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

YES 2.101 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ IFR

mainModule List

((delete :: (Eq a, Eq b) => (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

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

delete

deleteBy (==)

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

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

module Maybe where

import qualified List
import qualified Prelude

If Reductions:
The following If expression

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

is transformed to

deleteBy0 ys y eq x True = ys

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

mainModule List

((delete :: (Eq b, Eq a) => (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

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

delete

deleteBy (==)

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

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

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

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule List

((delete :: (Eq b, Eq a) => (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

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

delete

deleteBy (==)

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

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

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

module Maybe where

import qualified List
import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

delete

deleteBy (==)

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

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

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

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="delete\n  Eq a  Eq b",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
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1049 -> 6[label="",style="solid", color="burlywood", weight=3];
1050[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 1050[label="",style="solid", color="burlywood", weight=9];
1050 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="deleteBy (==) xy3 (xy40 : xy41)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="deleteBy (==) xy3 []\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="deleteBy0 xy41 xy40 (==) xy3 ((==) xy3 xy40)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1051[label="xy3/(xy30,xy31)",fontsize=10,color="white",style="solid",shape="box"];8 -> 1051[label="",style="solid", color="burlywood", weight=9];
1051 -> 10[label="",style="solid", color="burlywood", weight=3];
9[label="[]\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];10[label="deleteBy0 xy41 xy40 (==) (xy30,xy31) ((==) (xy30,xy31) xy40)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1052[label="xy40/(xy400,xy401)",fontsize=10,color="white",style="solid",shape="box"];10 -> 1052[label="",style="solid", color="burlywood", weight=9];
1052 -> 11[label="",style="solid", color="burlywood", weight=3];
11[label="deleteBy0 xy41 (xy400,xy401) (==) (xy30,xy31) ((==) (xy30,xy31) (xy400,xy401))\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12 -> 94[label="",style="dashed", color="red", weight=0];
12[label="deleteBy0 xy41 (xy400,xy401) (==) (xy30,xy31) (xy30 == xy400 && xy31 == xy401)\n  Eq a  Eq b",fontsize=16,color="magenta"];12 -> 95[label="",style="dashed", color="magenta", weight=3];
12 -> 96[label="",style="dashed", color="magenta", weight=3];
12 -> 97[label="",style="dashed", color="magenta", weight=3];
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12 -> 99[label="",style="dashed", color="magenta", weight=3];
12 -> 100[label="",style="dashed", color="magenta", weight=3];
95[label="xy41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];96[label="xy401\n  Eq a",fontsize=16,color="green",shape="box"];97[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];98 -> 374[label="",style="dashed", color="red", weight=0];
98[label="xy30 == xy400 && xy31 == xy401\n  Eq a  Eq b",fontsize=16,color="magenta"];98 -> 375[label="",style="dashed", color="magenta", weight=3];
98 -> 376[label="",style="dashed", color="magenta", weight=3];
99[label="xy31\n  Eq a",fontsize=16,color="green",shape="box"];100[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];94[label="deleteBy0 xy25 (xy26,xy27) (==) (xy28,xy29) xy30\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1055[label="xy30/False",fontsize=10,color="white",style="solid",shape="box"];94 -> 1055[label="",style="solid", color="burlywood", weight=9];
1055 -> 123[label="",style="solid", color="burlywood", weight=3];
1056[label="xy30/True",fontsize=10,color="white",style="solid",shape="box"];94 -> 1056[label="",style="solid", color="burlywood", weight=9];
1056 -> 124[label="",style="solid", color="burlywood", weight=3];
375[label="xy31 == xy401\n  Eq a",fontsize=16,color="blue",shape="box"];1057[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1057[label="",style="solid", color="blue", weight=9];
1057 -> 379[label="",style="solid", color="blue", weight=3];
1058[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1058[label="",style="solid", color="blue", weight=9];
1058 -> 380[label="",style="solid", color="blue", weight=3];
1059[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1059[label="",style="solid", color="blue", weight=9];
1059 -> 381[label="",style="solid", color="blue", weight=3];
1060[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1060[label="",style="solid", color="blue", weight=9];
1060 -> 382[label="",style="solid", color="blue", weight=3];
1061[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1061[label="",style="solid", color="blue", weight=9];
1061 -> 383[label="",style="solid", color="blue", weight=3];
1062[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1062[label="",style="solid", color="blue", weight=9];
1062 -> 384[label="",style="solid", color="blue", weight=3];
1063[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1063[label="",style="solid", color="blue", weight=9];
1063 -> 385[label="",style="solid", color="blue", weight=3];
1064[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1064[label="",style="solid", color="blue", weight=9];
1064 -> 386[label="",style="solid", color="blue", weight=3];
1065[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1065[label="",style="solid", color="blue", weight=9];
1065 -> 387[label="",style="solid", color="blue", weight=3];
1066[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1066[label="",style="solid", color="blue", weight=9];
1066 -> 388[label="",style="solid", color="blue", weight=3];
1067[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1067[label="",style="solid", color="blue", weight=9];
1067 -> 389[label="",style="solid", color="blue", weight=3];
1068[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1068[label="",style="solid", color="blue", weight=9];
1068 -> 390[label="",style="solid", color="blue", weight=3];
1069[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1069[label="",style="solid", color="blue", weight=9];
1069 -> 391[label="",style="solid", color="blue", weight=3];
1070[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];375 -> 1070[label="",style="solid", color="blue", weight=9];
1070 -> 392[label="",style="solid", color="blue", weight=3];
376[label="xy30 == xy400\n  Eq a",fontsize=16,color="blue",shape="box"];1071[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1071[label="",style="solid", color="blue", weight=9];
1071 -> 393[label="",style="solid", color="blue", weight=3];
1072[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1072[label="",style="solid", color="blue", weight=9];
1072 -> 394[label="",style="solid", color="blue", weight=3];
1073[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1073[label="",style="solid", color="blue", weight=9];
1073 -> 395[label="",style="solid", color="blue", weight=3];
1074[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1074[label="",style="solid", color="blue", weight=9];
1074 -> 396[label="",style="solid", color="blue", weight=3];
1075[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1075[label="",style="solid", color="blue", weight=9];
1075 -> 397[label="",style="solid", color="blue", weight=3];
1076[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1076[label="",style="solid", color="blue", weight=9];
1076 -> 398[label="",style="solid", color="blue", weight=3];
1077[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1077[label="",style="solid", color="blue", weight=9];
1077 -> 399[label="",style="solid", color="blue", weight=3];
1078[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1078[label="",style="solid", color="blue", weight=9];
1078 -> 400[label="",style="solid", color="blue", weight=3];
1079[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1079[label="",style="solid", color="blue", weight=9];
1079 -> 401[label="",style="solid", color="blue", weight=3];
1080[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1080[label="",style="solid", color="blue", weight=9];
1080 -> 402[label="",style="solid", color="blue", weight=3];
1081[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1081[label="",style="solid", color="blue", weight=9];
1081 -> 403[label="",style="solid", color="blue", weight=3];
1082[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1082[label="",style="solid", color="blue", weight=9];
1082 -> 404[label="",style="solid", color="blue", weight=3];
1083[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1083[label="",style="solid", color="blue", weight=9];
1083 -> 405[label="",style="solid", color="blue", weight=3];
1084[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];376 -> 1084[label="",style="solid", color="blue", weight=9];
1084 -> 406[label="",style="solid", color="blue", weight=3];
374[label="xy42 && xy43",fontsize=16,color="burlywood",shape="triangle"];1085[label="xy42/False",fontsize=10,color="white",style="solid",shape="box"];374 -> 1085[label="",style="solid", color="burlywood", weight=9];
1085 -> 407[label="",style="solid", color="burlywood", weight=3];
1086[label="xy42/True",fontsize=10,color="white",style="solid",shape="box"];374 -> 1086[label="",style="solid", color="burlywood", weight=9];
1086 -> 408[label="",style="solid", color="burlywood", weight=3];
123[label="deleteBy0 xy25 (xy26,xy27) (==) (xy28,xy29) False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];123 -> 141[label="",style="solid", color="black", weight=3];
124[label="deleteBy0 xy25 (xy26,xy27) (==) (xy28,xy29) True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];124 -> 142[label="",style="solid", color="black", weight=3];
379[label="xy31 == xy401",fontsize=16,color="black",shape="triangle"];379 -> 409[label="",style="solid", color="black", weight=3];
380[label="xy31 == xy401",fontsize=16,color="burlywood",shape="triangle"];1087[label="xy31/LT",fontsize=10,color="white",style="solid",shape="box"];380 -> 1087[label="",style="solid", color="burlywood", weight=9];
1087 -> 410[label="",style="solid", color="burlywood", weight=3];
1088[label="xy31/EQ",fontsize=10,color="white",style="solid",shape="box"];380 -> 1088[label="",style="solid", color="burlywood", weight=9];
1088 -> 411[label="",style="solid", color="burlywood", weight=3];
1089[label="xy31/GT",fontsize=10,color="white",style="solid",shape="box"];380 -> 1089[label="",style="solid", color="burlywood", weight=9];
1089 -> 412[label="",style="solid", color="burlywood", weight=3];
381[label="xy31 == xy401",fontsize=16,color="black",shape="triangle"];381 -> 413[label="",style="solid", color="black", weight=3];
382[label="xy31 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1090[label="xy31/xy310 : xy311",fontsize=10,color="white",style="solid",shape="box"];382 -> 1090[label="",style="solid", color="burlywood", weight=9];
1090 -> 414[label="",style="solid", color="burlywood", weight=3];
1091[label="xy31/[]",fontsize=10,color="white",style="solid",shape="box"];382 -> 1091[label="",style="solid", color="burlywood", weight=9];
1091 -> 415[label="",style="solid", color="burlywood", weight=3];
383[label="xy31 == xy401",fontsize=16,color="black",shape="triangle"];383 -> 416[label="",style="solid", color="black", weight=3];
384[label="xy31 == xy401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1092[label="xy31/(xy310,xy311)",fontsize=10,color="white",style="solid",shape="box"];384 -> 1092[label="",style="solid", color="burlywood", weight=9];
1092 -> 417[label="",style="solid", color="burlywood", weight=3];
385[label="xy31 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1093[label="xy31/Nothing",fontsize=10,color="white",style="solid",shape="box"];385 -> 1093[label="",style="solid", color="burlywood", weight=9];
1093 -> 418[label="",style="solid", color="burlywood", weight=3];
1094[label="xy31/Just xy310",fontsize=10,color="white",style="solid",shape="box"];385 -> 1094[label="",style="solid", color="burlywood", weight=9];
1094 -> 419[label="",style="solid", color="burlywood", weight=3];
386[label="xy31 == xy401",fontsize=16,color="burlywood",shape="triangle"];1095[label="xy31/False",fontsize=10,color="white",style="solid",shape="box"];386 -> 1095[label="",style="solid", color="burlywood", weight=9];
1095 -> 420[label="",style="solid", color="burlywood", weight=3];
1096[label="xy31/True",fontsize=10,color="white",style="solid",shape="box"];386 -> 1096[label="",style="solid", color="burlywood", weight=9];
1096 -> 421[label="",style="solid", color="burlywood", weight=3];
387[label="xy31 == xy401",fontsize=16,color="burlywood",shape="triangle"];1097[label="xy31/Integer xy310",fontsize=10,color="white",style="solid",shape="box"];387 -> 1097[label="",style="solid", color="burlywood", weight=9];
1097 -> 422[label="",style="solid", color="burlywood", weight=3];
388[label="xy31 == xy401\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];1098[label="xy31/xy310 :% xy311",fontsize=10,color="white",style="solid",shape="box"];388 -> 1098[label="",style="solid", color="burlywood", weight=9];
1098 -> 423[label="",style="solid", color="burlywood", weight=3];
389[label="xy31 == xy401",fontsize=16,color="black",shape="triangle"];389 -> 424[label="",style="solid", color="black", weight=3];
390[label="xy31 == xy401",fontsize=16,color="burlywood",shape="triangle"];1099[label="xy31/()",fontsize=10,color="white",style="solid",shape="box"];390 -> 1099[label="",style="solid", color="burlywood", weight=9];
1099 -> 425[label="",style="solid", color="burlywood", weight=3];
391[label="xy31 == xy401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1100[label="xy31/Left xy310",fontsize=10,color="white",style="solid",shape="box"];391 -> 1100[label="",style="solid", color="burlywood", weight=9];
1100 -> 426[label="",style="solid", color="burlywood", weight=3];
1101[label="xy31/Right xy310",fontsize=10,color="white",style="solid",shape="box"];391 -> 1101[label="",style="solid", color="burlywood", weight=9];
1101 -> 427[label="",style="solid", color="burlywood", weight=3];
392[label="xy31 == xy401\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];1102[label="xy31/(xy310,xy311,xy312)",fontsize=10,color="white",style="solid",shape="box"];392 -> 1102[label="",style="solid", color="burlywood", weight=9];
1102 -> 428[label="",style="solid", color="burlywood", weight=3];
393 -> 379[label="",style="dashed", color="red", weight=0];
393[label="xy30 == xy400",fontsize=16,color="magenta"];393 -> 429[label="",style="dashed", color="magenta", weight=3];
393 -> 430[label="",style="dashed", color="magenta", weight=3];
394 -> 380[label="",style="dashed", color="red", weight=0];
394[label="xy30 == xy400",fontsize=16,color="magenta"];394 -> 431[label="",style="dashed", color="magenta", weight=3];
394 -> 432[label="",style="dashed", color="magenta", weight=3];
395 -> 381[label="",style="dashed", color="red", weight=0];
395[label="xy30 == xy400",fontsize=16,color="magenta"];395 -> 433[label="",style="dashed", color="magenta", weight=3];
395 -> 434[label="",style="dashed", color="magenta", weight=3];
396 -> 382[label="",style="dashed", color="red", weight=0];
396[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];396 -> 435[label="",style="dashed", color="magenta", weight=3];
396 -> 436[label="",style="dashed", color="magenta", weight=3];
397 -> 383[label="",style="dashed", color="red", weight=0];
397[label="xy30 == xy400",fontsize=16,color="magenta"];397 -> 437[label="",style="dashed", color="magenta", weight=3];
397 -> 438[label="",style="dashed", color="magenta", weight=3];
398 -> 384[label="",style="dashed", color="red", weight=0];
398[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="magenta"];398 -> 439[label="",style="dashed", color="magenta", weight=3];
398 -> 440[label="",style="dashed", color="magenta", weight=3];
399 -> 385[label="",style="dashed", color="red", weight=0];
399[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];399 -> 441[label="",style="dashed", color="magenta", weight=3];
399 -> 442[label="",style="dashed", color="magenta", weight=3];
400 -> 386[label="",style="dashed", color="red", weight=0];
400[label="xy30 == xy400",fontsize=16,color="magenta"];400 -> 443[label="",style="dashed", color="magenta", weight=3];
400 -> 444[label="",style="dashed", color="magenta", weight=3];
401 -> 387[label="",style="dashed", color="red", weight=0];
401[label="xy30 == xy400",fontsize=16,color="magenta"];401 -> 445[label="",style="dashed", color="magenta", weight=3];
401 -> 446[label="",style="dashed", color="magenta", weight=3];
402 -> 388[label="",style="dashed", color="red", weight=0];
402[label="xy30 == xy400\n  Integral a",fontsize=16,color="magenta"];402 -> 447[label="",style="dashed", color="magenta", weight=3];
402 -> 448[label="",style="dashed", color="magenta", weight=3];
403 -> 389[label="",style="dashed", color="red", weight=0];
403[label="xy30 == xy400",fontsize=16,color="magenta"];403 -> 449[label="",style="dashed", color="magenta", weight=3];
403 -> 450[label="",style="dashed", color="magenta", weight=3];
404 -> 390[label="",style="dashed", color="red", weight=0];
404[label="xy30 == xy400",fontsize=16,color="magenta"];404 -> 451[label="",style="dashed", color="magenta", weight=3];
404 -> 452[label="",style="dashed", color="magenta", weight=3];
405 -> 391[label="",style="dashed", color="red", weight=0];
405[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="magenta"];405 -> 453[label="",style="dashed", color="magenta", weight=3];
405 -> 454[label="",style="dashed", color="magenta", weight=3];
406 -> 392[label="",style="dashed", color="red", weight=0];
406[label="xy30 == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];406 -> 455[label="",style="dashed", color="magenta", weight=3];
406 -> 456[label="",style="dashed", color="magenta", weight=3];
407[label="False && xy43",fontsize=16,color="black",shape="box"];407 -> 457[label="",style="solid", color="black", weight=3];
408[label="True && xy43",fontsize=16,color="black",shape="box"];408 -> 458[label="",style="solid", color="black", weight=3];
141[label="(xy26,xy27) : deleteBy (==) (xy28,xy29) xy25\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];141 -> 165[label="",style="dashed", color="green", weight=3];
142[label="xy25\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];409[label="primEqFloat xy31 xy401",fontsize=16,color="burlywood",shape="box"];1117[label="xy31/Float xy310 xy311",fontsize=10,color="white",style="solid",shape="box"];409 -> 1117[label="",style="solid", color="burlywood", weight=9];
1117 -> 459[label="",style="solid", color="burlywood", weight=3];
410[label="LT == xy401",fontsize=16,color="burlywood",shape="box"];1118[label="xy401/LT",fontsize=10,color="white",style="solid",shape="box"];410 -> 1118[label="",style="solid", color="burlywood", weight=9];
1118 -> 460[label="",style="solid", color="burlywood", weight=3];
1119[label="xy401/EQ",fontsize=10,color="white",style="solid",shape="box"];410 -> 1119[label="",style="solid", color="burlywood", weight=9];
1119 -> 461[label="",style="solid", color="burlywood", weight=3];
1120[label="xy401/GT",fontsize=10,color="white",style="solid",shape="box"];410 -> 1120[label="",style="solid", color="burlywood", weight=9];
1120 -> 462[label="",style="solid", color="burlywood", weight=3];
411[label="EQ == xy401",fontsize=16,color="burlywood",shape="box"];1121[label="xy401/LT",fontsize=10,color="white",style="solid",shape="box"];411 -> 1121[label="",style="solid", color="burlywood", weight=9];
1121 -> 463[label="",style="solid", color="burlywood", weight=3];
1122[label="xy401/EQ",fontsize=10,color="white",style="solid",shape="box"];411 -> 1122[label="",style="solid", color="burlywood", weight=9];
1122 -> 464[label="",style="solid", color="burlywood", weight=3];
1123[label="xy401/GT",fontsize=10,color="white",style="solid",shape="box"];411 -> 1123[label="",style="solid", color="burlywood", weight=9];
1123 -> 465[label="",style="solid", color="burlywood", weight=3];
412[label="GT == xy401",fontsize=16,color="burlywood",shape="box"];1124[label="xy401/LT",fontsize=10,color="white",style="solid",shape="box"];412 -> 1124[label="",style="solid", color="burlywood", weight=9];
1124 -> 466[label="",style="solid", color="burlywood", weight=3];
1125[label="xy401/EQ",fontsize=10,color="white",style="solid",shape="box"];412 -> 1125[label="",style="solid", color="burlywood", weight=9];
1125 -> 467[label="",style="solid", color="burlywood", weight=3];
1126[label="xy401/GT",fontsize=10,color="white",style="solid",shape="box"];412 -> 1126[label="",style="solid", color="burlywood", weight=9];
1126 -> 468[label="",style="solid", color="burlywood", weight=3];
413[label="primEqDouble xy31 xy401",fontsize=16,color="burlywood",shape="box"];1127[label="xy31/Double xy310 xy311",fontsize=10,color="white",style="solid",shape="box"];413 -> 1127[label="",style="solid", color="burlywood", weight=9];
1127 -> 469[label="",style="solid", color="burlywood", weight=3];
414[label="xy310 : xy311 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];1128[label="xy401/xy4010 : xy4011",fontsize=10,color="white",style="solid",shape="box"];414 -> 1128[label="",style="solid", color="burlywood", weight=9];
1128 -> 470[label="",style="solid", color="burlywood", weight=3];
1129[label="xy401/[]",fontsize=10,color="white",style="solid",shape="box"];414 -> 1129[label="",style="solid", color="burlywood", weight=9];
1129 -> 471[label="",style="solid", color="burlywood", weight=3];
415[label="[] == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];1130[label="xy401/xy4010 : xy4011",fontsize=10,color="white",style="solid",shape="box"];415 -> 1130[label="",style="solid", color="burlywood", weight=9];
1130 -> 472[label="",style="solid", color="burlywood", weight=3];
1131[label="xy401/[]",fontsize=10,color="white",style="solid",shape="box"];415 -> 1131[label="",style="solid", color="burlywood", weight=9];
1131 -> 473[label="",style="solid", color="burlywood", weight=3];
416[label="primEqChar xy31 xy401",fontsize=16,color="burlywood",shape="box"];1132[label="xy31/Char xy310",fontsize=10,color="white",style="solid",shape="box"];416 -> 1132[label="",style="solid", color="burlywood", weight=9];
1132 -> 474[label="",style="solid", color="burlywood", weight=3];
417[label="(xy310,xy311) == xy401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1133[label="xy401/(xy4010,xy4011)",fontsize=10,color="white",style="solid",shape="box"];417 -> 1133[label="",style="solid", color="burlywood", weight=9];
1133 -> 475[label="",style="solid", color="burlywood", weight=3];
418[label="Nothing == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];1134[label="xy401/Nothing",fontsize=10,color="white",style="solid",shape="box"];418 -> 1134[label="",style="solid", color="burlywood", weight=9];
1134 -> 476[label="",style="solid", color="burlywood", weight=3];
1135[label="xy401/Just xy4010",fontsize=10,color="white",style="solid",shape="box"];418 -> 1135[label="",style="solid", color="burlywood", weight=9];
1135 -> 477[label="",style="solid", color="burlywood", weight=3];
419[label="Just xy310 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];1136[label="xy401/Nothing",fontsize=10,color="white",style="solid",shape="box"];419 -> 1136[label="",style="solid", color="burlywood", weight=9];
1136 -> 478[label="",style="solid", color="burlywood", weight=3];
1137[label="xy401/Just xy4010",fontsize=10,color="white",style="solid",shape="box"];419 -> 1137[label="",style="solid", color="burlywood", weight=9];
1137 -> 479[label="",style="solid", color="burlywood", weight=3];
420[label="False == xy401",fontsize=16,color="burlywood",shape="box"];1138[label="xy401/False",fontsize=10,color="white",style="solid",shape="box"];420 -> 1138[label="",style="solid", color="burlywood", weight=9];
1138 -> 480[label="",style="solid", color="burlywood", weight=3];
1139[label="xy401/True",fontsize=10,color="white",style="solid",shape="box"];420 -> 1139[label="",style="solid", color="burlywood", weight=9];
1139 -> 481[label="",style="solid", color="burlywood", weight=3];
421[label="True == xy401",fontsize=16,color="burlywood",shape="box"];1140[label="xy401/False",fontsize=10,color="white",style="solid",shape="box"];421 -> 1140[label="",style="solid", color="burlywood", weight=9];
1140 -> 482[label="",style="solid", color="burlywood", weight=3];
1141[label="xy401/True",fontsize=10,color="white",style="solid",shape="box"];421 -> 1141[label="",style="solid", color="burlywood", weight=9];
1141 -> 483[label="",style="solid", color="burlywood", weight=3];
422[label="Integer xy310 == xy401",fontsize=16,color="burlywood",shape="box"];1142[label="xy401/Integer xy4010",fontsize=10,color="white",style="solid",shape="box"];422 -> 1142[label="",style="solid", color="burlywood", weight=9];
1142 -> 484[label="",style="solid", color="burlywood", weight=3];
423[label="xy310 :% xy311 == xy401\n  Integral a",fontsize=16,color="burlywood",shape="box"];1143[label="xy401/xy4010 :% xy4011",fontsize=10,color="white",style="solid",shape="box"];423 -> 1143[label="",style="solid", color="burlywood", weight=9];
1143 -> 485[label="",style="solid", color="burlywood", weight=3];
424[label="primEqInt xy31 xy401",fontsize=16,color="burlywood",shape="triangle"];1144[label="xy31/Pos xy310",fontsize=10,color="white",style="solid",shape="box"];424 -> 1144[label="",style="solid", color="burlywood", weight=9];
1144 -> 486[label="",style="solid", color="burlywood", weight=3];
1145[label="xy31/Neg xy310",fontsize=10,color="white",style="solid",shape="box"];424 -> 1145[label="",style="solid", color="burlywood", weight=9];
1145 -> 487[label="",style="solid", color="burlywood", weight=3];
425[label="() == xy401",fontsize=16,color="burlywood",shape="box"];1146[label="xy401/()",fontsize=10,color="white",style="solid",shape="box"];425 -> 1146[label="",style="solid", color="burlywood", weight=9];
1146 -> 488[label="",style="solid", color="burlywood", weight=3];
426[label="Left xy310 == xy401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1147[label="xy401/Left xy4010",fontsize=10,color="white",style="solid",shape="box"];426 -> 1147[label="",style="solid", color="burlywood", weight=9];
1147 -> 489[label="",style="solid", color="burlywood", weight=3];
1148[label="xy401/Right xy4010",fontsize=10,color="white",style="solid",shape="box"];426 -> 1148[label="",style="solid", color="burlywood", weight=9];
1148 -> 490[label="",style="solid", color="burlywood", weight=3];
427[label="Right xy310 == xy401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1149[label="xy401/Left xy4010",fontsize=10,color="white",style="solid",shape="box"];427 -> 1149[label="",style="solid", color="burlywood", weight=9];
1149 -> 491[label="",style="solid", color="burlywood", weight=3];
1150[label="xy401/Right xy4010",fontsize=10,color="white",style="solid",shape="box"];427 -> 1150[label="",style="solid", color="burlywood", weight=9];
1150 -> 492[label="",style="solid", color="burlywood", weight=3];
428[label="(xy310,xy311,xy312) == xy401\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1151[label="xy401/(xy4010,xy4011,xy4012)",fontsize=10,color="white",style="solid",shape="box"];428 -> 1151[label="",style="solid", color="burlywood", weight=9];
1151 -> 493[label="",style="solid", color="burlywood", weight=3];
429[label="xy30",fontsize=16,color="green",shape="box"];430[label="xy400",fontsize=16,color="green",shape="box"];431[label="xy30",fontsize=16,color="green",shape="box"];432[label="xy400",fontsize=16,color="green",shape="box"];433[label="xy30",fontsize=16,color="green",shape="box"];434[label="xy400",fontsize=16,color="green",shape="box"];435[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];436[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];437[label="xy30",fontsize=16,color="green",shape="box"];438[label="xy400",fontsize=16,color="green",shape="box"];439[label="xy30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];440[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];441[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];442[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];443[label="xy30",fontsize=16,color="green",shape="box"];444[label="xy400",fontsize=16,color="green",shape="box"];445[label="xy30",fontsize=16,color="green",shape="box"];446[label="xy400",fontsize=16,color="green",shape="box"];447[label="xy30\n  Integral a",fontsize=16,color="green",shape="box"];448[label="xy400\n  Integral a",fontsize=16,color="green",shape="box"];449[label="xy30",fontsize=16,color="green",shape="box"];450[label="xy400",fontsize=16,color="green",shape="box"];451[label="xy30",fontsize=16,color="green",shape="box"];452[label="xy400",fontsize=16,color="green",shape="box"];453[label="xy30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];454[label="xy400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];455[label="xy30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];456[label="xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];457[label="False",fontsize=16,color="green",shape="box"];458[label="xy43",fontsize=16,color="green",shape="box"];165 -> 5[label="",style="dashed", color="red", weight=0];
165[label="deleteBy (==) (xy28,xy29) xy25\n  Eq a  Eq b",fontsize=16,color="magenta"];165 -> 215[label="",style="dashed", color="magenta", weight=3];
165 -> 216[label="",style="dashed", color="magenta", weight=3];
459[label="primEqFloat (Float xy310 xy311) xy401",fontsize=16,color="burlywood",shape="box"];1153[label="xy401/Float xy4010 xy4011",fontsize=10,color="white",style="solid",shape="box"];459 -> 1153[label="",style="solid", color="burlywood", weight=9];
1153 -> 494[label="",style="solid", color="burlywood", weight=3];
460[label="LT == LT",fontsize=16,color="black",shape="box"];460 -> 495[label="",style="solid", color="black", weight=3];
461[label="LT == EQ",fontsize=16,color="black",shape="box"];461 -> 496[label="",style="solid", color="black", weight=3];
462[label="LT == GT",fontsize=16,color="black",shape="box"];462 -> 497[label="",style="solid", color="black", weight=3];
463[label="EQ == LT",fontsize=16,color="black",shape="box"];463 -> 498[label="",style="solid", color="black", weight=3];
464[label="EQ == EQ",fontsize=16,color="black",shape="box"];464 -> 499[label="",style="solid", color="black", weight=3];
465[label="EQ == GT",fontsize=16,color="black",shape="box"];465 -> 500[label="",style="solid", color="black", weight=3];
466[label="GT == LT",fontsize=16,color="black",shape="box"];466 -> 501[label="",style="solid", color="black", weight=3];
467[label="GT == EQ",fontsize=16,color="black",shape="box"];467 -> 502[label="",style="solid", color="black", weight=3];
468[label="GT == GT",fontsize=16,color="black",shape="box"];468 -> 503[label="",style="solid", color="black", weight=3];
469[label="primEqDouble (Double xy310 xy311) xy401",fontsize=16,color="burlywood",shape="box"];1154[label="xy401/Double xy4010 xy4011",fontsize=10,color="white",style="solid",shape="box"];469 -> 1154[label="",style="solid", color="burlywood", weight=9];
1154 -> 504[label="",style="solid", color="burlywood", weight=3];
470[label="xy310 : xy311 == xy4010 : xy4011\n  Eq a",fontsize=16,color="black",shape="box"];470 -> 505[label="",style="solid", color="black", weight=3];
471[label="xy310 : xy311 == []\n  Eq a",fontsize=16,color="black",shape="box"];471 -> 506[label="",style="solid", color="black", weight=3];
472[label="[] == xy4010 : xy4011\n  Eq a",fontsize=16,color="black",shape="box"];472 -> 507[label="",style="solid", color="black", weight=3];
473[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];473 -> 508[label="",style="solid", color="black", weight=3];
474[label="primEqChar (Char xy310) xy401",fontsize=16,color="burlywood",shape="box"];1155[label="xy401/Char xy4010",fontsize=10,color="white",style="solid",shape="box"];474 -> 1155[label="",style="solid", color="burlywood", weight=9];
1155 -> 509[label="",style="solid", color="burlywood", weight=3];
475[label="(xy310,xy311) == (xy4010,xy4011)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];475 -> 510[label="",style="solid", color="black", weight=3];
476[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];476 -> 511[label="",style="solid", color="black", weight=3];
477[label="Nothing == Just xy4010\n  Eq a",fontsize=16,color="black",shape="box"];477 -> 512[label="",style="solid", color="black", weight=3];
478[label="Just xy310 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];478 -> 513[label="",style="solid", color="black", weight=3];
479[label="Just xy310 == Just xy4010\n  Eq a",fontsize=16,color="black",shape="box"];479 -> 514[label="",style="solid", color="black", weight=3];
480[label="False == False",fontsize=16,color="black",shape="box"];480 -> 515[label="",style="solid", color="black", weight=3];
481[label="False == True",fontsize=16,color="black",shape="box"];481 -> 516[label="",style="solid", color="black", weight=3];
482[label="True == False",fontsize=16,color="black",shape="box"];482 -> 517[label="",style="solid", color="black", weight=3];
483[label="True == True",fontsize=16,color="black",shape="box"];483 -> 518[label="",style="solid", color="black", weight=3];
484[label="Integer xy310 == Integer xy4010",fontsize=16,color="black",shape="box"];484 -> 519[label="",style="solid", color="black", weight=3];
485[label="xy310 :% xy311 == xy4010 :% xy4011\n  Integral a",fontsize=16,color="black",shape="box"];485 -> 520[label="",style="solid", color="black", weight=3];
486[label="primEqInt (Pos xy310) xy401",fontsize=16,color="burlywood",shape="box"];1156[label="xy310/Succ xy3100",fontsize=10,color="white",style="solid",shape="box"];486 -> 1156[label="",style="solid", color="burlywood", weight=9];
1156 -> 521[label="",style="solid", color="burlywood", weight=3];
1157[label="xy310/Zero",fontsize=10,color="white",style="solid",shape="box"];486 -> 1157[label="",style="solid", color="burlywood", weight=9];
1157 -> 522[label="",style="solid", color="burlywood", weight=3];
487[label="primEqInt (Neg xy310) xy401",fontsize=16,color="burlywood",shape="box"];1158[label="xy310/Succ xy3100",fontsize=10,color="white",style="solid",shape="box"];487 -> 1158[label="",style="solid", color="burlywood", weight=9];
1158 -> 523[label="",style="solid", color="burlywood", weight=3];
1159[label="xy310/Zero",fontsize=10,color="white",style="solid",shape="box"];487 -> 1159[label="",style="solid", color="burlywood", weight=9];
1159 -> 524[label="",style="solid", color="burlywood", weight=3];
488[label="() == ()",fontsize=16,color="black",shape="box"];488 -> 525[label="",style="solid", color="black", weight=3];
489[label="Left xy310 == Left xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];489 -> 526[label="",style="solid", color="black", weight=3];
490[label="Left xy310 == Right xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];490 -> 527[label="",style="solid", color="black", weight=3];
491[label="Right xy310 == Left xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];491 -> 528[label="",style="solid", color="black", weight=3];
492[label="Right xy310 == Right xy4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];492 -> 529[label="",style="solid", color="black", weight=3];
493[label="(xy310,xy311,xy312) == (xy4010,xy4011,xy4012)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];493 -> 530[label="",style="solid", color="black", weight=3];
215[label="xy25\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];216[label="(xy28,xy29)\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];494[label="primEqFloat (Float xy310 xy311) (Float xy4010 xy4011)",fontsize=16,color="black",shape="box"];494 -> 531[label="",style="solid", color="black", weight=3];
495[label="True",fontsize=16,color="green",shape="box"];496[label="False",fontsize=16,color="green",shape="box"];497[label="False",fontsize=16,color="green",shape="box"];498[label="False",fontsize=16,color="green",shape="box"];499[label="True",fontsize=16,color="green",shape="box"];500[label="False",fontsize=16,color="green",shape="box"];501[label="False",fontsize=16,color="green",shape="box"];502[label="False",fontsize=16,color="green",shape="box"];503[label="True",fontsize=16,color="green",shape="box"];504[label="primEqDouble (Double xy310 xy311) (Double xy4010 xy4011)",fontsize=16,color="black",shape="box"];504 -> 532[label="",style="solid", color="black", weight=3];
505 -> 374[label="",style="dashed", color="red", weight=0];
505[label="xy310 == xy4010 && xy311 == xy4011\n  Eq a",fontsize=16,color="magenta"];505 -> 533[label="",style="dashed", color="magenta", weight=3];
505 -> 534[label="",style="dashed", color="magenta", weight=3];
506[label="False",fontsize=16,color="green",shape="box"];507[label="False",fontsize=16,color="green",shape="box"];508[label="True",fontsize=16,color="green",shape="box"];509[label="primEqChar (Char xy310) (Char xy4010)",fontsize=16,color="black",shape="box"];509 -> 535[label="",style="solid", color="black", weight=3];
510 -> 374[label="",style="dashed", color="red", weight=0];
510[label="xy310 == xy4010 && xy311 == xy4011\n  Eq a  Eq b",fontsize=16,color="magenta"];510 -> 536[label="",style="dashed", color="magenta", weight=3];
510 -> 537[label="",style="dashed", color="magenta", weight=3];
511[label="True",fontsize=16,color="green",shape="box"];512[label="False",fontsize=16,color="green",shape="box"];513[label="False",fontsize=16,color="green",shape="box"];514[label="xy310 == xy4010\n  Eq a",fontsize=16,color="blue",shape="box"];1162[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1162[label="",style="solid", color="blue", weight=9];
1162 -> 538[label="",style="solid", color="blue", weight=3];
1163[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1163[label="",style="solid", color="blue", weight=9];
1163 -> 539[label="",style="solid", color="blue", weight=3];
1164[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1164[label="",style="solid", color="blue", weight=9];
1164 -> 540[label="",style="solid", color="blue", weight=3];
1165[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1165[label="",style="solid", color="blue", weight=9];
1165 -> 541[label="",style="solid", color="blue", weight=3];
1166[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1166[label="",style="solid", color="blue", weight=9];
1166 -> 542[label="",style="solid", color="blue", weight=3];
1167[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1167[label="",style="solid", color="blue", weight=9];
1167 -> 543[label="",style="solid", color="blue", weight=3];
1168[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1168[label="",style="solid", color="blue", weight=9];
1168 -> 544[label="",style="solid", color="blue", weight=3];
1169[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1169[label="",style="solid", color="blue", weight=9];
1169 -> 545[label="",style="solid", color="blue", weight=3];
1170[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];514 -> 1170[label="",style="solid", color="blue", weight=9];
1170 -> 546[label="",style="solid", color="blue", weight=3];
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1220[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];534 -> 1220[label="",style="solid", color="blue", weight=9];
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904 -> 998[label="",style="dashed", color="magenta", weight=3];
905[label="xy310",fontsize=16,color="green",shape="box"];906[label="xy4010",fontsize=16,color="green",shape="box"];907[label="xy310",fontsize=16,color="green",shape="box"];908[label="xy4010",fontsize=16,color="green",shape="box"];909[label="xy310",fontsize=16,color="green",shape="box"];910[label="xy4010",fontsize=16,color="green",shape="box"];911[label="xy310\n  Eq a",fontsize=16,color="green",shape="box"];912[label="xy4010\n  Eq a",fontsize=16,color="green",shape="box"];913[label="xy310",fontsize=16,color="green",shape="box"];914[label="xy4010",fontsize=16,color="green",shape="box"];915[label="xy310\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];916[label="xy4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];917[label="xy310\n  Eq a",fontsize=16,color="green",shape="box"];918[label="xy4010\n  Eq a",fontsize=16,color="green",shape="box"];919[label="xy310",fontsize=16,color="green",shape="box"];920[label="xy4010",fontsize=16,color="green",shape="box"];921[label="xy310",fontsize=16,color="green",shape="box"];922[label="xy4010",fontsize=16,color="green",shape="box"];923[label="xy310\n  Integral a",fontsize=16,color="green",shape="box"];924[label="xy4010\n  Integral a",fontsize=16,color="green",shape="box"];925[label="xy310",fontsize=16,color="green",shape="box"];926[label="xy4010",fontsize=16,color="green",shape="box"];927[label="xy310",fontsize=16,color="green",shape="box"];928[label="xy4010",fontsize=16,color="green",shape="box"];929[label="xy310\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];930[label="xy4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];931[label="xy310\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];932[label="xy4010\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];933[label="primMulInt (Pos xy3100) xy4010",fontsize=16,color="burlywood",shape="box"];1462[label="xy4010/Pos xy40100",fontsize=10,color="white",style="solid",shape="box"];933 -> 1462[label="",style="solid", color="burlywood", weight=9];
1462 -> 999[label="",style="solid", color="burlywood", weight=3];
1463[label="xy4010/Neg xy40100",fontsize=10,color="white",style="solid",shape="box"];933 -> 1463[label="",style="solid", color="burlywood", weight=9];
1463 -> 1000[label="",style="solid", color="burlywood", weight=3];
934[label="primMulInt (Neg xy3100) xy4010",fontsize=16,color="burlywood",shape="box"];1464[label="xy4010/Pos xy40100",fontsize=10,color="white",style="solid",shape="box"];934 -> 1464[label="",style="solid", color="burlywood", weight=9];
1464 -> 1001[label="",style="solid", color="burlywood", weight=3];
1465[label="xy4010/Neg xy40100",fontsize=10,color="white",style="solid",shape="box"];934 -> 1465[label="",style="solid", color="burlywood", weight=9];
1465 -> 1002[label="",style="solid", color="burlywood", weight=3];
935 -> 535[label="",style="dashed", color="red", weight=0];
935[label="primEqNat xy3100 xy40100",fontsize=16,color="magenta"];935 -> 1003[label="",style="dashed", color="magenta", weight=3];
935 -> 1004[label="",style="dashed", color="magenta", weight=3];
936[label="False",fontsize=16,color="green",shape="box"];937[label="False",fontsize=16,color="green",shape="box"];938[label="True",fontsize=16,color="green",shape="box"];939[label="xy40100",fontsize=16,color="green",shape="box"];940[label="xy3100",fontsize=16,color="green",shape="box"];941[label="xy40100",fontsize=16,color="green",shape="box"];942[label="xy3100",fontsize=16,color="green",shape="box"];943[label="xy312",fontsize=16,color="green",shape="box"];944[label="xy4012",fontsize=16,color="green",shape="box"];945[label="xy312",fontsize=16,color="green",shape="box"];946[label="xy4012",fontsize=16,color="green",shape="box"];947[label="xy312",fontsize=16,color="green",shape="box"];948[label="xy4012",fontsize=16,color="green",shape="box"];949[label="xy312\n  Eq a",fontsize=16,color="green",shape="box"];950[label="xy4012\n  Eq a",fontsize=16,color="green",shape="box"];951[label="xy312",fontsize=16,color="green",shape="box"];952[label="xy4012",fontsize=16,color="green",shape="box"];953[label="xy312\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];954[label="xy4012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];955[label="xy312\n  Eq a",fontsize=16,color="green",shape="box"];956[label="xy4012\n  Eq a",fontsize=16,color="green",shape="box"];957[label="xy312",fontsize=16,color="green",shape="box"];958[label="xy4012",fontsize=16,color="green",shape="box"];959[label="xy312",fontsize=16,color="green",shape="box"];960[label="xy4012",fontsize=16,color="green",shape="box"];961[label="xy312\n  Integral a",fontsize=16,color="green",shape="box"];962[label="xy4012\n  Integral a",fontsize=16,color="green",shape="box"];963[label="xy312",fontsize=16,color="green",shape="box"];964[label="xy4012",fontsize=16,color="green",shape="box"];965[label="xy312",fontsize=16,color="green",shape="box"];966[label="xy4012",fontsize=16,color="green",shape="box"];967[label="xy312\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];968[label="xy4012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];969[label="xy312\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];970[label="xy4012\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];971[label="xy311",fontsize=16,color="green",shape="box"];972[label="xy4011",fontsize=16,color="green",shape="box"];973[label="xy311",fontsize=16,color="green",shape="box"];974[label="xy4011",fontsize=16,color="green",shape="box"];975[label="xy311",fontsize=16,color="green",shape="box"];976[label="xy4011",fontsize=16,color="green",shape="box"];977[label="xy311\n  Eq a",fontsize=16,color="green",shape="box"];978[label="xy4011\n  Eq a",fontsize=16,color="green",shape="box"];979[label="xy311",fontsize=16,color="green",shape="box"];980[label="xy4011",fontsize=16,color="green",shape="box"];981[label="xy311\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];982[label="xy4011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];983[label="xy311\n  Eq a",fontsize=16,color="green",shape="box"];984[label="xy4011\n  Eq a",fontsize=16,color="green",shape="box"];985[label="xy311",fontsize=16,color="green",shape="box"];986[label="xy4011",fontsize=16,color="green",shape="box"];987[label="xy311",fontsize=16,color="green",shape="box"];988[label="xy4011",fontsize=16,color="green",shape="box"];989[label="xy311\n  Integral a",fontsize=16,color="green",shape="box"];990[label="xy4011\n  Integral a",fontsize=16,color="green",shape="box"];991[label="xy311",fontsize=16,color="green",shape="box"];992[label="xy4011",fontsize=16,color="green",shape="box"];993[label="xy311",fontsize=16,color="green",shape="box"];994[label="xy4011",fontsize=16,color="green",shape="box"];995[label="xy311\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];996[label="xy4011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];997[label="xy311\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];998[label="xy4011\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];999[label="primMulInt (Pos xy3100) (Pos xy40100)",fontsize=16,color="black",shape="box"];999 -> 1005[label="",style="solid", color="black", weight=3];
1000[label="primMulInt (Pos xy3100) (Neg xy40100)",fontsize=16,color="black",shape="box"];1000 -> 1006[label="",style="solid", color="black", weight=3];
1001[label="primMulInt (Neg xy3100) (Pos xy40100)",fontsize=16,color="black",shape="box"];1001 -> 1007[label="",style="solid", color="black", weight=3];
1002[label="primMulInt (Neg xy3100) (Neg xy40100)",fontsize=16,color="black",shape="box"];1002 -> 1008[label="",style="solid", color="black", weight=3];
1003[label="xy40100",fontsize=16,color="green",shape="box"];1004[label="xy3100",fontsize=16,color="green",shape="box"];1005[label="Pos (primMulNat xy3100 xy40100)",fontsize=16,color="green",shape="box"];1005 -> 1009[label="",style="dashed", color="green", weight=3];
1006[label="Neg (primMulNat xy3100 xy40100)",fontsize=16,color="green",shape="box"];1006 -> 1010[label="",style="dashed", color="green", weight=3];
1007[label="Neg (primMulNat xy3100 xy40100)",fontsize=16,color="green",shape="box"];1007 -> 1011[label="",style="dashed", color="green", weight=3];
1008[label="Pos (primMulNat xy3100 xy40100)",fontsize=16,color="green",shape="box"];1008 -> 1012[label="",style="dashed", color="green", weight=3];
1009[label="primMulNat xy3100 xy40100",fontsize=16,color="burlywood",shape="triangle"];1467[label="xy3100/Succ xy31000",fontsize=10,color="white",style="solid",shape="box"];1009 -> 1467[label="",style="solid", color="burlywood", weight=9];
1467 -> 1013[label="",style="solid", color="burlywood", weight=3];
1468[label="xy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];1009 -> 1468[label="",style="solid", color="burlywood", weight=9];
1468 -> 1014[label="",style="solid", color="burlywood", weight=3];
1010 -> 1009[label="",style="dashed", color="red", weight=0];
1010[label="primMulNat xy3100 xy40100",fontsize=16,color="magenta"];1010 -> 1015[label="",style="dashed", color="magenta", weight=3];
1011 -> 1009[label="",style="dashed", color="red", weight=0];
1011[label="primMulNat xy3100 xy40100",fontsize=16,color="magenta"];1011 -> 1016[label="",style="dashed", color="magenta", weight=3];
1012 -> 1009[label="",style="dashed", color="red", weight=0];
1012[label="primMulNat xy3100 xy40100",fontsize=16,color="magenta"];1012 -> 1017[label="",style="dashed", color="magenta", weight=3];
1012 -> 1018[label="",style="dashed", color="magenta", weight=3];
1013[label="primMulNat (Succ xy31000) xy40100",fontsize=16,color="burlywood",shape="box"];1472[label="xy40100/Succ xy401000",fontsize=10,color="white",style="solid",shape="box"];1013 -> 1472[label="",style="solid", color="burlywood", weight=9];
1472 -> 1019[label="",style="solid", color="burlywood", weight=3];
1473[label="xy40100/Zero",fontsize=10,color="white",style="solid",shape="box"];1013 -> 1473[label="",style="solid", color="burlywood", weight=9];
1473 -> 1020[label="",style="solid", color="burlywood", weight=3];
1014[label="primMulNat Zero xy40100",fontsize=16,color="burlywood",shape="box"];1474[label="xy40100/Succ xy401000",fontsize=10,color="white",style="solid",shape="box"];1014 -> 1474[label="",style="solid", color="burlywood", weight=9];
1474 -> 1021[label="",style="solid", color="burlywood", weight=3];
1475[label="xy40100/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 1475[label="",style="solid", color="burlywood", weight=9];
1475 -> 1022[label="",style="solid", color="burlywood", weight=3];
1015[label="xy40100",fontsize=16,color="green",shape="box"];1016[label="xy3100",fontsize=16,color="green",shape="box"];1017[label="xy3100",fontsize=16,color="green",shape="box"];1018[label="xy40100",fontsize=16,color="green",shape="box"];1019[label="primMulNat (Succ xy31000) (Succ xy401000)",fontsize=16,color="black",shape="box"];1019 -> 1023[label="",style="solid", color="black", weight=3];
1020[label="primMulNat (Succ xy31000) Zero",fontsize=16,color="black",shape="box"];1020 -> 1024[label="",style="solid", color="black", weight=3];
1021[label="primMulNat Zero (Succ xy401000)",fontsize=16,color="black",shape="box"];1021 -> 1025[label="",style="solid", color="black", weight=3];
1022[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1022 -> 1026[label="",style="solid", color="black", weight=3];
1023 -> 1027[label="",style="dashed", color="red", weight=0];
1023[label="primPlusNat (primMulNat xy31000 (Succ xy401000)) (Succ xy401000)",fontsize=16,color="magenta"];1023 -> 1028[label="",style="dashed", color="magenta", weight=3];
1024[label="Zero",fontsize=16,color="green",shape="box"];1025[label="Zero",fontsize=16,color="green",shape="box"];1026[label="Zero",fontsize=16,color="green",shape="box"];1028 -> 1009[label="",style="dashed", color="red", weight=0];
1028[label="primMulNat xy31000 (Succ xy401000)",fontsize=16,color="magenta"];1028 -> 1029[label="",style="dashed", color="magenta", weight=3];
1028 -> 1030[label="",style="dashed", color="magenta", weight=3];
1027[label="primPlusNat xy44 (Succ xy401000)",fontsize=16,color="burlywood",shape="triangle"];1478[label="xy44/Succ xy440",fontsize=10,color="white",style="solid",shape="box"];1027 -> 1478[label="",style="solid", color="burlywood", weight=9];
1478 -> 1031[label="",style="solid", color="burlywood", weight=3];
1479[label="xy44/Zero",fontsize=10,color="white",style="solid",shape="box"];1027 -> 1479[label="",style="solid", color="burlywood", weight=9];
1479 -> 1032[label="",style="solid", color="burlywood", weight=3];
1029[label="xy31000",fontsize=16,color="green",shape="box"];1030[label="Succ xy401000",fontsize=16,color="green",shape="box"];1031[label="primPlusNat (Succ xy440) (Succ xy401000)",fontsize=16,color="black",shape="box"];1031 -> 1033[label="",style="solid", color="black", weight=3];
1032[label="primPlusNat Zero (Succ xy401000)",fontsize=16,color="black",shape="box"];1032 -> 1034[label="",style="solid", color="black", weight=3];
1033[label="Succ (Succ (primPlusNat xy440 xy401000))",fontsize=16,color="green",shape="box"];1033 -> 1035[label="",style="dashed", color="green", weight=3];
1034[label="Succ xy401000",fontsize=16,color="green",shape="box"];1035[label="primPlusNat xy440 xy401000",fontsize=16,color="burlywood",shape="triangle"];1480[label="xy440/Succ xy4400",fontsize=10,color="white",style="solid",shape="box"];1035 -> 1480[label="",style="solid", color="burlywood", weight=9];
1480 -> 1036[label="",style="solid", color="burlywood", weight=3];
1481[label="xy440/Zero",fontsize=10,color="white",style="solid",shape="box"];1035 -> 1481[label="",style="solid", color="burlywood", weight=9];
1481 -> 1037[label="",style="solid", color="burlywood", weight=3];
1036[label="primPlusNat (Succ xy4400) xy401000",fontsize=16,color="burlywood",shape="box"];1482[label="xy401000/Succ xy4010000",fontsize=10,color="white",style="solid",shape="box"];1036 -> 1482[label="",style="solid", color="burlywood", weight=9];
1482 -> 1038[label="",style="solid", color="burlywood", weight=3];
1483[label="xy401000/Zero",fontsize=10,color="white",style="solid",shape="box"];1036 -> 1483[label="",style="solid", color="burlywood", weight=9];
1483 -> 1039[label="",style="solid", color="burlywood", weight=3];
1037[label="primPlusNat Zero xy401000",fontsize=16,color="burlywood",shape="box"];1484[label="xy401000/Succ xy4010000",fontsize=10,color="white",style="solid",shape="box"];1037 -> 1484[label="",style="solid", color="burlywood", weight=9];
1484 -> 1040[label="",style="solid", color="burlywood", weight=3];
1485[label="xy401000/Zero",fontsize=10,color="white",style="solid",shape="box"];1037 -> 1485[label="",style="solid", color="burlywood", weight=9];
1485 -> 1041[label="",style="solid", color="burlywood", weight=3];
1038[label="primPlusNat (Succ xy4400) (Succ xy4010000)",fontsize=16,color="black",shape="box"];1038 -> 1042[label="",style="solid", color="black", weight=3];
1039[label="primPlusNat (Succ xy4400) Zero",fontsize=16,color="black",shape="box"];1039 -> 1043[label="",style="solid", color="black", weight=3];
1040[label="primPlusNat Zero (Succ xy4010000)",fontsize=16,color="black",shape="box"];1040 -> 1044[label="",style="solid", color="black", weight=3];
1041[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1041 -> 1045[label="",style="solid", color="black", weight=3];
1042[label="Succ (Succ (primPlusNat xy4400 xy4010000))",fontsize=16,color="green",shape="box"];1042 -> 1046[label="",style="dashed", color="green", weight=3];
1043[label="Succ xy4400",fontsize=16,color="green",shape="box"];1044[label="Succ xy4010000",fontsize=16,color="green",shape="box"];1045[label="Zero",fontsize=16,color="green",shape="box"];1046 -> 1035[label="",style="dashed", color="red", weight=0];
1046[label="primPlusNat xy4400 xy4010000",fontsize=16,color="magenta"];1046 -> 1047[label="",style="dashed", color="magenta", weight=3];
1046 -> 1048[label="",style="dashed", color="magenta", weight=3];
1047[label="xy4400",fontsize=16,color="green",shape="box"];1048[label="xy4010000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_primPlusNat(Succ(xy4400), Succ(xy4010000)) → new_primPlusNat(xy4400, xy4010000)

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(xy4400), Succ(xy4010000)) → new_primPlusNat(xy4400, xy4010000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_primMulNat(Succ(xy31000), Succ(xy401000)) → new_primMulNat(xy31000, Succ(xy401000))

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

new_primMulNat(Succ(xy31000), Succ(xy401000)) → new_primMulNat(xy31000, Succ(xy401000))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_primEqNat(Succ(xy3100), Succ(xy40100)) → new_primEqNat(xy3100, xy40100)

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_esEs2(Left(xy310), Left(xy4010), app(ty_[], gb), gc) → new_esEs(xy310, xy4010, gb)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_@2, bc), bd)) → new_esEs0(xy310, xy4010, bc, bd)
new_esEs2(Right(xy310), Right(xy4010), hd, app(ty_[], he)) → new_esEs(xy310, xy4010, he)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(app(ty_Either, bdg), bdh), bag, bcb) → new_esEs2(xy310, xy4010, bdg, bdh)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs3(xy312, xy4012, bbf, bbg, bbh)
new_esEs2(Left(xy310), Left(xy4010), app(app(ty_@2, gd), ge), gc) → new_esEs0(xy310, xy4010, gd, ge)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(ty_[], bah)) → new_esEs(xy312, xy4012, bah)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(ty_Maybe, bbc)) → new_esEs1(xy312, xy4012, bbc)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(app(ty_Either, ec), ed), dg) → new_esEs2(xy310, xy4010, ec, ed)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(app(ty_@2, bdd), bde), bag, bcb) → new_esEs0(xy310, xy4010, bdd, bde)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(app(ty_@3, bh), ca), cb)) → new_esEs3(xy310, xy4010, bh, ca, cb)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(ty_[], bdc), bag, bcb) → new_esEs(xy310, xy4010, bdc)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(app(ty_Either, bcf), bcg), bcb) → new_esEs2(xy311, xy4011, bcf, bcg)
new_esEs1(Just(xy310), Just(xy4010), app(app(app(ty_@3, fg), fh), ga)) → new_esEs3(xy310, xy4010, fg, fh, ga)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(ty_[], bca), bcb) → new_esEs(xy311, xy4011, bca)
new_esEs2(Left(xy310), Left(xy4010), app(app(ty_Either, gg), gh), gc) → new_esEs2(xy310, xy4010, gg, gh)
new_esEs2(Left(xy310), Left(xy4010), app(app(app(ty_@3, ha), hb), hc), gc) → new_esEs3(xy310, xy4010, ha, hb, hc)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(ty_Maybe, bdf), bag, bcb) → new_esEs1(xy310, xy4010, bdf)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(app(ty_@2, bcc), bcd), bcb) → new_esEs0(xy311, xy4011, bcc, bcd)
new_esEs2(Right(xy310), Right(xy4010), hd, app(app(ty_@2, hf), hg)) → new_esEs0(xy310, xy4010, hf, hg)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(ty_[], cd)) → new_esEs(xy311, xy4011, cd)
new_esEs1(Just(xy310), Just(xy4010), app(app(ty_@2, fa), fb)) → new_esEs0(xy310, xy4010, fa, fb)
new_esEs2(Left(xy310), Left(xy4010), app(ty_Maybe, gf), gc) → new_esEs1(xy310, xy4010, gf)
new_esEs1(Just(xy310), Just(xy4010), app(app(ty_Either, fd), ff)) → new_esEs2(xy310, xy4010, fd, ff)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(app(ty_Either, bbd), bbe)) → new_esEs2(xy312, xy4012, bbd, bbe)
new_esEs1(Just(xy310), Just(xy4010), app(ty_[], eh)) → new_esEs(xy310, xy4010, eh)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(app(app(ty_@3, bch), bda), bdb), bcb) → new_esEs3(xy311, xy4011, bch, bda, bdb)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), ba) → new_esEs(xy311, xy4011, ba)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_Either, bf), bg)) → new_esEs2(xy310, xy4010, bf, bg)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(app(app(ty_@3, ee), ef), eg), dg) → new_esEs3(xy310, xy4010, ee, ef, eg)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(app(ty_Either, da), db)) → new_esEs2(xy311, xy4011, da, db)
new_esEs2(Right(xy310), Right(xy4010), hd, app(app(ty_Either, baa), bab)) → new_esEs2(xy310, xy4010, baa, bab)
new_esEs1(Just(xy310), Just(xy4010), app(ty_Maybe, fc)) → new_esEs1(xy310, xy4010, fc)
new_esEs2(Right(xy310), Right(xy4010), hd, app(ty_Maybe, hh)) → new_esEs1(xy310, xy4010, hh)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(app(ty_@2, dh), ea), dg) → new_esEs0(xy310, xy4010, dh, ea)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(ty_[], df), dg) → new_esEs(xy310, xy4010, df)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(ty_Maybe, cg)) → new_esEs1(xy311, xy4011, cg)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(ty_Maybe, eb), dg) → new_esEs1(xy310, xy4010, eb)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(app(ty_@2, ce), cf)) → new_esEs0(xy311, xy4011, ce, cf)
new_esEs2(Right(xy310), Right(xy4010), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(xy310, xy4010, bac, bad, bae)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(app(ty_@2, bba), bbb)) → new_esEs0(xy312, xy4012, bba, bbb)
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(app(app(ty_@3, dc), dd), de)) → new_esEs3(xy311, xy4011, dc, dd, de)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_[], bb)) → new_esEs(xy310, xy4010, bb)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(app(app(ty_@3, bea), beb), bec), bag, bcb) → new_esEs3(xy310, xy4010, bea, beb, bec)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_Maybe, be)) → new_esEs1(xy310, xy4010, be)
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(ty_Maybe, bce), bcb) → new_esEs1(xy311, xy4011, bce)

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

new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_Either, bf), bg)) → new_esEs2(xy310, xy4010, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(app(ty_@3, bh), ca), cb)) → new_esEs3(xy310, xy4010, bh, ca, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(Just(xy310), Just(xy4010), app(app(ty_Either, fd), ff)) → new_esEs2(xy310, xy4010, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xy310), Just(xy4010), app(ty_[], eh)) → new_esEs(xy310, xy4010, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Just(xy310), Just(xy4010), app(app(app(ty_@3, fg), fh), ga)) → new_esEs3(xy310, xy4010, fg, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_@2, bc), bd)) → new_esEs0(xy310, xy4010, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_Maybe, be)) → new_esEs1(xy310, xy4010, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Just(xy310), Just(xy4010), app(app(ty_@2, fa), fb)) → new_esEs0(xy310, xy4010, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xy310), Just(xy4010), app(ty_Maybe, fc)) → new_esEs1(xy310, xy4010, fc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(xy310, xy311), :(xy4010, xy4011), ba) → new_esEs(xy311, xy4011, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_[], bb)) → new_esEs(xy310, xy4010, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(app(ty_Either, ec), ed), dg) → new_esEs2(xy310, xy4010, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(app(ty_Either, da), db)) → new_esEs2(xy311, xy4011, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Left(xy310), Left(xy4010), app(app(ty_Either, gg), gh), gc) → new_esEs2(xy310, xy4010, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(xy310), Right(xy4010), hd, app(app(ty_Either, baa), bab)) → new_esEs2(xy310, xy4010, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(app(ty_Either, bdg), bdh), bag, bcb) → new_esEs2(xy310, xy4010, bdg, bdh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(app(ty_Either, bcf), bcg), bcb) → new_esEs2(xy311, xy4011, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(app(ty_Either, bbd), bbe)) → new_esEs2(xy312, xy4012, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(ty_[], cd)) → new_esEs(xy311, xy4011, cd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(ty_[], df), dg) → new_esEs(xy310, xy4010, df)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(app(app(ty_@3, ee), ef), eg), dg) → new_esEs3(xy310, xy4010, ee, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(app(app(ty_@3, dc), dd), de)) → new_esEs3(xy311, xy4011, dc, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(app(ty_@2, dh), ea), dg) → new_esEs0(xy310, xy4010, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(app(ty_@2, ce), cf)) → new_esEs0(xy311, xy4011, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), cc, app(ty_Maybe, cg)) → new_esEs1(xy311, xy4011, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@2(xy310, xy311), @2(xy4010, xy4011), app(ty_Maybe, eb), dg) → new_esEs1(xy310, xy4010, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Left(xy310), Left(xy4010), app(ty_[], gb), gc) → new_esEs(xy310, xy4010, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(xy310), Right(xy4010), hd, app(ty_[], he)) → new_esEs(xy310, xy4010, he)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(ty_[], bah)) → new_esEs(xy312, xy4012, bah)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(ty_[], bdc), bag, bcb) → new_esEs(xy310, xy4010, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(ty_[], bca), bcb) → new_esEs(xy311, xy4011, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(xy310), Left(xy4010), app(app(app(ty_@3, ha), hb), hc), gc) → new_esEs3(xy310, xy4010, ha, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Right(xy310), Right(xy4010), hd, app(app(app(ty_@3, bac), bad), bae)) → new_esEs3(xy310, xy4010, bac, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(Left(xy310), Left(xy4010), app(app(ty_@2, gd), ge), gc) → new_esEs0(xy310, xy4010, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(xy310), Right(xy4010), hd, app(app(ty_@2, hf), hg)) → new_esEs0(xy310, xy4010, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Left(xy310), Left(xy4010), app(ty_Maybe, gf), gc) → new_esEs1(xy310, xy4010, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(xy310), Right(xy4010), hd, app(ty_Maybe, hh)) → new_esEs1(xy310, xy4010, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs3(xy312, xy4012, bbf, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(app(app(ty_@3, bch), bda), bdb), bcb) → new_esEs3(xy311, xy4011, bch, bda, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(app(app(ty_@3, bea), beb), bec), bag, bcb) → new_esEs3(xy310, xy4010, bea, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(app(ty_@2, bdd), bde), bag, bcb) → new_esEs0(xy310, xy4010, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(app(ty_@2, bcc), bcd), bcb) → new_esEs0(xy311, xy4011, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(app(ty_@2, bba), bbb)) → new_esEs0(xy312, xy4012, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, bag, app(ty_Maybe, bbc)) → new_esEs1(xy312, xy4012, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), app(ty_Maybe, bdf), bag, bcb) → new_esEs1(xy310, xy4010, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), baf, app(ty_Maybe, bce), bcb) → new_esEs1(xy311, xy4011, bce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_deleteBy(@2(xy30, xy31), :(@2(xy400, xy401), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy401, xy30, xy31, new_asAs(new_esEs5(xy30, xy400, bc), new_esEs4(xy31, xy401, bd)), bc, bd)
new_deleteBy0(xy25, xy26, xy27, xy28, xy29, False, ba, bb) → new_deleteBy(@2(xy28, xy29), xy25, ba, bb)

The TRS R consists of the following rules:

new_esEs7(Just(xy310), Just(xy4010), app(ty_Maybe, ca)) → new_esEs7(xy310, xy4010, ca)
new_esEs22(xy310, xy4010, ty_Integer) → new_esEs14(xy310, xy4010)
new_esEs20(xy312, xy4012, app(ty_Maybe, dg)) → new_esEs7(xy312, xy4012, dg)
new_esEs24(xy311, xy4011, app(ty_Ratio, beb)) → new_esEs15(xy311, xy4011, beb)
new_primPlusNat1(Succ(xy4400), Succ(xy4010000)) → Succ(Succ(new_primPlusNat1(xy4400, xy4010000)))
new_primEqInt(Neg(Succ(xy3100)), Pos(xy4010)) → False
new_primEqInt(Pos(Succ(xy3100)), Neg(xy4010)) → False
new_esEs7(Nothing, Just(xy4010), be) → False
new_esEs7(Just(xy310), Nothing, be) → False
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs25(xy310, xy4010, ty_Ordering) → new_esEs6(xy310, xy4010)
new_esEs18(Left(xy310), Left(xy4010), app(app(ty_Either, baa), bab), hc) → new_esEs18(xy310, xy4010, baa, bab)
new_esEs24(xy311, xy4011, app(app(ty_Either, bec), bed)) → new_esEs18(xy311, xy4011, bec, bed)
new_primEqInt(Neg(Zero), Pos(Succ(xy40100))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40100))) → False
new_esEs18(Left(xy310), Left(xy4010), app(ty_Maybe, hg), hc) → new_esEs7(xy310, xy4010, hg)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_@0) → new_esEs17(xy310, xy4010)
new_esEs21(xy311, xy4011, ty_Char) → new_esEs11(xy311, xy4011)
new_esEs8(Float(xy310, xy311), Float(xy4010, xy4011)) → new_esEs16(new_sr(xy310, xy4010), new_sr(xy311, xy4011))
new_esEs7(Just(xy310), Just(xy4010), ty_Double) → new_esEs9(xy310, xy4010)
new_esEs5(xy30, xy400, app(ty_[], bgb)) → new_esEs10(xy30, xy400, bgb)
new_esEs21(xy311, xy4011, ty_@0) → new_esEs17(xy311, xy4011)
new_primMulNat0(Zero, Zero) → Zero
new_esEs5(xy30, xy400, ty_Int) → new_esEs16(xy30, xy400)
new_esEs23(xy310, xy4010, ty_Ordering) → new_esEs6(xy310, xy4010)
new_esEs4(xy31, xy401, app(ty_Maybe, be)) → new_esEs7(xy31, xy401, be)
new_esEs22(xy310, xy4010, app(app(ty_Either, gf), gg)) → new_esEs18(xy310, xy4010, gf, gg)
new_esEs7(Just(xy310), Just(xy4010), app(app(app(ty_@3, ce), cf), cg)) → new_esEs19(xy310, xy4010, ce, cf, cg)
new_esEs18(Right(xy310), Right(xy4010), baf, app(ty_Ratio, bbc)) → new_esEs15(xy310, xy4010, bbc)
new_esEs21(xy311, xy4011, ty_Integer) → new_esEs14(xy311, xy4011)
new_esEs18(Left(xy310), Left(xy4010), ty_Double, hc) → new_esEs9(xy310, xy4010)
new_esEs5(xy30, xy400, ty_Double) → new_esEs9(xy30, xy400)
new_esEs24(xy311, xy4011, ty_Double) → new_esEs9(xy311, xy4011)
new_esEs21(xy311, xy4011, app(ty_[], ef)) → new_esEs10(xy311, xy4011, ef)
new_primPlusNat0(Zero, xy401000) → Succ(xy401000)
new_esEs23(xy310, xy4010, ty_Double) → new_esEs9(xy310, xy4010)
new_esEs23(xy310, xy4010, app(app(ty_@2, bcc), bcd)) → new_esEs12(xy310, xy4010, bcc, bcd)
new_esEs22(xy310, xy4010, ty_@0) → new_esEs17(xy310, xy4010)
new_esEs4(xy31, xy401, ty_Char) → new_esEs11(xy31, xy401)
new_sr(Pos(xy3100), Neg(xy40100)) → Neg(new_primMulNat0(xy3100, xy40100))
new_sr(Neg(xy3100), Pos(xy40100)) → Neg(new_primMulNat0(xy3100, xy40100))
new_esEs24(xy311, xy4011, ty_Bool) → new_esEs13(xy311, xy4011)
new_esEs18(Left(xy310), Left(xy4010), ty_Bool, hc) → new_esEs13(xy310, xy4010)
new_esEs23(xy310, xy4010, app(ty_[], bcb)) → new_esEs10(xy310, xy4010, bcb)
new_esEs21(xy311, xy4011, app(ty_Ratio, fb)) → new_esEs15(xy311, xy4011, fb)
new_esEs24(xy311, xy4011, app(app(app(ty_@3, bee), bef), beg)) → new_esEs19(xy311, xy4011, bee, bef, beg)
new_esEs22(xy310, xy4010, ty_Char) → new_esEs11(xy310, xy4010)
new_esEs20(xy312, xy4012, ty_Float) → new_esEs8(xy312, xy4012)
new_esEs5(xy30, xy400, app(app(ty_Either, bgg), bgh)) → new_esEs18(xy30, xy400, bgg, bgh)
new_esEs21(xy311, xy4011, app(ty_Maybe, fa)) → new_esEs7(xy311, xy4011, fa)
new_esEs7(Just(xy310), Just(xy4010), ty_Integer) → new_esEs14(xy310, xy4010)
new_esEs4(xy31, xy401, app(app(app(ty_@3, da), db), dc)) → new_esEs19(xy31, xy401, da, db, dc)
new_esEs24(xy311, xy4011, ty_@0) → new_esEs17(xy311, xy4011)
new_esEs20(xy312, xy4012, app(app(ty_@2, de), df)) → new_esEs12(xy312, xy4012, de, df)
new_esEs18(Left(xy310), Left(xy4010), ty_Ordering, hc) → new_esEs6(xy310, xy4010)
new_esEs20(xy312, xy4012, ty_Char) → new_esEs11(xy312, xy4012)
new_esEs26(xy311, xy4011, ty_Integer) → new_esEs14(xy311, xy4011)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Double) → new_esEs9(xy310, xy4010)
new_esEs23(xy310, xy4010, ty_Bool) → new_esEs13(xy310, xy4010)
new_esEs18(Left(xy310), Left(xy4010), app(app(ty_@2, he), hf), hc) → new_esEs12(xy310, xy4010, he, hf)
new_esEs5(xy30, xy400, ty_Integer) → new_esEs14(xy30, xy400)
new_esEs18(Right(xy310), Right(xy4010), baf, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs19(xy310, xy4010, bbf, bbg, bbh)
new_esEs25(xy310, xy4010, ty_Bool) → new_esEs13(xy310, xy4010)
new_primEqNat0(Zero, Succ(xy40100)) → False
new_primEqNat0(Succ(xy3100), Zero) → False
new_esEs21(xy311, xy4011, app(app(app(ty_@3, ff), fg), fh)) → new_esEs19(xy311, xy4011, ff, fg, fh)
new_esEs25(xy310, xy4010, ty_Double) → new_esEs9(xy310, xy4010)
new_esEs17(@0, @0) → True
new_esEs5(xy30, xy400, app(ty_Maybe, bge)) → new_esEs7(xy30, xy400, bge)
new_esEs25(xy310, xy4010, app(ty_[], beh)) → new_esEs10(xy310, xy4010, beh)
new_esEs20(xy312, xy4012, app(ty_[], dd)) → new_esEs10(xy312, xy4012, dd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(xy310, xy4010, app(app(app(ty_@3, gh), ha), hb)) → new_esEs19(xy310, xy4010, gh, ha, hb)
new_esEs22(xy310, xy4010, app(ty_Ratio, ge)) → new_esEs15(xy310, xy4010, ge)
new_esEs7(Just(xy310), Just(xy4010), app(ty_Ratio, cb)) → new_esEs15(xy310, xy4010, cb)
new_esEs25(xy310, xy4010, ty_Char) → new_esEs11(xy310, xy4010)
new_esEs4(xy31, xy401, app(ty_[], bca)) → new_esEs10(xy31, xy401, bca)
new_esEs25(xy310, xy4010, ty_Float) → new_esEs8(xy310, xy4010)
new_esEs20(xy312, xy4012, ty_Int) → new_esEs16(xy312, xy4012)
new_esEs4(xy31, xy401, app(ty_Ratio, bhd)) → new_esEs15(xy31, xy401, bhd)
new_esEs20(xy312, xy4012, ty_Ordering) → new_esEs6(xy312, xy4012)
new_esEs26(xy311, xy4011, ty_Int) → new_esEs16(xy311, xy4011)
new_esEs5(xy30, xy400, ty_Bool) → new_esEs13(xy30, xy400)
new_esEs6(GT, LT) → False
new_esEs6(LT, GT) → False
new_esEs24(xy311, xy4011, app(ty_Maybe, bea)) → new_esEs7(xy311, xy4011, bea)
new_esEs5(xy30, xy400, ty_@0) → new_esEs17(xy30, xy400)
new_esEs23(xy310, xy4010, app(ty_Maybe, bce)) → new_esEs7(xy310, xy4010, bce)
new_esEs25(xy310, xy4010, ty_Int) → new_esEs16(xy310, xy4010)
new_esEs25(xy310, xy4010, ty_Integer) → new_esEs14(xy310, xy4010)
new_esEs21(xy311, xy4011, app(app(ty_@2, eg), eh)) → new_esEs12(xy311, xy4011, eg, eh)
new_esEs21(xy311, xy4011, app(app(ty_Either, fc), fd)) → new_esEs18(xy311, xy4011, fc, fd)
new_esEs14(Integer(xy310), Integer(xy4010)) → new_primEqInt(xy310, xy4010)
new_esEs10(:(xy310, xy311), :(xy4010, xy4011), bca) → new_asAs(new_esEs23(xy310, xy4010, bca), new_esEs10(xy311, xy4011, bca))
new_esEs4(xy31, xy401, ty_Integer) → new_esEs14(xy31, xy401)
new_esEs7(Just(xy310), Just(xy4010), app(app(ty_Either, cc), cd)) → new_esEs18(xy310, xy4010, cc, cd)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Ordering) → new_esEs6(xy310, xy4010)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Float) → new_esEs8(xy310, xy4010)
new_esEs11(Char(xy310), Char(xy4010)) → new_primEqNat0(xy310, xy4010)
new_esEs25(xy310, xy4010, app(ty_Maybe, bfc)) → new_esEs7(xy310, xy4010, bfc)
new_esEs24(xy311, xy4011, app(ty_[], bdf)) → new_esEs10(xy311, xy4011, bdf)
new_esEs7(Just(xy310), Just(xy4010), ty_Float) → new_esEs8(xy310, xy4010)
new_esEs23(xy310, xy4010, app(ty_Ratio, bcf)) → new_esEs15(xy310, xy4010, bcf)
new_esEs18(Right(xy310), Right(xy4010), baf, app(ty_Maybe, bbb)) → new_esEs7(xy310, xy4010, bbb)
new_esEs21(xy311, xy4011, ty_Double) → new_esEs9(xy311, xy4011)
new_esEs18(Left(xy310), Left(xy4010), ty_Float, hc) → new_esEs8(xy310, xy4010)
new_esEs24(xy311, xy4011, app(app(ty_@2, bdg), bdh)) → new_esEs12(xy311, xy4011, bdg, bdh)
new_esEs18(Left(xy310), Left(xy4010), ty_Int, hc) → new_esEs16(xy310, xy4010)
new_esEs20(xy312, xy4012, app(app(app(ty_@3, ec), ed), ee)) → new_esEs19(xy312, xy4012, ec, ed, ee)
new_sr(Neg(xy3100), Neg(xy40100)) → Pos(new_primMulNat0(xy3100, xy40100))
new_esEs24(xy311, xy4011, ty_Char) → new_esEs11(xy311, xy4011)
new_esEs5(xy30, xy400, app(ty_Ratio, bgf)) → new_esEs15(xy30, xy400, bgf)
new_esEs4(xy31, xy401, ty_Float) → new_esEs8(xy31, xy401)
new_asAs(False, xy43) → False
new_sr(Pos(xy3100), Pos(xy40100)) → Pos(new_primMulNat0(xy3100, xy40100))
new_esEs18(Right(xy310), Right(xy4010), baf, app(app(ty_@2, bah), bba)) → new_esEs12(xy310, xy4010, bah, bba)
new_esEs24(xy311, xy4011, ty_Int) → new_esEs16(xy311, xy4011)
new_primEqNat0(Zero, Zero) → True
new_esEs18(Left(xy310), Left(xy4010), ty_Char, hc) → new_esEs11(xy310, xy4010)
new_esEs15(:%(xy310, xy311), :%(xy4010, xy4011), bhd) → new_asAs(new_esEs27(xy310, xy4010, bhd), new_esEs26(xy311, xy4011, bhd))
new_esEs25(xy310, xy4010, app(app(ty_@2, bfa), bfb)) → new_esEs12(xy310, xy4010, bfa, bfb)
new_primMulNat0(Zero, Succ(xy401000)) → Zero
new_primMulNat0(Succ(xy31000), Zero) → Zero
new_esEs21(xy311, xy4011, ty_Bool) → new_esEs13(xy311, xy4011)
new_esEs21(xy311, xy4011, ty_Int) → new_esEs16(xy311, xy4011)
new_esEs20(xy312, xy4012, app(ty_Ratio, dh)) → new_esEs15(xy312, xy4012, dh)
new_esEs18(Right(xy310), Right(xy4010), baf, app(app(ty_Either, bbd), bbe)) → new_esEs18(xy310, xy4010, bbd, bbe)
new_esEs22(xy310, xy4010, app(ty_[], ga)) → new_esEs10(xy310, xy4010, ga)
new_esEs20(xy312, xy4012, ty_Bool) → new_esEs13(xy312, xy4012)
new_esEs25(xy310, xy4010, app(app(ty_Either, bfe), bff)) → new_esEs18(xy310, xy4010, bfe, bff)
new_esEs5(xy30, xy400, app(app(ty_@2, bgc), bgd)) → new_esEs12(xy30, xy400, bgc, bgd)
new_esEs4(xy31, xy401, ty_Int) → new_esEs16(xy31, xy401)
new_esEs18(Right(xy310), Left(xy4010), baf, hc) → False
new_esEs18(Left(xy310), Right(xy4010), baf, hc) → False
new_esEs13(False, False) → True
new_esEs4(xy31, xy401, ty_Double) → new_esEs9(xy31, xy401)
new_esEs5(xy30, xy400, app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs19(xy30, xy400, bha, bhb, bhc)
new_esEs4(xy31, xy401, ty_Bool) → new_esEs13(xy31, xy401)
new_esEs22(xy310, xy4010, ty_Double) → new_esEs9(xy310, xy4010)
new_primPlusNat0(Succ(xy440), xy401000) → Succ(Succ(new_primPlusNat1(xy440, xy401000)))
new_esEs22(xy310, xy4010, ty_Float) → new_esEs8(xy310, xy4010)
new_esEs7(Just(xy310), Just(xy4010), app(ty_[], bf)) → new_esEs10(xy310, xy4010, bf)
new_esEs23(xy310, xy4010, ty_Int) → new_esEs16(xy310, xy4010)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Int) → new_esEs16(xy310, xy4010)
new_esEs20(xy312, xy4012, ty_Integer) → new_esEs14(xy312, xy4012)
new_esEs21(xy311, xy4011, ty_Ordering) → new_esEs6(xy311, xy4011)
new_esEs24(xy311, xy4011, ty_Integer) → new_esEs14(xy311, xy4011)
new_esEs27(xy310, xy4010, ty_Int) → new_esEs16(xy310, xy4010)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Integer) → new_esEs14(xy310, xy4010)
new_primEqInt(Neg(Succ(xy3100)), Neg(Succ(xy40100))) → new_primEqNat0(xy3100, xy40100)
new_esEs25(xy310, xy4010, app(app(app(ty_@3, bfg), bfh), bga)) → new_esEs19(xy310, xy4010, bfg, bfh, bga)
new_esEs7(Just(xy310), Just(xy4010), ty_Int) → new_esEs16(xy310, xy4010)
new_esEs20(xy312, xy4012, app(app(ty_Either, ea), eb)) → new_esEs18(xy312, xy4012, ea, eb)
new_esEs18(Left(xy310), Left(xy4010), ty_Integer, hc) → new_esEs14(xy310, xy4010)
new_primPlusNat1(Zero, Succ(xy4010000)) → Succ(xy4010000)
new_primPlusNat1(Succ(xy4400), Zero) → Succ(xy4400)
new_esEs6(GT, GT) → True
new_esEs6(GT, EQ) → False
new_esEs6(EQ, GT) → False
new_esEs16(xy31, xy401) → new_primEqInt(xy31, xy401)
new_esEs18(Left(xy310), Left(xy4010), app(ty_Ratio, hh), hc) → new_esEs15(xy310, xy4010, hh)
new_esEs5(xy30, xy400, ty_Ordering) → new_esEs6(xy30, xy400)
new_esEs4(xy31, xy401, app(app(ty_@2, bdd), bde)) → new_esEs12(xy31, xy401, bdd, bde)
new_esEs18(Left(xy310), Left(xy4010), app(ty_[], hd), hc) → new_esEs10(xy310, xy4010, hd)
new_esEs6(EQ, EQ) → True
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs23(xy310, xy4010, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs19(xy310, xy4010, bda, bdb, bdc)
new_esEs23(xy310, xy4010, ty_Char) → new_esEs11(xy310, xy4010)
new_esEs23(xy310, xy4010, app(app(ty_Either, bcg), bch)) → new_esEs18(xy310, xy4010, bcg, bch)
new_esEs25(xy310, xy4010, app(ty_Ratio, bfd)) → new_esEs15(xy310, xy4010, bfd)
new_primEqInt(Neg(Zero), Neg(Succ(xy40100))) → False
new_primEqInt(Neg(Succ(xy3100)), Neg(Zero)) → False
new_esEs5(xy30, xy400, ty_Float) → new_esEs8(xy30, xy400)
new_esEs18(Right(xy310), Right(xy4010), baf, app(ty_[], bag)) → new_esEs10(xy310, xy4010, bag)
new_esEs21(xy311, xy4011, ty_Float) → new_esEs8(xy311, xy4011)
new_esEs23(xy310, xy4010, ty_Float) → new_esEs8(xy310, xy4010)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Bool) → new_esEs13(xy310, xy4010)
new_esEs20(xy312, xy4012, ty_@0) → new_esEs17(xy312, xy4012)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs24(xy311, xy4011, ty_Float) → new_esEs8(xy311, xy4011)
new_esEs27(xy310, xy4010, ty_Integer) → new_esEs14(xy310, xy4010)
new_esEs18(Left(xy310), Left(xy4010), app(app(app(ty_@3, bac), bad), bae), hc) → new_esEs19(xy310, xy4010, bac, bad, bae)
new_esEs22(xy310, xy4010, app(app(ty_@2, gb), gc)) → new_esEs12(xy310, xy4010, gb, gc)
new_asAs(True, xy43) → xy43
new_esEs23(xy310, xy4010, ty_Integer) → new_esEs14(xy310, xy4010)
new_esEs10([], :(xy4010, xy4011), bca) → False
new_esEs10(:(xy310, xy311), [], bca) → False
new_primMulNat0(Succ(xy31000), Succ(xy401000)) → new_primPlusNat0(new_primMulNat0(xy31000, Succ(xy401000)), xy401000)
new_esEs20(xy312, xy4012, ty_Double) → new_esEs9(xy312, xy4012)
new_esEs25(xy310, xy4010, ty_@0) → new_esEs17(xy310, xy4010)
new_esEs13(True, True) → True
new_esEs24(xy311, xy4011, ty_Ordering) → new_esEs6(xy311, xy4011)
new_primEqInt(Pos(Succ(xy3100)), Pos(Succ(xy40100))) → new_primEqNat0(xy3100, xy40100)
new_esEs7(Just(xy310), Just(xy4010), ty_@0) → new_esEs17(xy310, xy4010)
new_esEs18(Right(xy310), Right(xy4010), baf, ty_Char) → new_esEs11(xy310, xy4010)
new_esEs12(@2(xy310, xy311), @2(xy4010, xy4011), bdd, bde) → new_asAs(new_esEs25(xy310, xy4010, bdd), new_esEs24(xy311, xy4011, bde))
new_esEs22(xy310, xy4010, ty_Bool) → new_esEs13(xy310, xy4010)
new_esEs4(xy31, xy401, ty_@0) → new_esEs17(xy31, xy401)
new_esEs22(xy310, xy4010, ty_Ordering) → new_esEs6(xy310, xy4010)
new_esEs6(EQ, LT) → False
new_esEs6(LT, EQ) → False
new_esEs10([], [], bca) → True
new_primEqNat0(Succ(xy3100), Succ(xy40100)) → new_primEqNat0(xy3100, xy40100)
new_esEs7(Just(xy310), Just(xy4010), ty_Bool) → new_esEs13(xy310, xy4010)
new_esEs9(Double(xy310, xy311), Double(xy4010, xy4011)) → new_esEs16(new_sr(xy310, xy4010), new_sr(xy311, xy4011))
new_esEs7(Just(xy310), Just(xy4010), app(app(ty_@2, bg), bh)) → new_esEs12(xy310, xy4010, bg, bh)
new_esEs7(Just(xy310), Just(xy4010), ty_Char) → new_esEs11(xy310, xy4010)
new_esEs4(xy31, xy401, ty_Ordering) → new_esEs6(xy31, xy401)
new_esEs7(Just(xy310), Just(xy4010), ty_Ordering) → new_esEs6(xy310, xy4010)
new_esEs18(Left(xy310), Left(xy4010), ty_@0, hc) → new_esEs17(xy310, xy4010)
new_esEs7(Nothing, Nothing, be) → True
new_primEqInt(Pos(Zero), Pos(Succ(xy40100))) → False
new_primEqInt(Pos(Succ(xy3100)), Pos(Zero)) → False
new_esEs6(LT, LT) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs22(xy310, xy4010, app(ty_Maybe, gd)) → new_esEs7(xy310, xy4010, gd)
new_esEs4(xy31, xy401, app(app(ty_Either, baf), hc)) → new_esEs18(xy31, xy401, baf, hc)
new_esEs23(xy310, xy4010, ty_@0) → new_esEs17(xy310, xy4010)
new_esEs5(xy30, xy400, ty_Char) → new_esEs11(xy30, xy400)
new_esEs19(@3(xy310, xy311, xy312), @3(xy4010, xy4011, xy4012), da, db, dc) → new_asAs(new_esEs22(xy310, xy4010, da), new_asAs(new_esEs21(xy311, xy4011, db), new_esEs20(xy312, xy4012, dc)))
new_esEs22(xy310, xy4010, ty_Int) → new_esEs16(xy310, xy4010)

The set Q consists of the following terms:

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

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

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

new_deleteBy0(xy25, xy26, xy27, xy28, xy29, False, ba, bb) → new_deleteBy(@2(xy28, xy29), xy25, ba, bb)
The graph contains the following edges 1 >= 2, 7 >= 3, 8 >= 4
new_deleteBy(@2(xy30, xy31), :(@2(xy400, xy401), xy41), bc, bd) → new_deleteBy0(xy41, xy400, xy401, xy30, xy31, new_asAs(new_esEs5(xy30, xy400, bc), new_esEs4(xy31, xy401, bd)), bc, bd)
The graph contains the following edges 2 > 1, 2 > 2, 2 > 3, 1 > 4, 1 > 5, 3 >= 7, 4 >= 8

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