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

YES 3.077 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 :: [Ordering] -> [Ordering] -> [Ordering]) :: [Ordering] -> [Ordering] -> [Ordering])

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 :: [Ordering] -> [Ordering] -> [Ordering]) :: [Ordering] -> [Ordering] -> [Ordering])

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 :: [Ordering] -> [Ordering] -> [Ordering]) :: [Ordering] -> [Ordering] -> [Ordering])

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'1 y ys xs True = nubBy' ys xs

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

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

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

nubBy'3 [] vy = []

nubBy'3 wz xu = nubBy'2 wz xu

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 :: [Ordering] -> [Ordering] -> [Ordering]) :: [Ordering] -> [Ordering] -> [Ordering])

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	wz xu	=	nubBy'2 wz xu

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 wz xu = nubBy'2 wz xu

are unpacked to the following functions on top level

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

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

nubByNubBy' xv [] vy = nubByNubBy'3 xv [] vy

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

nubByNubBy'3 xv [] vy = []

nubByNubBy'3 xv wz xu = nubByNubBy'2 xv wz xu

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

mainModule List

(union :: [Ordering] -> [Ordering] -> [Ordering])

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

nubByNubBy'0

xv y ys xs True

y : nubByNubBy' xv ys (y : xs)

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

nubByNubBy'2

xv (y : ys) xs

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

nubByNubBy'3	xv [] vy	=	[]
nubByNubBy'3	xv wz xu	=	nubByNubBy'2 xv wz xu

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

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11 -> 157[label="",style="dashed", color="magenta", weight=3];
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2058 -> 182[label="",style="solid", color="burlywood", weight=3];
2059[label="xw8/[]",fontsize=10,color="white",style="solid",shape="box"];153 -> 2059[label="",style="solid", color="burlywood", weight=9];
2059 -> 183[label="",style="solid", color="burlywood", weight=3];
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2060 -> 18[label="",style="solid", color="burlywood", weight=3];
2061[label="xw4/[]",fontsize=10,color="white",style="solid",shape="box"];15 -> 2061[label="",style="solid", color="burlywood", weight=9];
2061 -> 19[label="",style="solid", color="burlywood", weight=3];
182[label="(xw80 : xw81) ++ foldl (flip (deleteBy (==))) xw9 (xw10 : xw11)\n  Eq a",fontsize=16,color="black",shape="box"];182 -> 193[label="",style="solid", color="black", weight=3];
183[label="[] ++ foldl (flip (deleteBy (==))) xw9 (xw10 : xw11)\n  Eq a",fontsize=16,color="black",shape="box"];183 -> 194[label="",style="solid", color="black", weight=3];
18[label="nubByNubBy' (==) (xw40 : xw41) []",fontsize=16,color="black",shape="box"];18 -> 23[label="",style="solid", color="black", weight=3];
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194[label="foldl (flip (deleteBy (==))) xw9 (xw10 : xw11)\n  Eq a",fontsize=16,color="black",shape="box"];194 -> 205[label="",style="solid", color="black", weight=3];
23[label="nubByNubBy'2 (==) (xw40 : xw41) []",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];
204 -> 153[label="",style="dashed", color="red", weight=0];
204[label="xw81 ++ foldl (flip (deleteBy (==))) xw9 (xw10 : xw11)\n  Eq a",fontsize=16,color="magenta"];204 -> 218[label="",style="dashed", color="magenta", weight=3];
205[label="foldl (flip (deleteBy (==))) (flip (deleteBy (==)) xw9 xw10) xw11\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];2063[label="xw11/xw110 : xw111",fontsize=10,color="white",style="solid",shape="box"];205 -> 2063[label="",style="solid", color="burlywood", weight=9];
2063 -> 219[label="",style="solid", color="burlywood", weight=3];
2064[label="xw11/[]",fontsize=10,color="white",style="solid",shape="box"];205 -> 2064[label="",style="solid", color="burlywood", weight=9];
2064 -> 220[label="",style="solid", color="burlywood", weight=3];
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220[label="foldl (flip (deleteBy (==))) (flip (deleteBy (==)) xw9 xw10) []\n  Eq a",fontsize=16,color="black",shape="box"];220 -> 228[label="",style="solid", color="black", weight=3];
33[label="nubByNubBy'1 (==) xw40 xw41 [] False",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
227 -> 205[label="",style="dashed", color="red", weight=0];
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227 -> 236[label="",style="dashed", color="magenta", weight=3];
227 -> 237[label="",style="dashed", color="magenta", weight=3];
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235[label="xw110\n  Eq a",fontsize=16,color="green",shape="box"];236[label="xw111\n  Eq a",fontsize=16,color="green",shape="box"];237 -> 228[label="",style="dashed", color="red", weight=0];
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2067 -> 245[label="",style="solid", color="burlywood", weight=3];
2068[label="xw9/[]",fontsize=10,color="white",style="solid",shape="box"];238 -> 2068[label="",style="solid", color="burlywood", weight=9];
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259 -> 273[label="",style="dashed", color="red", weight=0];
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259 -> 275[label="",style="dashed", color="magenta", weight=3];
259 -> 276[label="",style="dashed", color="magenta", weight=3];
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56 -> 1382[label="",style="dashed", color="magenta", weight=3];
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2072[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2072[label="",style="solid", color="blue", weight=9];
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2073[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2073[label="",style="solid", color="blue", weight=9];
2073 -> 280[label="",style="solid", color="blue", weight=3];
2074[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2074[label="",style="solid", color="blue", weight=9];
2074 -> 281[label="",style="solid", color="blue", weight=3];
2075[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2075[label="",style="solid", color="blue", weight=9];
2075 -> 282[label="",style="solid", color="blue", weight=3];
2076[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2076[label="",style="solid", color="blue", weight=9];
2076 -> 283[label="",style="solid", color="blue", weight=3];
2077[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2077[label="",style="solid", color="blue", weight=9];
2077 -> 284[label="",style="solid", color="blue", weight=3];
2078[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2078[label="",style="solid", color="blue", weight=9];
2078 -> 285[label="",style="solid", color="blue", weight=3];
2079[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2079[label="",style="solid", color="blue", weight=9];
2079 -> 286[label="",style="solid", color="blue", weight=3];
2080[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2080[label="",style="solid", color="blue", weight=9];
2080 -> 287[label="",style="solid", color="blue", weight=3];
2081[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2081[label="",style="solid", color="blue", weight=9];
2081 -> 288[label="",style="solid", color="blue", weight=3];
2082[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2082[label="",style="solid", color="blue", weight=9];
2082 -> 289[label="",style="solid", color="blue", weight=3];
2083[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2083[label="",style="solid", color="blue", weight=9];
2083 -> 290[label="",style="solid", color="blue", weight=3];
2084[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];275 -> 2084[label="",style="solid", color="blue", weight=9];
2084 -> 291[label="",style="solid", color="blue", weight=3];
276[label="xw10\n  Eq a",fontsize=16,color="green",shape="box"];277[label="xw90\n  Eq a",fontsize=16,color="green",shape="box"];273[label="deleteBy0 xw17 xw18 (==) xw19 xw20\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];2085[label="xw20/False",fontsize=10,color="white",style="solid",shape="box"];273 -> 2085[label="",style="solid", color="burlywood", weight=9];
2085 -> 292[label="",style="solid", color="burlywood", weight=3];
2086[label="xw20/True",fontsize=10,color="white",style="solid",shape="box"];273 -> 2086[label="",style="solid", color="burlywood", weight=9];
2086 -> 293[label="",style="solid", color="burlywood", weight=3];
1380[label="xw41",fontsize=16,color="green",shape="box"];1381[label="xw40",fontsize=16,color="green",shape="box"];1382[label="[]",fontsize=16,color="green",shape="box"];1379[label="nubByNubBy' (==) xw106 (xw107 : xw108)\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];2087[label="xw106/xw1060 : xw1061",fontsize=10,color="white",style="solid",shape="box"];1379 -> 2087[label="",style="solid", color="burlywood", weight=9];
2087 -> 1554[label="",style="solid", color="burlywood", weight=3];
2088[label="xw106/[]",fontsize=10,color="white",style="solid",shape="box"];1379 -> 2088[label="",style="solid", color="burlywood", weight=9];
2088 -> 1555[label="",style="solid", color="burlywood", weight=3];
278[label="(==) xw10 xw90\n  Eq a",fontsize=16,color="black",shape="triangle"];278 -> 306[label="",style="solid", color="black", weight=3];
279[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];279 -> 307[label="",style="solid", color="black", weight=3];
280[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];280 -> 308[label="",style="solid", color="black", weight=3];
281[label="(==) xw10 xw90",fontsize=16,color="burlywood",shape="triangle"];2089[label="xw10/LT",fontsize=10,color="white",style="solid",shape="box"];281 -> 2089[label="",style="solid", color="burlywood", weight=9];
2089 -> 309[label="",style="solid", color="burlywood", weight=3];
2090[label="xw10/EQ",fontsize=10,color="white",style="solid",shape="box"];281 -> 2090[label="",style="solid", color="burlywood", weight=9];
2090 -> 310[label="",style="solid", color="burlywood", weight=3];
2091[label="xw10/GT",fontsize=10,color="white",style="solid",shape="box"];281 -> 2091[label="",style="solid", color="burlywood", weight=9];
2091 -> 311[label="",style="solid", color="burlywood", weight=3];
282[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];282 -> 312[label="",style="solid", color="black", weight=3];
283[label="(==) xw10 xw90\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];283 -> 313[label="",style="solid", color="black", weight=3];
284[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];284 -> 314[label="",style="solid", color="black", weight=3];
285[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];285 -> 315[label="",style="solid", color="black", weight=3];
286[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];286 -> 316[label="",style="solid", color="black", weight=3];
287[label="(==) xw10 xw90\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="triangle"];287 -> 317[label="",style="solid", color="black", weight=3];
288[label="(==) xw10 xw90\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];288 -> 318[label="",style="solid", color="black", weight=3];
289[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];289 -> 319[label="",style="solid", color="black", weight=3];
290[label="(==) xw10 xw90\n  Eq a",fontsize=16,color="black",shape="triangle"];290 -> 320[label="",style="solid", color="black", weight=3];
291[label="(==) xw10 xw90\n  Integral a",fontsize=16,color="black",shape="triangle"];291 -> 321[label="",style="solid", color="black", weight=3];
292[label="deleteBy0 xw17 xw18 (==) xw19 False\n  Eq a",fontsize=16,color="black",shape="box"];292 -> 322[label="",style="solid", color="black", weight=3];
293[label="deleteBy0 xw17 xw18 (==) xw19 True\n  Eq a",fontsize=16,color="black",shape="box"];293 -> 323[label="",style="solid", color="black", weight=3];
1554[label="nubByNubBy' (==) (xw1060 : xw1061) (xw107 : xw108)\n  Eq a",fontsize=16,color="black",shape="box"];1554 -> 1556[label="",style="solid", color="black", weight=3];
1555[label="nubByNubBy' (==) [] (xw107 : xw108)\n  Eq a",fontsize=16,color="black",shape="box"];1555 -> 1557[label="",style="solid", color="black", weight=3];
306[label="error []",fontsize=16,color="red",shape="box"];307[label="error []",fontsize=16,color="red",shape="box"];308[label="error []",fontsize=16,color="red",shape="box"];309[label="(==) LT xw90",fontsize=16,color="burlywood",shape="box"];2092[label="xw90/LT",fontsize=10,color="white",style="solid",shape="box"];309 -> 2092[label="",style="solid", color="burlywood", weight=9];
2092 -> 330[label="",style="solid", color="burlywood", weight=3];
2093[label="xw90/EQ",fontsize=10,color="white",style="solid",shape="box"];309 -> 2093[label="",style="solid", color="burlywood", weight=9];
2093 -> 331[label="",style="solid", color="burlywood", weight=3];
2094[label="xw90/GT",fontsize=10,color="white",style="solid",shape="box"];309 -> 2094[label="",style="solid", color="burlywood", weight=9];
2094 -> 332[label="",style="solid", color="burlywood", weight=3];
310[label="(==) EQ xw90",fontsize=16,color="burlywood",shape="box"];2095[label="xw90/LT",fontsize=10,color="white",style="solid",shape="box"];310 -> 2095[label="",style="solid", color="burlywood", weight=9];
2095 -> 333[label="",style="solid", color="burlywood", weight=3];
2096[label="xw90/EQ",fontsize=10,color="white",style="solid",shape="box"];310 -> 2096[label="",style="solid", color="burlywood", weight=9];
2096 -> 334[label="",style="solid", color="burlywood", weight=3];
2097[label="xw90/GT",fontsize=10,color="white",style="solid",shape="box"];310 -> 2097[label="",style="solid", color="burlywood", weight=9];
2097 -> 335[label="",style="solid", color="burlywood", weight=3];
311[label="(==) GT xw90",fontsize=16,color="burlywood",shape="box"];2098[label="xw90/LT",fontsize=10,color="white",style="solid",shape="box"];311 -> 2098[label="",style="solid", color="burlywood", weight=9];
2098 -> 336[label="",style="solid", color="burlywood", weight=3];
2099[label="xw90/EQ",fontsize=10,color="white",style="solid",shape="box"];311 -> 2099[label="",style="solid", color="burlywood", weight=9];
2099 -> 337[label="",style="solid", color="burlywood", weight=3];
2100[label="xw90/GT",fontsize=10,color="white",style="solid",shape="box"];311 -> 2100[label="",style="solid", color="burlywood", weight=9];
2100 -> 338[label="",style="solid", color="burlywood", weight=3];
312[label="error []",fontsize=16,color="red",shape="box"];313[label="error []",fontsize=16,color="red",shape="box"];314[label="error []",fontsize=16,color="red",shape="box"];315[label="error []",fontsize=16,color="red",shape="box"];316[label="error []",fontsize=16,color="red",shape="box"];317[label="error []",fontsize=16,color="red",shape="box"];318[label="error []",fontsize=16,color="red",shape="box"];319[label="error []",fontsize=16,color="red",shape="box"];320[label="error []",fontsize=16,color="red",shape="box"];321[label="error []",fontsize=16,color="red",shape="box"];322[label="xw18 : deleteBy (==) xw19 xw17\n  Eq a",fontsize=16,color="green",shape="box"];322 -> 339[label="",style="dashed", color="green", weight=3];
323[label="xw17\n  Eq a",fontsize=16,color="green",shape="box"];1556[label="nubByNubBy'2 (==) (xw1060 : xw1061) (xw107 : xw108)\n  Eq a",fontsize=16,color="black",shape="box"];1556 -> 1558[label="",style="solid", color="black", weight=3];
1557[label="nubByNubBy'3 (==) [] (xw107 : xw108)\n  Eq a",fontsize=16,color="black",shape="box"];1557 -> 1559[label="",style="solid", color="black", weight=3];
330[label="(==) LT LT",fontsize=16,color="black",shape="box"];330 -> 342[label="",style="solid", color="black", weight=3];
331[label="(==) LT EQ",fontsize=16,color="black",shape="box"];331 -> 343[label="",style="solid", color="black", weight=3];
332[label="(==) LT GT",fontsize=16,color="black",shape="box"];332 -> 344[label="",style="solid", color="black", weight=3];
333[label="(==) EQ LT",fontsize=16,color="black",shape="box"];333 -> 345[label="",style="solid", color="black", weight=3];
334[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];334 -> 346[label="",style="solid", color="black", weight=3];
335[label="(==) EQ GT",fontsize=16,color="black",shape="box"];335 -> 347[label="",style="solid", color="black", weight=3];
336[label="(==) GT LT",fontsize=16,color="black",shape="box"];336 -> 348[label="",style="solid", color="black", weight=3];
337[label="(==) GT EQ",fontsize=16,color="black",shape="box"];337 -> 349[label="",style="solid", color="black", weight=3];
338[label="(==) GT GT",fontsize=16,color="black",shape="box"];338 -> 350[label="",style="solid", color="black", weight=3];
339 -> 238[label="",style="dashed", color="red", weight=0];
339[label="deleteBy (==) xw19 xw17\n  Eq a",fontsize=16,color="magenta"];339 -> 351[label="",style="dashed", color="magenta", weight=3];
339 -> 352[label="",style="dashed", color="magenta", weight=3];
1558[label="nubByNubBy'1 (==) xw1060 xw1061 (xw107 : xw108) (elem_by (==) xw1060 (xw107 : xw108))\n  Eq a",fontsize=16,color="black",shape="box"];1558 -> 1560[label="",style="solid", color="black", weight=3];
1559[label="[]\n  Eq a",fontsize=16,color="green",shape="box"];342[label="True",fontsize=16,color="green",shape="box"];343[label="False",fontsize=16,color="green",shape="box"];344[label="False",fontsize=16,color="green",shape="box"];345[label="False",fontsize=16,color="green",shape="box"];346[label="True",fontsize=16,color="green",shape="box"];347[label="False",fontsize=16,color="green",shape="box"];348[label="False",fontsize=16,color="green",shape="box"];349[label="False",fontsize=16,color="green",shape="box"];350[label="True",fontsize=16,color="green",shape="box"];351[label="xw19\n  Eq a",fontsize=16,color="green",shape="box"];352[label="xw17\n  Eq a",fontsize=16,color="green",shape="box"];1560 -> 1936[label="",style="dashed", color="red", weight=0];
1560[label="nubByNubBy'1 (==) xw1060 xw1061 (xw107 : xw108) ((==) xw107 xw1060 || elem_by (==) xw1060 xw108)\n  Eq a",fontsize=16,color="magenta"];1560 -> 1937[label="",style="dashed", color="magenta", weight=3];
1560 -> 1938[label="",style="dashed", color="magenta", weight=3];
1560 -> 1939[label="",style="dashed", color="magenta", weight=3];
1560 -> 1940[label="",style="dashed", color="magenta", weight=3];
1560 -> 1941[label="",style="dashed", color="magenta", weight=3];
1560 -> 1942[label="",style="dashed", color="magenta", weight=3];
1937[label="xw108\n  Eq a",fontsize=16,color="green",shape="box"];1938[label="(==) xw107 xw1060\n  Eq a",fontsize=16,color="blue",shape="box"];2103[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2103[label="",style="solid", color="blue", weight=9];
2103 -> 1949[label="",style="solid", color="blue", weight=3];
2104[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2104[label="",style="solid", color="blue", weight=9];
2104 -> 1950[label="",style="solid", color="blue", weight=3];
2105[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2105[label="",style="solid", color="blue", weight=9];
2105 -> 1951[label="",style="solid", color="blue", weight=3];
2106[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2106[label="",style="solid", color="blue", weight=9];
2106 -> 1952[label="",style="solid", color="blue", weight=3];
2107[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2107[label="",style="solid", color="blue", weight=9];
2107 -> 1953[label="",style="solid", color="blue", weight=3];
2108[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2108[label="",style="solid", color="blue", weight=9];
2108 -> 1954[label="",style="solid", color="blue", weight=3];
2109[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2109[label="",style="solid", color="blue", weight=9];
2109 -> 1955[label="",style="solid", color="blue", weight=3];
2110[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2110[label="",style="solid", color="blue", weight=9];
2110 -> 1956[label="",style="solid", color="blue", weight=3];
2111[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2111[label="",style="solid", color="blue", weight=9];
2111 -> 1957[label="",style="solid", color="blue", weight=3];
2112[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2112[label="",style="solid", color="blue", weight=9];
2112 -> 1958[label="",style="solid", color="blue", weight=3];
2113[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2113[label="",style="solid", color="blue", weight=9];
2113 -> 1959[label="",style="solid", color="blue", weight=3];
2114[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2114[label="",style="solid", color="blue", weight=9];
2114 -> 1960[label="",style="solid", color="blue", weight=3];
2115[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2115[label="",style="solid", color="blue", weight=9];
2115 -> 1961[label="",style="solid", color="blue", weight=3];
2116[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1938 -> 2116[label="",style="solid", color="blue", weight=9];
2116 -> 1962[label="",style="solid", color="blue", weight=3];
1939[label="xw108\n  Eq a",fontsize=16,color="green",shape="box"];1940[label="xw107\n  Eq a",fontsize=16,color="green",shape="box"];1941[label="xw1061\n  Eq a",fontsize=16,color="green",shape="box"];1942[label="xw1060\n  Eq a",fontsize=16,color="green",shape="box"];1936[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (xw202 || elem_by (==) xw198 xw203)\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];2117[label="xw202/False",fontsize=10,color="white",style="solid",shape="box"];1936 -> 2117[label="",style="solid", color="burlywood", weight=9];
2117 -> 1963[label="",style="solid", color="burlywood", weight=3];
2118[label="xw202/True",fontsize=10,color="white",style="solid",shape="box"];1936 -> 2118[label="",style="solid", color="burlywood", weight=9];
2118 -> 1964[label="",style="solid", color="burlywood", weight=3];
1949 -> 278[label="",style="dashed", color="red", weight=0];
1949[label="(==) xw107 xw1060\n  Eq a",fontsize=16,color="magenta"];1949 -> 1965[label="",style="dashed", color="magenta", weight=3];
1949 -> 1966[label="",style="dashed", color="magenta", weight=3];
1950 -> 279[label="",style="dashed", color="red", weight=0];
1950[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1950 -> 1967[label="",style="dashed", color="magenta", weight=3];
1950 -> 1968[label="",style="dashed", color="magenta", weight=3];
1951 -> 280[label="",style="dashed", color="red", weight=0];
1951[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1951 -> 1969[label="",style="dashed", color="magenta", weight=3];
1951 -> 1970[label="",style="dashed", color="magenta", weight=3];
1952 -> 281[label="",style="dashed", color="red", weight=0];
1952[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1952 -> 1971[label="",style="dashed", color="magenta", weight=3];
1952 -> 1972[label="",style="dashed", color="magenta", weight=3];
1953 -> 282[label="",style="dashed", color="red", weight=0];
1953[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1953 -> 1973[label="",style="dashed", color="magenta", weight=3];
1953 -> 1974[label="",style="dashed", color="magenta", weight=3];
1954 -> 283[label="",style="dashed", color="red", weight=0];
1954[label="(==) xw107 xw1060\n  Eq a  Eq b",fontsize=16,color="magenta"];1954 -> 1975[label="",style="dashed", color="magenta", weight=3];
1954 -> 1976[label="",style="dashed", color="magenta", weight=3];
1955 -> 284[label="",style="dashed", color="red", weight=0];
1955[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1955 -> 1977[label="",style="dashed", color="magenta", weight=3];
1955 -> 1978[label="",style="dashed", color="magenta", weight=3];
1956 -> 285[label="",style="dashed", color="red", weight=0];
1956[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1956 -> 1979[label="",style="dashed", color="magenta", weight=3];
1956 -> 1980[label="",style="dashed", color="magenta", weight=3];
1957 -> 286[label="",style="dashed", color="red", weight=0];
1957[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1957 -> 1981[label="",style="dashed", color="magenta", weight=3];
1957 -> 1982[label="",style="dashed", color="magenta", weight=3];
1958 -> 287[label="",style="dashed", color="red", weight=0];
1958[label="(==) xw107 xw1060\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];1958 -> 1983[label="",style="dashed", color="magenta", weight=3];
1958 -> 1984[label="",style="dashed", color="magenta", weight=3];
1959 -> 288[label="",style="dashed", color="red", weight=0];
1959[label="(==) xw107 xw1060\n  Eq a  Eq b",fontsize=16,color="magenta"];1959 -> 1985[label="",style="dashed", color="magenta", weight=3];
1959 -> 1986[label="",style="dashed", color="magenta", weight=3];
1960 -> 289[label="",style="dashed", color="red", weight=0];
1960[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1960 -> 1987[label="",style="dashed", color="magenta", weight=3];
1960 -> 1988[label="",style="dashed", color="magenta", weight=3];
1961 -> 290[label="",style="dashed", color="red", weight=0];
1961[label="(==) xw107 xw1060\n  Eq a",fontsize=16,color="magenta"];1961 -> 1989[label="",style="dashed", color="magenta", weight=3];
1961 -> 1990[label="",style="dashed", color="magenta", weight=3];
1962 -> 291[label="",style="dashed", color="red", weight=0];
1962[label="(==) xw107 xw1060\n  Integral a",fontsize=16,color="magenta"];1962 -> 1991[label="",style="dashed", color="magenta", weight=3];
1962 -> 1992[label="",style="dashed", color="magenta", weight=3];
1963[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (False || elem_by (==) xw198 xw203)\n  Eq a",fontsize=16,color="black",shape="box"];1963 -> 1993[label="",style="solid", color="black", weight=3];
1964[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (True || elem_by (==) xw198 xw203)\n  Eq a",fontsize=16,color="black",shape="box"];1964 -> 1994[label="",style="solid", color="black", weight=3];
1965[label="xw107\n  Eq a",fontsize=16,color="green",shape="box"];1966[label="xw1060\n  Eq a",fontsize=16,color="green",shape="box"];1967[label="xw107",fontsize=16,color="green",shape="box"];1968[label="xw1060",fontsize=16,color="green",shape="box"];1969[label="xw107",fontsize=16,color="green",shape="box"];1970[label="xw1060",fontsize=16,color="green",shape="box"];1971[label="xw107",fontsize=16,color="green",shape="box"];1972[label="xw1060",fontsize=16,color="green",shape="box"];1973[label="xw107",fontsize=16,color="green",shape="box"];1974[label="xw1060",fontsize=16,color="green",shape="box"];1975[label="xw107\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1976[label="xw1060\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1977[label="xw107",fontsize=16,color="green",shape="box"];1978[label="xw1060",fontsize=16,color="green",shape="box"];1979[label="xw107",fontsize=16,color="green",shape="box"];1980[label="xw1060",fontsize=16,color="green",shape="box"];1981[label="xw107",fontsize=16,color="green",shape="box"];1982[label="xw1060",fontsize=16,color="green",shape="box"];1983[label="xw107\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1984[label="xw1060\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];1985[label="xw107\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1986[label="xw1060\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];1987[label="xw107",fontsize=16,color="green",shape="box"];1988[label="xw1060",fontsize=16,color="green",shape="box"];1989[label="xw107\n  Eq a",fontsize=16,color="green",shape="box"];1990[label="xw1060\n  Eq a",fontsize=16,color="green",shape="box"];1991[label="xw107\n  Integral a",fontsize=16,color="green",shape="box"];1992[label="xw1060\n  Integral a",fontsize=16,color="green",shape="box"];1993[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (elem_by (==) xw198 xw203)\n  Eq a",fontsize=16,color="burlywood",shape="box"];2133[label="xw203/xw2030 : xw2031",fontsize=10,color="white",style="solid",shape="box"];1993 -> 2133[label="",style="solid", color="burlywood", weight=9];
2133 -> 1995[label="",style="solid", color="burlywood", weight=3];
2134[label="xw203/[]",fontsize=10,color="white",style="solid",shape="box"];1993 -> 2134[label="",style="solid", color="burlywood", weight=9];
2134 -> 1996[label="",style="solid", color="burlywood", weight=3];
1994[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) True\n  Eq a",fontsize=16,color="black",shape="box"];1994 -> 1997[label="",style="solid", color="black", weight=3];
1995[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (elem_by (==) xw198 (xw2030 : xw2031))\n  Eq a",fontsize=16,color="black",shape="box"];1995 -> 1998[label="",style="solid", color="black", weight=3];
1996[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (elem_by (==) xw198 [])\n  Eq a",fontsize=16,color="black",shape="box"];1996 -> 1999[label="",style="solid", color="black", weight=3];
1997 -> 1379[label="",style="dashed", color="red", weight=0];
1997[label="nubByNubBy' (==) xw199 (xw200 : xw201)\n  Eq a",fontsize=16,color="magenta"];1997 -> 2000[label="",style="dashed", color="magenta", weight=3];
1997 -> 2001[label="",style="dashed", color="magenta", weight=3];
1997 -> 2002[label="",style="dashed", color="magenta", weight=3];
1998 -> 1936[label="",style="dashed", color="red", weight=0];
1998[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) ((==) xw2030 xw198 || elem_by (==) xw198 xw2031)\n  Eq a",fontsize=16,color="magenta"];1998 -> 2003[label="",style="dashed", color="magenta", weight=3];
1998 -> 2004[label="",style="dashed", color="magenta", weight=3];
1999[label="nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) False\n  Eq a",fontsize=16,color="black",shape="box"];1999 -> 2005[label="",style="solid", color="black", weight=3];
2000[label="xw199\n  Eq a",fontsize=16,color="green",shape="box"];2001[label="xw200\n  Eq a",fontsize=16,color="green",shape="box"];2002[label="xw201\n  Eq a",fontsize=16,color="green",shape="box"];2003[label="xw2031\n  Eq a",fontsize=16,color="green",shape="box"];2004[label="(==) xw2030 xw198\n  Eq a",fontsize=16,color="blue",shape="box"];2137[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2137[label="",style="solid", color="blue", weight=9];
2137 -> 2006[label="",style="solid", color="blue", weight=3];
2138[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2138[label="",style="solid", color="blue", weight=9];
2138 -> 2007[label="",style="solid", color="blue", weight=3];
2139[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2139[label="",style="solid", color="blue", weight=9];
2139 -> 2008[label="",style="solid", color="blue", weight=3];
2140[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2140[label="",style="solid", color="blue", weight=9];
2140 -> 2009[label="",style="solid", color="blue", weight=3];
2141[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2141[label="",style="solid", color="blue", weight=9];
2141 -> 2010[label="",style="solid", color="blue", weight=3];
2142[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2142[label="",style="solid", color="blue", weight=9];
2142 -> 2011[label="",style="solid", color="blue", weight=3];
2143[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2143[label="",style="solid", color="blue", weight=9];
2143 -> 2012[label="",style="solid", color="blue", weight=3];
2144[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2144[label="",style="solid", color="blue", weight=9];
2144 -> 2013[label="",style="solid", color="blue", weight=3];
2145[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2145[label="",style="solid", color="blue", weight=9];
2145 -> 2014[label="",style="solid", color="blue", weight=3];
2146[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2146[label="",style="solid", color="blue", weight=9];
2146 -> 2015[label="",style="solid", color="blue", weight=3];
2147[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2147[label="",style="solid", color="blue", weight=9];
2147 -> 2016[label="",style="solid", color="blue", weight=3];
2148[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2148[label="",style="solid", color="blue", weight=9];
2148 -> 2017[label="",style="solid", color="blue", weight=3];
2149[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2149[label="",style="solid", color="blue", weight=9];
2149 -> 2018[label="",style="solid", color="blue", weight=3];
2150[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2004 -> 2150[label="",style="solid", color="blue", weight=9];
2150 -> 2019[label="",style="solid", color="blue", weight=3];
2005[label="nubByNubBy'0 (==) xw198 xw199 (xw200 : xw201) otherwise\n  Eq a",fontsize=16,color="black",shape="box"];2005 -> 2020[label="",style="solid", color="black", weight=3];
2006 -> 278[label="",style="dashed", color="red", weight=0];
2006[label="(==) xw2030 xw198\n  Eq a",fontsize=16,color="magenta"];2006 -> 2021[label="",style="dashed", color="magenta", weight=3];
2006 -> 2022[label="",style="dashed", color="magenta", weight=3];
2007 -> 279[label="",style="dashed", color="red", weight=0];
2007[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2007 -> 2023[label="",style="dashed", color="magenta", weight=3];
2007 -> 2024[label="",style="dashed", color="magenta", weight=3];
2008 -> 280[label="",style="dashed", color="red", weight=0];
2008[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2008 -> 2025[label="",style="dashed", color="magenta", weight=3];
2008 -> 2026[label="",style="dashed", color="magenta", weight=3];
2009 -> 281[label="",style="dashed", color="red", weight=0];
2009[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2009 -> 2027[label="",style="dashed", color="magenta", weight=3];
2009 -> 2028[label="",style="dashed", color="magenta", weight=3];
2010 -> 282[label="",style="dashed", color="red", weight=0];
2010[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2010 -> 2029[label="",style="dashed", color="magenta", weight=3];
2010 -> 2030[label="",style="dashed", color="magenta", weight=3];
2011 -> 283[label="",style="dashed", color="red", weight=0];
2011[label="(==) xw2030 xw198\n  Eq a  Eq b",fontsize=16,color="magenta"];2011 -> 2031[label="",style="dashed", color="magenta", weight=3];
2011 -> 2032[label="",style="dashed", color="magenta", weight=3];
2012 -> 284[label="",style="dashed", color="red", weight=0];
2012[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2012 -> 2033[label="",style="dashed", color="magenta", weight=3];
2012 -> 2034[label="",style="dashed", color="magenta", weight=3];
2013 -> 285[label="",style="dashed", color="red", weight=0];
2013[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2013 -> 2035[label="",style="dashed", color="magenta", weight=3];
2013 -> 2036[label="",style="dashed", color="magenta", weight=3];
2014 -> 286[label="",style="dashed", color="red", weight=0];
2014[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2014 -> 2037[label="",style="dashed", color="magenta", weight=3];
2014 -> 2038[label="",style="dashed", color="magenta", weight=3];
2015 -> 287[label="",style="dashed", color="red", weight=0];
2015[label="(==) xw2030 xw198\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];2015 -> 2039[label="",style="dashed", color="magenta", weight=3];
2015 -> 2040[label="",style="dashed", color="magenta", weight=3];
2016 -> 288[label="",style="dashed", color="red", weight=0];
2016[label="(==) xw2030 xw198\n  Eq a  Eq b",fontsize=16,color="magenta"];2016 -> 2041[label="",style="dashed", color="magenta", weight=3];
2016 -> 2042[label="",style="dashed", color="magenta", weight=3];
2017 -> 289[label="",style="dashed", color="red", weight=0];
2017[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2017 -> 2043[label="",style="dashed", color="magenta", weight=3];
2017 -> 2044[label="",style="dashed", color="magenta", weight=3];
2018 -> 290[label="",style="dashed", color="red", weight=0];
2018[label="(==) xw2030 xw198\n  Eq a",fontsize=16,color="magenta"];2018 -> 2045[label="",style="dashed", color="magenta", weight=3];
2018 -> 2046[label="",style="dashed", color="magenta", weight=3];
2019 -> 291[label="",style="dashed", color="red", weight=0];
2019[label="(==) xw2030 xw198\n  Integral a",fontsize=16,color="magenta"];2019 -> 2047[label="",style="dashed", color="magenta", weight=3];
2019 -> 2048[label="",style="dashed", color="magenta", weight=3];
2020[label="nubByNubBy'0 (==) xw198 xw199 (xw200 : xw201) True\n  Eq a",fontsize=16,color="black",shape="box"];2020 -> 2049[label="",style="solid", color="black", weight=3];
2021[label="xw2030\n  Eq a",fontsize=16,color="green",shape="box"];2022[label="xw198\n  Eq a",fontsize=16,color="green",shape="box"];2023[label="xw2030",fontsize=16,color="green",shape="box"];2024[label="xw198",fontsize=16,color="green",shape="box"];2025[label="xw2030",fontsize=16,color="green",shape="box"];2026[label="xw198",fontsize=16,color="green",shape="box"];2027[label="xw2030",fontsize=16,color="green",shape="box"];2028[label="xw198",fontsize=16,color="green",shape="box"];2029[label="xw2030",fontsize=16,color="green",shape="box"];2030[label="xw198",fontsize=16,color="green",shape="box"];2031[label="xw2030\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];2032[label="xw198\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];2033[label="xw2030",fontsize=16,color="green",shape="box"];2034[label="xw198",fontsize=16,color="green",shape="box"];2035[label="xw2030",fontsize=16,color="green",shape="box"];2036[label="xw198",fontsize=16,color="green",shape="box"];2037[label="xw2030",fontsize=16,color="green",shape="box"];2038[label="xw198",fontsize=16,color="green",shape="box"];2039[label="xw2030\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];2040[label="xw198\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];2041[label="xw2030\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];2042[label="xw198\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];2043[label="xw2030",fontsize=16,color="green",shape="box"];2044[label="xw198",fontsize=16,color="green",shape="box"];2045[label="xw2030\n  Eq a",fontsize=16,color="green",shape="box"];2046[label="xw198\n  Eq a",fontsize=16,color="green",shape="box"];2047[label="xw2030\n  Integral a",fontsize=16,color="green",shape="box"];2048[label="xw198\n  Integral a",fontsize=16,color="green",shape="box"];2049[label="xw198 : nubByNubBy' (==) xw199 (xw198 : xw200 : xw201)\n  Eq a",fontsize=16,color="green",shape="box"];2049 -> 2050[label="",style="dashed", color="green", weight=3];
2050 -> 1379[label="",style="dashed", color="red", weight=0];
2050[label="nubByNubBy' (==) xw199 (xw198 : xw200 : xw201)\n  Eq a",fontsize=16,color="magenta"];2050 -> 2051[label="",style="dashed", color="magenta", weight=3];
2050 -> 2052[label="",style="dashed", color="magenta", weight=3];
2050 -> 2053[label="",style="dashed", color="magenta", weight=3];
2051[label="xw199\n  Eq a",fontsize=16,color="green",shape="box"];2052[label="xw198\n  Eq a",fontsize=16,color="green",shape="box"];2053[label="xw200 : xw201\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

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

new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) → new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) → new_nubByNubBy'(xw199, xw200, xw201, ba)
new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) → new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
new_nubByNubBy'(:(xw1060, xw1061), xw107, xw108, bb) → new_nubByNubBy'1(xw1060, xw1061, xw107, xw108, new_esEs0(xw107, xw1060, bb), xw108, bb)

The TRS R consists of the following rules:

new_esEs0(xw107, xw1060, app(ty_[], cf)) → new_esEs1(xw107, xw1060, cf)
new_esEs0(xw107, xw1060, ty_Ordering) → new_esEs4(xw107, xw1060)
new_esEs7(xw10, xw90) → error([])
new_esEs(xw2030, xw198, app(ty_[], bc)) → new_esEs1(xw2030, xw198, bc)
new_esEs0(xw107, xw1060, ty_@0) → new_esEs2(xw107, xw1060)
new_esEs4(EQ, LT) → False
new_esEs4(LT, EQ) → False
new_esEs0(xw107, xw1060, app(ty_Maybe, dg)) → new_esEs13(xw107, xw1060, dg)
new_esEs13(xw10, xw90, ea) → error([])
new_esEs(xw2030, xw198, ty_@0) → new_esEs2(xw2030, xw198)
new_esEs(xw2030, xw198, app(ty_Ratio, cd)) → new_esEs14(xw2030, xw198, cd)
new_esEs12(xw10, xw90) → error([])
new_esEs6(xw10, xw90, ec, ed) → error([])
new_esEs0(xw107, xw1060, ty_Bool) → new_esEs9(xw107, xw1060)
new_esEs4(GT, EQ) → False
new_esEs4(EQ, GT) → False
new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) → new_esEs10(xw2030, xw198, bf, bg, bh)
new_esEs10(xw10, xw90, ee, ef, eg) → error([])
new_esEs4(GT, LT) → False
new_esEs4(LT, GT) → False
new_esEs(xw2030, xw198, ty_Ordering) → new_esEs4(xw2030, xw198)
new_esEs(xw2030, xw198, app(ty_Maybe, cc)) → new_esEs13(xw2030, xw198, cc)
new_esEs14(xw10, xw90, ce) → error([])
new_esEs(xw2030, xw198, ty_Bool) → new_esEs9(xw2030, xw198)
new_esEs(xw2030, xw198, ty_Char) → new_esEs5(xw2030, xw198)
new_esEs0(xw107, xw1060, ty_Double) → new_esEs12(xw107, xw1060)
new_esEs0(xw107, xw1060, app(app(ty_Either, de), df)) → new_esEs11(xw107, xw1060, de, df)
new_esEs(xw2030, xw198, ty_Integer) → new_esEs7(xw2030, xw198)
new_esEs11(xw10, xw90, eh, fa) → error([])
new_esEs(xw2030, xw198, ty_Int) → new_esEs8(xw2030, xw198)
new_esEs0(xw107, xw1060, app(ty_Ratio, dh)) → new_esEs14(xw107, xw1060, dh)
new_esEs0(xw107, xw1060, app(app(ty_@2, cg), da)) → new_esEs6(xw107, xw1060, cg, da)
new_esEs5(xw10, xw90) → error([])
new_esEs2(xw10, xw90) → error([])
new_esEs3(xw10, xw90) → error([])
new_esEs0(xw107, xw1060, app(app(app(ty_@3, db), dc), dd)) → new_esEs10(xw107, xw1060, db, dc, dd)
new_esEs1(xw10, xw90, eb) → error([])
new_esEs(xw2030, xw198, ty_Float) → new_esEs3(xw2030, xw198)
new_esEs0(xw107, xw1060, ty_Char) → new_esEs5(xw107, xw1060)
new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) → new_esEs11(xw2030, xw198, ca, cb)
new_esEs0(xw107, xw1060, ty_Integer) → new_esEs7(xw107, xw1060)
new_esEs8(xw10, xw90) → error([])
new_esEs0(xw107, xw1060, ty_Float) → new_esEs3(xw107, xw1060)
new_esEs4(EQ, EQ) → True
new_esEs9(xw10, xw90) → error([])
new_esEs4(GT, GT) → True
new_esEs0(xw107, xw1060, ty_Int) → new_esEs8(xw107, xw1060)
new_esEs(xw2030, xw198, ty_Double) → new_esEs12(xw2030, xw198)
new_esEs(xw2030, xw198, app(app(ty_@2, bd), be)) → new_esEs6(xw2030, xw198, bd, be)
new_esEs4(LT, LT) → True

The set Q consists of the following terms:

new_esEs0(x0, x1, ty_Double)
new_esEs13(x0, x1, x2)
new_esEs14(x0, x1, x2)
new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs(x0, x1, ty_Char)
new_esEs0(x0, x1, app(ty_[], x2))
new_esEs0(x0, x1, ty_Char)
new_esEs2(x0, x1)
new_esEs10(x0, x1, x2, x3, x4)
new_esEs(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, x2, x3)
new_esEs4(GT, LT)
new_esEs4(LT, GT)
new_esEs(x0, x1, ty_Bool)
new_esEs5(x0, x1)
new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs0(x0, x1, app(ty_Maybe, x2))
new_esEs4(LT, LT)
new_esEs0(x0, x1, ty_Integer)
new_esEs(x0, x1, app(app(ty_Either, x2), x3))
new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs(x0, x1, ty_Double)
new_esEs0(x0, x1, ty_Bool)
new_esEs12(x0, x1)
new_esEs6(x0, x1, x2, x3)
new_esEs0(x0, x1, ty_Int)
new_esEs4(LT, EQ)
new_esEs4(EQ, LT)
new_esEs1(x0, x1, x2)
new_esEs9(x0, x1)
new_esEs0(x0, x1, ty_Float)
new_esEs(x0, x1, ty_Int)
new_esEs(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1)
new_esEs(x0, x1, ty_Ordering)
new_esEs(x0, x1, ty_@0)
new_esEs(x0, x1, app(app(ty_@2, x2), x3))
new_esEs0(x0, x1, app(ty_Ratio, x2))
new_esEs7(x0, x1)
new_esEs0(x0, x1, ty_@0)
new_esEs(x0, x1, ty_Float)
new_esEs(x0, x1, ty_Integer)
new_esEs0(x0, x1, ty_Ordering)
new_esEs4(EQ, EQ)
new_esEs3(x0, x1)
new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs(x0, x1, app(ty_Maybe, x2))
new_esEs4(GT, EQ)
new_esEs4(EQ, GT)
new_esEs4(GT, GT)

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'(:(xw1060, xw1061), xw107, xw108, bb) → new_nubByNubBy'1(xw1060, xw1061, xw107, xw108, new_esEs0(xw107, xw1060, bb), xw108, bb)
The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) → new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6, 7 >= 7
new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) → new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) → new_nubByNubBy'(xw199, xw200, xw201, 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

                        ↳ QDPSizeChangeProof

                      ↳ QDP

                      ↳ QDP

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

new_deleteBy0(xw17, xw18, xw19, False, ba) → new_deleteBy(xw19, xw17, ba)
new_deleteBy(xw10, :(xw90, xw91), bb) → new_deleteBy0(xw91, xw90, xw10, new_esEs15(xw10, xw90, bb), bb)

The TRS R consists of the following rules:

new_esEs11(xw10, xw90, cc, cd) → error([])
new_esEs15(xw10, xw90, app(app(ty_@2, bf), bg)) → new_esEs6(xw10, xw90, bf, bg)
new_esEs5(xw10, xw90) → error([])
new_esEs15(xw10, xw90, ty_Double) → new_esEs12(xw10, xw90)
new_esEs15(xw10, xw90, app(ty_Maybe, bd)) → new_esEs13(xw10, xw90, bd)
new_esEs7(xw10, xw90) → error([])
new_esEs2(xw10, xw90) → error([])
new_esEs4(LT, EQ) → False
new_esEs4(EQ, LT) → False
new_esEs3(xw10, xw90) → error([])
new_esEs15(xw10, xw90, app(ty_Ratio, bc)) → new_esEs14(xw10, xw90, bc)
new_esEs1(xw10, xw90, be) → error([])
new_esEs15(xw10, xw90, ty_Int) → new_esEs8(xw10, xw90)
new_esEs15(xw10, xw90, app(app(ty_Either, cc), cd)) → new_esEs11(xw10, xw90, cc, cd)
new_esEs15(xw10, xw90, ty_Char) → new_esEs5(xw10, xw90)
new_esEs13(xw10, xw90, bd) → error([])
new_esEs8(xw10, xw90) → error([])
new_esEs12(xw10, xw90) → error([])
new_esEs15(xw10, xw90, ty_Bool) → new_esEs9(xw10, xw90)
new_esEs6(xw10, xw90, bf, bg) → error([])
new_esEs15(xw10, xw90, app(app(app(ty_@3, bh), ca), cb)) → new_esEs10(xw10, xw90, bh, ca, cb)
new_esEs4(EQ, GT) → False
new_esEs4(GT, EQ) → False
new_esEs4(EQ, EQ) → True
new_esEs9(xw10, xw90) → error([])
new_esEs10(xw10, xw90, bh, ca, cb) → error([])
new_esEs15(xw10, xw90, ty_Ordering) → new_esEs4(xw10, xw90)
new_esEs4(LT, GT) → False
new_esEs4(GT, LT) → False
new_esEs15(xw10, xw90, ty_Integer) → new_esEs7(xw10, xw90)
new_esEs15(xw10, xw90, ty_@0) → new_esEs2(xw10, xw90)
new_esEs4(GT, GT) → True
new_esEs15(xw10, xw90, ty_Float) → new_esEs3(xw10, xw90)
new_esEs14(xw10, xw90, bc) → error([])
new_esEs15(xw10, xw90, app(ty_[], be)) → new_esEs1(xw10, xw90, be)
new_esEs4(LT, LT) → True

The set Q consists of the following terms:

new_esEs4(LT, EQ)
new_esEs4(EQ, LT)
new_esEs6(x0, x1, x2, x3)
new_esEs14(x0, x1, x2)
new_esEs9(x0, x1)
new_esEs15(x0, x1, app(ty_[], x2))
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_esEs15(x0, x1, ty_Ordering)
new_esEs8(x0, x1)
new_esEs15(x0, x1, ty_Double)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1)
new_esEs2(x0, x1)
new_esEs15(x0, x1, ty_@0)
new_esEs1(x0, x1, x2)
new_esEs15(x0, x1, ty_Float)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_esEs4(LT, GT)
new_esEs4(GT, LT)
new_esEs15(x0, x1, ty_Char)
new_esEs4(EQ, EQ)
new_esEs15(x0, x1, ty_Int)
new_esEs3(x0, x1)
new_esEs5(x0, x1)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(LT, LT)
new_esEs13(x0, x1, x2)
new_esEs4(GT, EQ)
new_esEs4(EQ, GT)
new_esEs10(x0, x1, x2, x3, x4)
new_esEs15(x0, x1, ty_Bool)
new_esEs12(x0, x1)
new_esEs11(x0, x1, x2, x3)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(GT, GT)
new_esEs15(x0, x1, ty_Integer)

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

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

new_deleteBy(xw10, :(xw90, xw91), bb) → new_deleteBy0(xw91, xw90, xw10, new_esEs15(xw10, xw90, bb), bb)
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
new_deleteBy0(xw17, xw18, xw19, False, ba) → new_deleteBy(xw19, xw17, ba)
The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ Narrow

                    ↳ AND

                      ↳ QDP

                      ↳ QDP

                      ↳ QDP

                        ↳ QDPSizeChangeProof

                      ↳ QDP

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

new_foldl(xw9, xw10, :(xw110, xw111), ba) → new_foldl(new_flip(xw9, xw10, ba), xw110, xw111, ba)

The TRS R consists of the following rules:

new_esEs11(xw10, xw90, cc, cd) → error([])
new_esEs15(xw10, xw90, app(app(ty_@2, bf), bg)) → new_esEs6(xw10, xw90, bf, bg)
new_esEs5(xw10, xw90) → error([])
new_esEs15(xw10, xw90, ty_Double) → new_esEs12(xw10, xw90)
new_esEs15(xw10, xw90, app(ty_Maybe, bc)) → new_esEs13(xw10, xw90, bc)
new_esEs7(xw10, xw90) → error([])
new_esEs2(xw10, xw90) → error([])
new_deleteBy00(xw17, xw18, xw19, True, bd) → xw17
new_esEs4(LT, EQ) → False
new_esEs4(EQ, LT) → False
new_esEs3(xw10, xw90) → error([])
new_esEs15(xw10, xw90, app(ty_Ratio, bb)) → new_esEs14(xw10, xw90, bb)
new_esEs1(xw10, xw90, be) → error([])
new_esEs15(xw10, xw90, ty_Int) → new_esEs8(xw10, xw90)
new_esEs15(xw10, xw90, app(app(ty_Either, cc), cd)) → new_esEs11(xw10, xw90, cc, cd)
new_esEs15(xw10, xw90, ty_Char) → new_esEs5(xw10, xw90)
new_esEs13(xw10, xw90, bc) → error([])
new_deleteBy1(xw10, [], ba) → []
new_esEs8(xw10, xw90) → error([])
new_esEs15(xw10, xw90, ty_Bool) → new_esEs9(xw10, xw90)
new_esEs12(xw10, xw90) → error([])
new_esEs15(xw10, xw90, app(app(app(ty_@3, bh), ca), cb)) → new_esEs10(xw10, xw90, bh, ca, cb)
new_esEs6(xw10, xw90, bf, bg) → error([])
new_deleteBy1(xw10, :(xw90, xw91), ba) → new_deleteBy00(xw91, xw90, xw10, new_esEs15(xw10, xw90, ba), ba)
new_esEs4(EQ, GT) → False
new_esEs4(GT, EQ) → False
new_deleteBy00(xw17, xw18, xw19, False, bd) → :(xw18, new_deleteBy1(xw19, xw17, bd))
new_esEs4(EQ, EQ) → True
new_esEs9(xw10, xw90) → error([])
new_esEs10(xw10, xw90, bh, ca, cb) → error([])
new_esEs15(xw10, xw90, ty_Ordering) → new_esEs4(xw10, xw90)
new_esEs4(LT, GT) → False
new_esEs4(GT, LT) → False
new_esEs15(xw10, xw90, ty_Integer) → new_esEs7(xw10, xw90)
new_esEs15(xw10, xw90, ty_@0) → new_esEs2(xw10, xw90)
new_esEs4(GT, GT) → True
new_esEs15(xw10, xw90, ty_Float) → new_esEs3(xw10, xw90)
new_flip(xw9, xw10, ba) → new_deleteBy1(xw10, xw9, ba)
new_esEs14(xw10, xw90, bb) → error([])
new_esEs15(xw10, xw90, app(ty_[], be)) → new_esEs1(xw10, xw90, be)
new_esEs4(LT, LT) → True

The set Q consists of the following terms:

new_deleteBy00(x0, x1, x2, False, x3)
new_esEs4(LT, EQ)
new_esEs4(EQ, LT)
new_deleteBy00(x0, x1, x2, True, x3)
new_esEs6(x0, x1, x2, x3)
new_esEs9(x0, x1)
new_esEs15(x0, x1, app(ty_[], x2))
new_deleteBy1(x0, :(x1, x2), x3)
new_esEs15(x0, x1, ty_Ordering)
new_flip(x0, x1, x2)
new_esEs8(x0, x1)
new_esEs15(x0, x1, ty_Double)
new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1)
new_esEs2(x0, x1)
new_esEs15(x0, x1, ty_@0)
new_esEs1(x0, x1, x2)
new_esEs15(x0, x1, ty_Float)
new_esEs4(LT, GT)
new_esEs4(GT, LT)
new_esEs4(EQ, EQ)
new_esEs15(x0, x1, ty_Char)
new_esEs15(x0, x1, ty_Int)
new_esEs14(x0, x1, x2)
new_esEs3(x0, x1)
new_deleteBy1(x0, [], x1)
new_esEs5(x0, x1)
new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(x0, x1, app(ty_Maybe, x2))
new_esEs4(LT, LT)
new_esEs4(EQ, GT)
new_esEs4(GT, EQ)
new_esEs10(x0, x1, x2, x3, x4)
new_esEs15(x0, x1, ty_Bool)
new_esEs15(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1)
new_esEs11(x0, x1, x2, x3)
new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(GT, GT)
new_esEs15(x0, x1, ty_Integer)
new_esEs13(x0, x1, x2)

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

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

new_foldl(xw9, xw10, :(xw110, xw111), ba) → new_foldl(new_flip(xw9, xw10, ba), xw110, xw111, 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

                        ↳ QDPSizeChangeProof

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

new_psPs(:(xw80, xw81), xw9, xw10, xw11, ba) → new_psPs(xw81, xw9, xw10, xw11, ba)

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_psPs(:(xw80, xw81), xw9, xw10, xw11, ba) → new_psPs(xw81, xw9, xw10, xw11, 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'	xv [] vy	= nubByNubBy'3 xv [] vy
nubByNubBy'	xv (y : ys) xs	= nubByNubBy'2 xv (y : ys) xs

nubByNubBy'3	xv [] vy	= []
nubByNubBy'3	xv wz xu	= nubByNubBy'2 xv wz xu

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