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

YES 1.942 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

  ↳ LR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

intersect

intersectBy (==)

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

intersectBy

eq xs ys

concatMap (\vv2 ->

case	vv2 of
	x	->	if any (eq x) ys then x : [] else []
	_	->	[]

) xs

module Maybe where

import qualified List
import qualified Prelude

Lambda Reductions:
The following Lambda expression

\vv2→

case vv2 of
x → if any (eq x) ys then x : [] else []

_ → []

is transformed to

intersectBy0 eq ys vv2 =

case vv2 of
x → if any (eq x) ys then x : [] else []

_ → []

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

intersect

intersectBy (==)

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

intersectBy

eq xs ys

concatMap (intersectBy0 eq ys) xs

intersectBy0

eq ys vv2

case	vv2 of
	x	->	if any (eq x) ys then x : [] else []
	_	->	[]

module Maybe where

import qualified List
import qualified Prelude

Case Reductions:
The following Case expression

case vv2 of
x → if any (eq x) ys then x : [] else []

_ → []

is transformed to

intersectBy00 eq ys x = if any (eq x) ys then x : [] else []

intersectBy00 eq ys _ = []

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

intersect

intersectBy (==)

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

intersectBy

eq xs ys

concatMap (intersectBy0 eq ys) xs

intersectBy0

eq ys vv2

intersectBy00 eq ys vv2

intersectBy00	eq ys x	=	if any (eq x) ys then x : [] else []
intersectBy00	eq ys _	=	[]

module Maybe where

import qualified List
import qualified Prelude

If Reductions:
The following If expression

if any (eq x) ys then x : [] else []

is transformed to

intersectBy000 x True = x : []

intersectBy000 x False = []

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

intersect

intersectBy (==)

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

intersectBy

eq xs ys

concatMap (intersectBy0 eq ys) xs

intersectBy0

eq ys vv2

intersectBy00 eq ys vv2

intersectBy00	eq ys x	=	intersectBy000 x (any (eq x) ys)
intersectBy00	eq ys _	=	[]

intersectBy000	x True	=	x : []
intersectBy000	x False	=	[]

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

intersect

intersectBy (==)

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

intersectBy

eq xs ys

concatMap (intersectBy0 eq ys) xs

intersectBy0

eq ys vv2

intersectBy00 eq ys vv2

intersectBy00	eq ys x	=	intersectBy000 x (any (eq x) ys)
intersectBy00	eq ys vw	=	[]

intersectBy000	x True	=	x : []
intersectBy000	x False	=	[]

module Maybe where

import qualified List
import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

intersect

intersectBy (==)

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

intersectBy

eq xs ys

concatMap (intersectBy0 eq ys) xs

intersectBy0

eq ys vv2

intersectBy00 eq ys vv2

intersectBy00	eq ys x	=	intersectBy000 x (any (eq x) ys)
intersectBy00	eq ys vw	=	[]

intersectBy000	x True	=	x : []
intersectBy000	x False	=	[]

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
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5[label="intersectBy (==) xx3 xx4\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="concatMap (intersectBy0 (==) xx4) xx3\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="concat . map (intersectBy0 (==) xx4)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="concat (map (intersectBy0 (==) xx4) xx3)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
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1012 -> 10[label="",style="solid", color="burlywood", weight=3];
1013[label="xx3/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 1013[label="",style="solid", color="burlywood", weight=9];
1013 -> 11[label="",style="solid", color="burlywood", weight=3];
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11[label="foldr (++) [] (map (intersectBy0 (==) xx4) [])\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="foldr (++) [] (intersectBy0 (==) xx4 xx30 : map (intersectBy0 (==) xx4) xx31)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="foldr (++) [] []\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14 -> 16[label="",style="dashed", color="red", weight=0];
14[label="(++) intersectBy0 (==) xx4 xx30 foldr (++) [] (map (intersectBy0 (==) xx4) xx31)\n  Eq a  Eq b",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
15[label="[]\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0];
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18[label="xx31\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];19[label="(++) intersectBy00 (==) xx4 xx30 xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
20[label="(++) intersectBy000 xx30 (any ((==) xx30) xx4) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
21[label="(++) intersectBy000 xx30 (or . map ((==) xx30)) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
22[label="(++) intersectBy000 xx30 (or (map ((==) xx30) xx4)) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
23[label="(++) intersectBy000 xx30 (foldr (||) False (map ((==) xx30) xx4)) xx5\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1016[label="xx4/xx40 : xx41",fontsize=10,color="white",style="solid",shape="box"];23 -> 1016[label="",style="solid", color="burlywood", weight=9];
1016 -> 24[label="",style="solid", color="burlywood", weight=3];
1017[label="xx4/[]",fontsize=10,color="white",style="solid",shape="box"];23 -> 1017[label="",style="solid", color="burlywood", weight=9];
1017 -> 25[label="",style="solid", color="burlywood", weight=3];
24[label="(++) intersectBy000 xx30 (foldr (||) False (map ((==) xx30) (xx40 : xx41))) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
25[label="(++) intersectBy000 xx30 (foldr (||) False (map ((==) xx30) [])) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
26[label="(++) intersectBy000 xx30 (foldr (||) False (((==) xx30 xx40) : map ((==) xx30) xx41)) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
27[label="(++) intersectBy000 xx30 (foldr (||) False []) xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
28[label="(++) intersectBy000 xx30 ((||) (==) xx30 xx40 foldr (||) False (map ((==) xx30) xx41)) xx5\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1018[label="xx30/(xx300,xx301)",fontsize=10,color="white",style="solid",shape="box"];28 -> 1018[label="",style="solid", color="burlywood", weight=9];
1018 -> 30[label="",style="solid", color="burlywood", weight=3];
29[label="(++) intersectBy000 xx30 False xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
30[label="(++) intersectBy000 (xx300,xx301) ((||) (==) (xx300,xx301) xx40 foldr (||) False (map ((==) (xx300,xx301)) xx41)) xx5\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1019[label="xx40/(xx400,xx401)",fontsize=10,color="white",style="solid",shape="box"];30 -> 1019[label="",style="solid", color="burlywood", weight=9];
1019 -> 32[label="",style="solid", color="burlywood", weight=3];
31[label="(++) [] xx5\n  Eq a  Eq b",fontsize=16,color="black",shape="triangle"];31 -> 33[label="",style="solid", color="black", weight=3];
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33[label="xx5\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];34 -> 116[label="",style="dashed", color="red", weight=0];
34[label="(++) intersectBy000 (xx300,xx301) ((||) xx300 == xx400 && xx301 == xx401 foldr (||) False (map ((==) (xx300,xx301)) xx41)) xx5\n  Eq a  Eq b",fontsize=16,color="magenta"];34 -> 117[label="",style="dashed", color="magenta", weight=3];
34 -> 118[label="",style="dashed", color="magenta", weight=3];
34 -> 119[label="",style="dashed", color="magenta", weight=3];
34 -> 120[label="",style="dashed", color="magenta", weight=3];
34 -> 121[label="",style="dashed", color="magenta", weight=3];
117[label="xx301\n  Eq a",fontsize=16,color="green",shape="box"];118[label="xx300\n  Eq a",fontsize=16,color="green",shape="box"];119[label="xx41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];120 -> 336[label="",style="dashed", color="red", weight=0];
120[label="xx300 == xx400 && xx301 == xx401\n  Eq a  Eq b",fontsize=16,color="magenta"];120 -> 337[label="",style="dashed", color="magenta", weight=3];
120 -> 338[label="",style="dashed", color="magenta", weight=3];
121[label="xx5\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];116[label="(++) intersectBy000 (xx25,xx26) ((||) xx27 foldr (||) False (map ((==) (xx25,xx26)) xx28)) xx29\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1022[label="xx27/False",fontsize=10,color="white",style="solid",shape="box"];116 -> 1022[label="",style="solid", color="burlywood", weight=9];
1022 -> 141[label="",style="solid", color="burlywood", weight=3];
1023[label="xx27/True",fontsize=10,color="white",style="solid",shape="box"];116 -> 1023[label="",style="solid", color="burlywood", weight=9];
1023 -> 142[label="",style="solid", color="burlywood", weight=3];
337[label="xx300 == xx400\n  Eq a",fontsize=16,color="blue",shape="box"];1024[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1024[label="",style="solid", color="blue", weight=9];
1024 -> 341[label="",style="solid", color="blue", weight=3];
1025[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1025[label="",style="solid", color="blue", weight=9];
1025 -> 342[label="",style="solid", color="blue", weight=3];
1026[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1026[label="",style="solid", color="blue", weight=9];
1026 -> 343[label="",style="solid", color="blue", weight=3];
1027[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1027[label="",style="solid", color="blue", weight=9];
1027 -> 344[label="",style="solid", color="blue", weight=3];
1028[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1028[label="",style="solid", color="blue", weight=9];
1028 -> 345[label="",style="solid", color="blue", weight=3];
1029[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1029[label="",style="solid", color="blue", weight=9];
1029 -> 346[label="",style="solid", color="blue", weight=3];
1030[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1030[label="",style="solid", color="blue", weight=9];
1030 -> 347[label="",style="solid", color="blue", weight=3];
1031[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1031[label="",style="solid", color="blue", weight=9];
1031 -> 348[label="",style="solid", color="blue", weight=3];
1032[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1032[label="",style="solid", color="blue", weight=9];
1032 -> 349[label="",style="solid", color="blue", weight=3];
1033[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1033[label="",style="solid", color="blue", weight=9];
1033 -> 350[label="",style="solid", color="blue", weight=3];
1034[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1034[label="",style="solid", color="blue", weight=9];
1034 -> 351[label="",style="solid", color="blue", weight=3];
1035[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1035[label="",style="solid", color="blue", weight=9];
1035 -> 352[label="",style="solid", color="blue", weight=3];
1036[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1036[label="",style="solid", color="blue", weight=9];
1036 -> 353[label="",style="solid", color="blue", weight=3];
1037[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];337 -> 1037[label="",style="solid", color="blue", weight=9];
1037 -> 354[label="",style="solid", color="blue", weight=3];
338[label="xx301 == xx401\n  Eq a",fontsize=16,color="blue",shape="box"];1038[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1038[label="",style="solid", color="blue", weight=9];
1038 -> 355[label="",style="solid", color="blue", weight=3];
1039[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1039[label="",style="solid", color="blue", weight=9];
1039 -> 356[label="",style="solid", color="blue", weight=3];
1040[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1040[label="",style="solid", color="blue", weight=9];
1040 -> 357[label="",style="solid", color="blue", weight=3];
1041[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1041[label="",style="solid", color="blue", weight=9];
1041 -> 358[label="",style="solid", color="blue", weight=3];
1042[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1042[label="",style="solid", color="blue", weight=9];
1042 -> 359[label="",style="solid", color="blue", weight=3];
1043[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1043[label="",style="solid", color="blue", weight=9];
1043 -> 360[label="",style="solid", color="blue", weight=3];
1044[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1044[label="",style="solid", color="blue", weight=9];
1044 -> 361[label="",style="solid", color="blue", weight=3];
1045[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1045[label="",style="solid", color="blue", weight=9];
1045 -> 362[label="",style="solid", color="blue", weight=3];
1046[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1046[label="",style="solid", color="blue", weight=9];
1046 -> 363[label="",style="solid", color="blue", weight=3];
1047[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1047[label="",style="solid", color="blue", weight=9];
1047 -> 364[label="",style="solid", color="blue", weight=3];
1048[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1048[label="",style="solid", color="blue", weight=9];
1048 -> 365[label="",style="solid", color="blue", weight=3];
1049[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1049[label="",style="solid", color="blue", weight=9];
1049 -> 366[label="",style="solid", color="blue", weight=3];
1050[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1050[label="",style="solid", color="blue", weight=9];
1050 -> 367[label="",style="solid", color="blue", weight=3];
1051[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];338 -> 1051[label="",style="solid", color="blue", weight=9];
1051 -> 368[label="",style="solid", color="blue", weight=3];
336[label="xx41 && xx42",fontsize=16,color="burlywood",shape="triangle"];1052[label="xx41/False",fontsize=10,color="white",style="solid",shape="box"];336 -> 1052[label="",style="solid", color="burlywood", weight=9];
1052 -> 369[label="",style="solid", color="burlywood", weight=3];
1053[label="xx41/True",fontsize=10,color="white",style="solid",shape="box"];336 -> 1053[label="",style="solid", color="burlywood", weight=9];
1053 -> 370[label="",style="solid", color="burlywood", weight=3];
141[label="(++) intersectBy000 (xx25,xx26) ((||) False foldr (||) False (map ((==) (xx25,xx26)) xx28)) xx29\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];141 -> 159[label="",style="solid", color="black", weight=3];
142[label="(++) intersectBy000 (xx25,xx26) ((||) True foldr (||) False (map ((==) (xx25,xx26)) xx28)) xx29\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];142 -> 160[label="",style="solid", color="black", weight=3];
341[label="xx300 == xx400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1054[label="xx300/xx3000 : xx3001",fontsize=10,color="white",style="solid",shape="box"];341 -> 1054[label="",style="solid", color="burlywood", weight=9];
1054 -> 372[label="",style="solid", color="burlywood", weight=3];
1055[label="xx300/[]",fontsize=10,color="white",style="solid",shape="box"];341 -> 1055[label="",style="solid", color="burlywood", weight=9];
1055 -> 373[label="",style="solid", color="burlywood", weight=3];
342[label="xx300 == xx400",fontsize=16,color="burlywood",shape="triangle"];1056[label="xx300/LT",fontsize=10,color="white",style="solid",shape="box"];342 -> 1056[label="",style="solid", color="burlywood", weight=9];
1056 -> 374[label="",style="solid", color="burlywood", weight=3];
1057[label="xx300/EQ",fontsize=10,color="white",style="solid",shape="box"];342 -> 1057[label="",style="solid", color="burlywood", weight=9];
1057 -> 375[label="",style="solid", color="burlywood", weight=3];
1058[label="xx300/GT",fontsize=10,color="white",style="solid",shape="box"];342 -> 1058[label="",style="solid", color="burlywood", weight=9];
1058 -> 376[label="",style="solid", color="burlywood", weight=3];
343[label="xx300 == xx400",fontsize=16,color="burlywood",shape="triangle"];1059[label="xx300/Integer xx3000",fontsize=10,color="white",style="solid",shape="box"];343 -> 1059[label="",style="solid", color="burlywood", weight=9];
1059 -> 377[label="",style="solid", color="burlywood", weight=3];
344[label="xx300 == xx400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];1060[label="xx300/(xx3000,xx3001,xx3002)",fontsize=10,color="white",style="solid",shape="box"];344 -> 1060[label="",style="solid", color="burlywood", weight=9];
1060 -> 378[label="",style="solid", color="burlywood", weight=3];
345[label="xx300 == xx400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1061[label="xx300/Left xx3000",fontsize=10,color="white",style="solid",shape="box"];345 -> 1061[label="",style="solid", color="burlywood", weight=9];
1061 -> 379[label="",style="solid", color="burlywood", weight=3];
1062[label="xx300/Right xx3000",fontsize=10,color="white",style="solid",shape="box"];345 -> 1062[label="",style="solid", color="burlywood", weight=9];
1062 -> 380[label="",style="solid", color="burlywood", weight=3];
346[label="xx300 == xx400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1063[label="xx300/(xx3000,xx3001)",fontsize=10,color="white",style="solid",shape="box"];346 -> 1063[label="",style="solid", color="burlywood", weight=9];
1063 -> 381[label="",style="solid", color="burlywood", weight=3];
347[label="xx300 == xx400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1064[label="xx300/Nothing",fontsize=10,color="white",style="solid",shape="box"];347 -> 1064[label="",style="solid", color="burlywood", weight=9];
1064 -> 382[label="",style="solid", color="burlywood", weight=3];
1065[label="xx300/Just xx3000",fontsize=10,color="white",style="solid",shape="box"];347 -> 1065[label="",style="solid", color="burlywood", weight=9];
1065 -> 383[label="",style="solid", color="burlywood", weight=3];
348[label="xx300 == xx400",fontsize=16,color="burlywood",shape="triangle"];1066[label="xx300/False",fontsize=10,color="white",style="solid",shape="box"];348 -> 1066[label="",style="solid", color="burlywood", weight=9];
1066 -> 384[label="",style="solid", color="burlywood", weight=3];
1067[label="xx300/True",fontsize=10,color="white",style="solid",shape="box"];348 -> 1067[label="",style="solid", color="burlywood", weight=9];
1067 -> 385[label="",style="solid", color="burlywood", weight=3];
349[label="xx300 == xx400",fontsize=16,color="burlywood",shape="triangle"];1068[label="xx300/()",fontsize=10,color="white",style="solid",shape="box"];349 -> 1068[label="",style="solid", color="burlywood", weight=9];
1068 -> 386[label="",style="solid", color="burlywood", weight=3];
350[label="xx300 == xx400",fontsize=16,color="black",shape="triangle"];350 -> 387[label="",style="solid", color="black", weight=3];
351[label="xx300 == xx400\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];1069[label="xx300/xx3000 :% xx3001",fontsize=10,color="white",style="solid",shape="box"];351 -> 1069[label="",style="solid", color="burlywood", weight=9];
1069 -> 388[label="",style="solid", color="burlywood", weight=3];
352[label="xx300 == xx400",fontsize=16,color="black",shape="triangle"];352 -> 389[label="",style="solid", color="black", weight=3];
353[label="xx300 == xx400",fontsize=16,color="black",shape="triangle"];353 -> 390[label="",style="solid", color="black", weight=3];
354[label="xx300 == xx400",fontsize=16,color="black",shape="triangle"];354 -> 391[label="",style="solid", color="black", weight=3];
355 -> 341[label="",style="dashed", color="red", weight=0];
355[label="xx301 == xx401\n  Eq a",fontsize=16,color="magenta"];355 -> 392[label="",style="dashed", color="magenta", weight=3];
355 -> 393[label="",style="dashed", color="magenta", weight=3];
356 -> 342[label="",style="dashed", color="red", weight=0];
356[label="xx301 == xx401",fontsize=16,color="magenta"];356 -> 394[label="",style="dashed", color="magenta", weight=3];
356 -> 395[label="",style="dashed", color="magenta", weight=3];
357 -> 343[label="",style="dashed", color="red", weight=0];
357[label="xx301 == xx401",fontsize=16,color="magenta"];357 -> 396[label="",style="dashed", color="magenta", weight=3];
357 -> 397[label="",style="dashed", color="magenta", weight=3];
358 -> 344[label="",style="dashed", color="red", weight=0];
358[label="xx301 == xx401\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];358 -> 398[label="",style="dashed", color="magenta", weight=3];
358 -> 399[label="",style="dashed", color="magenta", weight=3];
359 -> 345[label="",style="dashed", color="red", weight=0];
359[label="xx301 == xx401\n  Eq a  Eq b",fontsize=16,color="magenta"];359 -> 400[label="",style="dashed", color="magenta", weight=3];
359 -> 401[label="",style="dashed", color="magenta", weight=3];
360 -> 346[label="",style="dashed", color="red", weight=0];
360[label="xx301 == xx401\n  Eq a  Eq b",fontsize=16,color="magenta"];360 -> 402[label="",style="dashed", color="magenta", weight=3];
360 -> 403[label="",style="dashed", color="magenta", weight=3];
361 -> 347[label="",style="dashed", color="red", weight=0];
361[label="xx301 == xx401\n  Eq a",fontsize=16,color="magenta"];361 -> 404[label="",style="dashed", color="magenta", weight=3];
361 -> 405[label="",style="dashed", color="magenta", weight=3];
362 -> 348[label="",style="dashed", color="red", weight=0];
362[label="xx301 == xx401",fontsize=16,color="magenta"];362 -> 406[label="",style="dashed", color="magenta", weight=3];
362 -> 407[label="",style="dashed", color="magenta", weight=3];
363 -> 349[label="",style="dashed", color="red", weight=0];
363[label="xx301 == xx401",fontsize=16,color="magenta"];363 -> 408[label="",style="dashed", color="magenta", weight=3];
363 -> 409[label="",style="dashed", color="magenta", weight=3];
364 -> 350[label="",style="dashed", color="red", weight=0];
364[label="xx301 == xx401",fontsize=16,color="magenta"];364 -> 410[label="",style="dashed", color="magenta", weight=3];
364 -> 411[label="",style="dashed", color="magenta", weight=3];
365 -> 351[label="",style="dashed", color="red", weight=0];
365[label="xx301 == xx401\n  Integral a",fontsize=16,color="magenta"];365 -> 412[label="",style="dashed", color="magenta", weight=3];
365 -> 413[label="",style="dashed", color="magenta", weight=3];
366 -> 352[label="",style="dashed", color="red", weight=0];
366[label="xx301 == xx401",fontsize=16,color="magenta"];366 -> 414[label="",style="dashed", color="magenta", weight=3];
366 -> 415[label="",style="dashed", color="magenta", weight=3];
367 -> 353[label="",style="dashed", color="red", weight=0];
367[label="xx301 == xx401",fontsize=16,color="magenta"];367 -> 416[label="",style="dashed", color="magenta", weight=3];
367 -> 417[label="",style="dashed", color="magenta", weight=3];
368 -> 354[label="",style="dashed", color="red", weight=0];
368[label="xx301 == xx401",fontsize=16,color="magenta"];368 -> 418[label="",style="dashed", color="magenta", weight=3];
368 -> 419[label="",style="dashed", color="magenta", weight=3];
369[label="False && xx42",fontsize=16,color="black",shape="box"];369 -> 420[label="",style="solid", color="black", weight=3];
370[label="True && xx42",fontsize=16,color="black",shape="box"];370 -> 421[label="",style="solid", color="black", weight=3];
159 -> 23[label="",style="dashed", color="red", weight=0];
159[label="(++) intersectBy000 (xx25,xx26) (foldr (||) False (map ((==) (xx25,xx26)) xx28)) xx29\n  Eq a  Eq b",fontsize=16,color="magenta"];159 -> 183[label="",style="dashed", color="magenta", weight=3];
159 -> 184[label="",style="dashed", color="magenta", weight=3];
159 -> 185[label="",style="dashed", color="magenta", weight=3];
160[label="(++) intersectBy000 (xx25,xx26) True xx29\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];160 -> 186[label="",style="solid", color="black", weight=3];
372[label="xx3000 : xx3001 == xx400\n  Eq a",fontsize=16,color="burlywood",shape="box"];1085[label="xx400/xx4000 : xx4001",fontsize=10,color="white",style="solid",shape="box"];372 -> 1085[label="",style="solid", color="burlywood", weight=9];
1085 -> 422[label="",style="solid", color="burlywood", weight=3];
1086[label="xx400/[]",fontsize=10,color="white",style="solid",shape="box"];372 -> 1086[label="",style="solid", color="burlywood", weight=9];
1086 -> 423[label="",style="solid", color="burlywood", weight=3];
373[label="[] == xx400\n  Eq a",fontsize=16,color="burlywood",shape="box"];1087[label="xx400/xx4000 : xx4001",fontsize=10,color="white",style="solid",shape="box"];373 -> 1087[label="",style="solid", color="burlywood", weight=9];
1087 -> 424[label="",style="solid", color="burlywood", weight=3];
1088[label="xx400/[]",fontsize=10,color="white",style="solid",shape="box"];373 -> 1088[label="",style="solid", color="burlywood", weight=9];
1088 -> 425[label="",style="solid", color="burlywood", weight=3];
374[label="LT == xx400",fontsize=16,color="burlywood",shape="box"];1089[label="xx400/LT",fontsize=10,color="white",style="solid",shape="box"];374 -> 1089[label="",style="solid", color="burlywood", weight=9];
1089 -> 426[label="",style="solid", color="burlywood", weight=3];
1090[label="xx400/EQ",fontsize=10,color="white",style="solid",shape="box"];374 -> 1090[label="",style="solid", color="burlywood", weight=9];
1090 -> 427[label="",style="solid", color="burlywood", weight=3];
1091[label="xx400/GT",fontsize=10,color="white",style="solid",shape="box"];374 -> 1091[label="",style="solid", color="burlywood", weight=9];
1091 -> 428[label="",style="solid", color="burlywood", weight=3];
375[label="EQ == xx400",fontsize=16,color="burlywood",shape="box"];1092[label="xx400/LT",fontsize=10,color="white",style="solid",shape="box"];375 -> 1092[label="",style="solid", color="burlywood", weight=9];
1092 -> 429[label="",style="solid", color="burlywood", weight=3];
1093[label="xx400/EQ",fontsize=10,color="white",style="solid",shape="box"];375 -> 1093[label="",style="solid", color="burlywood", weight=9];
1093 -> 430[label="",style="solid", color="burlywood", weight=3];
1094[label="xx400/GT",fontsize=10,color="white",style="solid",shape="box"];375 -> 1094[label="",style="solid", color="burlywood", weight=9];
1094 -> 431[label="",style="solid", color="burlywood", weight=3];
376[label="GT == xx400",fontsize=16,color="burlywood",shape="box"];1095[label="xx400/LT",fontsize=10,color="white",style="solid",shape="box"];376 -> 1095[label="",style="solid", color="burlywood", weight=9];
1095 -> 432[label="",style="solid", color="burlywood", weight=3];
1096[label="xx400/EQ",fontsize=10,color="white",style="solid",shape="box"];376 -> 1096[label="",style="solid", color="burlywood", weight=9];
1096 -> 433[label="",style="solid", color="burlywood", weight=3];
1097[label="xx400/GT",fontsize=10,color="white",style="solid",shape="box"];376 -> 1097[label="",style="solid", color="burlywood", weight=9];
1097 -> 434[label="",style="solid", color="burlywood", weight=3];
377[label="Integer xx3000 == xx400",fontsize=16,color="burlywood",shape="box"];1098[label="xx400/Integer xx4000",fontsize=10,color="white",style="solid",shape="box"];377 -> 1098[label="",style="solid", color="burlywood", weight=9];
1098 -> 435[label="",style="solid", color="burlywood", weight=3];
378[label="(xx3000,xx3001,xx3002) == xx400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1099[label="xx400/(xx4000,xx4001,xx4002)",fontsize=10,color="white",style="solid",shape="box"];378 -> 1099[label="",style="solid", color="burlywood", weight=9];
1099 -> 436[label="",style="solid", color="burlywood", weight=3];
379[label="Left xx3000 == xx400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1100[label="xx400/Left xx4000",fontsize=10,color="white",style="solid",shape="box"];379 -> 1100[label="",style="solid", color="burlywood", weight=9];
1100 -> 437[label="",style="solid", color="burlywood", weight=3];
1101[label="xx400/Right xx4000",fontsize=10,color="white",style="solid",shape="box"];379 -> 1101[label="",style="solid", color="burlywood", weight=9];
1101 -> 438[label="",style="solid", color="burlywood", weight=3];
380[label="Right xx3000 == xx400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1102[label="xx400/Left xx4000",fontsize=10,color="white",style="solid",shape="box"];380 -> 1102[label="",style="solid", color="burlywood", weight=9];
1102 -> 439[label="",style="solid", color="burlywood", weight=3];
1103[label="xx400/Right xx4000",fontsize=10,color="white",style="solid",shape="box"];380 -> 1103[label="",style="solid", color="burlywood", weight=9];
1103 -> 440[label="",style="solid", color="burlywood", weight=3];
381[label="(xx3000,xx3001) == xx400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1104[label="xx400/(xx4000,xx4001)",fontsize=10,color="white",style="solid",shape="box"];381 -> 1104[label="",style="solid", color="burlywood", weight=9];
1104 -> 441[label="",style="solid", color="burlywood", weight=3];
382[label="Nothing == xx400\n  Eq a",fontsize=16,color="burlywood",shape="box"];1105[label="xx400/Nothing",fontsize=10,color="white",style="solid",shape="box"];382 -> 1105[label="",style="solid", color="burlywood", weight=9];
1105 -> 442[label="",style="solid", color="burlywood", weight=3];
1106[label="xx400/Just xx4000",fontsize=10,color="white",style="solid",shape="box"];382 -> 1106[label="",style="solid", color="burlywood", weight=9];
1106 -> 443[label="",style="solid", color="burlywood", weight=3];
383[label="Just xx3000 == xx400\n  Eq a",fontsize=16,color="burlywood",shape="box"];1107[label="xx400/Nothing",fontsize=10,color="white",style="solid",shape="box"];383 -> 1107[label="",style="solid", color="burlywood", weight=9];
1107 -> 444[label="",style="solid", color="burlywood", weight=3];
1108[label="xx400/Just xx4000",fontsize=10,color="white",style="solid",shape="box"];383 -> 1108[label="",style="solid", color="burlywood", weight=9];
1108 -> 445[label="",style="solid", color="burlywood", weight=3];
384[label="False == xx400",fontsize=16,color="burlywood",shape="box"];1109[label="xx400/False",fontsize=10,color="white",style="solid",shape="box"];384 -> 1109[label="",style="solid", color="burlywood", weight=9];
1109 -> 446[label="",style="solid", color="burlywood", weight=3];
1110[label="xx400/True",fontsize=10,color="white",style="solid",shape="box"];384 -> 1110[label="",style="solid", color="burlywood", weight=9];
1110 -> 447[label="",style="solid", color="burlywood", weight=3];
385[label="True == xx400",fontsize=16,color="burlywood",shape="box"];1111[label="xx400/False",fontsize=10,color="white",style="solid",shape="box"];385 -> 1111[label="",style="solid", color="burlywood", weight=9];
1111 -> 448[label="",style="solid", color="burlywood", weight=3];
1112[label="xx400/True",fontsize=10,color="white",style="solid",shape="box"];385 -> 1112[label="",style="solid", color="burlywood", weight=9];
1112 -> 449[label="",style="solid", color="burlywood", weight=3];
386[label="() == xx400",fontsize=16,color="burlywood",shape="box"];1113[label="xx400/()",fontsize=10,color="white",style="solid",shape="box"];386 -> 1113[label="",style="solid", color="burlywood", weight=9];
1113 -> 450[label="",style="solid", color="burlywood", weight=3];
387[label="primEqFloat xx300 xx400",fontsize=16,color="burlywood",shape="box"];1114[label="xx300/Float xx3000 xx3001",fontsize=10,color="white",style="solid",shape="box"];387 -> 1114[label="",style="solid", color="burlywood", weight=9];
1114 -> 451[label="",style="solid", color="burlywood", weight=3];
388[label="xx3000 :% xx3001 == xx400\n  Integral a",fontsize=16,color="burlywood",shape="box"];1115[label="xx400/xx4000 :% xx4001",fontsize=10,color="white",style="solid",shape="box"];388 -> 1115[label="",style="solid", color="burlywood", weight=9];
1115 -> 452[label="",style="solid", color="burlywood", weight=3];
389[label="primEqChar xx300 xx400",fontsize=16,color="burlywood",shape="box"];1116[label="xx300/Char xx3000",fontsize=10,color="white",style="solid",shape="box"];389 -> 1116[label="",style="solid", color="burlywood", weight=9];
1116 -> 453[label="",style="solid", color="burlywood", weight=3];
390[label="primEqInt xx300 xx400",fontsize=16,color="burlywood",shape="triangle"];1117[label="xx300/Pos xx3000",fontsize=10,color="white",style="solid",shape="box"];390 -> 1117[label="",style="solid", color="burlywood", weight=9];
1117 -> 454[label="",style="solid", color="burlywood", weight=3];
1118[label="xx300/Neg xx3000",fontsize=10,color="white",style="solid",shape="box"];390 -> 1118[label="",style="solid", color="burlywood", weight=9];
1118 -> 455[label="",style="solid", color="burlywood", weight=3];
391[label="primEqDouble xx300 xx400",fontsize=16,color="burlywood",shape="box"];1119[label="xx300/Double xx3000 xx3001",fontsize=10,color="white",style="solid",shape="box"];391 -> 1119[label="",style="solid", color="burlywood", weight=9];
1119 -> 456[label="",style="solid", color="burlywood", weight=3];
392[label="xx301\n  Eq a",fontsize=16,color="green",shape="box"];393[label="xx401\n  Eq a",fontsize=16,color="green",shape="box"];394[label="xx301",fontsize=16,color="green",shape="box"];395[label="xx401",fontsize=16,color="green",shape="box"];396[label="xx301",fontsize=16,color="green",shape="box"];397[label="xx401",fontsize=16,color="green",shape="box"];398[label="xx301\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];399[label="xx401\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];400[label="xx301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];401[label="xx401\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];402[label="xx301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];403[label="xx401\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];404[label="xx301\n  Eq a",fontsize=16,color="green",shape="box"];405[label="xx401\n  Eq a",fontsize=16,color="green",shape="box"];406[label="xx301",fontsize=16,color="green",shape="box"];407[label="xx401",fontsize=16,color="green",shape="box"];408[label="xx301",fontsize=16,color="green",shape="box"];409[label="xx401",fontsize=16,color="green",shape="box"];410[label="xx301",fontsize=16,color="green",shape="box"];411[label="xx401",fontsize=16,color="green",shape="box"];412[label="xx301\n  Integral a",fontsize=16,color="green",shape="box"];413[label="xx401\n  Integral a",fontsize=16,color="green",shape="box"];414[label="xx301",fontsize=16,color="green",shape="box"];415[label="xx401",fontsize=16,color="green",shape="box"];416[label="xx301",fontsize=16,color="green",shape="box"];417[label="xx401",fontsize=16,color="green",shape="box"];418[label="xx301",fontsize=16,color="green",shape="box"];419[label="xx401",fontsize=16,color="green",shape="box"];420[label="False",fontsize=16,color="green",shape="box"];421[label="xx42",fontsize=16,color="green",shape="box"];183[label="xx28\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];184[label="xx29\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];185[label="(xx25,xx26)\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];186[label="(++) ((xx25,xx26) : []) xx29\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];186 -> 236[label="",style="solid", color="black", weight=3];
422[label="xx3000 : xx3001 == xx4000 : xx4001\n  Eq a",fontsize=16,color="black",shape="box"];422 -> 457[label="",style="solid", color="black", weight=3];
423[label="xx3000 : xx3001 == []\n  Eq a",fontsize=16,color="black",shape="box"];423 -> 458[label="",style="solid", color="black", weight=3];
424[label="[] == xx4000 : xx4001\n  Eq a",fontsize=16,color="black",shape="box"];424 -> 459[label="",style="solid", color="black", weight=3];
425[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];425 -> 460[label="",style="solid", color="black", weight=3];
426[label="LT == LT",fontsize=16,color="black",shape="box"];426 -> 461[label="",style="solid", color="black", weight=3];
427[label="LT == EQ",fontsize=16,color="black",shape="box"];427 -> 462[label="",style="solid", color="black", weight=3];
428[label="LT == GT",fontsize=16,color="black",shape="box"];428 -> 463[label="",style="solid", color="black", weight=3];
429[label="EQ == LT",fontsize=16,color="black",shape="box"];429 -> 464[label="",style="solid", color="black", weight=3];
430[label="EQ == EQ",fontsize=16,color="black",shape="box"];430 -> 465[label="",style="solid", color="black", weight=3];
431[label="EQ == GT",fontsize=16,color="black",shape="box"];431 -> 466[label="",style="solid", color="black", weight=3];
432[label="GT == LT",fontsize=16,color="black",shape="box"];432 -> 467[label="",style="solid", color="black", weight=3];
433[label="GT == EQ",fontsize=16,color="black",shape="box"];433 -> 468[label="",style="solid", color="black", weight=3];
434[label="GT == GT",fontsize=16,color="black",shape="box"];434 -> 469[label="",style="solid", color="black", weight=3];
435[label="Integer xx3000 == Integer xx4000",fontsize=16,color="black",shape="box"];435 -> 470[label="",style="solid", color="black", weight=3];
436[label="(xx3000,xx3001,xx3002) == (xx4000,xx4001,xx4002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];436 -> 471[label="",style="solid", color="black", weight=3];
437[label="Left xx3000 == Left xx4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];437 -> 472[label="",style="solid", color="black", weight=3];
438[label="Left xx3000 == Right xx4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];438 -> 473[label="",style="solid", color="black", weight=3];
439[label="Right xx3000 == Left xx4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];439 -> 474[label="",style="solid", color="black", weight=3];
440[label="Right xx3000 == Right xx4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];440 -> 475[label="",style="solid", color="black", weight=3];
441[label="(xx3000,xx3001) == (xx4000,xx4001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];441 -> 476[label="",style="solid", color="black", weight=3];
442[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];442 -> 477[label="",style="solid", color="black", weight=3];
443[label="Nothing == Just xx4000\n  Eq a",fontsize=16,color="black",shape="box"];443 -> 478[label="",style="solid", color="black", weight=3];
444[label="Just xx3000 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];444 -> 479[label="",style="solid", color="black", weight=3];
445[label="Just xx3000 == Just xx4000\n  Eq a",fontsize=16,color="black",shape="box"];445 -> 480[label="",style="solid", color="black", weight=3];
446[label="False == False",fontsize=16,color="black",shape="box"];446 -> 481[label="",style="solid", color="black", weight=3];
447[label="False == True",fontsize=16,color="black",shape="box"];447 -> 482[label="",style="solid", color="black", weight=3];
448[label="True == False",fontsize=16,color="black",shape="box"];448 -> 483[label="",style="solid", color="black", weight=3];
449[label="True == True",fontsize=16,color="black",shape="box"];449 -> 484[label="",style="solid", color="black", weight=3];
450[label="() == ()",fontsize=16,color="black",shape="box"];450 -> 485[label="",style="solid", color="black", weight=3];
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1120 -> 486[label="",style="solid", color="burlywood", weight=3];
452[label="xx3000 :% xx3001 == xx4000 :% xx4001\n  Integral a",fontsize=16,color="black",shape="box"];452 -> 487[label="",style="solid", color="black", weight=3];
453[label="primEqChar (Char xx3000) xx400",fontsize=16,color="burlywood",shape="box"];1121[label="xx400/Char xx4000",fontsize=10,color="white",style="solid",shape="box"];453 -> 1121[label="",style="solid", color="burlywood", weight=9];
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1122 -> 489[label="",style="solid", color="burlywood", weight=3];
1123[label="xx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];454 -> 1123[label="",style="solid", color="burlywood", weight=9];
1123 -> 490[label="",style="solid", color="burlywood", weight=3];
455[label="primEqInt (Neg xx3000) xx400",fontsize=16,color="burlywood",shape="box"];1124[label="xx3000/Succ xx30000",fontsize=10,color="white",style="solid",shape="box"];455 -> 1124[label="",style="solid", color="burlywood", weight=9];
1124 -> 491[label="",style="solid", color="burlywood", weight=3];
1125[label="xx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];455 -> 1125[label="",style="solid", color="burlywood", weight=9];
1125 -> 492[label="",style="solid", color="burlywood", weight=3];
456[label="primEqDouble (Double xx3000 xx3001) xx400",fontsize=16,color="burlywood",shape="box"];1126[label="xx400/Double xx4000 xx4001",fontsize=10,color="white",style="solid",shape="box"];456 -> 1126[label="",style="solid", color="burlywood", weight=9];
1126 -> 493[label="",style="solid", color="burlywood", weight=3];
236[label="(xx25,xx26) : [] ++ xx29\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];236 -> 302[label="",style="dashed", color="green", weight=3];
457 -> 336[label="",style="dashed", color="red", weight=0];
457[label="xx3000 == xx4000 && xx3001 == xx4001\n  Eq a",fontsize=16,color="magenta"];457 -> 494[label="",style="dashed", color="magenta", weight=3];
457 -> 495[label="",style="dashed", color="magenta", weight=3];
458[label="False",fontsize=16,color="green",shape="box"];459[label="False",fontsize=16,color="green",shape="box"];460[label="True",fontsize=16,color="green",shape="box"];461[label="True",fontsize=16,color="green",shape="box"];462[label="False",fontsize=16,color="green",shape="box"];463[label="False",fontsize=16,color="green",shape="box"];464[label="False",fontsize=16,color="green",shape="box"];465[label="True",fontsize=16,color="green",shape="box"];466[label="False",fontsize=16,color="green",shape="box"];467[label="False",fontsize=16,color="green",shape="box"];468[label="False",fontsize=16,color="green",shape="box"];469[label="True",fontsize=16,color="green",shape="box"];470 -> 390[label="",style="dashed", color="red", weight=0];
470[label="primEqInt xx3000 xx4000",fontsize=16,color="magenta"];470 -> 496[label="",style="dashed", color="magenta", weight=3];
470 -> 497[label="",style="dashed", color="magenta", weight=3];
471 -> 336[label="",style="dashed", color="red", weight=0];
471[label="xx3000 == xx4000 && xx3001 == xx4001 && xx3002 == xx4002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];471 -> 498[label="",style="dashed", color="magenta", weight=3];
471 -> 499[label="",style="dashed", color="magenta", weight=3];
472[label="xx3000 == xx4000\n  Eq a",fontsize=16,color="blue",shape="box"];1130[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1130[label="",style="solid", color="blue", weight=9];
1130 -> 500[label="",style="solid", color="blue", weight=3];
1131[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1131[label="",style="solid", color="blue", weight=9];
1131 -> 501[label="",style="solid", color="blue", weight=3];
1132[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1132[label="",style="solid", color="blue", weight=9];
1132 -> 502[label="",style="solid", color="blue", weight=3];
1133[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1133[label="",style="solid", color="blue", weight=9];
1133 -> 503[label="",style="solid", color="blue", weight=3];
1134[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1134[label="",style="solid", color="blue", weight=9];
1134 -> 504[label="",style="solid", color="blue", weight=3];
1135[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1135[label="",style="solid", color="blue", weight=9];
1135 -> 505[label="",style="solid", color="blue", weight=3];
1136[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1136[label="",style="solid", color="blue", weight=9];
1136 -> 506[label="",style="solid", color="blue", weight=3];
1137[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1137[label="",style="solid", color="blue", weight=9];
1137 -> 507[label="",style="solid", color="blue", weight=3];
1138[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1138[label="",style="solid", color="blue", weight=9];
1138 -> 508[label="",style="solid", color="blue", weight=3];
1139[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1139[label="",style="solid", color="blue", weight=9];
1139 -> 509[label="",style="solid", color="blue", weight=3];
1140[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1140[label="",style="solid", color="blue", weight=9];
1140 -> 510[label="",style="solid", color="blue", weight=3];
1141[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1141[label="",style="solid", color="blue", weight=9];
1141 -> 511[label="",style="solid", color="blue", weight=3];
1142[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1142[label="",style="solid", color="blue", weight=9];
1142 -> 512[label="",style="solid", color="blue", weight=3];
1143[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];472 -> 1143[label="",style="solid", color="blue", weight=9];
1143 -> 513[label="",style="solid", color="blue", weight=3];
473[label="False",fontsize=16,color="green",shape="box"];474[label="False",fontsize=16,color="green",shape="box"];475[label="xx3000 == xx4000\n  Eq a",fontsize=16,color="blue",shape="box"];1144[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1144[label="",style="solid", color="blue", weight=9];
1144 -> 514[label="",style="solid", color="blue", weight=3];
1145[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1145[label="",style="solid", color="blue", weight=9];
1145 -> 515[label="",style="solid", color="blue", weight=3];
1146[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1146[label="",style="solid", color="blue", weight=9];
1146 -> 516[label="",style="solid", color="blue", weight=3];
1147[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1147[label="",style="solid", color="blue", weight=9];
1147 -> 517[label="",style="solid", color="blue", weight=3];
1148[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1148[label="",style="solid", color="blue", weight=9];
1148 -> 518[label="",style="solid", color="blue", weight=3];
1149[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1149[label="",style="solid", color="blue", weight=9];
1149 -> 519[label="",style="solid", color="blue", weight=3];
1150[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1150[label="",style="solid", color="blue", weight=9];
1150 -> 520[label="",style="solid", color="blue", weight=3];
1151[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1151[label="",style="solid", color="blue", weight=9];
1151 -> 521[label="",style="solid", color="blue", weight=3];
1152[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1152[label="",style="solid", color="blue", weight=9];
1152 -> 522[label="",style="solid", color="blue", weight=3];
1153[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1153[label="",style="solid", color="blue", weight=9];
1153 -> 523[label="",style="solid", color="blue", weight=3];
1154[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1154[label="",style="solid", color="blue", weight=9];
1154 -> 524[label="",style="solid", color="blue", weight=3];
1155[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1155[label="",style="solid", color="blue", weight=9];
1155 -> 525[label="",style="solid", color="blue", weight=3];
1156[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1156[label="",style="solid", color="blue", weight=9];
1156 -> 526[label="",style="solid", color="blue", weight=3];
1157[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];475 -> 1157[label="",style="solid", color="blue", weight=9];
1157 -> 527[label="",style="solid", color="blue", weight=3];
476 -> 336[label="",style="dashed", color="red", weight=0];
476[label="xx3000 == xx4000 && xx3001 == xx4001\n  Eq a  Eq b",fontsize=16,color="magenta"];476 -> 528[label="",style="dashed", color="magenta", weight=3];
476 -> 529[label="",style="dashed", color="magenta", weight=3];
477[label="True",fontsize=16,color="green",shape="box"];478[label="False",fontsize=16,color="green",shape="box"];479[label="False",fontsize=16,color="green",shape="box"];480[label="xx3000 == xx4000\n  Eq a",fontsize=16,color="blue",shape="box"];1159[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1159[label="",style="solid", color="blue", weight=9];
1159 -> 530[label="",style="solid", color="blue", weight=3];
1160[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1160[label="",style="solid", color="blue", weight=9];
1160 -> 531[label="",style="solid", color="blue", weight=3];
1161[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1161[label="",style="solid", color="blue", weight=9];
1161 -> 532[label="",style="solid", color="blue", weight=3];
1162[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1162[label="",style="solid", color="blue", weight=9];
1162 -> 533[label="",style="solid", color="blue", weight=3];
1163[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1163[label="",style="solid", color="blue", weight=9];
1163 -> 534[label="",style="solid", color="blue", weight=3];
1164[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1164[label="",style="solid", color="blue", weight=9];
1164 -> 535[label="",style="solid", color="blue", weight=3];
1165[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1165[label="",style="solid", color="blue", weight=9];
1165 -> 536[label="",style="solid", color="blue", weight=3];
1166[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1166[label="",style="solid", color="blue", weight=9];
1166 -> 537[label="",style="solid", color="blue", weight=3];
1167[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1167[label="",style="solid", color="blue", weight=9];
1167 -> 538[label="",style="solid", color="blue", weight=3];
1168[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1168[label="",style="solid", color="blue", weight=9];
1168 -> 539[label="",style="solid", color="blue", weight=3];
1169[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1169[label="",style="solid", color="blue", weight=9];
1169 -> 540[label="",style="solid", color="blue", weight=3];
1170[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1170[label="",style="solid", color="blue", weight=9];
1170 -> 541[label="",style="solid", color="blue", weight=3];
1171[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1171[label="",style="solid", color="blue", weight=9];
1171 -> 542[label="",style="solid", color="blue", weight=3];
1172[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];480 -> 1172[label="",style="solid", color="blue", weight=9];
1172 -> 543[label="",style="solid", color="blue", weight=3];
481[label="True",fontsize=16,color="green",shape="box"];482[label="False",fontsize=16,color="green",shape="box"];483[label="False",fontsize=16,color="green",shape="box"];484[label="True",fontsize=16,color="green",shape="box"];485[label="True",fontsize=16,color="green",shape="box"];486[label="primEqFloat (Float xx3000 xx3001) (Float xx4000 xx4001)",fontsize=16,color="black",shape="box"];486 -> 544[label="",style="solid", color="black", weight=3];
487 -> 336[label="",style="dashed", color="red", weight=0];
487[label="xx3000 == xx4000 && xx3001 == xx4001\n  Integral a",fontsize=16,color="magenta"];487 -> 545[label="",style="dashed", color="magenta", weight=3];
487 -> 546[label="",style="dashed", color="magenta", weight=3];
488[label="primEqChar (Char xx3000) (Char xx4000)",fontsize=16,color="black",shape="box"];488 -> 547[label="",style="solid", color="black", weight=3];
489[label="primEqInt (Pos (Succ xx30000)) xx400",fontsize=16,color="burlywood",shape="box"];1174[label="xx400/Pos xx4000",fontsize=10,color="white",style="solid",shape="box"];489 -> 1174[label="",style="solid", color="burlywood", weight=9];
1174 -> 548[label="",style="solid", color="burlywood", weight=3];
1175[label="xx400/Neg xx4000",fontsize=10,color="white",style="solid",shape="box"];489 -> 1175[label="",style="solid", color="burlywood", weight=9];
1175 -> 549[label="",style="solid", color="burlywood", weight=3];
490[label="primEqInt (Pos Zero) xx400",fontsize=16,color="burlywood",shape="box"];1176[label="xx400/Pos xx4000",fontsize=10,color="white",style="solid",shape="box"];490 -> 1176[label="",style="solid", color="burlywood", weight=9];
1176 -> 550[label="",style="solid", color="burlywood", weight=3];
1177[label="xx400/Neg xx4000",fontsize=10,color="white",style="solid",shape="box"];490 -> 1177[label="",style="solid", color="burlywood", weight=9];
1177 -> 551[label="",style="solid", color="burlywood", weight=3];
491[label="primEqInt (Neg (Succ xx30000)) xx400",fontsize=16,color="burlywood",shape="box"];1178[label="xx400/Pos xx4000",fontsize=10,color="white",style="solid",shape="box"];491 -> 1178[label="",style="solid", color="burlywood", weight=9];
1178 -> 552[label="",style="solid", color="burlywood", weight=3];
1179[label="xx400/Neg xx4000",fontsize=10,color="white",style="solid",shape="box"];491 -> 1179[label="",style="solid", color="burlywood", weight=9];
1179 -> 553[label="",style="solid", color="burlywood", weight=3];
492[label="primEqInt (Neg Zero) xx400",fontsize=16,color="burlywood",shape="box"];1180[label="xx400/Pos xx4000",fontsize=10,color="white",style="solid",shape="box"];492 -> 1180[label="",style="solid", color="burlywood", weight=9];
1180 -> 554[label="",style="solid", color="burlywood", weight=3];
1181[label="xx400/Neg xx4000",fontsize=10,color="white",style="solid",shape="box"];492 -> 1181[label="",style="solid", color="burlywood", weight=9];
1181 -> 555[label="",style="solid", color="burlywood", weight=3];
493[label="primEqDouble (Double xx3000 xx3001) (Double xx4000 xx4001)",fontsize=16,color="black",shape="box"];493 -> 556[label="",style="solid", color="black", weight=3];
302 -> 31[label="",style="dashed", color="red", weight=0];
302[label="[] ++ xx29\n  Eq a  Eq b",fontsize=16,color="magenta"];302 -> 371[label="",style="dashed", color="magenta", weight=3];
494[label="xx3000 == xx4000\n  Eq a",fontsize=16,color="blue",shape="box"];1183[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1183[label="",style="solid", color="blue", weight=9];
1183 -> 557[label="",style="solid", color="blue", weight=3];
1184[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1184[label="",style="solid", color="blue", weight=9];
1184 -> 558[label="",style="solid", color="blue", weight=3];
1185[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1185[label="",style="solid", color="blue", weight=9];
1185 -> 559[label="",style="solid", color="blue", weight=3];
1186[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1186[label="",style="solid", color="blue", weight=9];
1186 -> 560[label="",style="solid", color="blue", weight=3];
1187[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1187[label="",style="solid", color="blue", weight=9];
1187 -> 561[label="",style="solid", color="blue", weight=3];
1188[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1188[label="",style="solid", color="blue", weight=9];
1188 -> 562[label="",style="solid", color="blue", weight=3];
1189[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1189[label="",style="solid", color="blue", weight=9];
1189 -> 563[label="",style="solid", color="blue", weight=3];
1190[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1190[label="",style="solid", color="blue", weight=9];
1190 -> 564[label="",style="solid", color="blue", weight=3];
1191[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1191[label="",style="solid", color="blue", weight=9];
1191 -> 565[label="",style="solid", color="blue", weight=3];
1192[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1192[label="",style="solid", color="blue", weight=9];
1192 -> 566[label="",style="solid", color="blue", weight=3];
1193[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1193[label="",style="solid", color="blue", weight=9];
1193 -> 567[label="",style="solid", color="blue", weight=3];
1194[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1194[label="",style="solid", color="blue", weight=9];
1194 -> 568[label="",style="solid", color="blue", weight=3];
1195[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1195[label="",style="solid", color="blue", weight=9];
1195 -> 569[label="",style="solid", color="blue", weight=3];
1196[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];494 -> 1196[label="",style="solid", color="blue", weight=9];
1196 -> 570[label="",style="solid", color="blue", weight=3];
495 -> 341[label="",style="dashed", color="red", weight=0];
495[label="xx3001 == xx4001\n  Eq a",fontsize=16,color="magenta"];495 -> 571[label="",style="dashed", color="magenta", weight=3];
495 -> 572[label="",style="dashed", color="magenta", weight=3];
496[label="xx3000",fontsize=16,color="green",shape="box"];497[label="xx4000",fontsize=16,color="green",shape="box"];498[label="xx3000 == xx4000\n  Eq a",fontsize=16,color="blue",shape="box"];1198[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];498 -> 1198[label="",style="solid", color="blue", weight=9];
1198 -> 573[label="",style="solid", color="blue", weight=3];
1199[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];498 -> 1199[label="",style="solid", color="blue", weight=9];
1199 -> 574[label="",style="solid", color="blue", weight=3];
1200[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];498 -> 1200[label="",style="solid", color="blue", weight=9];
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710[label="primEqInt (Pos (Succ xx30000)) (Pos Zero)",fontsize=16,color="black",shape="box"];710 -> 881[label="",style="solid", color="black", weight=3];
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↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

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

new_primPlusNat(Succ(xx4300), Succ(xx4000000)) → new_primPlusNat(xx4300, xx4000000)

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

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

new_primPlusNat(Succ(xx4300), Succ(xx4000000)) → new_primPlusNat(xx4300, xx4000000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

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

new_primMulNat(Succ(xx300000), Succ(xx400000)) → new_primMulNat(xx300000, Succ(xx400000))

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

new_primMulNat(Succ(xx300000), Succ(xx400000)) → new_primMulNat(xx300000, Succ(xx400000))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

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

new_primEqNat(Succ(xx30000), Succ(xx40000)) → new_primEqNat(xx30000, xx40000)

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

new_primEqNat(Succ(xx30000), Succ(xx40000)) → new_primEqNat(xx30000, xx40000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

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

new_esEs1(Right(xx3000), Right(xx4000), he, app(ty_Maybe, baf)) → new_esEs3(xx3000, xx4000, baf)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(app(ty_Either, ff), fg)) → new_esEs1(xx3002, xx4002, ff, fg)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(ty_Maybe, df), cd, ce) → new_esEs3(xx3000, xx4000, df)
new_esEs1(Left(xx3000), Left(xx4000), app(app(app(ty_@3, ge), gf), gg), gd) → new_esEs0(xx3000, xx4000, ge, gf, gg)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(app(ty_@2, bch), bda)) → new_esEs2(xx3001, xx4001, bch, bda)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(app(ty_@2, ef), eg), ce) → new_esEs2(xx3001, xx4001, ef, eg)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(app(ty_Either, db), dc), cd, ce) → new_esEs1(xx3000, xx4000, db, dc)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(ty_Maybe, bbh), bah) → new_esEs3(xx3000, xx4000, bbh)
new_esEs1(Right(xx3000), Right(xx4000), he, app(app(app(ty_@3, hg), hh), baa)) → new_esEs0(xx3000, xx4000, hg, hh, baa)
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(app(ty_@2, bg), bh)) → new_esEs2(xx3000, xx4000, bg, bh)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(app(ty_@2, bbf), bbg), bah) → new_esEs2(xx3000, xx4000, bbf, bbg)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(ty_Maybe, bdb)) → new_esEs3(xx3001, xx4001, bdb)
new_esEs1(Left(xx3000), Left(xx4000), app(app(ty_Either, gh), ha), gd) → new_esEs1(xx3000, xx4000, gh, ha)
new_esEs1(Right(xx3000), Right(xx4000), he, app(app(ty_Either, bab), bac)) → new_esEs1(xx3000, xx4000, bab, bac)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(app(app(ty_@3, ea), eb), ec), ce) → new_esEs0(xx3001, xx4001, ea, eb, ec)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(app(ty_@2, dd), de), cd, ce) → new_esEs2(xx3000, xx4000, dd, de)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(ty_[], fa)) → new_esEs(xx3002, xx4002, fa)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(app(ty_Either, ed), ee), ce) → new_esEs1(xx3001, xx4001, ed, ee)
new_esEs1(Left(xx3000), Left(xx4000), app(app(ty_@2, hb), hc), gd) → new_esEs2(xx3000, xx4000, hb, hc)
new_esEs3(Just(xx3000), Just(xx4000), app(app(ty_@2, bea), beb)) → new_esEs2(xx3000, xx4000, bea, beb)
new_esEs3(Just(xx3000), Just(xx4000), app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs0(xx3000, xx4000, bdd, bde, bdf)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(ty_Maybe, eh), ce) → new_esEs3(xx3001, xx4001, eh)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(ty_Maybe, gb)) → new_esEs3(xx3002, xx4002, gb)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(app(ty_Either, bcf), bcg)) → new_esEs1(xx3001, xx4001, bcf, bcg)
new_esEs3(Just(xx3000), Just(xx4000), app(ty_[], bdc)) → new_esEs(xx3000, xx4000, bdc)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(app(ty_@2, fh), ga)) → new_esEs2(xx3002, xx4002, fh, ga)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(ty_[], cc), cd, ce) → new_esEs(xx3000, xx4000, cc)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(xx3001, xx4001, bcc, bcd, bce)
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), cb) → new_esEs(xx3001, xx4001, cb)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(ty_[], bcb)) → new_esEs(xx3001, xx4001, bcb)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(app(app(ty_@3, fb), fc), fd)) → new_esEs0(xx3002, xx4002, fb, fc, fd)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(ty_[], dh), ce) → new_esEs(xx3001, xx4001, dh)
new_esEs1(Right(xx3000), Right(xx4000), he, app(app(ty_@2, bad), bae)) → new_esEs2(xx3000, xx4000, bad, bae)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(xx3000, xx4000, bba, bbb, bbc)
new_esEs3(Just(xx3000), Just(xx4000), app(ty_Maybe, bec)) → new_esEs3(xx3000, xx4000, bec)
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(xx3000, xx4000, bb, bc, bd)
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(ty_Maybe, ca)) → new_esEs3(xx3000, xx4000, ca)
new_esEs1(Left(xx3000), Left(xx4000), app(ty_Maybe, hd), gd) → new_esEs3(xx3000, xx4000, hd)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(ty_[], bag), bah) → new_esEs(xx3000, xx4000, bag)
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(app(ty_Either, be), bf)) → new_esEs1(xx3000, xx4000, be, bf)
new_esEs1(Right(xx3000), Right(xx4000), he, app(ty_[], hf)) → new_esEs(xx3000, xx4000, hf)
new_esEs1(Left(xx3000), Left(xx4000), app(ty_[], gc), gd) → new_esEs(xx3000, xx4000, gc)
new_esEs3(Just(xx3000), Just(xx4000), app(app(ty_Either, bdg), bdh)) → new_esEs1(xx3000, xx4000, bdg, bdh)
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(app(ty_Either, bbd), bbe), bah) → new_esEs1(xx3000, xx4000, bbd, bbe)
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(ty_[], ba)) → new_esEs(xx3000, xx4000, ba)
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(app(app(ty_@3, cf), cg), da), cd, ce) → new_esEs0(xx3000, xx4000, cf, cg, da)

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

new_esEs3(Just(xx3000), Just(xx4000), app(app(ty_Either, bdg), bdh)) → new_esEs1(xx3000, xx4000, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(xx3000), Just(xx4000), app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs0(xx3000, xx4000, bdd, bde, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(xx3000), Just(xx4000), app(app(ty_@2, bea), beb)) → new_esEs2(xx3000, xx4000, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(app(ty_Either, be), bf)) → new_esEs1(xx3000, xx4000, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(app(app(ty_@3, bb), bc), bd)) → new_esEs0(xx3000, xx4000, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(app(ty_@2, bg), bh)) → new_esEs2(xx3000, xx4000, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(xx3000), Just(xx4000), app(ty_[], bdc)) → new_esEs(xx3000, xx4000, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xx3000), Just(xx4000), app(ty_Maybe, bec)) → new_esEs3(xx3000, xx4000, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(ty_Maybe, ca)) → new_esEs3(xx3000, xx4000, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Left(xx3000), Left(xx4000), app(app(ty_Either, gh), ha), gd) → new_esEs1(xx3000, xx4000, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Right(xx3000), Right(xx4000), he, app(app(ty_Either, bab), bac)) → new_esEs1(xx3000, xx4000, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(app(ty_Either, ff), fg)) → new_esEs1(xx3002, xx4002, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(app(ty_Either, db), dc), cd, ce) → new_esEs1(xx3000, xx4000, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(app(ty_Either, ed), ee), ce) → new_esEs1(xx3001, xx4001, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(app(ty_Either, bcf), bcg)) → new_esEs1(xx3001, xx4001, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(app(ty_Either, bbd), bbe), bah) → new_esEs1(xx3000, xx4000, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Left(xx3000), Left(xx4000), app(app(app(ty_@3, ge), gf), gg), gd) → new_esEs0(xx3000, xx4000, ge, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(Right(xx3000), Right(xx4000), he, app(app(app(ty_@3, hg), hh), baa)) → new_esEs0(xx3000, xx4000, hg, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(Left(xx3000), Left(xx4000), app(app(ty_@2, hb), hc), gd) → new_esEs2(xx3000, xx4000, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Right(xx3000), Right(xx4000), he, app(app(ty_@2, bad), bae)) → new_esEs2(xx3000, xx4000, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(Right(xx3000), Right(xx4000), he, app(ty_[], hf)) → new_esEs(xx3000, xx4000, hf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Left(xx3000), Left(xx4000), app(ty_[], gc), gd) → new_esEs(xx3000, xx4000, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Right(xx3000), Right(xx4000), he, app(ty_Maybe, baf)) → new_esEs3(xx3000, xx4000, baf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(Left(xx3000), Left(xx4000), app(ty_Maybe, hd), gd) → new_esEs3(xx3000, xx4000, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(app(app(ty_@3, ea), eb), ec), ce) → new_esEs0(xx3001, xx4001, ea, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(app(app(ty_@3, fb), fc), fd)) → new_esEs0(xx3002, xx4002, fb, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(app(app(ty_@3, cf), cg), da), cd, ce) → new_esEs0(xx3000, xx4000, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(xx3001, xx4001, bcc, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(app(app(ty_@3, bba), bbb), bbc), bah) → new_esEs0(xx3000, xx4000, bba, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(app(ty_@2, ef), eg), ce) → new_esEs2(xx3001, xx4001, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(app(ty_@2, dd), de), cd, ce) → new_esEs2(xx3000, xx4000, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(app(ty_@2, fh), ga)) → new_esEs2(xx3002, xx4002, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(ty_[], fa)) → new_esEs(xx3002, xx4002, fa)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(ty_[], cc), cd, ce) → new_esEs(xx3000, xx4000, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(ty_[], dh), ce) → new_esEs(xx3001, xx4001, dh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), app(ty_Maybe, df), cd, ce) → new_esEs3(xx3000, xx4000, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, app(ty_Maybe, eh), ce) → new_esEs3(xx3001, xx4001, eh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), dg, cd, app(ty_Maybe, gb)) → new_esEs3(xx3002, xx4002, gb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(app(ty_@2, bch), bda)) → new_esEs2(xx3001, xx4001, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(app(ty_@2, bbf), bbg), bah) → new_esEs2(xx3000, xx4000, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(ty_[], bcb)) → new_esEs(xx3001, xx4001, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(ty_[], bag), bah) → new_esEs(xx3000, xx4000, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), app(ty_Maybe, bbh), bah) → new_esEs3(xx3000, xx4000, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@2(xx3000, xx3001), @2(xx4000, xx4001), bca, app(ty_Maybe, bdb)) → new_esEs3(xx3001, xx4001, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), cb) → new_esEs(xx3001, xx4001, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(:(xx3000, xx3001), :(xx4000, xx4001), app(ty_[], ba)) → new_esEs(xx3000, xx4000, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

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

new_psPs(xx25, xx26, False, xx28, xx29, ba, bb) → new_psPs0(@2(xx25, xx26), xx28, xx29, ba, bb)
new_psPs0(@2(xx300, xx301), :(@2(xx400, xx401), xx41), xx5, bc, bd) → new_psPs(xx300, xx301, new_asAs(new_esEs4(xx300, xx400, bc), new_esEs5(xx301, xx401, bd)), xx41, xx5, bc, bd)

The TRS R consists of the following rules:

new_esEs15(Just(xx3000), Just(xx4000), app(app(ty_Either, bgg), bgh)) → new_esEs13(xx3000, xx4000, bgg, bgh)
new_primPlusNat1(Succ(xx4300), Succ(xx4000000)) → Succ(Succ(new_primPlusNat1(xx4300, xx4000000)))
new_esEs27(xx3001, xx4001, ty_Char) → new_esEs19(xx3001, xx4001)
new_esEs26(xx3000, xx4000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs12(xx3000, xx4000, bdh, bea, beb)
new_esEs4(xx300, xx400, ty_@0) → new_esEs16(xx300, xx400)
new_primEqInt(Pos(Succ(xx30000)), Neg(xx4000)) → False
new_primEqInt(Neg(Succ(xx30000)), Pos(xx4000)) → False
new_esEs20(xx3000, xx4000, ty_@0) → new_esEs16(xx3000, xx4000)
new_esEs15(Just(xx3000), Just(xx4000), app(ty_Ratio, bhd)) → new_esEs18(xx3000, xx4000, bhd)
new_esEs27(xx3001, xx4001, app(ty_Ratio, bgb)) → new_esEs18(xx3001, xx4001, bgb)
new_esEs22(xx3002, xx4002, ty_Ordering) → new_esEs7(xx3002, xx4002)
new_esEs26(xx3000, xx4000, ty_Int) → new_esEs9(xx3000, xx4000)
new_esEs11(Integer(xx3000), Integer(xx4000)) → new_primEqInt(xx3000, xx4000)
new_primEqInt(Pos(Zero), Neg(Succ(xx40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xx40000))) → False
new_esEs13(Left(xx3000), Left(xx4000), ty_Bool, cb) → new_esEs6(xx3000, xx4000)
new_esEs26(xx3000, xx4000, ty_Integer) → new_esEs11(xx3000, xx4000)
new_esEs15(Just(xx3000), Just(xx4000), ty_Integer) → new_esEs11(xx3000, xx4000)
new_esEs13(Left(xx3000), Left(xx4000), app(app(ty_Either, hc), hd), cb) → new_esEs13(xx3000, xx4000, hc, hd)
new_esEs23(xx3000, xx4000, app(app(ty_Either, bbg), bbh)) → new_esEs13(xx3000, xx4000, bbg, bbh)
new_esEs20(xx3000, xx4000, ty_Int) → new_esEs9(xx3000, xx4000)
new_esEs22(xx3002, xx4002, ty_@0) → new_esEs16(xx3002, xx4002)
new_esEs23(xx3000, xx4000, ty_Float) → new_esEs17(xx3000, xx4000)
new_esEs20(xx3000, xx4000, ty_Char) → new_esEs19(xx3000, xx4000)
new_esEs26(xx3000, xx4000, ty_Float) → new_esEs17(xx3000, xx4000)
new_esEs5(xx301, xx401, app(ty_[], bce)) → new_esEs10(xx301, xx401, bce)
new_esEs7(LT, GT) → False
new_esEs7(GT, LT) → False
new_primMulNat0(Zero, Zero) → Zero
new_esEs15(Just(xx3000), Just(xx4000), ty_Double) → new_esEs8(xx3000, xx4000)
new_esEs5(xx301, xx401, app(ty_Ratio, bdf)) → new_esEs18(xx301, xx401, bdf)
new_esEs4(xx300, xx400, app(ty_Ratio, cf)) → new_esEs18(xx300, xx400, cf)
new_esEs26(xx3000, xx4000, app(ty_Maybe, beg)) → new_esEs15(xx3000, xx4000, beg)
new_esEs13(Right(xx3000), Right(xx4000), ca, app(app(ty_@2, bag), bah)) → new_esEs14(xx3000, xx4000, bag, bah)
new_esEs21(xx3001, xx4001, ty_Ordering) → new_esEs7(xx3001, xx4001)
new_esEs23(xx3000, xx4000, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs12(xx3000, xx4000, bbd, bbe, bbf)
new_esEs20(xx3000, xx4000, app(app(ty_@2, df), dg)) → new_esEs14(xx3000, xx4000, df, dg)
new_esEs21(xx3001, xx4001, app(ty_[], eb)) → new_esEs10(xx3001, xx4001, eb)
new_primPlusNat0(Zero, xx400000) → Succ(xx400000)
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Integer) → new_esEs11(xx3000, xx4000)
new_esEs26(xx3000, xx4000, app(ty_Ratio, beh)) → new_esEs18(xx3000, xx4000, beh)
new_esEs13(Left(xx3000), Left(xx4000), ty_Char, cb) → new_esEs19(xx3000, xx4000)
new_esEs15(Just(xx3000), Just(xx4000), ty_Bool) → new_esEs6(xx3000, xx4000)
new_esEs20(xx3000, xx4000, app(app(app(ty_@3, da), db), dc)) → new_esEs12(xx3000, xx4000, da, db, dc)
new_esEs12(@3(xx3000, xx3001, xx3002), @3(xx4000, xx4001, xx4002), bf, bg, bh) → new_asAs(new_esEs20(xx3000, xx4000, bf), new_asAs(new_esEs21(xx3001, xx4001, bg), new_esEs22(xx3002, xx4002, bh)))
new_sr(Neg(xx30000), Pos(xx40000)) → Neg(new_primMulNat0(xx30000, xx40000))
new_sr(Pos(xx30000), Neg(xx40000)) → Neg(new_primMulNat0(xx30000, xx40000))
new_esEs22(xx3002, xx4002, ty_Integer) → new_esEs11(xx3002, xx4002)
new_esEs15(Just(xx3000), Just(xx4000), ty_Float) → new_esEs17(xx3000, xx4000)
new_esEs23(xx3000, xx4000, app(ty_[], bbc)) → new_esEs10(xx3000, xx4000, bbc)
new_esEs26(xx3000, xx4000, app(ty_[], bdg)) → new_esEs10(xx3000, xx4000, bdg)
new_esEs26(xx3000, xx4000, ty_Double) → new_esEs8(xx3000, xx4000)
new_esEs25(xx3001, xx4001, ty_Integer) → new_esEs11(xx3001, xx4001)
new_esEs7(LT, LT) → True
new_esEs20(xx3000, xx4000, app(app(ty_Either, dd), de)) → new_esEs13(xx3000, xx4000, dd, de)
new_esEs15(Just(xx3000), Just(xx4000), app(ty_[], bgc)) → new_esEs10(xx3000, xx4000, bgc)
new_esEs24(xx3000, xx4000, ty_Integer) → new_esEs11(xx3000, xx4000)
new_esEs22(xx3002, xx4002, app(app(ty_Either, ga), gb)) → new_esEs13(xx3002, xx4002, ga, gb)
new_esEs23(xx3000, xx4000, app(ty_Maybe, bcc)) → new_esEs15(xx3000, xx4000, bcc)
new_esEs4(xx300, xx400, ty_Float) → new_esEs17(xx300, xx400)
new_esEs26(xx3000, xx4000, ty_Bool) → new_esEs6(xx3000, xx4000)
new_esEs4(xx300, xx400, ty_Ordering) → new_esEs7(xx300, xx400)
new_esEs13(Left(xx3000), Left(xx4000), ty_Ordering, cb) → new_esEs7(xx3000, xx4000)
new_esEs22(xx3002, xx4002, app(ty_Ratio, gf)) → new_esEs18(xx3002, xx4002, gf)
new_primEqNat0(Zero, Succ(xx40000)) → False
new_primEqNat0(Succ(xx30000), Zero) → False
new_esEs21(xx3001, xx4001, ty_Int) → new_esEs9(xx3001, xx4001)
new_esEs22(xx3002, xx4002, ty_Float) → new_esEs17(xx3002, xx4002)
new_esEs15(Just(xx3000), Just(xx4000), ty_Int) → new_esEs9(xx3000, xx4000)
new_esEs17(Float(xx3000, xx3001), Float(xx4000, xx4001)) → new_esEs9(new_sr(xx3000, xx4000), new_sr(xx3001, xx4001))
new_esEs22(xx3002, xx4002, app(app(ty_@2, gc), gd)) → new_esEs14(xx3002, xx4002, gc, gd)
new_esEs20(xx3000, xx4000, app(ty_[], cg)) → new_esEs10(xx3000, xx4000, cg)
new_esEs27(xx3001, xx4001, app(app(ty_Either, bfe), bff)) → new_esEs13(xx3001, xx4001, bfe, bff)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(xx3000, xx4000, app(ty_Ratio, bcd)) → new_esEs18(xx3000, xx4000, bcd)
new_esEs13(Left(xx3000), Left(xx4000), app(app(ty_@2, he), hf), cb) → new_esEs14(xx3000, xx4000, he, hf)
new_esEs20(xx3000, xx4000, ty_Bool) → new_esEs6(xx3000, xx4000)
new_esEs21(xx3001, xx4001, app(app(ty_@2, eh), fa)) → new_esEs14(xx3001, xx4001, eh, fa)
new_esEs27(xx3001, xx4001, ty_@0) → new_esEs16(xx3001, xx4001)
new_esEs13(Left(xx3000), Left(xx4000), ty_Double, cb) → new_esEs8(xx3000, xx4000)
new_esEs22(xx3002, xx4002, ty_Int) → new_esEs9(xx3002, xx4002)
new_esEs4(xx300, xx400, app(ty_[], be)) → new_esEs10(xx300, xx400, be)
new_esEs21(xx3001, xx4001, app(app(app(ty_@3, ec), ed), ee)) → new_esEs12(xx3001, xx4001, ec, ed, ee)
new_esEs22(xx3002, xx4002, app(app(app(ty_@3, ff), fg), fh)) → new_esEs12(xx3002, xx4002, ff, fg, fh)
new_esEs15(Nothing, Nothing, ce) → True
new_esEs5(xx301, xx401, ty_Bool) → new_esEs6(xx301, xx401)
new_esEs13(Left(xx3000), Left(xx4000), ty_@0, cb) → new_esEs16(xx3000, xx4000)
new_esEs27(xx3001, xx4001, ty_Float) → new_esEs17(xx3001, xx4001)
new_esEs27(xx3001, xx4001, app(ty_Maybe, bga)) → new_esEs15(xx3001, xx4001, bga)
new_esEs23(xx3000, xx4000, ty_Double) → new_esEs8(xx3000, xx4000)
new_esEs5(xx301, xx401, ty_Double) → new_esEs8(xx301, xx401)
new_esEs4(xx300, xx400, ty_Integer) → new_esEs11(xx300, xx400)
new_esEs24(xx3000, xx4000, ty_Int) → new_esEs9(xx3000, xx4000)
new_esEs7(EQ, EQ) → True
new_esEs22(xx3002, xx4002, ty_Bool) → new_esEs6(xx3002, xx4002)
new_esEs23(xx3000, xx4000, ty_Ordering) → new_esEs7(xx3000, xx4000)
new_esEs4(xx300, xx400, ty_Char) → new_esEs19(xx300, xx400)
new_esEs6(True, True) → True
new_esEs27(xx3001, xx4001, ty_Int) → new_esEs9(xx3001, xx4001)
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Float) → new_esEs17(xx3000, xx4000)
new_esEs26(xx3000, xx4000, ty_Char) → new_esEs19(xx3000, xx4000)
new_esEs10(:(xx3000, xx3001), :(xx4000, xx4001), be) → new_asAs(new_esEs23(xx3000, xx4000, be), new_esEs10(xx3001, xx4001, be))
new_esEs20(xx3000, xx4000, app(ty_Ratio, ea)) → new_esEs18(xx3000, xx4000, ea)
new_esEs13(Left(xx3000), Left(xx4000), ty_Int, cb) → new_esEs9(xx3000, xx4000)
new_esEs5(xx301, xx401, ty_@0) → new_esEs16(xx301, xx401)
new_esEs27(xx3001, xx4001, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs12(xx3001, xx4001, bfb, bfc, bfd)
new_esEs26(xx3000, xx4000, app(app(ty_@2, bee), bef)) → new_esEs14(xx3000, xx4000, bee, bef)
new_esEs19(Char(xx3000), Char(xx4000)) → new_primEqNat0(xx3000, xx4000)
new_esEs22(xx3002, xx4002, ty_Char) → new_esEs19(xx3002, xx4002)
new_esEs15(Just(xx3000), Just(xx4000), app(app(ty_@2, bha), bhb)) → new_esEs14(xx3000, xx4000, bha, bhb)
new_esEs13(Right(xx3000), Right(xx4000), ca, app(ty_[], baa)) → new_esEs10(xx3000, xx4000, baa)
new_esEs27(xx3001, xx4001, ty_Bool) → new_esEs6(xx3001, xx4001)
new_esEs7(EQ, GT) → False
new_esEs7(GT, EQ) → False
new_esEs26(xx3000, xx4000, ty_Ordering) → new_esEs7(xx3000, xx4000)
new_esEs20(xx3000, xx4000, ty_Ordering) → new_esEs7(xx3000, xx4000)
new_sr(Neg(xx30000), Neg(xx40000)) → Pos(new_primMulNat0(xx30000, xx40000))
new_esEs20(xx3000, xx4000, ty_Integer) → new_esEs11(xx3000, xx4000)
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_@0) → new_esEs16(xx3000, xx4000)
new_sr(Pos(xx30000), Pos(xx40000)) → Pos(new_primMulNat0(xx30000, xx40000))
new_asAs(False, xx42) → False
new_esEs23(xx3000, xx4000, ty_@0) → new_esEs16(xx3000, xx4000)
new_primEqNat0(Zero, Zero) → True
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Int) → new_esEs9(xx3000, xx4000)
new_primMulNat0(Zero, Succ(xx400000)) → Zero
new_primMulNat0(Succ(xx300000), Zero) → Zero
new_esEs15(Just(xx3000), Just(xx4000), ty_Char) → new_esEs19(xx3000, xx4000)
new_esEs15(Just(xx3000), Just(xx4000), ty_Ordering) → new_esEs7(xx3000, xx4000)
new_esEs21(xx3001, xx4001, ty_Bool) → new_esEs6(xx3001, xx4001)
new_esEs5(xx301, xx401, ty_Char) → new_esEs19(xx301, xx401)
new_esEs22(xx3002, xx4002, app(ty_[], fd)) → new_esEs10(xx3002, xx4002, fd)
new_esEs23(xx3000, xx4000, ty_Int) → new_esEs9(xx3000, xx4000)
new_esEs26(xx3000, xx4000, ty_@0) → new_esEs16(xx3000, xx4000)
new_esEs21(xx3001, xx4001, app(ty_Maybe, fb)) → new_esEs15(xx3001, xx4001, fb)
new_esEs27(xx3001, xx4001, ty_Ordering) → new_esEs7(xx3001, xx4001)
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Bool) → new_esEs6(xx3000, xx4000)
new_esEs5(xx301, xx401, app(ty_Maybe, bde)) → new_esEs15(xx301, xx401, bde)
new_esEs13(Right(xx3000), Right(xx4000), ca, app(ty_Maybe, bba)) → new_esEs15(xx3000, xx4000, bba)
new_esEs13(Left(xx3000), Left(xx4000), app(app(app(ty_@3, gh), ha), hb), cb) → new_esEs12(xx3000, xx4000, gh, ha, hb)
new_esEs13(Right(xx3000), Right(xx4000), ca, app(ty_Ratio, bbb)) → new_esEs18(xx3000, xx4000, bbb)
new_esEs4(xx300, xx400, ty_Bool) → new_esEs6(xx300, xx400)
new_esEs4(xx300, xx400, app(app(app(ty_@3, bf), bg), bh)) → new_esEs12(xx300, xx400, bf, bg, bh)
new_esEs4(xx300, xx400, app(ty_Maybe, ce)) → new_esEs15(xx300, xx400, ce)
new_esEs5(xx301, xx401, app(app(ty_@2, bdc), bdd)) → new_esEs14(xx301, xx401, bdc, bdd)
new_esEs5(xx301, xx401, app(app(ty_Either, bda), bdb)) → new_esEs13(xx301, xx401, bda, bdb)
new_esEs16(@0, @0) → True
new_esEs5(xx301, xx401, ty_Int) → new_esEs9(xx301, xx401)
new_primPlusNat0(Succ(xx430), xx400000) → Succ(Succ(new_primPlusNat1(xx430, xx400000)))
new_esEs20(xx3000, xx4000, ty_Double) → new_esEs8(xx3000, xx4000)
new_esEs27(xx3001, xx4001, app(ty_[], bfa)) → new_esEs10(xx3001, xx4001, bfa)
new_esEs27(xx3001, xx4001, app(app(ty_@2, bfg), bfh)) → new_esEs14(xx3001, xx4001, bfg, bfh)
new_primEqInt(Neg(Succ(xx30000)), Neg(Succ(xx40000))) → new_primEqNat0(xx30000, xx40000)
new_esEs20(xx3000, xx4000, ty_Float) → new_esEs17(xx3000, xx4000)
new_esEs13(Right(xx3000), Left(xx4000), ca, cb) → False
new_esEs13(Left(xx3000), Right(xx4000), ca, cb) → False
new_esEs13(Right(xx3000), Right(xx4000), ca, app(app(ty_Either, bae), baf)) → new_esEs13(xx3000, xx4000, bae, baf)
new_esEs5(xx301, xx401, ty_Float) → new_esEs17(xx301, xx401)
new_esEs5(xx301, xx401, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs12(xx301, xx401, bcf, bcg, bch)
new_esEs4(xx300, xx400, ty_Double) → new_esEs8(xx300, xx400)
new_esEs15(Just(xx3000), Just(xx4000), app(ty_Maybe, bhc)) → new_esEs15(xx3000, xx4000, bhc)
new_primPlusNat1(Zero, Succ(xx4000000)) → Succ(xx4000000)
new_primPlusNat1(Succ(xx4300), Zero) → Succ(xx4300)
new_esEs14(@2(xx3000, xx3001), @2(xx4000, xx4001), cc, cd) → new_asAs(new_esEs26(xx3000, xx4000, cc), new_esEs27(xx3001, xx4001, cd))
new_esEs27(xx3001, xx4001, ty_Double) → new_esEs8(xx3001, xx4001)
new_esEs21(xx3001, xx4001, ty_@0) → new_esEs16(xx3001, xx4001)
new_esEs8(Double(xx3000, xx3001), Double(xx4000, xx4001)) → new_esEs9(new_sr(xx3000, xx4000), new_sr(xx3001, xx4001))
new_esEs5(xx301, xx401, ty_Ordering) → new_esEs7(xx301, xx401)
new_esEs22(xx3002, xx4002, app(ty_Maybe, ge)) → new_esEs15(xx3002, xx4002, ge)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs23(xx3000, xx4000, ty_Char) → new_esEs19(xx3000, xx4000)
new_esEs4(xx300, xx400, app(app(ty_Either, ca), cb)) → new_esEs13(xx300, xx400, ca, cb)
new_esEs20(xx3000, xx4000, app(ty_Maybe, dh)) → new_esEs15(xx3000, xx4000, dh)
new_esEs21(xx3001, xx4001, ty_Double) → new_esEs8(xx3001, xx4001)
new_esEs15(Just(xx3000), Just(xx4000), ty_@0) → new_esEs16(xx3000, xx4000)
new_esEs21(xx3001, xx4001, ty_Integer) → new_esEs11(xx3001, xx4001)
new_esEs5(xx301, xx401, ty_Integer) → new_esEs11(xx301, xx401)
new_esEs13(Left(xx3000), Left(xx4000), app(ty_Maybe, hg), cb) → new_esEs15(xx3000, xx4000, hg)
new_esEs18(:%(xx3000, xx3001), :%(xx4000, xx4001), cf) → new_asAs(new_esEs24(xx3000, xx4000, cf), new_esEs25(xx3001, xx4001, cf))
new_esEs7(EQ, LT) → False
new_esEs7(LT, EQ) → False
new_primEqInt(Neg(Succ(xx30000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xx40000))) → False
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Ordering) → new_esEs7(xx3000, xx4000)
new_esEs21(xx3001, xx4001, app(app(ty_Either, ef), eg)) → new_esEs13(xx3001, xx4001, ef, eg)
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Double) → new_esEs8(xx3000, xx4000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs21(xx3001, xx4001, ty_Float) → new_esEs17(xx3001, xx4001)
new_asAs(True, xx42) → xx42
new_esEs10([], :(xx4000, xx4001), be) → False
new_esEs10(:(xx3000, xx3001), [], be) → False
new_primMulNat0(Succ(xx300000), Succ(xx400000)) → new_primPlusNat0(new_primMulNat0(xx300000, Succ(xx400000)), xx400000)
new_esEs15(Nothing, Just(xx4000), ce) → False
new_esEs15(Just(xx3000), Nothing, ce) → False
new_esEs27(xx3001, xx4001, ty_Integer) → new_esEs11(xx3001, xx4001)
new_esEs22(xx3002, xx4002, ty_Double) → new_esEs8(xx3002, xx4002)
new_esEs23(xx3000, xx4000, ty_Bool) → new_esEs6(xx3000, xx4000)
new_primEqInt(Pos(Succ(xx30000)), Pos(Succ(xx40000))) → new_primEqNat0(xx30000, xx40000)
new_esEs13(Left(xx3000), Left(xx4000), ty_Float, cb) → new_esEs17(xx3000, xx4000)
new_esEs13(Left(xx3000), Left(xx4000), ty_Integer, cb) → new_esEs11(xx3000, xx4000)
new_esEs6(True, False) → False
new_esEs6(False, True) → False
new_esEs25(xx3001, xx4001, ty_Int) → new_esEs9(xx3001, xx4001)
new_esEs13(Right(xx3000), Right(xx4000), ca, app(app(app(ty_@3, bab), bac), bad)) → new_esEs12(xx3000, xx4000, bab, bac, bad)
new_esEs10([], [], be) → True
new_esEs6(False, False) → True
new_primEqNat0(Succ(xx30000), Succ(xx40000)) → new_primEqNat0(xx30000, xx40000)
new_esEs23(xx3000, xx4000, ty_Integer) → new_esEs11(xx3000, xx4000)
new_esEs9(xx300, xx400) → new_primEqInt(xx300, xx400)
new_esEs13(Right(xx3000), Right(xx4000), ca, ty_Char) → new_esEs19(xx3000, xx4000)
new_esEs4(xx300, xx400, ty_Int) → new_esEs9(xx300, xx400)
new_esEs23(xx3000, xx4000, app(app(ty_@2, bca), bcb)) → new_esEs14(xx3000, xx4000, bca, bcb)
new_esEs7(GT, GT) → True
new_esEs13(Left(xx3000), Left(xx4000), app(ty_[], gg), cb) → new_esEs10(xx3000, xx4000, gg)
new_esEs4(xx300, xx400, app(app(ty_@2, cc), cd)) → new_esEs14(xx300, xx400, cc, cd)
new_esEs21(xx3001, xx4001, ty_Char) → new_esEs19(xx3001, xx4001)
new_primEqInt(Pos(Succ(xx30000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xx40000))) → False
new_esEs26(xx3000, xx4000, app(app(ty_Either, bec), bed)) → new_esEs13(xx3000, xx4000, bec, bed)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs21(xx3001, xx4001, app(ty_Ratio, fc)) → new_esEs18(xx3001, xx4001, fc)
new_esEs15(Just(xx3000), Just(xx4000), app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs12(xx3000, xx4000, bgd, bge, bgf)
new_esEs13(Left(xx3000), Left(xx4000), app(ty_Ratio, hh), cb) → new_esEs18(xx3000, xx4000, hh)

The set Q consists of the following terms:

new_esEs23(x0, x1, ty_Bool)
new_esEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(LT, EQ)
new_esEs7(EQ, LT)
new_esEs9(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10([], [], x0)
new_esEs11(Integer(x0), Integer(x1))
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_esEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs4(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Double)
new_esEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs15(Just(x0), Just(x1), ty_Bool)
new_esEs22(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Zero)
new_esEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs13(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(Left(x0), Left(x1), ty_Double, x2)
new_esEs15(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Bool)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(LT, LT)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs7(GT, LT)
new_esEs7(LT, GT)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Integer)
new_esEs13(Left(x0), Right(x1), x2, x3)
new_esEs13(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, ty_Int)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, ty_Float)
new_primMulNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs10(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs21(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(@0, @0)
new_asAs(True, x0)
new_esEs20(x0, x1, ty_Ordering)
new_esEs13(Left(x0), Left(x1), ty_@0, x2)
new_primPlusNat0(Zero, x0)
new_esEs23(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_esEs19(Char(x0), Char(x1))
new_esEs5(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(Nothing, Nothing, x0)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, ty_@0)
new_esEs15(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Double)
new_esEs7(GT, GT)
new_esEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs4(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs15(Just(x0), Just(x1), ty_@0)
new_esEs6(False, False)
new_esEs13(Left(x0), Left(x1), ty_Int, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs10([], :(x0, x1), x2)
new_esEs26(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs27(x0, x1, ty_Float)
new_esEs4(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Zero)
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Integer)
new_esEs13(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(x0, x1, ty_Char)
new_esEs13(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs15(Just(x0), Just(x1), app(ty_[], x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_sr(Neg(x0), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(GT, EQ)
new_esEs7(EQ, GT)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Int)
new_esEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs15(Just(x0), Just(x1), ty_Char)
new_esEs15(Just(x0), Just(x1), ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs15(Nothing, Just(x0), x1)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(x0, x1, ty_Integer)
new_esEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Int)
new_esEs13(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs13(Right(x0), Right(x1), x2, ty_Integer)
new_esEs5(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs13(Right(x0), Right(x1), x2, ty_Float)
new_sr(Pos(x0), Pos(x1))
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_esEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Char)
new_esEs23(x0, x1, ty_Char)
new_asAs(False, x0)
new_esEs6(True, True)
new_esEs15(Just(x0), Just(x1), ty_Double)
new_esEs5(x0, x1, ty_Ordering)
new_esEs15(Just(x0), Just(x1), ty_Integer)
new_esEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs26(x0, x1, ty_Char)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(EQ, EQ)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs15(Just(x0), Just(x1), ty_Ordering)
new_esEs6(True, False)
new_esEs6(False, True)
new_esEs21(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_esEs4(x0, x1, ty_Float)
new_esEs5(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Float)
new_esEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs4(x0, x1, ty_Integer)
new_esEs26(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_psPs0(@2(xx300, xx301), :(@2(xx400, xx401), xx41), xx5, bc, bd) → new_psPs(xx300, xx301, new_asAs(new_esEs4(xx300, xx400, bc), new_esEs5(xx301, xx401, bd)), xx41, xx5, bc, bd)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 4, 3 >= 5, 4 >= 6, 5 >= 7
new_psPs(xx25, xx26, False, xx28, xx29, ba, bb) → new_psPs0(@2(xx25, xx26), xx28, xx29, ba, bb)
The graph contains the following edges 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ CR

        ↳ HASKELL

          ↳ IFR

            ↳ HASKELL

              ↳ BR

                ↳ HASKELL

                  ↳ COR

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

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

new_foldr(xx4, :(xx30, xx31), ba, bb) → new_foldr(xx4, xx31, ba, bb)

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

new_foldr(xx4, :(xx30, xx31), ba, bb) → new_foldr(xx4, xx31, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4

intersectBy00	eq ys x	= if any (eq x) ys then x : [] else []
intersectBy00	eq ys _	= []