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

YES 88.616 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

((union :: [Ratio Int] -> [Ratio Int] -> [Ratio Int]) :: [Ratio Int] -> [Ratio Int] -> [Ratio Int])

module List where

import qualified Maybe
import qualified Prelude

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

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

elem_by	_ _ []	=	False
elem_by	eq y (x : xs)	=	x `eq` y \|\| elem_by eq y xs

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

nubBy

eq l

nubBy' l []

where

nubBy'

[] _

[]

nubBy'

(y : ys) xs

elem_by eq y xs

nubBy' ys xs

otherwise

y : nubBy' ys (y : xs)

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

union

unionBy (==)

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

unionBy

eq xs ys

xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs

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

((union :: [Ratio Int] -> [Ratio Int] -> [Ratio Int]) :: [Ratio Int] -> [Ratio Int] -> [Ratio Int])

module List where

import qualified Maybe
import qualified Prelude

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

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

elem_by	_ _ []	=	False
elem_by	eq y (x : xs)	=	x `eq` y \|\| elem_by eq y xs

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

nubBy

eq l

nubBy' l []

where

nubBy'

[] _

[]

nubBy'

(y : ys) xs

elem_by eq y xs

nubBy' ys xs

otherwise

y : nubBy' ys (y : xs)

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

union

unionBy (==)

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

unionBy

eq xs ys

xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs

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

((union :: [Ratio Int] -> [Ratio Int] -> [Ratio Int]) :: [Ratio Int] -> [Ratio Int] -> [Ratio Int])

module List where

import qualified Maybe
import qualified Prelude

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

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

elem_by	vz wu []	=	False
elem_by	eq y (x : xs)	=	x `eq` y \|\| elem_by eq y xs

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

nubBy

eq l

nubBy' l []

where

nubBy'

[] vy

[]

nubBy'

(y : ys) xs

elem_by eq y xs

nubBy' ys xs

otherwise

y : nubBy' ys (y : xs)

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

union

unionBy (==)

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

unionBy

eq xs ys

xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs

module Maybe where

import qualified List
import qualified Prelude

Cond Reductions:
The following Function with conditions

nubBy' [] vy = []

nubBy' (y : ys) xs

| elem_by eq y xs

= nubBy' ys xs

| otherwise

= y : nubBy' ys (y : xs)

is transformed to

nubBy' [] vy = nubBy'3 [] vy

nubBy' (y : ys) xs = nubBy'2 (y : ys) xs

nubBy'0 y ys xs True = y : nubBy' ys (y : xs)

nubBy'1 y ys xs True = nubBy' ys xs

nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise

nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs)

nubBy'3 [] vy = []

nubBy'3 xv xw = nubBy'2 xv xw

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

              ↳ LetRed

mainModule List

((union :: [Ratio Int] -> [Ratio Int] -> [Ratio Int]) :: [Ratio Int] -> [Ratio Int] -> [Ratio Int])

module List where

import qualified Maybe
import qualified Prelude

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

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

elem_by	vz wu []	=	False
elem_by	eq y (x : xs)	=	x `eq` y \|\| elem_by eq y xs

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

nubBy

eq l

nubBy' l []

where

nubBy'	[] vy	=	nubBy'3 [] vy
nubBy'	(y : ys) xs	=	nubBy'2 (y : ys) xs

nubBy'0

y ys xs True

y : nubBy' ys (y : xs)

nubBy'1	y ys xs True	=	nubBy' ys xs
nubBy'1	y ys xs False	=	nubBy'0 y ys xs otherwise

nubBy'2

(y : ys) xs

nubBy'1 y ys xs (elem_by eq y xs)

nubBy'3	[] vy	=	[]
nubBy'3	xv xw	=	nubBy'2 xv xw

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

union

unionBy (==)

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

unionBy

eq xs ys

xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs

module Maybe where

import qualified List
import qualified Prelude

Let/Where Reductions:
The bindings of the following Let/Where expression

nubBy' l []

where

nubBy' [] vy = nubBy'3 [] vy

nubBy' (y : ys) xs = nubBy'2 (y : ys) xs

nubBy'0 y ys xs True = y : nubBy' ys (y : xs)

nubBy'1 y ys xs True = nubBy' ys xs

nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise

nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs)

nubBy'3 [] vy = []

nubBy'3 xv xw = nubBy'2 xv xw

are unpacked to the following functions on top level

nubByNubBy' xx [] vy = nubByNubBy'3 xx [] vy

nubByNubBy' xx (y : ys) xs = nubByNubBy'2 xx (y : ys) xs

nubByNubBy'3 xx [] vy = []

nubByNubBy'3 xx xv xw = nubByNubBy'2 xx xv xw

nubByNubBy'0 xx y ys xs True = y : nubByNubBy' xx ys (y : xs)

nubByNubBy'2 xx (y : ys) xs = nubByNubBy'1 xx y ys xs (elem_by xx y xs)

nubByNubBy'1 xx y ys xs True = nubByNubBy' xx ys xs

nubByNubBy'1 xx y ys xs False = nubByNubBy'0 xx y ys xs otherwise

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

mainModule List

(union :: [Ratio Int] -> [Ratio Int] -> [Ratio Int])

module List where

import qualified Maybe
import qualified Prelude

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

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

elem_by	vz wu []	=	False
elem_by	eq y (x : xs)	=	x `eq` y \|\| elem_by eq y xs

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

nubBy

eq l

nubByNubBy' eq l []

nubByNubBy'	xx [] vy	=	nubByNubBy'3 xx [] vy
nubByNubBy'	xx (y : ys) xs	=	nubByNubBy'2 xx (y : ys) xs

nubByNubBy'0

xx y ys xs True

y : nubByNubBy' xx ys (y : xs)

nubByNubBy'1	xx y ys xs True	=	nubByNubBy' xx ys xs
nubByNubBy'1	xx y ys xs False	=	nubByNubBy'0 xx y ys xs otherwise

nubByNubBy'2

xx (y : ys) xs

nubByNubBy'1 xx y ys xs (elem_by xx y xs)

nubByNubBy'3	xx [] vy	=	[]
nubByNubBy'3	xx xv xw	=	nubByNubBy'2 xx xv xw

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

union

unionBy (==)

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

unionBy

eq xs ys

xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="union",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
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4[label="union xy3 xy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="unionBy (==) xy3 xy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
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12637 -> 7[label="",style="solid", color="burlywood", weight=3];
12638[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 12638[label="",style="solid", color="burlywood", weight=9];
12638 -> 8[label="",style="solid", color="burlywood", weight=3];
7[label="(xy30 : xy31) ++ foldl (flip (deleteBy (==))) (nubBy (==) xy4) (xy30 : xy31)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="[] ++ foldl (flip (deleteBy (==))) (nubBy (==) xy4) []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
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10[label="foldl (flip (deleteBy (==))) (nubBy (==) xy4) []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11 -> 119[label="",style="dashed", color="red", weight=0];
11[label="xy31 ++ foldl (flip (deleteBy (==))) (nubBy (==) xy4) (xy30 : xy31)",fontsize=16,color="magenta"];11 -> 120[label="",style="dashed", color="magenta", weight=3];
11 -> 121[label="",style="dashed", color="magenta", weight=3];
11 -> 122[label="",style="dashed", color="magenta", weight=3];
11 -> 123[label="",style="dashed", color="magenta", weight=3];
12[label="nubBy (==) xy4",fontsize=16,color="black",shape="triangle"];12 -> 15[label="",style="solid", color="black", weight=3];
120[label="xy31",fontsize=16,color="green",shape="box"];121 -> 12[label="",style="dashed", color="red", weight=0];
121[label="nubBy (==) xy4",fontsize=16,color="magenta"];122[label="xy30",fontsize=16,color="green",shape="box"];123[label="xy31",fontsize=16,color="green",shape="box"];119[label="xy8 ++ foldl (flip (deleteBy (==))) xy9 (xy10 : xy11)\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12641[label="xy8/xy80 : xy81",fontsize=10,color="white",style="solid",shape="box"];119 -> 12641[label="",style="solid", color="burlywood", weight=9];
12641 -> 148[label="",style="solid", color="burlywood", weight=3];
12642[label="xy8/[]",fontsize=10,color="white",style="solid",shape="box"];119 -> 12642[label="",style="solid", color="burlywood", weight=9];
12642 -> 149[label="",style="solid", color="burlywood", weight=3];
15[label="nubByNubBy' (==) xy4 []",fontsize=16,color="burlywood",shape="box"];12643[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];15 -> 12643[label="",style="solid", color="burlywood", weight=9];
12643 -> 18[label="",style="solid", color="burlywood", weight=3];
12644[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];15 -> 12644[label="",style="solid", color="burlywood", weight=9];
12644 -> 19[label="",style="solid", color="burlywood", weight=3];
148[label="(xy80 : xy81) ++ foldl (flip (deleteBy (==))) xy9 (xy10 : xy11)\n  Eq a",fontsize=16,color="black",shape="box"];148 -> 151[label="",style="solid", color="black", weight=3];
149[label="[] ++ foldl (flip (deleteBy (==))) xy9 (xy10 : xy11)\n  Eq a",fontsize=16,color="black",shape="box"];149 -> 152[label="",style="solid", color="black", weight=3];
18[label="nubByNubBy' (==) (xy40 : xy41) []",fontsize=16,color="black",shape="box"];18 -> 23[label="",style="solid", color="black", weight=3];
19[label="nubByNubBy' (==) [] []",fontsize=16,color="black",shape="box"];19 -> 24[label="",style="solid", color="black", weight=3];
151[label="xy80 : xy81 ++ foldl (flip (deleteBy (==))) xy9 (xy10 : xy11)\n  Eq a",fontsize=16,color="green",shape="box"];151 -> 155[label="",style="dashed", color="green", weight=3];
152[label="foldl (flip (deleteBy (==))) xy9 (xy10 : xy11)\n  Eq a",fontsize=16,color="black",shape="box"];152 -> 156[label="",style="solid", color="black", weight=3];
23[label="nubByNubBy'2 (==) (xy40 : xy41) []",fontsize=16,color="black",shape="box"];23 -> 28[label="",style="solid", color="black", weight=3];
24[label="nubByNubBy'3 (==) [] []",fontsize=16,color="black",shape="box"];24 -> 29[label="",style="solid", color="black", weight=3];
155 -> 119[label="",style="dashed", color="red", weight=0];
155[label="xy81 ++ foldl (flip (deleteBy (==))) xy9 (xy10 : xy11)\n  Eq a",fontsize=16,color="magenta"];155 -> 161[label="",style="dashed", color="magenta", weight=3];
156[label="foldl (flip (deleteBy (==))) (flip (deleteBy (==)) xy9 xy10) xy11\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12646[label="xy11/xy110 : xy111",fontsize=10,color="white",style="solid",shape="box"];156 -> 12646[label="",style="solid", color="burlywood", weight=9];
12646 -> 162[label="",style="solid", color="burlywood", weight=3];
12647[label="xy11/[]",fontsize=10,color="white",style="solid",shape="box"];156 -> 12647[label="",style="solid", color="burlywood", weight=9];
12647 -> 163[label="",style="solid", color="burlywood", weight=3];
28[label="nubByNubBy'1 (==) xy40 xy41 [] (elem_by (==) xy40 [])",fontsize=16,color="black",shape="box"];28 -> 33[label="",style="solid", color="black", weight=3];
29[label="[]",fontsize=16,color="green",shape="box"];161[label="xy81\n  Eq a",fontsize=16,color="green",shape="box"];162[label="foldl (flip (deleteBy (==))) (flip (deleteBy (==)) xy9 xy10) (xy110 : xy111)\n  Eq a",fontsize=16,color="black",shape="box"];162 -> 172[label="",style="solid", color="black", weight=3];
163[label="foldl (flip (deleteBy (==))) (flip (deleteBy (==)) xy9 xy10) []\n  Eq a",fontsize=16,color="black",shape="box"];163 -> 173[label="",style="solid", color="black", weight=3];
33[label="nubByNubBy'1 (==) xy40 xy41 [] False",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
172 -> 156[label="",style="dashed", color="red", weight=0];
172[label="foldl (flip (deleteBy (==))) (flip (deleteBy (==)) (flip (deleteBy (==)) xy9 xy10) xy110) xy111\n  Eq a",fontsize=16,color="magenta"];172 -> 188[label="",style="dashed", color="magenta", weight=3];
172 -> 189[label="",style="dashed", color="magenta", weight=3];
172 -> 190[label="",style="dashed", color="magenta", weight=3];
173[label="flip (deleteBy (==)) xy9 xy10\n  Eq a",fontsize=16,color="black",shape="triangle"];173 -> 191[label="",style="solid", color="black", weight=3];
37[label="nubByNubBy'0 (==) xy40 xy41 [] otherwise",fontsize=16,color="black",shape="box"];37 -> 42[label="",style="solid", color="black", weight=3];
188[label="xy111\n  Eq a",fontsize=16,color="green",shape="box"];189 -> 173[label="",style="dashed", color="red", weight=0];
189[label="flip (deleteBy (==)) xy9 xy10\n  Eq a",fontsize=16,color="magenta"];190[label="xy110\n  Eq a",fontsize=16,color="green",shape="box"];191[label="deleteBy (==) xy10 xy9\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12650[label="xy9/xy90 : xy91",fontsize=10,color="white",style="solid",shape="box"];191 -> 12650[label="",style="solid", color="burlywood", weight=9];
12650 -> 206[label="",style="solid", color="burlywood", weight=3];
12651[label="xy9/[]",fontsize=10,color="white",style="solid",shape="box"];191 -> 12651[label="",style="solid", color="burlywood", weight=9];
12651 -> 207[label="",style="solid", color="burlywood", weight=3];
42[label="nubByNubBy'0 (==) xy40 xy41 [] True",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
206[label="deleteBy (==) xy10 (xy90 : xy91)\n  Eq a",fontsize=16,color="black",shape="box"];206 -> 224[label="",style="solid", color="black", weight=3];
207[label="deleteBy (==) xy10 []\n  Eq a",fontsize=16,color="black",shape="box"];207 -> 225[label="",style="solid", color="black", weight=3];
49[label="xy40 : nubByNubBy' (==) xy41 (xy40 : [])",fontsize=16,color="green",shape="box"];49 -> 54[label="",style="dashed", color="green", weight=3];
224 -> 246[label="",style="dashed", color="red", weight=0];
224[label="deleteBy0 xy91 xy90 (==) xy10 ((==) xy10 xy90)\n  Eq a",fontsize=16,color="magenta"];224 -> 247[label="",style="dashed", color="magenta", weight=3];
224 -> 248[label="",style="dashed", color="magenta", weight=3];
224 -> 249[label="",style="dashed", color="magenta", weight=3];
224 -> 250[label="",style="dashed", color="magenta", weight=3];
225[label="[]\n  Eq a",fontsize=16,color="green",shape="box"];54 -> 10684[label="",style="dashed", color="red", weight=0];
54[label="nubByNubBy' (==) xy41 (xy40 : [])",fontsize=16,color="magenta"];54 -> 10685[label="",style="dashed", color="magenta", weight=3];
54 -> 10686[label="",style="dashed", color="magenta", weight=3];
54 -> 10687[label="",style="dashed", color="magenta", weight=3];
247[label="(==) xy10 xy90\n  Eq a",fontsize=16,color="blue",shape="box"];12654[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12654[label="",style="solid", color="blue", weight=9];
12654 -> 251[label="",style="solid", color="blue", weight=3];
12655[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12655[label="",style="solid", color="blue", weight=9];
12655 -> 252[label="",style="solid", color="blue", weight=3];
12656[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12656[label="",style="solid", color="blue", weight=9];
12656 -> 253[label="",style="solid", color="blue", weight=3];
12657[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12657[label="",style="solid", color="blue", weight=9];
12657 -> 254[label="",style="solid", color="blue", weight=3];
12658[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12658[label="",style="solid", color="blue", weight=9];
12658 -> 255[label="",style="solid", color="blue", weight=3];
12659[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12659[label="",style="solid", color="blue", weight=9];
12659 -> 256[label="",style="solid", color="blue", weight=3];
12660[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12660[label="",style="solid", color="blue", weight=9];
12660 -> 257[label="",style="solid", color="blue", weight=3];
12661[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12661[label="",style="solid", color="blue", weight=9];
12661 -> 258[label="",style="solid", color="blue", weight=3];
12662[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12662[label="",style="solid", color="blue", weight=9];
12662 -> 259[label="",style="solid", color="blue", weight=3];
12663[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12663[label="",style="solid", color="blue", weight=9];
12663 -> 260[label="",style="solid", color="blue", weight=3];
12664[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12664[label="",style="solid", color="blue", weight=9];
12664 -> 261[label="",style="solid", color="blue", weight=3];
12665[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12665[label="",style="solid", color="blue", weight=9];
12665 -> 262[label="",style="solid", color="blue", weight=3];
12666[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12666[label="",style="solid", color="blue", weight=9];
12666 -> 263[label="",style="solid", color="blue", weight=3];
12667[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];247 -> 12667[label="",style="solid", color="blue", weight=9];
12667 -> 264[label="",style="solid", color="blue", weight=3];
248[label="xy91\n  Eq a",fontsize=16,color="green",shape="box"];249[label="xy10\n  Eq a",fontsize=16,color="green",shape="box"];250[label="xy90\n  Eq a",fontsize=16,color="green",shape="box"];246[label="deleteBy0 xy17 xy18 (==) xy19 xy20\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12668[label="xy20/False",fontsize=10,color="white",style="solid",shape="box"];246 -> 12668[label="",style="solid", color="burlywood", weight=9];
12668 -> 265[label="",style="solid", color="burlywood", weight=3];
12669[label="xy20/True",fontsize=10,color="white",style="solid",shape="box"];246 -> 12669[label="",style="solid", color="burlywood", weight=9];
12669 -> 266[label="",style="solid", color="burlywood", weight=3];
10685[label="xy40",fontsize=16,color="green",shape="box"];10686[label="[]",fontsize=16,color="green",shape="box"];10687[label="xy41",fontsize=16,color="green",shape="box"];10684[label="nubByNubBy' (==) xy827 (xy828 : xy829)\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12670[label="xy827/xy8270 : xy8271",fontsize=10,color="white",style="solid",shape="box"];10684 -> 12670[label="",style="solid", color="burlywood", weight=9];
12670 -> 12137[label="",style="solid", color="burlywood", weight=3];
12671[label="xy827/[]",fontsize=10,color="white",style="solid",shape="box"];10684 -> 12671[label="",style="solid", color="burlywood", weight=9];
12671 -> 12138[label="",style="solid", color="burlywood", weight=3];
251[label="(==) xy10 xy90\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="triangle"];251 -> 291[label="",style="solid", color="black", weight=3];
252[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];252 -> 292[label="",style="solid", color="black", weight=3];
253[label="(==) xy10 xy90\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];12672[label="xy10/xy100 :% xy101",fontsize=10,color="white",style="solid",shape="box"];253 -> 12672[label="",style="solid", color="burlywood", weight=9];
12672 -> 293[label="",style="solid", color="burlywood", weight=3];
254[label="(==) xy10 xy90\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];254 -> 294[label="",style="solid", color="black", weight=3];
255[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];255 -> 295[label="",style="solid", color="black", weight=3];
256[label="(==) xy10 xy90\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];256 -> 296[label="",style="solid", color="black", weight=3];
257[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];257 -> 297[label="",style="solid", color="black", weight=3];
258[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];258 -> 298[label="",style="solid", color="black", weight=3];
259[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];259 -> 299[label="",style="solid", color="black", weight=3];
260[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];260 -> 300[label="",style="solid", color="black", weight=3];
261[label="(==) xy10 xy90\n  Eq a",fontsize=16,color="black",shape="triangle"];261 -> 301[label="",style="solid", color="black", weight=3];
262[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];262 -> 302[label="",style="solid", color="black", weight=3];
263[label="(==) xy10 xy90\n  Eq a",fontsize=16,color="black",shape="triangle"];263 -> 303[label="",style="solid", color="black", weight=3];
264[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];264 -> 304[label="",style="solid", color="black", weight=3];
265[label="deleteBy0 xy17 xy18 (==) xy19 False\n  Eq a",fontsize=16,color="black",shape="box"];265 -> 305[label="",style="solid", color="black", weight=3];
266[label="deleteBy0 xy17 xy18 (==) xy19 True\n  Eq a",fontsize=16,color="black",shape="box"];266 -> 306[label="",style="solid", color="black", weight=3];
12137[label="nubByNubBy' (==) (xy8270 : xy8271) (xy828 : xy829)\n  Eq a",fontsize=16,color="black",shape="box"];12137 -> 12139[label="",style="solid", color="black", weight=3];
12138[label="nubByNubBy' (==) [] (xy828 : xy829)\n  Eq a",fontsize=16,color="black",shape="box"];12138 -> 12140[label="",style="solid", color="black", weight=3];
291[label="error []",fontsize=16,color="red",shape="box"];292[label="error []",fontsize=16,color="red",shape="box"];293[label="(==) xy100 :% xy101 xy90\n  Integral a",fontsize=16,color="burlywood",shape="box"];12673[label="xy90/xy900 :% xy901",fontsize=10,color="white",style="solid",shape="box"];293 -> 12673[label="",style="solid", color="burlywood", weight=9];
12673 -> 309[label="",style="solid", color="burlywood", weight=3];
294[label="error []",fontsize=16,color="red",shape="box"];295[label="error []",fontsize=16,color="red",shape="box"];296[label="error []",fontsize=16,color="red",shape="box"];297[label="error []",fontsize=16,color="red",shape="box"];298[label="error []",fontsize=16,color="red",shape="box"];299[label="error []",fontsize=16,color="red",shape="box"];300[label="error []",fontsize=16,color="red",shape="box"];301[label="error []",fontsize=16,color="red",shape="box"];302[label="primEqInt xy10 xy90",fontsize=16,color="burlywood",shape="box"];12674[label="xy10/Pos xy100",fontsize=10,color="white",style="solid",shape="box"];302 -> 12674[label="",style="solid", color="burlywood", weight=9];
12674 -> 310[label="",style="solid", color="burlywood", weight=3];
12675[label="xy10/Neg xy100",fontsize=10,color="white",style="solid",shape="box"];302 -> 12675[label="",style="solid", color="burlywood", weight=9];
12675 -> 311[label="",style="solid", color="burlywood", weight=3];
303[label="error []",fontsize=16,color="red",shape="box"];304[label="error []",fontsize=16,color="red",shape="box"];305[label="xy18 : deleteBy (==) xy19 xy17\n  Eq a",fontsize=16,color="green",shape="box"];305 -> 312[label="",style="dashed", color="green", weight=3];
306[label="xy17\n  Eq a",fontsize=16,color="green",shape="box"];12139[label="nubByNubBy'2 (==) (xy8270 : xy8271) (xy828 : xy829)\n  Eq a",fontsize=16,color="black",shape="box"];12139 -> 12141[label="",style="solid", color="black", weight=3];
12140[label="nubByNubBy'3 (==) [] (xy828 : xy829)\n  Eq a",fontsize=16,color="black",shape="box"];12140 -> 12142[label="",style="solid", color="black", weight=3];
309[label="(==) xy100 :% xy101 xy900 :% xy901\n  Integral a",fontsize=16,color="black",shape="box"];309 -> 315[label="",style="solid", color="black", weight=3];
310[label="primEqInt (Pos xy100) xy90",fontsize=16,color="burlywood",shape="box"];12676[label="xy100/Succ xy1000",fontsize=10,color="white",style="solid",shape="box"];310 -> 12676[label="",style="solid", color="burlywood", weight=9];
12676 -> 316[label="",style="solid", color="burlywood", weight=3];
12677[label="xy100/Zero",fontsize=10,color="white",style="solid",shape="box"];310 -> 12677[label="",style="solid", color="burlywood", weight=9];
12677 -> 317[label="",style="solid", color="burlywood", weight=3];
311[label="primEqInt (Neg xy100) xy90",fontsize=16,color="burlywood",shape="box"];12678[label="xy100/Succ xy1000",fontsize=10,color="white",style="solid",shape="box"];311 -> 12678[label="",style="solid", color="burlywood", weight=9];
12678 -> 318[label="",style="solid", color="burlywood", weight=3];
12679[label="xy100/Zero",fontsize=10,color="white",style="solid",shape="box"];311 -> 12679[label="",style="solid", color="burlywood", weight=9];
12679 -> 319[label="",style="solid", color="burlywood", weight=3];
312 -> 191[label="",style="dashed", color="red", weight=0];
312[label="deleteBy (==) xy19 xy17\n  Eq a",fontsize=16,color="magenta"];312 -> 320[label="",style="dashed", color="magenta", weight=3];
312 -> 321[label="",style="dashed", color="magenta", weight=3];
12141[label="nubByNubBy'1 (==) xy8270 xy8271 (xy828 : xy829) (elem_by (==) xy8270 (xy828 : xy829))\n  Eq a",fontsize=16,color="black",shape="box"];12141 -> 12143[label="",style="solid", color="black", weight=3];
12142[label="[]\n  Eq a",fontsize=16,color="green",shape="box"];315 -> 324[label="",style="dashed", color="red", weight=0];
315[label="xy100 == xy900 && xy101 == xy901\n  Integral a",fontsize=16,color="magenta"];315 -> 325[label="",style="dashed", color="magenta", weight=3];
315 -> 326[label="",style="dashed", color="magenta", weight=3];
315 -> 327[label="",style="dashed", color="magenta", weight=3];
316[label="primEqInt (Pos (Succ xy1000)) xy90",fontsize=16,color="burlywood",shape="box"];12682[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];316 -> 12682[label="",style="solid", color="burlywood", weight=9];
12682 -> 328[label="",style="solid", color="burlywood", weight=3];
12683[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];316 -> 12683[label="",style="solid", color="burlywood", weight=9];
12683 -> 329[label="",style="solid", color="burlywood", weight=3];
317[label="primEqInt (Pos Zero) xy90",fontsize=16,color="burlywood",shape="box"];12684[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];317 -> 12684[label="",style="solid", color="burlywood", weight=9];
12684 -> 330[label="",style="solid", color="burlywood", weight=3];
12685[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];317 -> 12685[label="",style="solid", color="burlywood", weight=9];
12685 -> 331[label="",style="solid", color="burlywood", weight=3];
318[label="primEqInt (Neg (Succ xy1000)) xy90",fontsize=16,color="burlywood",shape="box"];12686[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];318 -> 12686[label="",style="solid", color="burlywood", weight=9];
12686 -> 332[label="",style="solid", color="burlywood", weight=3];
12687[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];318 -> 12687[label="",style="solid", color="burlywood", weight=9];
12687 -> 333[label="",style="solid", color="burlywood", weight=3];
319[label="primEqInt (Neg Zero) xy90",fontsize=16,color="burlywood",shape="box"];12688[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];319 -> 12688[label="",style="solid", color="burlywood", weight=9];
12688 -> 334[label="",style="solid", color="burlywood", weight=3];
12689[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];319 -> 12689[label="",style="solid", color="burlywood", weight=9];
12689 -> 335[label="",style="solid", color="burlywood", weight=3];
320[label="xy17\n  Eq a",fontsize=16,color="green",shape="box"];321[label="xy19\n  Eq a",fontsize=16,color="green",shape="box"];12143 -> 12519[label="",style="dashed", color="red", weight=0];
12143[label="nubByNubBy'1 (==) xy8270 xy8271 (xy828 : xy829) ((==) xy828 xy8270 || elem_by (==) xy8270 xy829)\n  Eq a",fontsize=16,color="magenta"];12143 -> 12520[label="",style="dashed", color="magenta", weight=3];
12143 -> 12521[label="",style="dashed", color="magenta", weight=3];
12143 -> 12522[label="",style="dashed", color="magenta", weight=3];
12143 -> 12523[label="",style="dashed", color="magenta", weight=3];
12143 -> 12524[label="",style="dashed", color="magenta", weight=3];
12143 -> 12525[label="",style="dashed", color="magenta", weight=3];
325[label="xy901\n  Integral a",fontsize=16,color="green",shape="box"];326[label="xy100 == xy900\n  Integral a",fontsize=16,color="blue",shape="box"];12691[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];326 -> 12691[label="",style="solid", color="blue", weight=9];
12691 -> 336[label="",style="solid", color="blue", weight=3];
12692[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];326 -> 12692[label="",style="solid", color="blue", weight=9];
12692 -> 337[label="",style="solid", color="blue", weight=3];
327[label="xy101\n  Integral a",fontsize=16,color="green",shape="box"];324[label="xy28 && xy29 == xy30\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12693[label="xy28/False",fontsize=10,color="white",style="solid",shape="box"];324 -> 12693[label="",style="solid", color="burlywood", weight=9];
12693 -> 338[label="",style="solid", color="burlywood", weight=3];
12694[label="xy28/True",fontsize=10,color="white",style="solid",shape="box"];324 -> 12694[label="",style="solid", color="burlywood", weight=9];
12694 -> 339[label="",style="solid", color="burlywood", weight=3];
328[label="primEqInt (Pos (Succ xy1000)) (Pos xy900)",fontsize=16,color="burlywood",shape="box"];12695[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];328 -> 12695[label="",style="solid", color="burlywood", weight=9];
12695 -> 342[label="",style="solid", color="burlywood", weight=3];
12696[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];328 -> 12696[label="",style="solid", color="burlywood", weight=9];
12696 -> 343[label="",style="solid", color="burlywood", weight=3];
329[label="primEqInt (Pos (Succ xy1000)) (Neg xy900)",fontsize=16,color="black",shape="box"];329 -> 344[label="",style="solid", color="black", weight=3];
330[label="primEqInt (Pos Zero) (Pos xy900)",fontsize=16,color="burlywood",shape="box"];12697[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];330 -> 12697[label="",style="solid", color="burlywood", weight=9];
12697 -> 345[label="",style="solid", color="burlywood", weight=3];
12698[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];330 -> 12698[label="",style="solid", color="burlywood", weight=9];
12698 -> 346[label="",style="solid", color="burlywood", weight=3];
331[label="primEqInt (Pos Zero) (Neg xy900)",fontsize=16,color="burlywood",shape="box"];12699[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];331 -> 12699[label="",style="solid", color="burlywood", weight=9];
12699 -> 347[label="",style="solid", color="burlywood", weight=3];
12700[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];331 -> 12700[label="",style="solid", color="burlywood", weight=9];
12700 -> 348[label="",style="solid", color="burlywood", weight=3];
332[label="primEqInt (Neg (Succ xy1000)) (Pos xy900)",fontsize=16,color="black",shape="box"];332 -> 349[label="",style="solid", color="black", weight=3];
333[label="primEqInt (Neg (Succ xy1000)) (Neg xy900)",fontsize=16,color="burlywood",shape="box"];12701[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];333 -> 12701[label="",style="solid", color="burlywood", weight=9];
12701 -> 350[label="",style="solid", color="burlywood", weight=3];
12702[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];333 -> 12702[label="",style="solid", color="burlywood", weight=9];
12702 -> 351[label="",style="solid", color="burlywood", weight=3];
334[label="primEqInt (Neg Zero) (Pos xy900)",fontsize=16,color="burlywood",shape="box"];12703[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];334 -> 12703[label="",style="solid", color="burlywood", weight=9];
12703 -> 352[label="",style="solid", color="burlywood", weight=3];
12704[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];334 -> 12704[label="",style="solid", color="burlywood", weight=9];
12704 -> 353[label="",style="solid", color="burlywood", weight=3];
335[label="primEqInt (Neg Zero) (Neg xy900)",fontsize=16,color="burlywood",shape="box"];12705[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];335 -> 12705[label="",style="solid", color="burlywood", weight=9];
12705 -> 354[label="",style="solid", color="burlywood", weight=3];
12706[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];335 -> 12706[label="",style="solid", color="burlywood", weight=9];
12706 -> 355[label="",style="solid", color="burlywood", weight=3];
12520[label="xy829\n  Eq a",fontsize=16,color="green",shape="box"];12521[label="(==) xy828 xy8270\n  Eq a",fontsize=16,color="blue",shape="box"];12707[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12707[label="",style="solid", color="blue", weight=9];
12707 -> 12532[label="",style="solid", color="blue", weight=3];
12708[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12708[label="",style="solid", color="blue", weight=9];
12708 -> 12533[label="",style="solid", color="blue", weight=3];
12709[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12709[label="",style="solid", color="blue", weight=9];
12709 -> 12534[label="",style="solid", color="blue", weight=3];
12710[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12710[label="",style="solid", color="blue", weight=9];
12710 -> 12535[label="",style="solid", color="blue", weight=3];
12711[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12711[label="",style="solid", color="blue", weight=9];
12711 -> 12536[label="",style="solid", color="blue", weight=3];
12712[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12712[label="",style="solid", color="blue", weight=9];
12712 -> 12537[label="",style="solid", color="blue", weight=3];
12713[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12713[label="",style="solid", color="blue", weight=9];
12713 -> 12538[label="",style="solid", color="blue", weight=3];
12714[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12714[label="",style="solid", color="blue", weight=9];
12714 -> 12539[label="",style="solid", color="blue", weight=3];
12715[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12715[label="",style="solid", color="blue", weight=9];
12715 -> 12540[label="",style="solid", color="blue", weight=3];
12716[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12716[label="",style="solid", color="blue", weight=9];
12716 -> 12541[label="",style="solid", color="blue", weight=3];
12717[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12717[label="",style="solid", color="blue", weight=9];
12717 -> 12542[label="",style="solid", color="blue", weight=3];
12718[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12718[label="",style="solid", color="blue", weight=9];
12718 -> 12543[label="",style="solid", color="blue", weight=3];
12719[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12719[label="",style="solid", color="blue", weight=9];
12719 -> 12544[label="",style="solid", color="blue", weight=3];
12720[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];12521 -> 12720[label="",style="solid", color="blue", weight=9];
12720 -> 12545[label="",style="solid", color="blue", weight=3];
12522[label="xy8271\n  Eq a",fontsize=16,color="green",shape="box"];12523[label="xy828\n  Eq a",fontsize=16,color="green",shape="box"];12524[label="xy829\n  Eq a",fontsize=16,color="green",shape="box"];12525[label="xy8270\n  Eq a",fontsize=16,color="green",shape="box"];12519[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) (xy923 || elem_by (==) xy919 xy924)\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];12721[label="xy923/False",fontsize=10,color="white",style="solid",shape="box"];12519 -> 12721[label="",style="solid", color="burlywood", weight=9];
12721 -> 12546[label="",style="solid", color="burlywood", weight=3];
12722[label="xy923/True",fontsize=10,color="white",style="solid",shape="box"];12519 -> 12722[label="",style="solid", color="burlywood", weight=9];
12722 -> 12547[label="",style="solid", color="burlywood", weight=3];
336 -> 255[label="",style="dashed", color="red", weight=0];
336[label="xy100 == xy900",fontsize=16,color="magenta"];336 -> 356[label="",style="dashed", color="magenta", weight=3];
336 -> 357[label="",style="dashed", color="magenta", weight=3];
337 -> 262[label="",style="dashed", color="red", weight=0];
337[label="xy100 == xy900",fontsize=16,color="magenta"];337 -> 358[label="",style="dashed", color="magenta", weight=3];
337 -> 359[label="",style="dashed", color="magenta", weight=3];
338[label="False && xy29 == xy30\n  Eq a",fontsize=16,color="black",shape="box"];338 -> 360[label="",style="solid", color="black", weight=3];
339[label="True && xy29 == xy30\n  Eq a",fontsize=16,color="black",shape="box"];339 -> 361[label="",style="solid", color="black", weight=3];
342[label="primEqInt (Pos (Succ xy1000)) (Pos (Succ xy9000))",fontsize=16,color="black",shape="box"];342 -> 377[label="",style="solid", color="black", weight=3];
343[label="primEqInt (Pos (Succ xy1000)) (Pos Zero)",fontsize=16,color="black",shape="box"];343 -> 378[label="",style="solid", color="black", weight=3];
344[label="False",fontsize=16,color="green",shape="box"];345[label="primEqInt (Pos Zero) (Pos (Succ xy9000))",fontsize=16,color="black",shape="box"];345 -> 379[label="",style="solid", color="black", weight=3];
346[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];346 -> 380[label="",style="solid", color="black", weight=3];
347[label="primEqInt (Pos Zero) (Neg (Succ xy9000))",fontsize=16,color="black",shape="box"];347 -> 381[label="",style="solid", color="black", weight=3];
348[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];348 -> 382[label="",style="solid", color="black", weight=3];
349[label="False",fontsize=16,color="green",shape="box"];350[label="primEqInt (Neg (Succ xy1000)) (Neg (Succ xy9000))",fontsize=16,color="black",shape="box"];350 -> 383[label="",style="solid", color="black", weight=3];
351[label="primEqInt (Neg (Succ xy1000)) (Neg Zero)",fontsize=16,color="black",shape="box"];351 -> 384[label="",style="solid", color="black", weight=3];
352[label="primEqInt (Neg Zero) (Pos (Succ xy9000))",fontsize=16,color="black",shape="box"];352 -> 385[label="",style="solid", color="black", weight=3];
353[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];353 -> 386[label="",style="solid", color="black", weight=3];
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12533[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12533 -> 12550[label="",style="dashed", color="magenta", weight=3];
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12537[label="(==) xy828 xy8270\n  Eq a  Eq b",fontsize=16,color="magenta"];12537 -> 12558[label="",style="dashed", color="magenta", weight=3];
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12538[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12538 -> 12560[label="",style="dashed", color="magenta", weight=3];
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12539[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12539 -> 12562[label="",style="dashed", color="magenta", weight=3];
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12540[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12540 -> 12564[label="",style="dashed", color="magenta", weight=3];
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12541[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12541 -> 12566[label="",style="dashed", color="magenta", weight=3];
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12542 -> 261[label="",style="dashed", color="red", weight=0];
12542[label="(==) xy828 xy8270\n  Eq a",fontsize=16,color="magenta"];12542 -> 12568[label="",style="dashed", color="magenta", weight=3];
12542 -> 12569[label="",style="dashed", color="magenta", weight=3];
12543 -> 262[label="",style="dashed", color="red", weight=0];
12543[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12543 -> 12570[label="",style="dashed", color="magenta", weight=3];
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12544 -> 263[label="",style="dashed", color="red", weight=0];
12544[label="(==) xy828 xy8270\n  Eq a",fontsize=16,color="magenta"];12544 -> 12572[label="",style="dashed", color="magenta", weight=3];
12544 -> 12573[label="",style="dashed", color="magenta", weight=3];
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12545[label="(==) xy828 xy8270",fontsize=16,color="magenta"];12545 -> 12574[label="",style="dashed", color="magenta", weight=3];
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12546[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) (False || elem_by (==) xy919 xy924)\n  Eq a",fontsize=16,color="black",shape="box"];12546 -> 12576[label="",style="solid", color="black", weight=3];
12547[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) (True || elem_by (==) xy919 xy924)\n  Eq a",fontsize=16,color="black",shape="box"];12547 -> 12577[label="",style="solid", color="black", weight=3];
356[label="xy900",fontsize=16,color="green",shape="box"];357[label="xy100",fontsize=16,color="green",shape="box"];358[label="xy900",fontsize=16,color="green",shape="box"];359[label="xy100",fontsize=16,color="green",shape="box"];360[label="False",fontsize=16,color="green",shape="box"];361[label="xy29 == xy30\n  Eq a",fontsize=16,color="blue",shape="box"];12739[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12739[label="",style="solid", color="blue", weight=9];
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12740[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12740[label="",style="solid", color="blue", weight=9];
12740 -> 390[label="",style="solid", color="blue", weight=3];
12741[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12741[label="",style="solid", color="blue", weight=9];
12741 -> 391[label="",style="solid", color="blue", weight=3];
12742[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12742[label="",style="solid", color="blue", weight=9];
12742 -> 392[label="",style="solid", color="blue", weight=3];
12743[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12743[label="",style="solid", color="blue", weight=9];
12743 -> 393[label="",style="solid", color="blue", weight=3];
12744[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12744[label="",style="solid", color="blue", weight=9];
12744 -> 394[label="",style="solid", color="blue", weight=3];
12745[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12745[label="",style="solid", color="blue", weight=9];
12745 -> 395[label="",style="solid", color="blue", weight=3];
12746[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12746[label="",style="solid", color="blue", weight=9];
12746 -> 396[label="",style="solid", color="blue", weight=3];
12747[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12747[label="",style="solid", color="blue", weight=9];
12747 -> 397[label="",style="solid", color="blue", weight=3];
12748[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12748[label="",style="solid", color="blue", weight=9];
12748 -> 398[label="",style="solid", color="blue", weight=3];
12749[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12749[label="",style="solid", color="blue", weight=9];
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12750[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12750[label="",style="solid", color="blue", weight=9];
12750 -> 400[label="",style="solid", color="blue", weight=3];
12751[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12751[label="",style="solid", color="blue", weight=9];
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12752[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];361 -> 12752[label="",style="solid", color="blue", weight=9];
12752 -> 402[label="",style="solid", color="blue", weight=3];
377[label="primEqNat xy1000 xy9000",fontsize=16,color="burlywood",shape="triangle"];12753[label="xy1000/Succ xy10000",fontsize=10,color="white",style="solid",shape="box"];377 -> 12753[label="",style="solid", color="burlywood", weight=9];
12753 -> 405[label="",style="solid", color="burlywood", weight=3];
12754[label="xy1000/Zero",fontsize=10,color="white",style="solid",shape="box"];377 -> 12754[label="",style="solid", color="burlywood", weight=9];
12754 -> 406[label="",style="solid", color="burlywood", weight=3];
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383[label="primEqNat xy1000 xy9000",fontsize=16,color="magenta"];383 -> 407[label="",style="dashed", color="magenta", weight=3];
383 -> 408[label="",style="dashed", color="magenta", weight=3];
384[label="False",fontsize=16,color="green",shape="box"];385[label="False",fontsize=16,color="green",shape="box"];386[label="True",fontsize=16,color="green",shape="box"];387[label="False",fontsize=16,color="green",shape="box"];388[label="True",fontsize=16,color="green",shape="box"];12548[label="xy8270\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];12549[label="xy828\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];12550[label="xy8270",fontsize=16,color="green",shape="box"];12551[label="xy828",fontsize=16,color="green",shape="box"];12552[label="xy8270\n  Integral a",fontsize=16,color="green",shape="box"];12553[label="xy828\n  Integral a",fontsize=16,color="green",shape="box"];12554[label="xy8270\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12555[label="xy828\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12556[label="xy8270",fontsize=16,color="green",shape="box"];12557[label="xy828",fontsize=16,color="green",shape="box"];12558[label="xy8270\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12559[label="xy828\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12560[label="xy8270",fontsize=16,color="green",shape="box"];12561[label="xy828",fontsize=16,color="green",shape="box"];12562[label="xy8270",fontsize=16,color="green",shape="box"];12563[label="xy828",fontsize=16,color="green",shape="box"];12564[label="xy8270",fontsize=16,color="green",shape="box"];12565[label="xy828",fontsize=16,color="green",shape="box"];12566[label="xy8270",fontsize=16,color="green",shape="box"];12567[label="xy828",fontsize=16,color="green",shape="box"];12568[label="xy8270\n  Eq a",fontsize=16,color="green",shape="box"];12569[label="xy828\n  Eq a",fontsize=16,color="green",shape="box"];12570[label="xy8270",fontsize=16,color="green",shape="box"];12571[label="xy828",fontsize=16,color="green",shape="box"];12572[label="xy8270\n  Eq a",fontsize=16,color="green",shape="box"];12573[label="xy828\n  Eq a",fontsize=16,color="green",shape="box"];12574[label="xy8270",fontsize=16,color="green",shape="box"];12575[label="xy828",fontsize=16,color="green",shape="box"];12576[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) (elem_by (==) xy919 xy924)\n  Eq a",fontsize=16,color="burlywood",shape="box"];12756[label="xy924/xy9240 : xy9241",fontsize=10,color="white",style="solid",shape="box"];12576 -> 12756[label="",style="solid", color="burlywood", weight=9];
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12757[label="xy924/[]",fontsize=10,color="white",style="solid",shape="box"];12576 -> 12757[label="",style="solid", color="burlywood", weight=9];
12757 -> 12579[label="",style="solid", color="burlywood", weight=3];
12577[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) True\n  Eq a",fontsize=16,color="black",shape="box"];12577 -> 12580[label="",style="solid", color="black", weight=3];
389 -> 251[label="",style="dashed", color="red", weight=0];
389[label="xy29 == xy30\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];389 -> 409[label="",style="dashed", color="magenta", weight=3];
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390[label="xy29 == xy30",fontsize=16,color="magenta"];390 -> 411[label="",style="dashed", color="magenta", weight=3];
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391[label="xy29 == xy30\n  Integral a",fontsize=16,color="magenta"];391 -> 413[label="",style="dashed", color="magenta", weight=3];
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393[label="xy29 == xy30",fontsize=16,color="magenta"];393 -> 417[label="",style="dashed", color="magenta", weight=3];
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396[label="xy29 == xy30",fontsize=16,color="magenta"];396 -> 423[label="",style="dashed", color="magenta", weight=3];
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397 -> 259[label="",style="dashed", color="red", weight=0];
397[label="xy29 == xy30",fontsize=16,color="magenta"];397 -> 425[label="",style="dashed", color="magenta", weight=3];
397 -> 426[label="",style="dashed", color="magenta", weight=3];
398 -> 260[label="",style="dashed", color="red", weight=0];
398[label="xy29 == xy30",fontsize=16,color="magenta"];398 -> 427[label="",style="dashed", color="magenta", weight=3];
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399 -> 261[label="",style="dashed", color="red", weight=0];
399[label="xy29 == xy30\n  Eq a",fontsize=16,color="magenta"];399 -> 429[label="",style="dashed", color="magenta", weight=3];
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400[label="xy29 == xy30",fontsize=16,color="magenta"];400 -> 431[label="",style="dashed", color="magenta", weight=3];
400 -> 432[label="",style="dashed", color="magenta", weight=3];
401 -> 263[label="",style="dashed", color="red", weight=0];
401[label="xy29 == xy30\n  Eq a",fontsize=16,color="magenta"];401 -> 433[label="",style="dashed", color="magenta", weight=3];
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402 -> 264[label="",style="dashed", color="red", weight=0];
402[label="xy29 == xy30",fontsize=16,color="magenta"];402 -> 435[label="",style="dashed", color="magenta", weight=3];
402 -> 436[label="",style="dashed", color="magenta", weight=3];
405[label="primEqNat (Succ xy10000) xy9000",fontsize=16,color="burlywood",shape="box"];12772[label="xy9000/Succ xy90000",fontsize=10,color="white",style="solid",shape="box"];405 -> 12772[label="",style="solid", color="burlywood", weight=9];
12772 -> 439[label="",style="solid", color="burlywood", weight=3];
12773[label="xy9000/Zero",fontsize=10,color="white",style="solid",shape="box"];405 -> 12773[label="",style="solid", color="burlywood", weight=9];
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406[label="primEqNat Zero xy9000",fontsize=16,color="burlywood",shape="box"];12774[label="xy9000/Succ xy90000",fontsize=10,color="white",style="solid",shape="box"];406 -> 12774[label="",style="solid", color="burlywood", weight=9];
12774 -> 441[label="",style="solid", color="burlywood", weight=3];
12775[label="xy9000/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 12775[label="",style="solid", color="burlywood", weight=9];
12775 -> 442[label="",style="solid", color="burlywood", weight=3];
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12580 -> 10684[label="",style="dashed", color="red", weight=0];
12580[label="nubByNubBy' (==) xy920 (xy921 : xy922)\n  Eq a",fontsize=16,color="magenta"];12580 -> 12583[label="",style="dashed", color="magenta", weight=3];
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12580 -> 12585[label="",style="dashed", color="magenta", weight=3];
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441[label="primEqNat Zero (Succ xy90000)",fontsize=16,color="black",shape="box"];441 -> 447[label="",style="solid", color="black", weight=3];
442[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];442 -> 448[label="",style="solid", color="black", weight=3];
12581 -> 12519[label="",style="dashed", color="red", weight=0];
12581[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) ((==) xy9240 xy919 || elem_by (==) xy919 xy9241)\n  Eq a",fontsize=16,color="magenta"];12581 -> 12586[label="",style="dashed", color="magenta", weight=3];
12581 -> 12587[label="",style="dashed", color="magenta", weight=3];
12582[label="nubByNubBy'1 (==) xy919 xy920 (xy921 : xy922) False\n  Eq a",fontsize=16,color="black",shape="box"];12582 -> 12588[label="",style="solid", color="black", weight=3];
12583[label="xy921\n  Eq a",fontsize=16,color="green",shape="box"];12584[label="xy922\n  Eq a",fontsize=16,color="green",shape="box"];12585[label="xy920\n  Eq a",fontsize=16,color="green",shape="box"];445 -> 377[label="",style="dashed", color="red", weight=0];
445[label="primEqNat xy10000 xy90000",fontsize=16,color="magenta"];445 -> 466[label="",style="dashed", color="magenta", weight=3];
445 -> 467[label="",style="dashed", color="magenta", weight=3];
446[label="False",fontsize=16,color="green",shape="box"];447[label="False",fontsize=16,color="green",shape="box"];448[label="True",fontsize=16,color="green",shape="box"];12586[label="(==) xy9240 xy919\n  Eq a",fontsize=16,color="blue",shape="box"];12779[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12779[label="",style="solid", color="blue", weight=9];
12779 -> 12589[label="",style="solid", color="blue", weight=3];
12780[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12780[label="",style="solid", color="blue", weight=9];
12780 -> 12590[label="",style="solid", color="blue", weight=3];
12781[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12781[label="",style="solid", color="blue", weight=9];
12781 -> 12591[label="",style="solid", color="blue", weight=3];
12782[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12782[label="",style="solid", color="blue", weight=9];
12782 -> 12592[label="",style="solid", color="blue", weight=3];
12783[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12783[label="",style="solid", color="blue", weight=9];
12783 -> 12593[label="",style="solid", color="blue", weight=3];
12784[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12784[label="",style="solid", color="blue", weight=9];
12784 -> 12594[label="",style="solid", color="blue", weight=3];
12785[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12785[label="",style="solid", color="blue", weight=9];
12785 -> 12595[label="",style="solid", color="blue", weight=3];
12786[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12786[label="",style="solid", color="blue", weight=9];
12786 -> 12596[label="",style="solid", color="blue", weight=3];
12787[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12787[label="",style="solid", color="blue", weight=9];
12787 -> 12597[label="",style="solid", color="blue", weight=3];
12788[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12788[label="",style="solid", color="blue", weight=9];
12788 -> 12598[label="",style="solid", color="blue", weight=3];
12789[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12789[label="",style="solid", color="blue", weight=9];
12789 -> 12599[label="",style="solid", color="blue", weight=3];
12790[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12790[label="",style="solid", color="blue", weight=9];
12790 -> 12600[label="",style="solid", color="blue", weight=3];
12791[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12791[label="",style="solid", color="blue", weight=9];
12791 -> 12601[label="",style="solid", color="blue", weight=3];
12792[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];12586 -> 12792[label="",style="solid", color="blue", weight=9];
12792 -> 12602[label="",style="solid", color="blue", weight=3];
12587[label="xy9241\n  Eq a",fontsize=16,color="green",shape="box"];12588[label="nubByNubBy'0 (==) xy919 xy920 (xy921 : xy922) otherwise\n  Eq a",fontsize=16,color="black",shape="box"];12588 -> 12603[label="",style="solid", color="black", weight=3];
466[label="xy90000",fontsize=16,color="green",shape="box"];467[label="xy10000",fontsize=16,color="green",shape="box"];12589 -> 251[label="",style="dashed", color="red", weight=0];
12589[label="(==) xy9240 xy919\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];12589 -> 12604[label="",style="dashed", color="magenta", weight=3];
12589 -> 12605[label="",style="dashed", color="magenta", weight=3];
12590 -> 252[label="",style="dashed", color="red", weight=0];
12590[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12590 -> 12606[label="",style="dashed", color="magenta", weight=3];
12590 -> 12607[label="",style="dashed", color="magenta", weight=3];
12591 -> 253[label="",style="dashed", color="red", weight=0];
12591[label="(==) xy9240 xy919\n  Integral a",fontsize=16,color="magenta"];12591 -> 12608[label="",style="dashed", color="magenta", weight=3];
12591 -> 12609[label="",style="dashed", color="magenta", weight=3];
12592 -> 254[label="",style="dashed", color="red", weight=0];
12592[label="(==) xy9240 xy919\n  Eq a  Eq b",fontsize=16,color="magenta"];12592 -> 12610[label="",style="dashed", color="magenta", weight=3];
12592 -> 12611[label="",style="dashed", color="magenta", weight=3];
12593 -> 255[label="",style="dashed", color="red", weight=0];
12593[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12593 -> 12612[label="",style="dashed", color="magenta", weight=3];
12593 -> 12613[label="",style="dashed", color="magenta", weight=3];
12594 -> 256[label="",style="dashed", color="red", weight=0];
12594[label="(==) xy9240 xy919\n  Eq a  Eq b",fontsize=16,color="magenta"];12594 -> 12614[label="",style="dashed", color="magenta", weight=3];
12594 -> 12615[label="",style="dashed", color="magenta", weight=3];
12595 -> 257[label="",style="dashed", color="red", weight=0];
12595[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12595 -> 12616[label="",style="dashed", color="magenta", weight=3];
12595 -> 12617[label="",style="dashed", color="magenta", weight=3];
12596 -> 258[label="",style="dashed", color="red", weight=0];
12596[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12596 -> 12618[label="",style="dashed", color="magenta", weight=3];
12596 -> 12619[label="",style="dashed", color="magenta", weight=3];
12597 -> 259[label="",style="dashed", color="red", weight=0];
12597[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12597 -> 12620[label="",style="dashed", color="magenta", weight=3];
12597 -> 12621[label="",style="dashed", color="magenta", weight=3];
12598 -> 260[label="",style="dashed", color="red", weight=0];
12598[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12598 -> 12622[label="",style="dashed", color="magenta", weight=3];
12598 -> 12623[label="",style="dashed", color="magenta", weight=3];
12599 -> 261[label="",style="dashed", color="red", weight=0];
12599[label="(==) xy9240 xy919\n  Eq a",fontsize=16,color="magenta"];12599 -> 12624[label="",style="dashed", color="magenta", weight=3];
12599 -> 12625[label="",style="dashed", color="magenta", weight=3];
12600 -> 262[label="",style="dashed", color="red", weight=0];
12600[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12600 -> 12626[label="",style="dashed", color="magenta", weight=3];
12600 -> 12627[label="",style="dashed", color="magenta", weight=3];
12601 -> 263[label="",style="dashed", color="red", weight=0];
12601[label="(==) xy9240 xy919\n  Eq a",fontsize=16,color="magenta"];12601 -> 12628[label="",style="dashed", color="magenta", weight=3];
12601 -> 12629[label="",style="dashed", color="magenta", weight=3];
12602 -> 264[label="",style="dashed", color="red", weight=0];
12602[label="(==) xy9240 xy919",fontsize=16,color="magenta"];12602 -> 12630[label="",style="dashed", color="magenta", weight=3];
12602 -> 12631[label="",style="dashed", color="magenta", weight=3];
12603[label="nubByNubBy'0 (==) xy919 xy920 (xy921 : xy922) True\n  Eq a",fontsize=16,color="black",shape="box"];12603 -> 12632[label="",style="solid", color="black", weight=3];
12604[label="xy919\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];12605[label="xy9240\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];12606[label="xy919",fontsize=16,color="green",shape="box"];12607[label="xy9240",fontsize=16,color="green",shape="box"];12608[label="xy919\n  Integral a",fontsize=16,color="green",shape="box"];12609[label="xy9240\n  Integral a",fontsize=16,color="green",shape="box"];12610[label="xy919\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12611[label="xy9240\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12612[label="xy919",fontsize=16,color="green",shape="box"];12613[label="xy9240",fontsize=16,color="green",shape="box"];12614[label="xy919\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12615[label="xy9240\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];12616[label="xy919",fontsize=16,color="green",shape="box"];12617[label="xy9240",fontsize=16,color="green",shape="box"];12618[label="xy919",fontsize=16,color="green",shape="box"];12619[label="xy9240",fontsize=16,color="green",shape="box"];12620[label="xy919",fontsize=16,color="green",shape="box"];12621[label="xy9240",fontsize=16,color="green",shape="box"];12622[label="xy919",fontsize=16,color="green",shape="box"];12623[label="xy9240",fontsize=16,color="green",shape="box"];12624[label="xy919\n  Eq a",fontsize=16,color="green",shape="box"];12625[label="xy9240\n  Eq a",fontsize=16,color="green",shape="box"];12626[label="xy919",fontsize=16,color="green",shape="box"];12627[label="xy9240",fontsize=16,color="green",shape="box"];12628[label="xy919\n  Eq a",fontsize=16,color="green",shape="box"];12629[label="xy9240\n  Eq a",fontsize=16,color="green",shape="box"];12630[label="xy919",fontsize=16,color="green",shape="box"];12631[label="xy9240",fontsize=16,color="green",shape="box"];12632[label="xy919 : nubByNubBy' (==) xy920 (xy919 : xy921 : xy922)\n  Eq a",fontsize=16,color="green",shape="box"];12632 -> 12633[label="",style="dashed", color="green", weight=3];
12633 -> 10684[label="",style="dashed", color="red", weight=0];
12633[label="nubByNubBy' (==) xy920 (xy919 : xy921 : xy922)\n  Eq a",fontsize=16,color="magenta"];12633 -> 12634[label="",style="dashed", color="magenta", weight=3];
12633 -> 12635[label="",style="dashed", color="magenta", weight=3];
12633 -> 12636[label="",style="dashed", color="magenta", weight=3];
12634[label="xy919\n  Eq a",fontsize=16,color="green",shape="box"];12635[label="xy921 : xy922\n  Eq a",fontsize=16,color="green",shape="box"];12636[label="xy920\n  Eq a",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

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

new_primEqNat(Succ(xy10000), Succ(xy90000)) → new_primEqNat(xy10000, xy90000)

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_primEqNat(Succ(xy10000), Succ(xy90000)) → new_primEqNat(xy10000, xy90000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

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

new_esEs(:%(xy100, xy101), :%(xy900, xy901), ba) → new_asAs(new_esEs0(xy100, xy900, ba), xy101, xy901, ba)
new_asAs(True, xy29, xy30, app(ty_Ratio, bb)) → new_esEs(xy29, xy30, bb)

The TRS R consists of the following rules:

new_primEqNat0(Zero, Succ(xy90000)) → False
new_primEqNat0(Succ(xy10000), Zero) → False
new_esEs1(Neg(Succ(xy1000)), Neg(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)
new_esEs0(xy100, xy900, ty_Integer) → new_esEs2(xy100, xy900)
new_esEs1(Pos(Zero), Pos(Zero)) → True
new_esEs2(xy10, xy90) → error([])
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(xy10000), Succ(xy90000)) → new_primEqNat0(xy10000, xy90000)
new_esEs1(Neg(Succ(xy1000)), Pos(xy900)) → False
new_esEs1(Pos(Succ(xy1000)), Neg(xy900)) → False
new_esEs1(Neg(Succ(xy1000)), Neg(Zero)) → False
new_esEs1(Neg(Zero), Neg(Succ(xy9000))) → False
new_esEs1(Pos(Zero), Neg(Succ(xy9000))) → False
new_esEs1(Neg(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Succ(xy1000)), Pos(Zero)) → False
new_esEs1(Neg(Zero), Neg(Zero)) → True
new_esEs1(Pos(Zero), Neg(Zero)) → True
new_esEs1(Neg(Zero), Pos(Zero)) → True
new_esEs0(xy100, xy900, ty_Int) → new_esEs1(xy100, xy900)
new_esEs1(Pos(Succ(xy1000)), Pos(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)

The set Q consists of the following terms:

new_esEs0(x0, x1, ty_Integer)
new_esEs1(Neg(Succ(x0)), Neg(Succ(x1)))
new_primEqNat0(Zero, Zero)
new_primEqNat0(Succ(x0), Zero)
new_esEs1(Pos(Succ(x0)), Neg(x1))
new_esEs1(Neg(Succ(x0)), Pos(x1))
new_esEs1(Pos(Zero), Pos(Succ(x0)))
new_primEqNat0(Zero, Succ(x0))
new_esEs1(Neg(Zero), Neg(Succ(x0)))
new_esEs1(Neg(Zero), Neg(Zero))
new_esEs1(Pos(Succ(x0)), Pos(Zero))
new_esEs1(Neg(Succ(x0)), Neg(Zero))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs2(x0, x1)
new_esEs1(Pos(Zero), Pos(Zero))
new_esEs1(Pos(Zero), Neg(Succ(x0)))
new_esEs1(Neg(Zero), Pos(Succ(x0)))
new_esEs1(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs1(Pos(Zero), Neg(Zero))
new_esEs1(Neg(Zero), Pos(Zero))
new_esEs0(x0, x1, ty_Int)

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_esEs(:%(xy100, xy101), :%(xy900, xy901), ba) → new_asAs(new_esEs0(xy100, xy900, ba), xy101, xy901, ba)
The graph contains the following edges 1 > 2, 2 > 3, 3 >= 4
new_asAs(True, xy29, xy30, app(ty_Ratio, bb)) → new_esEs(xy29, xy30, bb)
The graph contains the following edges 2 >= 1, 3 >= 2, 4 > 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

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

new_nubByNubBy'(:(xy8270, xy8271), xy828, xy829, bb) → new_nubByNubBy'1(xy8270, xy8271, xy828, xy829, new_esEs4(xy828, xy8270, bb), xy829, bb)
new_nubByNubBy'1(xy919, xy920, xy921, xy922, False, :(xy9240, xy9241), ba) → new_nubByNubBy'1(xy919, xy920, xy921, xy922, new_esEs3(xy9240, xy919, ba), xy9241, ba)
new_nubByNubBy'1(xy919, xy920, xy921, xy922, False, [], ba) → new_nubByNubBy'(xy920, xy919, :(xy921, xy922), ba)
new_nubByNubBy'1(xy919, xy920, xy921, xy922, True, xy924, ba) → new_nubByNubBy'(xy920, xy921, xy922, ba)

The TRS R consists of the following rules:

new_asAs0(False, xy29, xy30, ce) → False
new_asAs0(True, xy29, xy30, ty_Ordering) → new_esEs6(xy29, xy30)
new_asAs0(True, xy29, xy30, ty_@0) → new_esEs12(xy29, xy30)
new_esEs4(xy828, xy8270, ty_Float) → new_esEs8(xy828, xy8270)
new_asAs0(True, xy29, xy30, ty_Int) → new_esEs1(xy29, xy30)
new_esEs3(xy9240, xy919, ty_Ordering) → new_esEs6(xy9240, xy919)
new_primEqNat0(Zero, Zero) → True
new_esEs16(xy10, xy90) → error([])
new_esEs1(Pos(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Succ(xy1000)), Pos(Zero)) → False
new_esEs3(xy9240, xy919, ty_@0) → new_esEs12(xy9240, xy919)
new_esEs13(xy10, xy90) → error([])
new_esEs4(xy828, xy8270, ty_Bool) → new_esEs16(xy828, xy8270)
new_esEs3(xy9240, xy919, app(ty_Maybe, gd)) → new_esEs14(xy9240, xy919, gd)
new_esEs3(xy9240, xy919, ty_Integer) → new_esEs2(xy9240, xy919)
new_esEs12(xy10, xy90) → error([])
new_asAs0(True, xy29, xy30, app(ty_[], dh)) → new_esEs15(xy29, xy30, dh)
new_primEqNat0(Zero, Succ(xy90000)) → False
new_primEqNat0(Succ(xy10000), Zero) → False
new_esEs1(Neg(Succ(xy1000)), Neg(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)
new_asAs0(True, xy29, xy30, ty_Char) → new_esEs13(xy29, xy30)
new_esEs3(xy9240, xy919, app(ty_[], ge)) → new_esEs15(xy9240, xy919, ge)
new_esEs4(xy828, xy8270, app(app(ty_@2, bg), bh)) → new_esEs10(xy828, xy8270, bg, bh)
new_esEs4(xy828, xy8270, app(ty_Ratio, bf)) → new_esEs9(xy828, xy8270, bf)
new_esEs14(xy10, xy90, eb) → error([])
new_esEs4(xy828, xy8270, app(app(ty_Either, ca), cb)) → new_esEs11(xy828, xy8270, ca, cb)
new_asAs0(True, xy29, xy30, ty_Bool) → new_esEs16(xy29, xy30)
new_esEs3(xy9240, xy919, ty_Float) → new_esEs8(xy9240, xy919)
new_esEs4(xy828, xy8270, ty_Double) → new_esEs5(xy828, xy8270)
new_esEs4(xy828, xy8270, ty_@0) → new_esEs12(xy828, xy8270)
new_esEs11(xy10, xy90, ef, eg) → error([])
new_esEs10(xy10, xy90, fa, fb) → error([])
new_esEs5(xy10, xy90) → error([])
new_esEs2(xy10, xy90) → error([])
new_asAs0(True, xy29, xy30, app(ty_Ratio, db)) → new_esEs9(xy29, xy30, db)
new_esEs3(xy9240, xy919, ty_Char) → new_esEs13(xy9240, xy919)
new_esEs4(xy828, xy8270, ty_Char) → new_esEs13(xy828, xy8270)
new_esEs3(xy9240, xy919, ty_Int) → new_esEs1(xy9240, xy919)
new_esEs3(xy9240, xy919, app(app(ty_@2, fh), ga)) → new_esEs10(xy9240, xy919, fh, ga)
new_asAs0(True, xy29, xy30, app(ty_Maybe, dg)) → new_esEs14(xy29, xy30, dg)
new_primEqNat0(Succ(xy10000), Succ(xy90000)) → new_primEqNat0(xy10000, xy90000)
new_asAs0(True, xy29, xy30, ty_Double) → new_esEs5(xy29, xy30)
new_esEs4(xy828, xy8270, ty_Integer) → new_esEs2(xy828, xy8270)
new_asAs0(True, xy29, xy30, ty_Float) → new_esEs8(xy29, xy30)
new_esEs1(Neg(Succ(xy1000)), Pos(xy900)) → False
new_esEs1(Pos(Succ(xy1000)), Neg(xy900)) → False
new_esEs4(xy828, xy8270, app(ty_Maybe, cc)) → new_esEs14(xy828, xy8270, cc)
new_esEs1(Pos(Zero), Neg(Succ(xy9000))) → False
new_esEs1(Neg(Zero), Pos(Succ(xy9000))) → False
new_asAs0(True, xy29, xy30, app(app(ty_Either, de), df)) → new_esEs11(xy29, xy30, de, df)
new_esEs4(xy828, xy8270, app(app(app(ty_@3, bc), bd), be)) → new_esEs7(xy828, xy8270, bc, bd, be)
new_asAs0(True, xy29, xy30, app(app(app(ty_@3, cf), cg), da)) → new_esEs7(xy29, xy30, cf, cg, da)
new_esEs4(xy828, xy8270, app(ty_[], cd)) → new_esEs15(xy828, xy8270, cd)
new_esEs1(Neg(Zero), Neg(Zero)) → True
new_esEs1(Pos(Zero), Neg(Zero)) → True
new_asAs0(True, xy29, xy30, ty_Integer) → new_esEs2(xy29, xy30)
new_esEs1(Neg(Zero), Pos(Zero)) → True
new_esEs0(xy100, xy900, ty_Int) → new_esEs1(xy100, xy900)
new_esEs8(xy10, xy90) → error([])
new_esEs3(xy9240, xy919, app(app(app(ty_@3, fc), fd), ff)) → new_esEs7(xy9240, xy919, fc, fd, ff)
new_asAs0(True, xy29, xy30, app(app(ty_@2, dc), dd)) → new_esEs10(xy29, xy30, dc, dd)
new_esEs4(xy828, xy8270, ty_Ordering) → new_esEs6(xy828, xy8270)
new_esEs0(xy100, xy900, ty_Integer) → new_esEs2(xy100, xy900)
new_esEs1(Pos(Zero), Pos(Zero)) → True
new_esEs3(xy9240, xy919, app(app(ty_Either, gb), gc)) → new_esEs11(xy9240, xy919, gb, gc)
new_esEs3(xy9240, xy919, ty_Double) → new_esEs5(xy9240, xy919)
new_esEs3(xy9240, xy919, ty_Bool) → new_esEs16(xy9240, xy919)
new_esEs9(:%(xy100, xy101), :%(xy900, xy901), eh) → new_asAs0(new_esEs0(xy100, xy900, eh), xy101, xy901, eh)
new_esEs1(Neg(Succ(xy1000)), Neg(Zero)) → False
new_esEs1(Neg(Zero), Neg(Succ(xy9000))) → False
new_esEs4(xy828, xy8270, ty_Int) → new_esEs1(xy828, xy8270)
new_esEs3(xy9240, xy919, app(ty_Ratio, fg)) → new_esEs9(xy9240, xy919, fg)
new_esEs6(xy10, xy90) → error([])
new_esEs7(xy10, xy90, ec, ed, ee) → error([])
new_esEs15(xy10, xy90, ea) → error([])
new_esEs1(Pos(Succ(xy1000)), Pos(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)

The set Q consists of the following terms:

new_asAs0(True, x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, x2)
new_esEs1(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(x0, x1)
new_esEs1(Pos(Succ(x0)), Neg(x1))
new_esEs1(Neg(Succ(x0)), Pos(x1))
new_esEs4(x0, x1, ty_Int)
new_esEs3(x0, x1, ty_Integer)
new_esEs1(Pos(Zero), Pos(Succ(x0)))
new_asAs0(True, x0, x1, ty_Float)
new_asAs0(True, x0, x1, app(ty_[], x2))
new_asAs0(True, x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs1(Neg(Succ(x0)), Neg(Zero))
new_asAs0(False, x0, x1, x2)
new_esEs6(x0, x1)
new_esEs3(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs1(Pos(Zero), Pos(Zero))
new_esEs3(x0, x1, ty_@0)
new_asAs0(True, x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs3(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(x0, x1, x2)
new_esEs1(Neg(Zero), Neg(Succ(x0)))
new_esEs3(x0, x1, ty_Float)
new_esEs13(x0, x1)
new_esEs1(Neg(Zero), Neg(Zero))
new_esEs3(x0, x1, ty_Bool)
new_esEs4(x0, x1, ty_Bool)
new_esEs5(x0, x1)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1)
new_esEs4(x0, x1, ty_Ordering)
new_esEs11(x0, x1, x2, x3)
new_esEs2(x0, x1)
new_asAs0(True, x0, x1, app(ty_Ratio, x2))
new_asAs0(True, x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs0(x0, x1, ty_Int)
new_asAs0(True, x0, x1, ty_Int)
new_asAs0(True, x0, x1, ty_Ordering)
new_asAs0(True, x0, x1, ty_Integer)
new_esEs10(x0, x1, x2, x3)
new_esEs7(x0, x1, x2, x3, x4)
new_primEqNat0(Zero, Succ(x0))
new_asAs0(True, x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Integer)
new_esEs8(x0, x1)
new_esEs3(x0, x1, app(ty_Maybe, x2))
new_asAs0(True, x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs3(x0, x1, app(app(ty_Either, x2), x3))
new_asAs0(True, x0, x1, ty_Bool)
new_esEs3(x0, x1, app(ty_Ratio, x2))
new_esEs1(Neg(Zero), Pos(Succ(x0)))
new_esEs1(Pos(Zero), Neg(Succ(x0)))
new_esEs1(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs3(x0, x1, ty_Int)
new_esEs0(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_esEs3(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs1(Pos(Succ(x0)), Pos(Zero))
new_esEs3(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs3(x0, x1, app(ty_[], x2))
new_esEs1(Pos(Zero), Neg(Zero))
new_esEs1(Neg(Zero), Pos(Zero))
new_esEs4(x0, x1, ty_Double)
new_esEs3(x0, x1, app(app(ty_@2, x2), x3))
new_asAs0(True, x0, 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_nubByNubBy'1(xy919, xy920, xy921, xy922, False, :(xy9240, xy9241), ba) → new_nubByNubBy'1(xy919, xy920, xy921, xy922, new_esEs3(xy9240, xy919, ba), xy9241, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6, 7 >= 7
new_nubByNubBy'(:(xy8270, xy8271), xy828, xy829, bb) → new_nubByNubBy'1(xy8270, xy8271, xy828, xy829, new_esEs4(xy828, xy8270, bb), xy829, bb)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
new_nubByNubBy'1(xy919, xy920, xy921, xy922, False, [], ba) → new_nubByNubBy'(xy920, xy919, :(xy921, xy922), ba)
The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
new_nubByNubBy'1(xy919, xy920, xy921, xy922, True, xy924, ba) → new_nubByNubBy'(xy920, xy921, xy922, ba)
The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

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

new_deleteBy(xy10, :(xy90, xy91), bb) → new_deleteBy0(xy91, xy90, xy10, new_esEs17(xy10, xy90, bb), bb)
new_deleteBy0(xy17, xy18, xy19, False, ba) → new_deleteBy(xy19, xy17, ba)

The TRS R consists of the following rules:

new_asAs0(False, xy29, xy30, bc) → False
new_asAs0(True, xy29, xy30, ty_Ordering) → new_esEs6(xy29, xy30)
new_esEs17(xy10, xy90, app(app(ty_Either, dg), dh)) → new_esEs11(xy10, xy90, dg, dh)
new_asAs0(True, xy29, xy30, ty_@0) → new_esEs12(xy29, xy30)
new_asAs0(True, xy29, xy30, ty_Int) → new_esEs1(xy29, xy30)
new_primEqNat0(Zero, Zero) → True
new_esEs17(xy10, xy90, ty_Char) → new_esEs13(xy10, xy90)
new_esEs16(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_Integer) → new_esEs2(xy10, xy90)
new_esEs1(Pos(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Succ(xy1000)), Pos(Zero)) → False
new_esEs13(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_@0) → new_esEs12(xy10, xy90)
new_esEs17(xy10, xy90, ty_Float) → new_esEs8(xy10, xy90)
new_esEs17(xy10, xy90, app(app(app(ty_@3, da), db), dc)) → new_esEs7(xy10, xy90, da, db, dc)
new_esEs12(xy10, xy90) → error([])
new_primEqNat0(Zero, Succ(xy90000)) → False
new_primEqNat0(Succ(xy10000), Zero) → False
new_asAs0(True, xy29, xy30, app(ty_[], ce)) → new_esEs15(xy29, xy30, ce)
new_esEs1(Neg(Succ(xy1000)), Neg(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)
new_asAs0(True, xy29, xy30, ty_Char) → new_esEs13(xy29, xy30)
new_esEs17(xy10, xy90, app(ty_Maybe, cg)) → new_esEs14(xy10, xy90, cg)
new_esEs14(xy10, xy90, cg) → error([])
new_asAs0(True, xy29, xy30, ty_Bool) → new_esEs16(xy29, xy30)
new_esEs17(xy10, xy90, ty_Int) → new_esEs1(xy10, xy90)
new_esEs17(xy10, xy90, app(ty_Ratio, dd)) → new_esEs9(xy10, xy90, dd)
new_esEs11(xy10, xy90, dg, dh) → error([])
new_esEs10(xy10, xy90, de, df) → error([])
new_esEs5(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_Double) → new_esEs5(xy10, xy90)
new_asAs0(True, xy29, xy30, app(ty_Ratio, bg)) → new_esEs9(xy29, xy30, bg)
new_esEs2(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_Ordering) → new_esEs6(xy10, xy90)
new_primEqNat0(Succ(xy10000), Succ(xy90000)) → new_primEqNat0(xy10000, xy90000)
new_asAs0(True, xy29, xy30, app(ty_Maybe, cd)) → new_esEs14(xy29, xy30, cd)
new_asAs0(True, xy29, xy30, ty_Double) → new_esEs5(xy29, xy30)
new_asAs0(True, xy29, xy30, ty_Float) → new_esEs8(xy29, xy30)
new_esEs1(Neg(Succ(xy1000)), Pos(xy900)) → False
new_esEs1(Pos(Succ(xy1000)), Neg(xy900)) → False
new_esEs1(Neg(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Zero), Neg(Succ(xy9000))) → False
new_asAs0(True, xy29, xy30, app(app(ty_Either, cb), cc)) → new_esEs11(xy29, xy30, cb, cc)
new_asAs0(True, xy29, xy30, app(app(app(ty_@3, bd), be), bf)) → new_esEs7(xy29, xy30, bd, be, bf)
new_esEs1(Neg(Zero), Neg(Zero)) → True
new_esEs1(Neg(Zero), Pos(Zero)) → True
new_esEs1(Pos(Zero), Neg(Zero)) → True
new_asAs0(True, xy29, xy30, ty_Integer) → new_esEs2(xy29, xy30)
new_esEs17(xy10, xy90, app(ty_[], cf)) → new_esEs15(xy10, xy90, cf)
new_esEs0(xy100, xy900, ty_Int) → new_esEs1(xy100, xy900)
new_esEs8(xy10, xy90) → error([])
new_asAs0(True, xy29, xy30, app(app(ty_@2, bh), ca)) → new_esEs10(xy29, xy30, bh, ca)
new_esEs0(xy100, xy900, ty_Integer) → new_esEs2(xy100, xy900)
new_esEs1(Pos(Zero), Pos(Zero)) → True
new_esEs17(xy10, xy90, ty_Bool) → new_esEs16(xy10, xy90)
new_esEs9(:%(xy100, xy101), :%(xy900, xy901), dd) → new_asAs0(new_esEs0(xy100, xy900, dd), xy101, xy901, dd)
new_esEs1(Neg(Zero), Neg(Succ(xy9000))) → False
new_esEs1(Neg(Succ(xy1000)), Neg(Zero)) → False
new_esEs7(xy10, xy90, da, db, dc) → error([])
new_esEs6(xy10, xy90) → error([])
new_esEs15(xy10, xy90, cf) → error([])
new_esEs17(xy10, xy90, app(app(ty_@2, de), df)) → new_esEs10(xy10, xy90, de, df)
new_esEs1(Pos(Succ(xy1000)), Pos(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)

The set Q consists of the following terms:

new_esEs1(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(x0, x1)
new_esEs17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs1(Pos(Succ(x0)), Neg(x1))
new_esEs1(Neg(Succ(x0)), Pos(x1))
new_esEs1(Pos(Zero), Pos(Succ(x0)))
new_asAs0(True, x0, x1, ty_Float)
new_esEs1(Neg(Succ(x0)), Neg(Zero))
new_esEs6(x0, x1)
new_asAs0(False, x0, x1, x2)
new_asAs0(True, x0, x1, app(ty_Maybe, x2))
new_esEs1(Pos(Zero), Pos(Zero))
new_asAs0(True, x0, x1, app(ty_[], x2))
new_esEs17(x0, x1, app(ty_Ratio, x2))
new_esEs1(Neg(Zero), Neg(Succ(x0)))
new_esEs13(x0, x1)
new_esEs1(Neg(Zero), Neg(Zero))
new_esEs15(x0, x1, x2)
new_asAs0(True, x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, x2, x3)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(x0, x1)
new_esEs12(x0, x1)
new_esEs2(x0, x1)
new_esEs7(x0, x1, x2, x3, x4)
new_esEs17(x0, x1, ty_Bool)
new_esEs17(x0, x1, ty_@0)
new_esEs0(x0, x1, ty_Int)
new_esEs17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs0(True, x0, x1, ty_Int)
new_asAs0(True, x0, x1, app(app(ty_@2, x2), x3))
new_asAs0(True, x0, x1, ty_Ordering)
new_esEs17(x0, x1, app(ty_[], x2))
new_esEs14(x0, x1, x2)
new_asAs0(True, x0, x1, ty_Integer)
new_esEs17(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_asAs0(True, x0, x1, ty_Double)
new_esEs8(x0, x1)
new_esEs17(x0, x1, app(app(ty_Either, x2), x3))
new_asAs0(True, x0, x1, ty_@0)
new_esEs17(x0, x1, ty_Char)
new_esEs17(x0, x1, app(ty_Maybe, x2))
new_asAs0(True, x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, x2, x3)
new_asAs0(True, x0, x1, ty_Bool)
new_asAs0(True, x0, x1, app(ty_Ratio, x2))
new_esEs1(Pos(Zero), Neg(Succ(x0)))
new_esEs1(Neg(Zero), Pos(Succ(x0)))
new_esEs1(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(x0, x1, ty_Ordering)
new_esEs0(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_primEqNat0(Succ(x0), Zero)
new_esEs17(x0, x1, ty_Double)
new_esEs1(Pos(Succ(x0)), Pos(Zero))
new_esEs17(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs17(x0, x1, ty_Float)
new_esEs1(Pos(Zero), Neg(Zero))
new_esEs1(Neg(Zero), Pos(Zero))
new_asAs0(True, x0, 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_deleteBy0(xy17, xy18, xy19, False, ba) → new_deleteBy(xy19, xy17, ba)
The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
new_deleteBy(xy10, :(xy90, xy91), bb) → new_deleteBy0(xy91, xy90, xy10, new_esEs17(xy10, xy90, bb), bb)
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

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

new_foldl(xy9, xy10, :(xy110, xy111), ba) → new_foldl(new_flip(xy9, xy10, ba), xy110, xy111, ba)

The TRS R consists of the following rules:

new_asAs0(False, xy29, xy30, bb) → False
new_asAs0(True, xy29, xy30, ty_Ordering) → new_esEs6(xy29, xy30)
new_esEs17(xy10, xy90, app(app(ty_Either, dg), dh)) → new_esEs11(xy10, xy90, dg, dh)
new_asAs0(True, xy29, xy30, ty_@0) → new_esEs12(xy29, xy30)
new_asAs0(True, xy29, xy30, ty_Int) → new_esEs1(xy29, xy30)
new_primEqNat0(Zero, Zero) → True
new_esEs17(xy10, xy90, ty_Char) → new_esEs13(xy10, xy90)
new_esEs16(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_Integer) → new_esEs2(xy10, xy90)
new_esEs1(Pos(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Succ(xy1000)), Pos(Zero)) → False
new_esEs13(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_@0) → new_esEs12(xy10, xy90)
new_deleteBy1(xy10, [], ba) → []
new_esEs17(xy10, xy90, ty_Float) → new_esEs8(xy10, xy90)
new_esEs17(xy10, xy90, app(app(app(ty_@3, da), db), dc)) → new_esEs7(xy10, xy90, da, db, dc)
new_esEs12(xy10, xy90) → error([])
new_primEqNat0(Zero, Succ(xy90000)) → False
new_primEqNat0(Succ(xy10000), Zero) → False
new_asAs0(True, xy29, xy30, app(ty_[], cd)) → new_esEs15(xy29, xy30, cd)
new_esEs1(Neg(Succ(xy1000)), Neg(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)
new_asAs0(True, xy29, xy30, ty_Char) → new_esEs13(xy29, xy30)
new_deleteBy00(xy17, xy18, xy19, False, cf) → :(xy18, new_deleteBy1(xy19, xy17, cf))
new_esEs17(xy10, xy90, app(ty_Maybe, cg)) → new_esEs14(xy10, xy90, cg)
new_esEs14(xy10, xy90, cg) → error([])
new_asAs0(True, xy29, xy30, ty_Bool) → new_esEs16(xy29, xy30)
new_esEs17(xy10, xy90, ty_Int) → new_esEs1(xy10, xy90)
new_esEs17(xy10, xy90, app(ty_Ratio, dd)) → new_esEs9(xy10, xy90, dd)
new_esEs11(xy10, xy90, dg, dh) → error([])
new_esEs10(xy10, xy90, de, df) → error([])
new_esEs5(xy10, xy90) → error([])
new_esEs17(xy10, xy90, ty_Double) → new_esEs5(xy10, xy90)
new_esEs2(xy10, xy90) → error([])
new_asAs0(True, xy29, xy30, app(ty_Ratio, bf)) → new_esEs9(xy29, xy30, bf)
new_deleteBy00(xy17, xy18, xy19, True, cf) → xy17
new_esEs17(xy10, xy90, ty_Ordering) → new_esEs6(xy10, xy90)
new_primEqNat0(Succ(xy10000), Succ(xy90000)) → new_primEqNat0(xy10000, xy90000)
new_asAs0(True, xy29, xy30, app(ty_Maybe, cc)) → new_esEs14(xy29, xy30, cc)
new_asAs0(True, xy29, xy30, ty_Double) → new_esEs5(xy29, xy30)
new_asAs0(True, xy29, xy30, ty_Float) → new_esEs8(xy29, xy30)
new_esEs1(Neg(Succ(xy1000)), Pos(xy900)) → False
new_esEs1(Pos(Succ(xy1000)), Neg(xy900)) → False
new_deleteBy1(xy10, :(xy90, xy91), ba) → new_deleteBy00(xy91, xy90, xy10, new_esEs17(xy10, xy90, ba), ba)
new_esEs1(Neg(Zero), Pos(Succ(xy9000))) → False
new_esEs1(Pos(Zero), Neg(Succ(xy9000))) → False
new_asAs0(True, xy29, xy30, app(app(ty_Either, ca), cb)) → new_esEs11(xy29, xy30, ca, cb)
new_asAs0(True, xy29, xy30, app(app(app(ty_@3, bc), bd), be)) → new_esEs7(xy29, xy30, bc, bd, be)
new_esEs1(Neg(Zero), Neg(Zero)) → True
new_esEs1(Neg(Zero), Pos(Zero)) → True
new_esEs1(Pos(Zero), Neg(Zero)) → True
new_asAs0(True, xy29, xy30, ty_Integer) → new_esEs2(xy29, xy30)
new_esEs17(xy10, xy90, app(ty_[], ce)) → new_esEs15(xy10, xy90, ce)
new_esEs0(xy100, xy900, ty_Int) → new_esEs1(xy100, xy900)
new_esEs8(xy10, xy90) → error([])
new_asAs0(True, xy29, xy30, app(app(ty_@2, bg), bh)) → new_esEs10(xy29, xy30, bg, bh)
new_esEs0(xy100, xy900, ty_Integer) → new_esEs2(xy100, xy900)
new_esEs1(Pos(Zero), Pos(Zero)) → True
new_esEs17(xy10, xy90, ty_Bool) → new_esEs16(xy10, xy90)
new_esEs9(:%(xy100, xy101), :%(xy900, xy901), dd) → new_asAs0(new_esEs0(xy100, xy900, dd), xy101, xy901, dd)
new_esEs1(Neg(Zero), Neg(Succ(xy9000))) → False
new_esEs1(Neg(Succ(xy1000)), Neg(Zero)) → False
new_flip(xy9, xy10, ba) → new_deleteBy1(xy10, xy9, ba)
new_esEs6(xy10, xy90) → error([])
new_esEs7(xy10, xy90, da, db, dc) → error([])
new_esEs15(xy10, xy90, ce) → error([])
new_esEs17(xy10, xy90, app(app(ty_@2, de), df)) → new_esEs10(xy10, xy90, de, df)
new_esEs1(Pos(Succ(xy1000)), Pos(Succ(xy9000))) → new_primEqNat0(xy1000, xy9000)

The set Q consists of the following terms:

new_asAs0(False, x0, x1, x2)
new_esEs1(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(x0, x1)
new_esEs17(x0, x1, app(app(ty_@2, x2), x3))
new_esEs1(Pos(Succ(x0)), Neg(x1))
new_esEs1(Neg(Succ(x0)), Pos(x1))
new_deleteBy00(x0, x1, x2, True, x3)
new_esEs1(Pos(Zero), Pos(Succ(x0)))
new_asAs0(True, x0, x1, ty_Float)
new_esEs1(Neg(Succ(x0)), Neg(Zero))
new_esEs15(x0, x1, x2)
new_esEs6(x0, x1)
new_asAs0(True, x0, x1, app(ty_[], x2))
new_esEs1(Pos(Zero), Pos(Zero))
new_esEs17(x0, x1, app(ty_[], x2))
new_esEs17(x0, x1, app(ty_Ratio, x2))
new_asAs0(True, x0, x1, app(app(ty_@2, x2), x3))
new_esEs1(Neg(Zero), Neg(Succ(x0)))
new_esEs13(x0, x1)
new_esEs1(Neg(Zero), Neg(Zero))
new_esEs11(x0, x1, x2, x3)
new_esEs9(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(x0, x1)
new_esEs12(x0, x1)
new_esEs2(x0, x1)
new_esEs7(x0, x1, x2, x3, x4)
new_esEs17(x0, x1, ty_Bool)
new_esEs0(x0, x1, ty_Int)
new_esEs17(x0, x1, ty_@0)
new_esEs17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_asAs0(True, x0, x1, ty_Int)
new_asAs0(True, x0, x1, ty_Ordering)
new_esEs14(x0, x1, x2)
new_asAs0(True, x0, x1, ty_Integer)
new_asAs0(True, x0, x1, app(app(ty_Either, x2), x3))
new_esEs17(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_asAs0(True, x0, x1, ty_Double)
new_deleteBy1(x0, :(x1, x2), x3)
new_esEs8(x0, x1)
new_esEs17(x0, x1, app(app(ty_Either, x2), x3))
new_asAs0(True, x0, x1, ty_@0)
new_esEs17(x0, x1, ty_Char)
new_asAs0(True, x0, x1, app(ty_Ratio, x2))
new_esEs17(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, x2, x3)
new_deleteBy1(x0, [], x1)
new_asAs0(True, x0, x1, ty_Bool)
new_deleteBy00(x0, x1, x2, False, x3)
new_esEs1(Pos(Zero), Neg(Succ(x0)))
new_esEs1(Neg(Zero), Pos(Succ(x0)))
new_esEs1(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs17(x0, x1, ty_Ordering)
new_asAs0(True, x0, x1, app(ty_Maybe, x2))
new_esEs0(x0, x1, ty_Integer)
new_primEqNat0(Zero, Zero)
new_asAs0(True, x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Succ(x0), Zero)
new_flip(x0, x1, x2)
new_esEs17(x0, x1, ty_Double)
new_esEs1(Pos(Succ(x0)), Pos(Zero))
new_esEs17(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs17(x0, x1, ty_Float)
new_esEs1(Neg(Zero), Pos(Zero))
new_esEs1(Pos(Zero), Neg(Zero))
new_asAs0(True, x0, 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_foldl(xy9, xy10, :(xy110, xy111), ba) → new_foldl(new_flip(xy9, xy10, ba), xy110, xy111, ba)
The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

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

new_psPs(:(xy80, xy81), xy9, xy10, xy11, ba) → new_psPs(xy81, xy9, xy10, xy11, ba)

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

new_psPs(:(xy80, xy81), xy9, xy10, xy11, ba) → new_psPs(xy81, xy9, xy10, xy11, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5

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

nubBy'	[] vy	= nubBy'3 [] vy
nubBy'	(y : ys) xs	= nubBy'2 (y : ys) xs

nubBy'1	y ys xs True	= nubBy' ys xs
nubBy'1	y ys xs False	= nubBy'0 y ys xs otherwise

nubByNubBy'	xx [] vy	= nubByNubBy'3 xx [] vy
nubByNubBy'	xx (y : ys) xs	= nubByNubBy'2 xx (y : ys) xs

nubByNubBy'3	xx [] vy	= []
nubByNubBy'3	xx xv xw	= nubByNubBy'2 xx xv xw

nubByNubBy'1	xx y ys xs True	= nubByNubBy' xx ys xs
nubByNubBy'1	xx y ys xs False	= nubByNubBy'0 xx y ys xs otherwise