style="solid", color="burlywood", weight=3];
705[label="primMulNat Zero xy40010",fontsize=16,color="burlywood",shape="box"];1174[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];705 -> 1174[label="",style="solid", color="burlywood", weight=9];
1174 -> 712[label="",style="solid", color="burlywood", weight=3];
1175[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];705 -> 1175[label="",style="solid", color="burlywood", weight=9];
1175 -> 713[label="",style="solid", color="burlywood", weight=3];
706[label="xy40010",fontsize=16,color="green",shape="box"];707[label="xy3010",fontsize=16,color="green",shape="box"];708[label="xy3010",fontsize=16,color="green",shape="box"];709[label="xy40010",fontsize=16,color="green",shape="box"];710[label="primMulNat (Succ xy30100) (Succ xy400100)",fontsize=16,color="black",shape="box"];710 -> 714[label="",style="solid", color="black", weight=3];
711[label="primMulNat (Succ xy30100) Zero",fontsize=16,color="black",shape="box"];711 -> 715[label="",style="solid", color="black", weight=3];
712[label="primMulNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];712 -> 716[label="",style="solid", color="black", weight=3];
713[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];713 -> 717[label="",style="solid", color="black", weight=3];
714 -> 718[label="",style="dashed", color="red", weight=0];
714[label="primPlusNat (primMulNat xy30100 (Succ xy400100)) (Succ xy400100)",fontsize=16,color="magenta"];714 -> 719[label="",style="dashed", color="magenta", weight=3];
715[label="Zero",fontsize=16,color="green",shape="box"];716[label="Zero",fontsize=16,color="green",shape="box"];717[label="Zero",fontsize=16,color="green",shape="box"];719 -> 700[label="",style="dashed", color="red", weight=0];
719[label="primMulNat xy30100 (Succ xy400100)",fontsize=16,color="magenta"];719 -> 720[label="",style="dashed", color="magenta", weight=3];
719 -> 721[label="",style="dashed", color="magenta", weight=3];
718[label="primPlusNat xy29 (Succ xy400100)",fontsize=16,color="burlywood",shape="triangle"];1178[label="xy29/Succ xy290",fontsize=10,color="white",style="solid",shape="box"];718 -> 1178[label="",style="solid", color="burlywood", weight=9];
1178 -> 722[label="",style="solid", color="burlywood", weight=3];
1179[label="xy29/Zero",fontsize=10,color="white",style="solid",shape="box"];718 -> 1179[label="",style="solid", color="burlywood", weight=9];
1179 -> 723[label="",style="solid", color="burlywood", weight=3];
720[label="xy30100",fontsize=16,color="green",shape="box"];721[label="Succ xy400100",fontsize=16,color="green",shape="box"];722[label="primPlusNat (Succ xy290) (Succ xy400100)",fontsize=16,color="black",shape="box"];722 -> 724[label="",style="solid", color="black", weight=3];
723[label="primPlusNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];723 -> 725[label="",style="solid", color="black", weight=3];
724[label="Succ (Succ (primPlusNat xy290 xy400100))",fontsize=16,color="green",shape="box"];724 -> 726[label="",style="dashed", color="green", weight=3];
725[label="Succ xy400100",fontsize=16,color="green",shape="box"];726[label="primPlusNat xy290 xy400100",fontsize=16,color="burlywood",shape="triangle"];1180[label="xy290/Succ xy2900",fontsize=10,color="white",style="solid",shape="box"];726 -> 1180[label="",style="solid", color="burlywood", weight=9];
1180 -> 727[label="",style="solid", color="burlywood", weight=3];
1181[label="xy290/Zero",fontsize=10,color="white",style="solid",shape="box"];726 -> 1181[label="",style="solid", color="burlywood", weight=9];
1181 -> 728[label="",style="solid", color="burlywood", weight=3];
727[label="primPlusNat (Succ xy2900) xy400100",fontsize=16,color="burlywood",shape="box"];1182[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];727 -> 1182[label="",style="solid", color="burlywood", weight=9];
1182 -> 729[label="",style="solid", color="burlywood", weight=3];
1183[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];727 -> 1183[label="",style="solid", color="burlywood", weight=9];
1183 -> 730[label="",style="solid", color="burlywood", weight=3];
728[label="primPlusNat Zero xy400100",fontsize=16,color="burlywood",shape="box"];1184[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];728 -> 1184[label="",style="solid", color="burlywood", weight=9];
1184 -> 731[label="",style="solid", color="burlywood", weight=3];
1185[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];728 -> 1185[label="",style="solid", color="burlywood", weight=9];
1185 -> 732[label="",style="solid", color="burlywood", weight=3];
729[label="primPlusNat (Succ xy2900) (Succ xy4001000)",fontsize=16,color="black",shape="box"];729 -> 733[label="",style="solid", color="black", weight=3];
730[label="primPlusNat (Succ xy2900) Zero",fontsize=16,color="black",shape="box"];730 -> 734[label="",style="solid", color="black", weight=3];
731[label="primPlusNat Zero (Succ xy4001000)",fontsize=16,color="black",shape="box"];731 -> 735[label="",style="solid", color="black", weight=3];
732[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];732 -> 736[label="",style="solid", color="black", weight=3];
733[label="Succ (Succ (primPlusNat xy2900 xy4001000))",fontsize=16,color="green",shape="box"];733 -> 737[label="",style="dashed", color="green", weight=3];
734[label="Succ xy2900",fontsize=16,color="green",shape="box"];735[label="Succ xy4001000",fontsize=16,color="green",shape="box"];736[label="Zero",fontsize=16,color="green",shape="box"];737 -> 726[label="",style="dashed", color="red", weight=0];
737[label="primPlusNat xy2900 xy4001000",fontsize=16,color="magenta"];737 -> 738[label="",style="dashed", color="magenta", weight=3];
737 -> 739[label="",style="dashed", color="magenta", weight=3];
738[label="xy2900",fontsize=16,color="green",shape="box"];739[label="xy4001000",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(xy2900), Succ(xy4001000)) → new_primPlusNat(xy2900, xy4001000)

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(xy2900), Succ(xy4001000)) → new_primPlusNat(xy2900, xy4001000)
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(xy30100), Succ(xy400100)) → new_primMulNat(xy30100, Succ(xy400100))

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

new_primMulNat(Succ(xy30100), Succ(xy400100)) → new_primMulNat(xy30100, Succ(xy400100))
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(xy3000), Succ(xy40000)) → new_primEqNat(xy3000, xy40000)

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

new_primEqNat(Succ(xy3000), Succ(xy40000)) → new_primEqNat(xy3000, xy40000)
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_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(app(ty_@2, ed), ee), dh) → new_esEs1(xy301, xy4001, ed, ee)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(app(ty_@3, hg), hh), baa), hf) → new_esEs0(xy300, xy4000, hg, hh, baa)
new_esEs3(Right(xy300), Right(xy4000), bdb, app(ty_[], bdc)) → new_esEs(xy300, xy4000, bdc)
new_esEs2(Just(xy300), Just(xy4000), app(ty_[], bag)) → new_esEs(xy300, xy4000, bag)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(app(ty_Either, de), df)) → new_esEs3(xy302, xy4002, de, df)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_Maybe, fh), cd, dh) → new_esEs2(xy300, xy4000, fh)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(ty_Maybe, dd)) → new_esEs2(xy302, xy4002, dd)
new_esEs3(Right(xy300), Right(xy4000), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(xy300, xy4000, beb, bec)
new_esEs3(Left(xy300), Left(xy4000), app(ty_[], bbh), bca) → new_esEs(xy300, xy4000, bbh)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(ty_[], ce)) → new_esEs(xy302, xy4002, ce)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(app(app(ty_@3, ea), eb), ec), dh) → new_esEs0(xy301, xy4001, ea, eb, ec)
new_esEs2(Just(xy300), Just(xy4000), app(ty_Maybe, bbe)) → new_esEs2(xy300, xy4000, bbe)
new_esEs3(Right(xy300), Right(xy4000), bdb, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs0(xy300, xy4000, bdd, bde, bdf)
new_esEs3(Left(xy300), Left(xy4000), app(app(ty_Either, bch), bda), bca) → new_esEs3(xy300, xy4000, bch, bda)
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_@2, bbc), bbd)) → new_esEs1(xy300, xy4000, bbc, bbd)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(ty_[], gd)) → new_esEs(xy301, xy4001, gd)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_Maybe, bad), hf) → new_esEs2(xy300, xy4000, bad)
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(ty_Maybe, bh)) → new_esEs2(xy300, xy4000, bh)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_[], he), hf) → new_esEs(xy300, xy4000, he)
new_esEs3(Left(xy300), Left(xy4000), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_esEs0(xy300, xy4000, bcb, bcc, bcd)
new_esEs2(Just(xy300), Just(xy4000), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(xy300, xy4000, bah, bba, bbb)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(app(ty_Either, hc), hd)) → new_esEs3(xy301, xy4001, hc, hd)
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(app(ty_@2, bf), bg)) → new_esEs1(xy300, xy4000, bf, bg)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(app(ty_@2, gh), ha)) → new_esEs1(xy301, xy4001, gh, ha)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(app(ty_@2, db), dc)) → new_esEs1(xy302, xy4002, db, dc)
new_esEs3(Left(xy300), Left(xy4000), app(ty_Maybe, bcg), bca) → new_esEs2(xy300, xy4000, bcg)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_[], fa), cd, dh) → new_esEs(xy300, xy4000, fa)
new_esEs(:(xy300, xy301), :(xy4000, xy4001), ba) → new_esEs(xy301, xy4001, ba)
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(app(ty_Either, ca), cb)) → new_esEs3(xy300, xy4000, ca, cb)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(xy302, xy4002, cf, cg, da)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(ty_[], dg), dh) → new_esEs(xy301, xy4001, dg)
new_esEs3(Left(xy300), Left(xy4000), app(app(ty_@2, bce), bcf), bca) → new_esEs1(xy300, xy4000, bce, bcf)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_Either, ga), gb), cd, dh) → new_esEs3(xy300, xy4000, ga, gb)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_@2, bab), bac), hf) → new_esEs1(xy300, xy4000, bab, bac)
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(app(app(ty_@3, bc), bd), be)) → new_esEs0(xy300, xy4000, bc, bd, be)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_@2, ff), fg), cd, dh) → new_esEs1(xy300, xy4000, ff, fg)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_Either, bae), baf), hf) → new_esEs3(xy300, xy4000, bae, baf)
new_esEs3(Right(xy300), Right(xy4000), bdb, app(ty_Maybe, bea)) → new_esEs2(xy300, xy4000, bea)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(ty_Maybe, hb)) → new_esEs2(xy301, xy4001, hb)
new_esEs3(Right(xy300), Right(xy4000), bdb, app(app(ty_@2, bdg), bdh)) → new_esEs1(xy300, xy4000, bdg, bdh)
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_Either, bbf), bbg)) → new_esEs3(xy300, xy4000, bbf, bbg)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(ty_Maybe, ef), dh) → new_esEs2(xy301, xy4001, ef)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(app(ty_Either, eg), eh), dh) → new_esEs3(xy301, xy4001, eg, eh)
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(ty_[], bb)) → new_esEs(xy300, xy4000, bb)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(app(app(ty_@3, ge), gf), gg)) → new_esEs0(xy301, xy4001, ge, gf, gg)
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, fb), fc), fd), cd, dh) → new_esEs0(xy300, xy4000, fb, fc, fd)

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

new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(app(ty_@2, bf), bg)) → new_esEs1(xy300, xy4000, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(app(app(ty_@3, bc), bd), be)) → new_esEs0(xy300, xy4000, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(app(ty_Either, ca), cb)) → new_esEs3(xy300, xy4000, ca, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(ty_Maybe, bh)) → new_esEs2(xy300, xy4000, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_@2, bbc), bbd)) → new_esEs1(xy300, xy4000, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy300), Just(xy4000), app(app(app(ty_@3, bah), bba), bbb)) → new_esEs0(xy300, xy4000, bah, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_Either, bbf), bbg)) → new_esEs3(xy300, xy4000, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy300), Just(xy4000), app(ty_Maybe, bbe)) → new_esEs2(xy300, xy4000, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Just(xy300), Just(xy4000), app(ty_[], bag)) → new_esEs(xy300, xy4000, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(app(ty_@2, ed), ee), dh) → new_esEs1(xy301, xy4001, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(app(ty_@2, db), dc)) → new_esEs1(xy302, xy4002, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_@2, ff), fg), cd, dh) → new_esEs1(xy300, xy4000, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(app(app(ty_@3, ea), eb), ec), dh) → new_esEs0(xy301, xy4001, ea, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(xy302, xy4002, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, fb), fc), fd), cd, dh) → new_esEs0(xy300, xy4000, fb, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(app(ty_Either, de), df)) → new_esEs3(xy302, xy4002, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_Either, ga), gb), cd, dh) → new_esEs3(xy300, xy4000, ga, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(app(ty_Either, eg), eh), dh) → new_esEs3(xy301, xy4001, eg, eh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(ty_Maybe, dd)) → new_esEs2(xy302, xy4002, dd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_Maybe, fh), cd, dh) → new_esEs2(xy300, xy4000, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(ty_Maybe, ef), dh) → new_esEs2(xy301, xy4001, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, cd, app(ty_[], ce)) → new_esEs(xy302, xy4002, ce)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_[], fa), cd, dh) → new_esEs(xy300, xy4000, fa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cc, app(ty_[], dg), dh) → new_esEs(xy301, xy4001, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(app(ty_@2, gh), ha)) → new_esEs1(xy301, xy4001, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_@2, bab), bac), hf) → new_esEs1(xy300, xy4000, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Left(xy300), Left(xy4000), app(app(ty_@2, bce), bcf), bca) → new_esEs1(xy300, xy4000, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Right(xy300), Right(xy4000), bdb, app(app(ty_@2, bdg), bdh)) → new_esEs1(xy300, xy4000, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(app(ty_@3, hg), hh), baa), hf) → new_esEs0(xy300, xy4000, hg, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(app(app(ty_@3, ge), gf), gg)) → new_esEs0(xy301, xy4001, ge, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(app(ty_Either, hc), hd)) → new_esEs3(xy301, xy4001, hc, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_Either, bae), baf), hf) → new_esEs3(xy300, xy4000, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_Maybe, bad), hf) → new_esEs2(xy300, xy4000, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(ty_Maybe, hb)) → new_esEs2(xy301, xy4001, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), gc, app(ty_[], gd)) → new_esEs(xy301, xy4001, gd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_[], he), hf) → new_esEs(xy300, xy4000, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy300), Right(xy4000), bdb, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs0(xy300, xy4000, bdd, bde, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(Left(xy300), Left(xy4000), app(app(app(ty_@3, bcb), bcc), bcd), bca) → new_esEs0(xy300, xy4000, bcb, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(xy300, xy301), :(xy4000, xy4001), ba) → new_esEs(xy301, xy4001, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(:(xy300, xy301), :(xy4000, xy4001), app(ty_[], bb)) → new_esEs(xy300, xy4000, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy300), Right(xy4000), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(xy300, xy4000, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(Left(xy300), Left(xy4000), app(app(ty_Either, bch), bda), bca) → new_esEs3(xy300, xy4000, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Left(xy300), Left(xy4000), app(ty_Maybe, bcg), bca) → new_esEs2(xy300, xy4000, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy300), Right(xy4000), bdb, app(ty_Maybe, bea)) → new_esEs2(xy300, xy4000, bea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(Right(xy300), Right(xy4000), bdb, app(ty_[], bdc)) → new_esEs(xy300, xy4000, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(Left(xy300), Left(xy4000), app(ty_[], bbh), bca) → new_esEs(xy300, xy4000, bbh)
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

                    ↳ DependencyGraphProof

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

new_deleteBy0(xy10, xy11, xy12, False, ba, bb) → new_deleteBy(Left(xy12), xy10, ba, bb)
new_deleteBy(Right(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy(Right(xy30), xy41, bc, bd)
new_deleteBy(Left(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy30, new_esEs4(xy30, xy400, bc), bc, bd)
new_deleteBy00(xy19, xy20, xy21, False, be, bf) → new_deleteBy(Right(xy21), xy19, be, bf)
new_deleteBy(Right(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy00(xy41, xy400, xy30, new_esEs5(xy30, xy400, bd), bc, bd)
new_deleteBy(Left(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy(Left(xy30), xy41, bc, bd)

The TRS R consists of the following rules:

new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs5(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs5(xy30, xy400, app(app(ty_@2, bdd), bde)) → new_esEs15(xy30, xy400, bdd, bde)
new_esEs5(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs13([], [], gb) → True
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_primMulNat0(Zero, Zero) → Zero
new_esEs16(Nothing, Nothing, gf) → True
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs4(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs4(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs4(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_esEs4(xy30, xy400, app(ty_Ratio, gc)) → new_esEs14(xy30, xy400, gc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs20(@0, @0) → True
new_esEs5(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs5(xy30, xy400, app(ty_[], bcg)) → new_esEs13(xy30, xy400, bcg)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs5(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs5(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs4(xy30, xy400, app(app(ty_Either, gg), gh)) → new_esEs22(xy30, xy400, gg, gh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs17(LT, LT) → True
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs5(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_asAs(False, xy28) → False
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primEqNat0(Zero, Zero) → True
new_esEs4(xy30, xy400, app(app(ty_@2, gd), ge)) → new_esEs15(xy30, xy400, gd, ge)
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs5(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs5(xy30, xy400, app(ty_Maybe, bdf)) → new_esEs16(xy30, xy400, bdf)
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs17(EQ, EQ) → True
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_asAs(True, xy28) → xy28
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs17(GT, GT) → True
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_[], gb)) → new_esEs13(xy30, xy400, gb)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs5(xy30, xy400, app(app(ty_Either, bdg), bdh)) → new_esEs22(xy30, xy400, bdg, bdh)
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_Maybe, gf)) → new_esEs16(xy30, xy400, gf)
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs5(xy30, xy400, app(ty_Ratio, bdc)) → new_esEs14(xy30, xy400, bdc)
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs5(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs5(xy30, xy400, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs8(xy30, xy400, bch, bda, bdb)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs4(xy30, xy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs8(xy30, xy400, bg, bh, ca)
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs18(False, False) → True
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ UsableRulesProof

                        ↳ QDP

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

new_deleteBy(Right(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy(Right(xy30), xy41, bc, bd)
new_deleteBy00(xy19, xy20, xy21, False, be, bf) → new_deleteBy(Right(xy21), xy19, be, bf)
new_deleteBy(Right(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy00(xy41, xy400, xy30, new_esEs5(xy30, xy400, bd), bc, bd)

The TRS R consists of the following rules:

new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs5(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs5(xy30, xy400, app(app(ty_@2, bdd), bde)) → new_esEs15(xy30, xy400, bdd, bde)
new_esEs5(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs13([], [], gb) → True
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_primMulNat0(Zero, Zero) → Zero
new_esEs16(Nothing, Nothing, gf) → True
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs4(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs4(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs4(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_esEs4(xy30, xy400, app(ty_Ratio, gc)) → new_esEs14(xy30, xy400, gc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs20(@0, @0) → True
new_esEs5(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs5(xy30, xy400, app(ty_[], bcg)) → new_esEs13(xy30, xy400, bcg)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs5(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs5(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs4(xy30, xy400, app(app(ty_Either, gg), gh)) → new_esEs22(xy30, xy400, gg, gh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs17(LT, LT) → True
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs5(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_asAs(False, xy28) → False
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primEqNat0(Zero, Zero) → True
new_esEs4(xy30, xy400, app(app(ty_@2, gd), ge)) → new_esEs15(xy30, xy400, gd, ge)
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs5(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs5(xy30, xy400, app(ty_Maybe, bdf)) → new_esEs16(xy30, xy400, bdf)
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs17(EQ, EQ) → True
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_asAs(True, xy28) → xy28
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs17(GT, GT) → True
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_[], gb)) → new_esEs13(xy30, xy400, gb)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs5(xy30, xy400, app(app(ty_Either, bdg), bdh)) → new_esEs22(xy30, xy400, bdg, bdh)
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_Maybe, gf)) → new_esEs16(xy30, xy400, gf)
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs5(xy30, xy400, app(ty_Ratio, bdc)) → new_esEs14(xy30, xy400, bdc)
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs5(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs5(xy30, xy400, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs8(xy30, xy400, bch, bda, bdb)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs4(xy30, xy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs8(xy30, xy400, bg, bh, ca)
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs18(False, False) → True
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

                        ↳ QDP

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

new_deleteBy(Right(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy(Right(xy30), xy41, bc, bd)
new_deleteBy00(xy19, xy20, xy21, False, be, bf) → new_deleteBy(Right(xy21), xy19, be, bf)
new_deleteBy(Right(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy00(xy41, xy400, xy30, new_esEs5(xy30, xy400, bd), bc, bd)

The TRS R consists of the following rules:

new_esEs5(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs5(xy30, xy400, app(app(ty_@2, bdd), bde)) → new_esEs15(xy30, xy400, bdd, bde)
new_esEs5(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs5(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs5(xy30, xy400, app(ty_[], bcg)) → new_esEs13(xy30, xy400, bcg)
new_esEs5(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs5(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs5(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs5(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs5(xy30, xy400, app(ty_Maybe, bdf)) → new_esEs16(xy30, xy400, bdf)
new_esEs5(xy30, xy400, app(app(ty_Either, bdg), bdh)) → new_esEs22(xy30, xy400, bdg, bdh)
new_esEs5(xy30, xy400, app(ty_Ratio, bdc)) → new_esEs14(xy30, xy400, bdc)
new_esEs5(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs5(xy30, xy400, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs8(xy30, xy400, bch, bda, bdb)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_asAs(False, xy28) → False
new_asAs(True, xy28) → xy28
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_esEs16(Nothing, Nothing, gf) → True
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs13([], [], gb) → True
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs20(@0, @0) → True
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs17(LT, LT) → True
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs17(EQ, EQ) → True
new_esEs17(GT, GT) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

                                ↳ QDP

                                  ↳ QDPSizeChangeProof

                        ↳ QDP

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

new_deleteBy(Right(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy(Right(xy30), xy41, bc, bd)
new_deleteBy00(xy19, xy20, xy21, False, be, bf) → new_deleteBy(Right(xy21), xy19, be, bf)
new_deleteBy(Right(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy00(xy41, xy400, xy30, new_esEs5(xy30, xy400, bd), bc, bd)

The TRS R consists of the following rules:

new_esEs5(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs5(xy30, xy400, app(app(ty_@2, bdd), bde)) → new_esEs15(xy30, xy400, bdd, bde)
new_esEs5(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs5(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs5(xy30, xy400, app(ty_[], bcg)) → new_esEs13(xy30, xy400, bcg)
new_esEs5(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs5(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs5(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs5(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs5(xy30, xy400, app(ty_Maybe, bdf)) → new_esEs16(xy30, xy400, bdf)
new_esEs5(xy30, xy400, app(app(ty_Either, bdg), bdh)) → new_esEs22(xy30, xy400, bdg, bdh)
new_esEs5(xy30, xy400, app(ty_Ratio, bdc)) → new_esEs14(xy30, xy400, bdc)
new_esEs5(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs5(xy30, xy400, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs8(xy30, xy400, bch, bda, bdb)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_asAs(False, xy28) → False
new_asAs(True, xy28) → xy28
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_esEs16(Nothing, Nothing, gf) → True
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs13([], [], gb) → True
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs20(@0, @0) → True
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs17(LT, LT) → True
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs17(EQ, EQ) → True
new_esEs17(GT, GT) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)

The set Q consists of the following terms:

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

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_deleteBy(Right(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy(Right(xy30), xy41, bc, bd)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
new_deleteBy(Right(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy00(xy41, xy400, xy30, new_esEs5(xy30, xy400, bd), bc, bd)
The graph contains the following edges 2 > 1, 2 > 2, 1 > 3, 3 >= 5, 4 >= 6
new_deleteBy00(xy19, xy20, xy21, False, be, bf) → new_deleteBy(Right(xy21), xy19, be, bf)
The graph contains the following edges 1 >= 2, 5 >= 3, 6 >= 4

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ UsableRulesProof

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

new_deleteBy0(xy10, xy11, xy12, False, ba, bb) → new_deleteBy(Left(xy12), xy10, ba, bb)
new_deleteBy(Left(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy30, new_esEs4(xy30, xy400, bc), bc, bd)
new_deleteBy(Left(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy(Left(xy30), xy41, bc, bd)

The TRS R consists of the following rules:

new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs5(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs5(xy30, xy400, app(app(ty_@2, bdd), bde)) → new_esEs15(xy30, xy400, bdd, bde)
new_esEs5(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs13([], [], gb) → True
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_primMulNat0(Zero, Zero) → Zero
new_esEs16(Nothing, Nothing, gf) → True
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs4(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs4(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs4(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_esEs4(xy30, xy400, app(ty_Ratio, gc)) → new_esEs14(xy30, xy400, gc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs20(@0, @0) → True
new_esEs5(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs5(xy30, xy400, app(ty_[], bcg)) → new_esEs13(xy30, xy400, bcg)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs5(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs5(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs4(xy30, xy400, app(app(ty_Either, gg), gh)) → new_esEs22(xy30, xy400, gg, gh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs17(LT, LT) → True
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs5(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_asAs(False, xy28) → False
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primEqNat0(Zero, Zero) → True
new_esEs4(xy30, xy400, app(app(ty_@2, gd), ge)) → new_esEs15(xy30, xy400, gd, ge)
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs5(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs5(xy30, xy400, app(ty_Maybe, bdf)) → new_esEs16(xy30, xy400, bdf)
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs17(EQ, EQ) → True
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_asAs(True, xy28) → xy28
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs17(GT, GT) → True
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_[], gb)) → new_esEs13(xy30, xy400, gb)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs5(xy30, xy400, app(app(ty_Either, bdg), bdh)) → new_esEs22(xy30, xy400, bdg, bdh)
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_Maybe, gf)) → new_esEs16(xy30, xy400, gf)
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs5(xy30, xy400, app(ty_Ratio, bdc)) → new_esEs14(xy30, xy400, bdc)
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs5(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs5(xy30, xy400, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs8(xy30, xy400, bch, bda, bdb)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs4(xy30, xy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs8(xy30, xy400, bg, bh, ca)
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs18(False, False) → True
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

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

new_deleteBy0(xy10, xy11, xy12, False, ba, bb) → new_deleteBy(Left(xy12), xy10, ba, bb)
new_deleteBy(Left(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy30, new_esEs4(xy30, xy400, bc), bc, bd)
new_deleteBy(Left(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy(Left(xy30), xy41, bc, bd)

The TRS R consists of the following rules:

new_esEs4(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs4(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs4(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs4(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs4(xy30, xy400, app(ty_Ratio, gc)) → new_esEs14(xy30, xy400, gc)
new_esEs4(xy30, xy400, app(app(ty_Either, gg), gh)) → new_esEs22(xy30, xy400, gg, gh)
new_esEs4(xy30, xy400, app(app(ty_@2, gd), ge)) → new_esEs15(xy30, xy400, gd, ge)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs4(xy30, xy400, app(ty_[], gb)) → new_esEs13(xy30, xy400, gb)
new_esEs4(xy30, xy400, app(ty_Maybe, gf)) → new_esEs16(xy30, xy400, gf)
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs4(xy30, xy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs8(xy30, xy400, bg, bh, ca)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_asAs(False, xy28) → False
new_asAs(True, xy28) → xy28
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_esEs16(Nothing, Nothing, gf) → True
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs13([], [], gb) → True
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs20(@0, @0) → True
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs17(LT, LT) → True
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs17(EQ, EQ) → True
new_esEs17(GT, GT) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)

The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

                                ↳ QDP

                                  ↳ QDPSizeChangeProof

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

new_deleteBy0(xy10, xy11, xy12, False, ba, bb) → new_deleteBy(Left(xy12), xy10, ba, bb)
new_deleteBy(Left(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy30, new_esEs4(xy30, xy400, bc), bc, bd)
new_deleteBy(Left(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy(Left(xy30), xy41, bc, bd)

The TRS R consists of the following rules:

new_esEs4(xy30, xy400, ty_Int) → new_esEs7(xy30, xy400)
new_esEs4(xy30, xy400, ty_Char) → new_esEs21(xy30, xy400)
new_esEs4(xy30, xy400, ty_@0) → new_esEs20(xy30, xy400)
new_esEs4(xy30, xy400, ty_Float) → new_esEs6(xy30, xy400)
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs4(xy30, xy400, app(ty_Ratio, gc)) → new_esEs14(xy30, xy400, gc)
new_esEs4(xy30, xy400, app(app(ty_Either, gg), gh)) → new_esEs22(xy30, xy400, gg, gh)
new_esEs4(xy30, xy400, app(app(ty_@2, gd), ge)) → new_esEs15(xy30, xy400, gd, ge)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs12(xy30, xy400)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs18(xy30, xy400)
new_esEs4(xy30, xy400, app(ty_[], gb)) → new_esEs13(xy30, xy400, gb)
new_esEs4(xy30, xy400, app(ty_Maybe, gf)) → new_esEs16(xy30, xy400, gf)
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs17(xy30, xy400)
new_esEs4(xy30, xy400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs8(xy30, xy400, bg, bh, ca)
new_esEs8(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, ca) → new_asAs(new_esEs11(xy300, xy4000, bg), new_asAs(new_esEs10(xy301, xy4001, bh), new_esEs9(xy302, xy4002, ca)))
new_esEs11(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_[], eg)) → new_esEs13(xy300, xy4000, eg)
new_esEs11(xy300, xy4000, app(app(ty_@2, fd), ff)) → new_esEs15(xy300, xy4000, fd, ff)
new_esEs11(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs11(xy300, xy4000, app(ty_Ratio, fc)) → new_esEs14(xy300, xy4000, fc)
new_esEs11(xy300, xy4000, app(app(app(ty_@3, eh), fa), fb)) → new_esEs8(xy300, xy4000, eh, fa, fb)
new_esEs11(xy300, xy4000, app(ty_Maybe, fg)) → new_esEs16(xy300, xy4000, fg)
new_esEs11(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs11(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs11(xy300, xy4000, app(app(ty_Either, fh), ga)) → new_esEs22(xy300, xy4000, fh, ga)
new_esEs10(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs10(xy301, xy4001, app(app(app(ty_@3, df), dg), dh)) → new_esEs8(xy301, xy4001, df, dg, dh)
new_esEs10(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_[], de)) → new_esEs13(xy301, xy4001, de)
new_esEs10(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Maybe, ed)) → new_esEs16(xy301, xy4001, ed)
new_esEs10(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs10(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)
new_esEs10(xy301, xy4001, app(ty_Ratio, ea)) → new_esEs14(xy301, xy4001, ea)
new_esEs10(xy301, xy4001, app(app(ty_Either, ee), ef)) → new_esEs22(xy301, xy4001, ee, ef)
new_esEs10(xy301, xy4001, app(app(ty_@2, eb), ec)) → new_esEs15(xy301, xy4001, eb, ec)
new_esEs10(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs9(xy302, xy4002, app(ty_[], cb)) → new_esEs13(xy302, xy4002, cb)
new_esEs9(xy302, xy4002, ty_@0) → new_esEs20(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Float) → new_esEs6(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Char) → new_esEs21(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Integer) → new_esEs12(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(ty_Either, dc), dd)) → new_esEs22(xy302, xy4002, dc, dd)
new_esEs9(xy302, xy4002, app(app(ty_@2, cg), da)) → new_esEs15(xy302, xy4002, cg, da)
new_esEs9(xy302, xy4002, ty_Bool) → new_esEs18(xy302, xy4002)
new_esEs9(xy302, xy4002, app(ty_Ratio, cf)) → new_esEs14(xy302, xy4002, cf)
new_esEs9(xy302, xy4002, ty_Ordering) → new_esEs17(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Int) → new_esEs7(xy302, xy4002)
new_esEs9(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs9(xy302, xy4002, app(app(app(ty_@3, cc), cd), ce)) → new_esEs8(xy302, xy4002, cc, cd, ce)
new_esEs9(xy302, xy4002, app(ty_Maybe, db)) → new_esEs16(xy302, xy4002, db)
new_asAs(False, xy28) → False
new_asAs(True, xy28) → xy28
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs8(xy300, xy4000, bgf, bgg, bgh)
new_esEs16(Nothing, Nothing, gf) → True
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_Either, bce), bcf)) → new_esEs22(xy300, xy4000, bce, bcf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Maybe, bcd)) → new_esEs16(xy300, xy4000, bcd)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_Either, bbc), bbd), gh) → new_esEs22(xy300, xy4000, bbc, bbd)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Maybe, bbb), gh) → new_esEs16(xy300, xy4000, bbb)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, bhd)) → new_esEs16(xy300, xy4000, bhd)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, bhe), bhf)) → new_esEs22(xy300, xy4000, bhe, bhf)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs21(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, bhb), bhc)) → new_esEs15(xy300, xy4000, bhb, bhc)
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs20(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs6(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs7(xy300, xy4000)
new_esEs16(Nothing, Just(xy4000), gf) → False
new_esEs16(Just(xy300), Nothing, gf) → False
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], bge)) → new_esEs13(xy300, xy4000, bge)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, bha)) → new_esEs14(xy300, xy4000, bha)
new_esEs14(:%(xy300, xy301), :%(xy4000, xy4001), gc) → new_asAs(new_esEs24(xy300, xy4000, gc), new_esEs23(xy301, xy4001, gc))
new_esEs24(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs24(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs12(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs7(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_primPlusNat0(Succ(xy290), xy400100) → Succ(Succ(new_primPlusNat1(xy290, xy400100)))
new_primPlusNat1(Succ(xy2900), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy2900, xy4001000)))
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy2900), Zero) → Succ(xy2900)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs13([], [], gb) → True
new_esEs13([], :(xy4000, xy4001), gb) → False
new_esEs13(:(xy300, xy301), [], gb) → False
new_esEs13(:(xy300, xy301), :(xy4000, xy4001), gb) → new_asAs(new_esEs25(xy300, xy4000, gb), new_esEs13(xy301, xy4001, gb))
new_esEs25(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_@2, hf), hg)) → new_esEs15(xy300, xy4000, hf, hg)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs25(xy300, xy4000, app(app(ty_Either, baa), bab)) → new_esEs22(xy300, xy4000, baa, bab)
new_esEs25(xy300, xy4000, app(app(app(ty_@3, hb), hc), hd)) → new_esEs8(xy300, xy4000, hb, hc, hd)
new_esEs25(xy300, xy4000, app(ty_Ratio, he)) → new_esEs14(xy300, xy4000, he)
new_esEs25(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_[], ha)) → new_esEs13(xy300, xy4000, ha)
new_esEs25(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, app(ty_Maybe, hh)) → new_esEs16(xy300, xy4000, hh)
new_esEs25(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs20(@0, @0) → True
new_esEs21(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs18(True, True) → True
new_esEs18(True, False) → False
new_esEs18(False, True) → False
new_esEs18(False, False) → True
new_esEs6(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs7(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Float, gh) → new_esEs6(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Char, gh) → new_esEs21(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(ty_@2, bcb), bcc)) → new_esEs15(xy300, xy4000, bcb, bcc)
new_esEs22(Left(xy300), Left(xy4000), ty_@0, gh) → new_esEs20(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Int, gh) → new_esEs7(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(ty_@2, bah), bba), gh) → new_esEs15(xy300, xy4000, bah, bba)
new_esEs22(Left(xy300), Left(xy4000), app(ty_[], bac), gh) → new_esEs13(xy300, xy4000, bac)
new_esEs22(Right(xy300), Right(xy4000), gg, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs8(xy300, xy4000, bbf, bbg, bbh)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Ordering, gh) → new_esEs17(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Integer, gh) → new_esEs12(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(ty_Ratio, bag), gh) → new_esEs14(xy300, xy4000, bag)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), ty_Double, gh) → new_esEs19(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs22(Left(xy300), Left(xy4000), app(app(app(ty_@3, bad), bae), baf), gh) → new_esEs8(xy300, xy4000, bad, bae, baf)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_Ratio, bca)) → new_esEs14(xy300, xy4000, bca)
new_esEs22(Left(xy300), Left(xy4000), ty_Bool, gh) → new_esEs18(xy300, xy4000)
new_esEs22(Right(xy300), Left(xy4000), gg, gh) → False
new_esEs22(Left(xy300), Right(xy4000), gg, gh) → False
new_esEs22(Right(xy300), Right(xy4000), gg, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs22(Right(xy300), Right(xy4000), gg, app(ty_[], bbe)) → new_esEs13(xy300, xy4000, bbe)
new_esEs17(LT, LT) → True
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs17(EQ, EQ) → True
new_esEs17(GT, GT) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs15(@2(xy300, xy301), @2(xy4000, xy4001), gd, ge) → new_asAs(new_esEs27(xy300, xy4000, gd), new_esEs26(xy301, xy4001, ge))
new_esEs27(xy300, xy4000, app(app(ty_@2, bfh), bga)) → new_esEs15(xy300, xy4000, bfh, bga)
new_esEs27(xy300, xy4000, ty_Integer) → new_esEs12(xy300, xy4000)
new_esEs27(xy300, xy4000, app(app(ty_Either, bgc), bgd)) → new_esEs22(xy300, xy4000, bgc, bgd)
new_esEs27(xy300, xy4000, app(ty_Maybe, bgb)) → new_esEs16(xy300, xy4000, bgb)
new_esEs27(xy300, xy4000, app(ty_Ratio, bfg)) → new_esEs14(xy300, xy4000, bfg)
new_esEs27(xy300, xy4000, ty_Int) → new_esEs7(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Float) → new_esEs6(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_@0) → new_esEs20(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Char) → new_esEs21(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Ordering) → new_esEs17(xy300, xy4000)
new_esEs27(xy300, xy4000, ty_Bool) → new_esEs18(xy300, xy4000)
new_esEs27(xy300, xy4000, app(ty_[], bfc)) → new_esEs13(xy300, xy4000, bfc)
new_esEs27(xy300, xy4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs8(xy300, xy4000, bfd, bfe, bff)
new_esEs27(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs26(xy301, xy4001, ty_Bool) → new_esEs18(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_@2, bef), beg)) → new_esEs15(xy301, xy4001, bef, beg)
new_esEs26(xy301, xy4001, app(ty_Ratio, bee)) → new_esEs14(xy301, xy4001, bee)
new_esEs26(xy301, xy4001, ty_Float) → new_esEs6(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs8(xy301, xy4001, beb, bec, bed)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs7(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs12(xy301, xy4001)
new_esEs26(xy301, xy4001, app(ty_[], bea)) → new_esEs13(xy301, xy4001, bea)
new_esEs26(xy301, xy4001, ty_Ordering) → new_esEs17(xy301, xy4001)
new_esEs26(xy301, xy4001, app(app(ty_Either, bfa), bfb)) → new_esEs22(xy301, xy4001, bfa, bfb)
new_esEs26(xy301, xy4001, app(ty_Maybe, beh)) → new_esEs16(xy301, xy4001, beh)
new_esEs26(xy301, xy4001, ty_@0) → new_esEs20(xy301, xy4001)
new_esEs26(xy301, xy4001, ty_Char) → new_esEs21(xy301, xy4001)

The set Q consists of the following terms:

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

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_deleteBy(Left(xy30), :(Left(xy400), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy30, new_esEs4(xy30, xy400, bc), bc, bd)
The graph contains the following edges 2 > 1, 2 > 2, 1 > 3, 3 >= 5, 4 >= 6
new_deleteBy(Left(xy30), :(Right(xy400), xy41), bc, bd) → new_deleteBy(Left(xy30), xy41, bc, bd)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
new_deleteBy0(xy10, xy11, xy12, False, ba, bb) → new_deleteBy(Left(xy12), xy10, ba, bb)
The graph contains the following edges 1 >= 2, 5 >= 3, 6 >= 4

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