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

YES 2.085 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 => [a] -> [[a]] -> [[a]]) :: Eq a => [a] -> [[a]] -> [[a]])

module List where

import qualified Maybe
import qualified Prelude

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

delete

deleteBy (==)

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

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

module Maybe where

import qualified List
import qualified Prelude

If Reductions:
The following If expression

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

is transformed to

deleteBy0 ys y eq x True = ys

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

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

delete

deleteBy (==)

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

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

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

module Maybe where

import qualified List
import qualified Prelude

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 => [a] -> [[a]] -> [[a]])

module List where

import qualified Maybe
import qualified Prelude

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

delete

deleteBy (==)

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

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

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

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="delete\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="delete xy3\n  Eq a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="delete xy3 xy4\n  Eq a",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="deleteBy (==) xy3 xy4\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];997[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];5 -> 997[label="",style="solid", color="burlywood", weight=9];
997 -> 6[label="",style="solid", color="burlywood", weight=3];
998[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 998[label="",style="solid", color="burlywood", weight=9];
998 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="deleteBy (==) xy3 (xy40 : xy41)\n  Eq a",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="deleteBy (==) xy3 []\n  Eq a",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",fontsize=16,color="burlywood",shape="box"];999[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];8 -> 999[label="",style="solid", color="burlywood", weight=9];
999 -> 10[label="",style="solid", color="burlywood", weight=3];
1000[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];8 -> 1000[label="",style="solid", color="burlywood", weight=9];
1000 -> 11[label="",style="solid", color="burlywood", weight=3];
9[label="[]\n  Eq a",fontsize=16,color="green",shape="box"];10[label="deleteBy0 xy41 xy40 (==) (xy30 : xy31) ((==) xy30 : xy31 xy40)\n  Eq a",fontsize=16,color="burlywood",shape="box"];1001[label="xy40/xy400 : xy401",fontsize=10,color="white",style="solid",shape="box"];10 -> 1001[label="",style="solid", color="burlywood", weight=9];
1001 -> 12[label="",style="solid", color="burlywood", weight=3];
1002[label="xy40/[]",fontsize=10,color="white",style="solid",shape="box"];10 -> 1002[label="",style="solid", color="burlywood", weight=9];
1002 -> 13[label="",style="solid", color="burlywood", weight=3];
11[label="deleteBy0 xy41 xy40 (==) [] ((==) [] xy40)\n  Eq a",fontsize=16,color="burlywood",shape="box"];1003[label="xy40/xy400 : xy401",fontsize=10,color="white",style="solid",shape="box"];11 -> 1003[label="",style="solid", color="burlywood", weight=9];
1003 -> 14[label="",style="solid", color="burlywood", weight=3];
1004[label="xy40/[]",fontsize=10,color="white",style="solid",shape="box"];11 -> 1004[label="",style="solid", color="burlywood", weight=9];
1004 -> 15[label="",style="solid", color="burlywood", weight=3];
12[label="deleteBy0 xy41 (xy400 : xy401) (==) (xy30 : xy31) ((==) xy30 : xy31 xy400 : xy401)\n  Eq a",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="deleteBy0 xy41 [] (==) (xy30 : xy31) ((==) xy30 : xy31 [])\n  Eq a",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="deleteBy0 xy41 (xy400 : xy401) (==) [] ((==) [] xy400 : xy401)\n  Eq a",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="deleteBy0 xy41 [] (==) [] ((==) [] [])\n  Eq a",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16 -> 110[label="",style="dashed", color="red", weight=0];
16[label="deleteBy0 xy41 (xy400 : xy401) (==) (xy30 : xy31) (xy30 == xy400 && xy31 == xy401)\n  Eq a",fontsize=16,color="magenta"];16 -> 111[label="",style="dashed", color="magenta", weight=3];
16 -> 112[label="",style="dashed", color="magenta", weight=3];
16 -> 113[label="",style="dashed", color="magenta", weight=3];
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16 -> 115[label="",style="dashed", color="magenta", weight=3];
16 -> 116[label="",style="dashed", color="magenta", weight=3];
17[label="deleteBy0 xy41 [] (==) (xy30 : xy31) False\n  Eq a",fontsize=16,color="black",shape="box"];17 -> 27[label="",style="solid", color="black", weight=3];
18[label="deleteBy0 xy41 (xy400 : xy401) (==) [] False\n  Eq a",fontsize=16,color="black",shape="box"];18 -> 28[label="",style="solid", color="black", weight=3];
19[label="deleteBy0 xy41 [] (==) [] True\n  Eq a",fontsize=16,color="black",shape="box"];19 -> 29[label="",style="solid", color="black", weight=3];
111[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];112[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];113 -> 362[label="",style="dashed", color="red", weight=0];
113[label="xy30 == xy400 && xy31 == xy401\n  Eq a",fontsize=16,color="magenta"];113 -> 363[label="",style="dashed", color="magenta", weight=3];
113 -> 364[label="",style="dashed", color="magenta", weight=3];
114[label="xy401\n  Eq a",fontsize=16,color="green",shape="box"];115[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];116[label="xy31\n  Eq a",fontsize=16,color="green",shape="box"];110[label="deleteBy0 xy12 (xy13 : xy14) (==) (xy15 : xy16) xy18\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1007[label="xy18/False",fontsize=10,color="white",style="solid",shape="box"];110 -> 1007[label="",style="solid", color="burlywood", weight=9];
1007 -> 124[label="",style="solid", color="burlywood", weight=3];
1008[label="xy18/True",fontsize=10,color="white",style="solid",shape="box"];110 -> 1008[label="",style="solid", color="burlywood", weight=9];
1008 -> 125[label="",style="solid", color="burlywood", weight=3];
27[label="[] : deleteBy (==) (xy30 : xy31) xy41\n  Eq a",fontsize=16,color="green",shape="box"];27 -> 46[label="",style="dashed", color="green", weight=3];
28[label="(xy400 : xy401) : deleteBy (==) [] xy41\n  Eq a",fontsize=16,color="green",shape="box"];28 -> 47[label="",style="dashed", color="green", weight=3];
29[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];363[label="xy30 == xy400\n  Eq a",fontsize=16,color="blue",shape="box"];1009[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1009[label="",style="solid", color="blue", weight=9];
1009 -> 367[label="",style="solid", color="blue", weight=3];
1010[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1010[label="",style="solid", color="blue", weight=9];
1010 -> 368[label="",style="solid", color="blue", weight=3];
1011[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1011[label="",style="solid", color="blue", weight=9];
1011 -> 369[label="",style="solid", color="blue", weight=3];
1012[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1012[label="",style="solid", color="blue", weight=9];
1012 -> 370[label="",style="solid", color="blue", weight=3];
1013[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1013[label="",style="solid", color="blue", weight=9];
1013 -> 371[label="",style="solid", color="blue", weight=3];
1014[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1014[label="",style="solid", color="blue", weight=9];
1014 -> 372[label="",style="solid", color="blue", weight=3];
1015[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1015[label="",style="solid", color="blue", weight=9];
1015 -> 373[label="",style="solid", color="blue", weight=3];
1016[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1016[label="",style="solid", color="blue", weight=9];
1016 -> 374[label="",style="solid", color="blue", weight=3];
1017[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1017[label="",style="solid", color="blue", weight=9];
1017 -> 375[label="",style="solid", color="blue", weight=3];
1018[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1018[label="",style="solid", color="blue", weight=9];
1018 -> 376[label="",style="solid", color="blue", weight=3];
1019[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1019[label="",style="solid", color="blue", weight=9];
1019 -> 377[label="",style="solid", color="blue", weight=3];
1020[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1020[label="",style="solid", color="blue", weight=9];
1020 -> 378[label="",style="solid", color="blue", weight=3];
1021[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1021[label="",style="solid", color="blue", weight=9];
1021 -> 379[label="",style="solid", color="blue", weight=3];
1022[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];363 -> 1022[label="",style="solid", color="blue", weight=9];
1022 -> 380[label="",style="solid", color="blue", weight=3];
364[label="xy31 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1023[label="xy31/xy310 : xy311",fontsize=10,color="white",style="solid",shape="box"];364 -> 1023[label="",style="solid", color="burlywood", weight=9];
1023 -> 381[label="",style="solid", color="burlywood", weight=3];
1024[label="xy31/[]",fontsize=10,color="white",style="solid",shape="box"];364 -> 1024[label="",style="solid", color="burlywood", weight=9];
1024 -> 382[label="",style="solid", color="burlywood", weight=3];
362[label="xy30 && xy31",fontsize=16,color="burlywood",shape="triangle"];1025[label="xy30/False",fontsize=10,color="white",style="solid",shape="box"];362 -> 1025[label="",style="solid", color="burlywood", weight=9];
1025 -> 383[label="",style="solid", color="burlywood", weight=3];
1026[label="xy30/True",fontsize=10,color="white",style="solid",shape="box"];362 -> 1026[label="",style="solid", color="burlywood", weight=9];
1026 -> 384[label="",style="solid", color="burlywood", weight=3];
124[label="deleteBy0 xy12 (xy13 : xy14) (==) (xy15 : xy16) False\n  Eq a",fontsize=16,color="black",shape="box"];124 -> 142[label="",style="solid", color="black", weight=3];
125[label="deleteBy0 xy12 (xy13 : xy14) (==) (xy15 : xy16) True\n  Eq a",fontsize=16,color="black",shape="box"];125 -> 143[label="",style="solid", color="black", weight=3];
46 -> 5[label="",style="dashed", color="red", weight=0];
46[label="deleteBy (==) (xy30 : xy31) xy41\n  Eq a",fontsize=16,color="magenta"];46 -> 70[label="",style="dashed", color="magenta", weight=3];
46 -> 71[label="",style="dashed", color="magenta", weight=3];
47 -> 5[label="",style="dashed", color="red", weight=0];
47[label="deleteBy (==) [] xy41\n  Eq a",fontsize=16,color="magenta"];47 -> 72[label="",style="dashed", color="magenta", weight=3];
47 -> 73[label="",style="dashed", color="magenta", weight=3];
367[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];367 -> 385[label="",style="solid", color="black", weight=3];
368[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];1029[label="xy30/LT",fontsize=10,color="white",style="solid",shape="box"];368 -> 1029[label="",style="solid", color="burlywood", weight=9];
1029 -> 386[label="",style="solid", color="burlywood", weight=3];
1030[label="xy30/EQ",fontsize=10,color="white",style="solid",shape="box"];368 -> 1030[label="",style="solid", color="burlywood", weight=9];
1030 -> 387[label="",style="solid", color="burlywood", weight=3];
1031[label="xy30/GT",fontsize=10,color="white",style="solid",shape="box"];368 -> 1031[label="",style="solid", color="burlywood", weight=9];
1031 -> 388[label="",style="solid", color="burlywood", weight=3];
369 -> 364[label="",style="dashed", color="red", weight=0];
369[label="xy30 == xy400\n  Eq a",fontsize=16,color="magenta"];369 -> 389[label="",style="dashed", color="magenta", weight=3];
369 -> 390[label="",style="dashed", color="magenta", weight=3];
370[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];370 -> 391[label="",style="solid", color="black", weight=3];
371[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];1033[label="xy30/Integer xy300",fontsize=10,color="white",style="solid",shape="box"];371 -> 1033[label="",style="solid", color="burlywood", weight=9];
1033 -> 392[label="",style="solid", color="burlywood", weight=3];
372[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];372 -> 393[label="",style="solid", color="black", weight=3];
373[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];1034[label="xy30/()",fontsize=10,color="white",style="solid",shape="box"];373 -> 1034[label="",style="solid", color="burlywood", weight=9];
1034 -> 394[label="",style="solid", color="burlywood", weight=3];
374[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1035[label="xy30/Left xy300",fontsize=10,color="white",style="solid",shape="box"];374 -> 1035[label="",style="solid", color="burlywood", weight=9];
1035 -> 395[label="",style="solid", color="burlywood", weight=3];
1036[label="xy30/Right xy300",fontsize=10,color="white",style="solid",shape="box"];374 -> 1036[label="",style="solid", color="burlywood", weight=9];
1036 -> 396[label="",style="solid", color="burlywood", weight=3];
375[label="xy30 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1037[label="xy30/(xy300,xy301)",fontsize=10,color="white",style="solid",shape="box"];375 -> 1037[label="",style="solid", color="burlywood", weight=9];
1037 -> 397[label="",style="solid", color="burlywood", weight=3];
376[label="xy30 == xy400",fontsize=16,color="burlywood",shape="triangle"];1038[label="xy30/False",fontsize=10,color="white",style="solid",shape="box"];376 -> 1038[label="",style="solid", color="burlywood", weight=9];
1038 -> 398[label="",style="solid", color="burlywood", weight=3];
1039[label="xy30/True",fontsize=10,color="white",style="solid",shape="box"];376 -> 1039[label="",style="solid", color="burlywood", weight=9];
1039 -> 399[label="",style="solid", color="burlywood", weight=3];
377[label="xy30 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1040[label="xy30/Nothing",fontsize=10,color="white",style="solid",shape="box"];377 -> 1040[label="",style="solid", color="burlywood", weight=9];
1040 -> 400[label="",style="solid", color="burlywood", weight=3];
1041[label="xy30/Just xy300",fontsize=10,color="white",style="solid",shape="box"];377 -> 1041[label="",style="solid", color="burlywood", weight=9];
1041 -> 401[label="",style="solid", color="burlywood", weight=3];
378[label="xy30 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];1042[label="xy30/xy300 :% xy301",fontsize=10,color="white",style="solid",shape="box"];378 -> 1042[label="",style="solid", color="burlywood", weight=9];
1042 -> 402[label="",style="solid", color="burlywood", weight=3];
379[label="xy30 == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];1043[label="xy30/(xy300,xy301,xy302)",fontsize=10,color="white",style="solid",shape="box"];379 -> 1043[label="",style="solid", color="burlywood", weight=9];
1043 -> 403[label="",style="solid", color="burlywood", weight=3];
380[label="xy30 == xy400",fontsize=16,color="black",shape="triangle"];380 -> 404[label="",style="solid", color="black", weight=3];
381[label="xy310 : xy311 == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];1044[label="xy401/xy4010 : xy4011",fontsize=10,color="white",style="solid",shape="box"];381 -> 1044[label="",style="solid", color="burlywood", weight=9];
1044 -> 405[label="",style="solid", color="burlywood", weight=3];
1045[label="xy401/[]",fontsize=10,color="white",style="solid",shape="box"];381 -> 1045[label="",style="solid", color="burlywood", weight=9];
1045 -> 406[label="",style="solid", color="burlywood", weight=3];
382[label="[] == xy401\n  Eq a",fontsize=16,color="burlywood",shape="box"];1046[label="xy401/xy4010 : xy4011",fontsize=10,color="white",style="solid",shape="box"];382 -> 1046[label="",style="solid", color="burlywood", weight=9];
1046 -> 407[label="",style="solid", color="burlywood", weight=3];
1047[label="xy401/[]",fontsize=10,color="white",style="solid",shape="box"];382 -> 1047[label="",style="solid", color="burlywood", weight=9];
1047 -> 408[label="",style="solid", color="burlywood", weight=3];
383[label="False && xy31",fontsize=16,color="black",shape="box"];383 -> 409[label="",style="solid", color="black", weight=3];
384[label="True && xy31",fontsize=16,color="black",shape="box"];384 -> 410[label="",style="solid", color="black", weight=3];
142[label="(xy13 : xy14) : deleteBy (==) (xy15 : xy16) xy12\n  Eq a",fontsize=16,color="green",shape="box"];142 -> 166[label="",style="dashed", color="green", weight=3];
143[label="xy12\n  Eq a",fontsize=16,color="green",shape="box"];70[label="xy30 : xy31\n  Eq a",fontsize=16,color="green",shape="box"];71[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];72[label="[]\n  Eq a",fontsize=16,color="green",shape="box"];73[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];385[label="primEqFloat xy30 xy400",fontsize=16,color="burlywood",shape="box"];1048[label="xy30/Float xy300 xy301",fontsize=10,color="white",style="solid",shape="box"];385 -> 1048[label="",style="solid", color="burlywood", weight=9];
1048 -> 411[label="",style="solid", color="burlywood", weight=3];
386[label="LT == xy400",fontsize=16,color="burlywood",shape="box"];1049[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];386 -> 1049[label="",style="solid", color="burlywood", weight=9];
1049 -> 412[label="",style="solid", color="burlywood", weight=3];
1050[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];386 -> 1050[label="",style="solid", color="burlywood", weight=9];
1050 -> 413[label="",style="solid", color="burlywood", weight=3];
1051[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];386 -> 1051[label="",style="solid", color="burlywood", weight=9];
1051 -> 414[label="",style="solid", color="burlywood", weight=3];
387[label="EQ == xy400",fontsize=16,color="burlywood",shape="box"];1052[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];387 -> 1052[label="",style="solid", color="burlywood", weight=9];
1052 -> 415[label="",style="solid", color="burlywood", weight=3];
1053[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];387 -> 1053[label="",style="solid", color="burlywood", weight=9];
1053 -> 416[label="",style="solid", color="burlywood", weight=3];
1054[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];387 -> 1054[label="",style="solid", color="burlywood", weight=9];
1054 -> 417[label="",style="solid", color="burlywood", weight=3];
388[label="GT == xy400",fontsize=16,color="burlywood",shape="box"];1055[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];388 -> 1055[label="",style="solid", color="burlywood", weight=9];
1055 -> 418[label="",style="solid", color="burlywood", weight=3];
1056[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];388 -> 1056[label="",style="solid", color="burlywood", weight=9];
1056 -> 419[label="",style="solid", color="burlywood", weight=3];
1057[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];388 -> 1057[label="",style="solid", color="burlywood", weight=9];
1057 -> 420[label="",style="solid", color="burlywood", weight=3];
389[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];390[label="xy30\n  Eq a",fontsize=16,color="green",shape="box"];391[label="primEqChar xy30 xy400",fontsize=16,color="burlywood",shape="box"];1058[label="xy30/Char xy300",fontsize=10,color="white",style="solid",shape="box"];391 -> 1058[label="",style="solid", color="burlywood", weight=9];
1058 -> 421[label="",style="solid", color="burlywood", weight=3];
392[label="Integer xy300 == xy400",fontsize=16,color="burlywood",shape="box"];1059[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];392 -> 1059[label="",style="solid", color="burlywood", weight=9];
1059 -> 422[label="",style="solid", color="burlywood", weight=3];
393[label="primEqInt xy30 xy400",fontsize=16,color="burlywood",shape="triangle"];1060[label="xy30/Pos xy300",fontsize=10,color="white",style="solid",shape="box"];393 -> 1060[label="",style="solid", color="burlywood", weight=9];
1060 -> 423[label="",style="solid", color="burlywood", weight=3];
1061[label="xy30/Neg xy300",fontsize=10,color="white",style="solid",shape="box"];393 -> 1061[label="",style="solid", color="burlywood", weight=9];
1061 -> 424[label="",style="solid", color="burlywood", weight=3];
394[label="() == xy400",fontsize=16,color="burlywood",shape="box"];1062[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];394 -> 1062[label="",style="solid", color="burlywood", weight=9];
1062 -> 425[label="",style="solid", color="burlywood", weight=3];
395[label="Left xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1063[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];395 -> 1063[label="",style="solid", color="burlywood", weight=9];
1063 -> 426[label="",style="solid", color="burlywood", weight=3];
1064[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];395 -> 1064[label="",style="solid", color="burlywood", weight=9];
1064 -> 427[label="",style="solid", color="burlywood", weight=3];
396[label="Right xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1065[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];396 -> 1065[label="",style="solid", color="burlywood", weight=9];
1065 -> 428[label="",style="solid", color="burlywood", weight=3];
1066[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];396 -> 1066[label="",style="solid", color="burlywood", weight=9];
1066 -> 429[label="",style="solid", color="burlywood", weight=3];
397[label="(xy300,xy301) == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1067[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];397 -> 1067[label="",style="solid", color="burlywood", weight=9];
1067 -> 430[label="",style="solid", color="burlywood", weight=3];
398[label="False == xy400",fontsize=16,color="burlywood",shape="box"];1068[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];398 -> 1068[label="",style="solid", color="burlywood", weight=9];
1068 -> 431[label="",style="solid", color="burlywood", weight=3];
1069[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];398 -> 1069[label="",style="solid", color="burlywood", weight=9];
1069 -> 432[label="",style="solid", color="burlywood", weight=3];
399[label="True == xy400",fontsize=16,color="burlywood",shape="box"];1070[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];399 -> 1070[label="",style="solid", color="burlywood", weight=9];
1070 -> 433[label="",style="solid", color="burlywood", weight=3];
1071[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];399 -> 1071[label="",style="solid", color="burlywood", weight=9];
1071 -> 434[label="",style="solid", color="burlywood", weight=3];
400[label="Nothing == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];1072[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];400 -> 1072[label="",style="solid", color="burlywood", weight=9];
1072 -> 435[label="",style="solid", color="burlywood", weight=3];
1073[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];400 -> 1073[label="",style="solid", color="burlywood", weight=9];
1073 -> 436[label="",style="solid", color="burlywood", weight=3];
401[label="Just xy300 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];1074[label="xy400/Nothing",fontsize=10,color="white",style="solid",shape="box"];401 -> 1074[label="",style="solid", color="burlywood", weight=9];
1074 -> 437[label="",style="solid", color="burlywood", weight=3];
1075[label="xy400/Just xy4000",fontsize=10,color="white",style="solid",shape="box"];401 -> 1075[label="",style="solid", color="burlywood", weight=9];
1075 -> 438[label="",style="solid", color="burlywood", weight=3];
402[label="xy300 :% xy301 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="box"];1076[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];402 -> 1076[label="",style="solid", color="burlywood", weight=9];
1076 -> 439[label="",style="solid", color="burlywood", weight=3];
403[label="(xy300,xy301,xy302) == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1077[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];403 -> 1077[label="",style="solid", color="burlywood", weight=9];
1077 -> 440[label="",style="solid", color="burlywood", weight=3];
404[label="primEqDouble xy30 xy400",fontsize=16,color="burlywood",shape="box"];1078[label="xy30/Double xy300 xy301",fontsize=10,color="white",style="solid",shape="box"];404 -> 1078[label="",style="solid", color="burlywood", weight=9];
1078 -> 441[label="",style="solid", color="burlywood", weight=3];
405[label="xy310 : xy311 == xy4010 : xy4011\n  Eq a",fontsize=16,color="black",shape="box"];405 -> 442[label="",style="solid", color="black", weight=3];
406[label="xy310 : xy311 == []\n  Eq a",fontsize=16,color="black",shape="box"];406 -> 443[label="",style="solid", color="black", weight=3];
407[label="[] == xy4010 : xy4011\n  Eq a",fontsize=16,color="black",shape="box"];407 -> 444[label="",style="solid", color="black", weight=3];
408[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];408 -> 445[label="",style="solid", color="black", weight=3];
409[label="False",fontsize=16,color="green",shape="box"];410[label="xy31",fontsize=16,color="green",shape="box"];166 -> 5[label="",style="dashed", color="red", weight=0];
166[label="deleteBy (==) (xy15 : xy16) xy12\n  Eq a",fontsize=16,color="magenta"];166 -> 216[label="",style="dashed", color="magenta", weight=3];
166 -> 217[label="",style="dashed", color="magenta", weight=3];
411[label="primEqFloat (Float xy300 xy301) xy400",fontsize=16,color="burlywood",shape="box"];1080[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];411 -> 1080[label="",style="solid", color="burlywood", weight=9];
1080 -> 446[label="",style="solid", color="burlywood", weight=3];
412[label="LT == LT",fontsize=16,color="black",shape="box"];412 -> 447[label="",style="solid", color="black", weight=3];
413[label="LT == EQ",fontsize=16,color="black",shape="box"];413 -> 448[label="",style="solid", color="black", weight=3];
414[label="LT == GT",fontsize=16,color="black",shape="box"];414 -> 449[label="",style="solid", color="black", weight=3];
415[label="EQ == LT",fontsize=16,color="black",shape="box"];415 -> 450[label="",style="solid", color="black", weight=3];
416[label="EQ == EQ",fontsize=16,color="black",shape="box"];416 -> 451[label="",style="solid", color="black", weight=3];
417[label="EQ == GT",fontsize=16,color="black",shape="box"];417 -> 452[label="",style="solid", color="black", weight=3];
418[label="GT == LT",fontsize=16,color="black",shape="box"];418 -> 453[label="",style="solid", color="black", weight=3];
419[label="GT == EQ",fontsize=16,color="black",shape="box"];419 -> 454[label="",style="solid", color="black", weight=3];
420[label="GT == GT",fontsize=16,color="black",shape="box"];420 -> 455[label="",style="solid", color="black", weight=3];
421[label="primEqChar (Char xy300) xy400",fontsize=16,color="burlywood",shape="box"];1081[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];421 -> 1081[label="",style="solid", color="burlywood", weight=9];
1081 -> 456[label="",style="solid", color="burlywood", weight=3];
422[label="Integer xy300 == Integer xy4000",fontsize=16,color="black",shape="box"];422 -> 457[label="",style="solid", color="black", weight=3];
423[label="primEqInt (Pos xy300) xy400",fontsize=16,color="burlywood",shape="box"];1082[label="xy300/Succ xy3000",fontsize=10,color="white",style="solid",shape="box"];423 -> 1082[label="",style="solid", color="burlywood", weight=9];
1082 -> 458[label="",style="solid", color="burlywood", weight=3];
1083[label="xy300/Zero",fontsize=10,color="white",style="solid",shape="box"];423 -> 1083[label="",style="solid", color="burlywood", weight=9];
1083 -> 459[label="",style="solid", color="burlywood", weight=3];
424[label="primEqInt (Neg xy300) xy400",fontsize=16,color="burlywood",shape="box"];1084[label="xy300/Succ xy3000",fontsize=10,color="white",style="solid",shape="box"];424 -> 1084[label="",style="solid", color="burlywood", weight=9];
1084 -> 460[label="",style="solid", color="burlywood", weight=3];
1085[label="xy300/Zero",fontsize=10,color="white",style="solid",shape="box"];424 -> 1085[label="",style="solid", color="burlywood", weight=9];
1085 -> 461[label="",style="solid", color="burlywood", weight=3];
425[label="() == ()",fontsize=16,color="black",shape="box"];425 -> 462[label="",style="solid", color="black", weight=3];
426[label="Left xy300 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];426 -> 463[label="",style="solid", color="black", weight=3];
427[label="Left xy300 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];427 -> 464[label="",style="solid", color="black", weight=3];
428[label="Right xy300 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];428 -> 465[label="",style="solid", color="black", weight=3];
429[label="Right xy300 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];429 -> 466[label="",style="solid", color="black", weight=3];
430[label="(xy300,xy301) == (xy4000,xy4001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];430 -> 467[label="",style="solid", color="black", weight=3];
431[label="False == False",fontsize=16,color="black",shape="box"];431 -> 468[label="",style="solid", color="black", weight=3];
432[label="False == True",fontsize=16,color="black",shape="box"];432 -> 469[label="",style="solid", color="black", weight=3];
433[label="True == False",fontsize=16,color="black",shape="box"];433 -> 470[label="",style="solid", color="black", weight=3];
434[label="True == True",fontsize=16,color="black",shape="box"];434 -> 471[label="",style="solid", color="black", weight=3];
435[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];435 -> 472[label="",style="solid", color="black", weight=3];
436[label="Nothing == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];436 -> 473[label="",style="solid", color="black", weight=3];
437[label="Just xy300 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];437 -> 474[label="",style="solid", color="black", weight=3];
438[label="Just xy300 == Just xy4000\n  Eq a",fontsize=16,color="black",shape="box"];438 -> 475[label="",style="solid", color="black", weight=3];
439[label="xy300 :% xy301 == xy4000 :% xy4001\n  Integral a",fontsize=16,color="black",shape="box"];439 -> 476[label="",style="solid", color="black", weight=3];
440[label="(xy300,xy301,xy302) == (xy4000,xy4001,xy4002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];440 -> 477[label="",style="solid", color="black", weight=3];
441[label="primEqDouble (Double xy300 xy301) xy400",fontsize=16,color="burlywood",shape="box"];1086[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];441 -> 1086[label="",style="solid", color="burlywood", weight=9];
1086 -> 478[label="",style="solid", color="burlywood", weight=3];
442 -> 362[label="",style="dashed", color="red", weight=0];
442[label="xy310 == xy4010 && xy311 == xy4011\n  Eq a",fontsize=16,color="magenta"];442 -> 479[label="",style="dashed", color="magenta", weight=3];
442 -> 480[label="",style="dashed", color="magenta", weight=3];
443[label="False",fontsize=16,color="green",shape="box"];444[label="False",fontsize=16,color="green",shape="box"];445[label="True",fontsize=16,color="green",shape="box"];216[label="xy15 : xy16\n  Eq a",fontsize=16,color="green",shape="box"];217[label="xy12\n  Eq a",fontsize=16,color="green",shape="box"];446[label="primEqFloat (Float xy300 xy301) (Float xy4000 xy4001)",fontsize=16,color="black",shape="box"];446 -> 481[label="",style="solid", color="black", weight=3];
447[label="True",fontsize=16,color="green",shape="box"];448[label="False",fontsize=16,color="green",shape="box"];449[label="False",fontsize=16,color="green",shape="box"];450[label="False",fontsize=16,color="green",shape="box"];451[label="True",fontsize=16,color="green",shape="box"];452[label="False",fontsize=16,color="green",shape="box"];453[label="False",fontsize=16,color="green",shape="box"];454[label="False",fontsize=16,color="green",shape="box"];455[label="True",fontsize=16,color="green",shape="box"];456[label="primEqChar (Char xy300) (Char xy4000)",fontsize=16,color="black",shape="box"];456 -> 482[label="",style="solid", color="black", weight=3];
457 -> 393[label="",style="dashed", color="red", weight=0];
457[label="primEqInt xy300 xy4000",fontsize=16,color="magenta"];457 -> 483[label="",style="dashed", color="magenta", weight=3];
457 -> 484[label="",style="dashed", color="magenta", weight=3];
458[label="primEqInt (Pos (Succ xy3000)) xy400",fontsize=16,color="burlywood",shape="box"];1089[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];458 -> 1089[label="",style="solid", color="burlywood", weight=9];
1089 -> 485[label="",style="solid", color="burlywood", weight=3];
1090[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];458 -> 1090[label="",style="solid", color="burlywood", weight=9];
1090 -> 486[label="",style="solid", color="burlywood", weight=3];
459[label="primEqInt (Pos Zero) xy400",fontsize=16,color="burlywood",shape="box"];1091[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];459 -> 1091[label="",style="solid", color="burlywood", weight=9];
1091 -> 487[label="",style="solid", color="burlywood", weight=3];
1092[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];459 -> 1092[label="",style="solid", color="burlywood", weight=9];
1092 -> 488[label="",style="solid", color="burlywood", weight=3];
460[label="primEqInt (Neg (Succ xy3000)) xy400",fontsize=16,color="burlywood",shape="box"];1093[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];460 -> 1093[label="",style="solid", color="burlywood", weight=9];
1093 -> 489[label="",style="solid", color="burlywood", weight=3];
1094[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];460 -> 1094[label="",style="solid", color="burlywood", weight=9];
1094 -> 490[label="",style="solid", color="burlywood", weight=3];
461[label="primEqInt (Neg Zero) xy400",fontsize=16,color="burlywood",shape="box"];1095[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];461 -> 1095[label="",style="solid", color="burlywood", weight=9];
1095 -> 491[label="",style="solid", color="burlywood", weight=3];
1096[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];461 -> 1096[label="",style="solid", color="burlywood", weight=9];
1096 -> 492[label="",style="solid", color="burlywood", weight=3];
462[label="True",fontsize=16,color="green",shape="box"];463[label="xy300 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];1097[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1097[label="",style="solid", color="blue", weight=9];
1097 -> 493[label="",style="solid", color="blue", weight=3];
1098[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1098[label="",style="solid", color="blue", weight=9];
1098 -> 494[label="",style="solid", color="blue", weight=3];
1099[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1099[label="",style="solid", color="blue", weight=9];
1099 -> 495[label="",style="solid", color="blue", weight=3];
1100[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1100[label="",style="solid", color="blue", weight=9];
1100 -> 496[label="",style="solid", color="blue", weight=3];
1101[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1101[label="",style="solid", color="blue", weight=9];
1101 -> 497[label="",style="solid", color="blue", weight=3];
1102[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1102[label="",style="solid", color="blue", weight=9];
1102 -> 498[label="",style="solid", color="blue", weight=3];
1103[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1103[label="",style="solid", color="blue", weight=9];
1103 -> 499[label="",style="solid", color="blue", weight=3];
1104[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1104[label="",style="solid", color="blue", weight=9];
1104 -> 500[label="",style="solid", color="blue", weight=3];
1105[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1105[label="",style="solid", color="blue", weight=9];
1105 -> 501[label="",style="solid", color="blue", weight=3];
1106[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1106[label="",style="solid", color="blue", weight=9];
1106 -> 502[label="",style="solid", color="blue", weight=3];
1107[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1107[label="",style="solid", color="blue", weight=9];
1107 -> 503[label="",style="solid", color="blue", weight=3];
1108[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1108[label="",style="solid", color="blue", weight=9];
1108 -> 504[label="",style="solid", color="blue", weight=3];
1109[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1109[label="",style="solid", color="blue", weight=9];
1109 -> 505[label="",style="solid", color="blue", weight=3];
1110[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];463 -> 1110[label="",style="solid", color="blue", weight=9];
1110 -> 506[label="",style="solid", color="blue", weight=3];
464[label="False",fontsize=16,color="green",shape="box"];465[label="False",fontsize=16,color="green",shape="box"];466[label="xy300 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];1111[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1111[label="",style="solid", color="blue", weight=9];
1111 -> 507[label="",style="solid", color="blue", weight=3];
1112[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1112[label="",style="solid", color="blue", weight=9];
1112 -> 508[label="",style="solid", color="blue", weight=3];
1113[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1113[label="",style="solid", color="blue", weight=9];
1113 -> 509[label="",style="solid", color="blue", weight=3];
1114[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1114[label="",style="solid", color="blue", weight=9];
1114 -> 510[label="",style="solid", color="blue", weight=3];
1115[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1115[label="",style="solid", color="blue", weight=9];
1115 -> 511[label="",style="solid", color="blue", weight=3];
1116[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1116[label="",style="solid", color="blue", weight=9];
1116 -> 512[label="",style="solid", color="blue", weight=3];
1117[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1117[label="",style="solid", color="blue", weight=9];
1117 -> 513[label="",style="solid", color="blue", weight=3];
1118[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1118[label="",style="solid", color="blue", weight=9];
1118 -> 514[label="",style="solid", color="blue", weight=3];
1119[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1119[label="",style="solid", color="blue", weight=9];
1119 -> 515[label="",style="solid", color="blue", weight=3];
1120[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1120[label="",style="solid", color="blue", weight=9];
1120 -> 516[label="",style="solid", color="blue", weight=3];
1121[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];466 -> 1121[label="",style="solid", color="blue", weight=9];
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480 -> 364[label="",style="dashed", color="red", weight=0];
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480 -> 557[label="",style="dashed", color="magenta", weight=3];
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1165[label="xy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];488 -> 1165[label="",style="solid", color="burlywood", weight=9];
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1211[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];521 -> 1211[label="",style="solid", color="blue", weight=9];
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1213[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];521 -> 1213[label="",style="solid", color="blue", weight=9];
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1217[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];522 -> 1217[label="",style="solid", color="blue", weight=9];
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1219[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];522 -> 1219[label="",style="solid", color="blue", weight=9];
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1227[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];522 -> 1227[label="",style="solid", color="blue", weight=9];
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523 -> 367[label="",style="dashed", color="red", weight=0];
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524 -> 368[label="",style="dashed", color="red", weight=0];
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527 -> 371[label="",style="dashed", color="red", weight=0];
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529 -> 373[label="",style="dashed", color="red", weight=0];
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533 -> 377[label="",style="dashed", color="red", weight=0];
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533 -> 681[label="",style="dashed", color="magenta", weight=3];
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1243[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];537 -> 1243[label="",style="solid", color="blue", weight=9];
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1245[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];538 -> 1245[label="",style="solid", color="blue", weight=9];
1245 -> 691[label="",style="solid", color="blue", weight=3];
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1249[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];539 -> 1249[label="",style="solid", color="blue", weight=9];
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1250[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];539 -> 1250[label="",style="solid", color="blue", weight=9];
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1255[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];539 -> 1255[label="",style="solid", color="blue", weight=9];
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1259[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];539 -> 1259[label="",style="solid", color="blue", weight=9];
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563[label="primEqInt (Pos (Succ xy3000)) (Pos Zero)",fontsize=16,color="black",shape="box"];563 -> 746[label="",style="solid", color="black", weight=3];
564[label="False",fontsize=16,color="green",shape="box"];565[label="primEqInt (Pos Zero) (Pos (Succ xy40000))",fontsize=16,color="black",shape="box"];565 -> 747[label="",style="solid", color="black", weight=3];
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568[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];568 -> 750[label="",style="solid", color="black", weight=3];
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883[label="primEqNat xy3000 xy40000",fontsize=16,color="magenta"];883 -> 951[label="",style="dashed", color="magenta", weight=3];
883 -> 952[label="",style="dashed", color="magenta", weight=3];
884[label="False",fontsize=16,color="green",shape="box"];885[label="False",fontsize=16,color="green",shape="box"];886[label="True",fontsize=16,color="green",shape="box"];887[label="xy40000",fontsize=16,color="green",shape="box"];888[label="xy3000",fontsize=16,color="green",shape="box"];889[label="xy40000",fontsize=16,color="green",shape="box"];890[label="xy3000",fontsize=16,color="green",shape="box"];891[label="xy4001",fontsize=16,color="green",shape="box"];892[label="xy301",fontsize=16,color="green",shape="box"];893[label="xy4001",fontsize=16,color="green",shape="box"];894[label="xy301",fontsize=16,color="green",shape="box"];895[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];896[label="xy301\n  Eq a",fontsize=16,color="green",shape="box"];897[label="xy4001",fontsize=16,color="green",shape="box"];898[label="xy301",fontsize=16,color="green",shape="box"];899[label="xy4001",fontsize=16,color="green",shape="box"];900[label="xy301",fontsize=16,color="green",shape="box"];901[label="xy4001",fontsize=16,color="green",shape="box"];902[label="xy301",fontsize=16,color="green",shape="box"];903[label="xy4001",fontsize=16,color="green",shape="box"];904[label="xy301",fontsize=16,color="green",shape="box"];905[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];906[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];907[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];908[label="xy301\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];909[label="xy4001",fontsize=16,color="green",shape="box"];910[label="xy301",fontsize=16,color="green",shape="box"];911[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];912[label="xy301\n  Eq a",fontsize=16,color="green",shape="box"];913[label="xy4001\n  Integral a",fontsize=16,color="green",shape="box"];914[label="xy301\n  Integral a",fontsize=16,color="green",shape="box"];915[label="xy4001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];916[label="xy301\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];917[label="xy4001",fontsize=16,color="green",shape="box"];918[label="xy301",fontsize=16,color="green",shape="box"];919[label="xy4002",fontsize=16,color="green",shape="box"];920[label="xy302",fontsize=16,color="green",shape="box"];921[label="xy4002",fontsize=16,color="green",shape="box"];922[label="xy302",fontsize=16,color="green",shape="box"];923[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];924[label="xy302\n  Eq a",fontsize=16,color="green",shape="box"];925[label="xy4002",fontsize=16,color="green",shape="box"];926[label="xy302",fontsize=16,color="green",shape="box"];927[label="xy4002",fontsize=16,color="green",shape="box"];928[label="xy302",fontsize=16,color="green",shape="box"];929[label="xy4002",fontsize=16,color="green",shape="box"];930[label="xy302",fontsize=16,color="green",shape="box"];931[label="xy4002",fontsize=16,color="green",shape="box"];932[label="xy302",fontsize=16,color="green",shape="box"];933[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];934[label="xy302\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];935[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];936[label="xy302\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];937[label="xy4002",fontsize=16,color="green",shape="box"];938[label="xy302",fontsize=16,color="green",shape="box"];939[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];940[label="xy302\n  Eq a",fontsize=16,color="green",shape="box"];941[label="xy4002\n  Integral a",fontsize=16,color="green",shape="box"];942[label="xy302\n  Integral a",fontsize=16,color="green",shape="box"];943[label="xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];944[label="xy302\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];945[label="xy4002",fontsize=16,color="green",shape="box"];946[label="xy302",fontsize=16,color="green",shape="box"];947[label="primMulInt (Pos xy3010) (Pos xy40010)",fontsize=16,color="black",shape="box"];947 -> 953[label="",style="solid", color="black", weight=3];
948[label="primMulInt (Pos xy3010) (Neg xy40010)",fontsize=16,color="black",shape="box"];948 -> 954[label="",style="solid", color="black", weight=3];
949[label="primMulInt (Neg xy3010) (Pos xy40010)",fontsize=16,color="black",shape="box"];949 -> 955[label="",style="solid", color="black", weight=3];
950[label="primMulInt (Neg xy3010) (Neg xy40010)",fontsize=16,color="black",shape="box"];950 -> 956[label="",style="solid", color="black", weight=3];
951[label="xy40000",fontsize=16,color="green",shape="box"];952[label="xy3000",fontsize=16,color="green",shape="box"];953[label="Pos (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];953 -> 957[label="",style="dashed", color="green", weight=3];
954[label="Neg (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];954 -> 958[label="",style="dashed", color="green", weight=3];
955[label="Neg (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];955 -> 959[label="",style="dashed", color="green", weight=3];
956[label="Pos (primMulNat xy3010 xy40010)",fontsize=16,color="green",shape="box"];956 -> 960[label="",style="dashed", color="green", weight=3];
957[label="primMulNat xy3010 xy40010",fontsize=16,color="burlywood",shape="triangle"];1394[label="xy3010/Succ xy30100",fontsize=10,color="white",style="solid",shape="box"];957 -> 1394[label="",style="solid", color="burlywood", weight=9];
1394 -> 961[label="",style="solid", color="burlywood", weight=3];
1395[label="xy3010/Zero",fontsize=10,color="white",style="solid",shape="box"];957 -> 1395[label="",style="solid", color="burlywood", weight=9];
1395 -> 962[label="",style="solid", color="burlywood", weight=3];
958 -> 957[label="",style="dashed", color="red", weight=0];
958[label="primMulNat xy3010 xy40010",fontsize=16,color="magenta"];958 -> 963[label="",style="dashed", color="magenta", weight=3];
959 -> 957[label="",style="dashed", color="red", weight=0];
959[label="primMulNat xy3010 xy40010",fontsize=16,color="magenta"];959 -> 964[label="",style="dashed", color="magenta", weight=3];
960 -> 957[label="",style="dashed", color="red", weight=0];
960[label="primMulNat xy3010 xy40010",fontsize=16,color="magenta"];960 -> 965[label="",style="dashed", color="magenta", weight=3];
960 -> 966[label="",style="dashed", color="magenta", weight=3];
961[label="primMulNat (Succ xy30100) xy40010",fontsize=16,color="burlywood",shape="box"];1399[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];961 -> 1399[label="",style="solid", color="burlywood", weight=9];
1399 -> 967[label="",style="solid", color="burlywood", weight=3];
1400[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];961 -> 1400[label="",style="solid", color="burlywood", weight=9];
1400 -> 968[label="",style="solid", color="burlywood", weight=3];
962[label="primMulNat Zero xy40010",fontsize=16,color="burlywood",shape="box"];1401[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];962 -> 1401[label="",style="solid", color="burlywood", weight=9];
1401 -> 969[label="",style="solid", color="burlywood", weight=3];
1402[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];962 -> 1402[label="",style="solid", color="burlywood", weight=9];
1402 -> 970[label="",style="solid", color="burlywood", weight=3];
963[label="xy40010",fontsize=16,color="green",shape="box"];964[label="xy3010",fontsize=16,color="green",shape="box"];965[label="xy40010",fontsize=16,color="green",shape="box"];966[label="xy3010",fontsize=16,color="green",shape="box"];967[label="primMulNat (Succ xy30100) (Succ xy400100)",fontsize=16,color="black",shape="box"];967 -> 971[label="",style="solid", color="black", weight=3];
968[label="primMulNat (Succ xy30100) Zero",fontsize=16,color="black",shape="box"];968 -> 972[label="",style="solid", color="black", weight=3];
969[label="primMulNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];969 -> 973[label="",style="solid", color="black", weight=3];
970[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];970 -> 974[label="",style="solid", color="black", weight=3];
971 -> 975[label="",style="dashed", color="red", weight=0];
971[label="primPlusNat (primMulNat xy30100 (Succ xy400100)) (Succ xy400100)",fontsize=16,color="magenta"];971 -> 976[label="",style="dashed", color="magenta", weight=3];
972[label="Zero",fontsize=16,color="green",shape="box"];973[label="Zero",fontsize=16,color="green",shape="box"];974[label="Zero",fontsize=16,color="green",shape="box"];976 -> 957[label="",style="dashed", color="red", weight=0];
976[label="primMulNat xy30100 (Succ xy400100)",fontsize=16,color="magenta"];976 -> 977[label="",style="dashed", color="magenta", weight=3];
976 -> 978[label="",style="dashed", color="magenta", weight=3];
975[label="primPlusNat xy32 (Succ xy400100)",fontsize=16,color="burlywood",shape="triangle"];1405[label="xy32/Succ xy320",fontsize=10,color="white",style="solid",shape="box"];975 -> 1405[label="",style="solid", color="burlywood", weight=9];
1405 -> 979[label="",style="solid", color="burlywood", weight=3];
1406[label="xy32/Zero",fontsize=10,color="white",style="solid",shape="box"];975 -> 1406[label="",style="solid", color="burlywood", weight=9];
1406 -> 980[label="",style="solid", color="burlywood", weight=3];
977[label="Succ xy400100",fontsize=16,color="green",shape="box"];978[label="xy30100",fontsize=16,color="green",shape="box"];979[label="primPlusNat (Succ xy320) (Succ xy400100)",fontsize=16,color="black",shape="box"];979 -> 981[label="",style="solid", color="black", weight=3];
980[label="primPlusNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];980 -> 982[label="",style="solid", color="black", weight=3];
981[label="Succ (Succ (primPlusNat xy320 xy400100))",fontsize=16,color="green",shape="box"];981 -> 983[label="",style="dashed", color="green", weight=3];
982[label="Succ xy400100",fontsize=16,color="green",shape="box"];983[label="primPlusNat xy320 xy400100",fontsize=16,color="burlywood",shape="triangle"];1407[label="xy320/Succ xy3200",fontsize=10,color="white",style="solid",shape="box"];983 -> 1407[label="",style="solid", color="burlywood", weight=9];
1407 -> 984[label="",style="solid", color="burlywood", weight=3];
1408[label="xy320/Zero",fontsize=10,color="white",style="solid",shape="box"];983 -> 1408[label="",style="solid", color="burlywood", weight=9];
1408 -> 985[label="",style="solid", color="burlywood", weight=3];
984[label="primPlusNat (Succ xy3200) xy400100",fontsize=16,color="burlywood",shape="box"];1409[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];984 -> 1409[label="",style="solid", color="burlywood", weight=9];
1409 -> 986[label="",style="solid", color="burlywood", weight=3];
1410[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];984 -> 1410[label="",style="solid", color="burlywood", weight=9];
1410 -> 987[label="",style="solid", color="burlywood", weight=3];
985[label="primPlusNat Zero xy400100",fontsize=16,color="burlywood",shape="box"];1411[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];985 -> 1411[label="",style="solid", color="burlywood", weight=9];
1411 -> 988[label="",style="solid", color="burlywood", weight=3];
1412[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];985 -> 1412[label="",style="solid", color="burlywood", weight=9];
1412 -> 989[label="",style="solid", color="burlywood", weight=3];
986[label="primPlusNat (Succ xy3200) (Succ xy4001000)",fontsize=16,color="black",shape="box"];986 -> 990[label="",style="solid", color="black", weight=3];
987[label="primPlusNat (Succ xy3200) Zero",fontsize=16,color="black",shape="box"];987 -> 991[label="",style="solid", color="black", weight=3];
988[label="primPlusNat Zero (Succ xy4001000)",fontsize=16,color="black",shape="box"];988 -> 992[label="",style="solid", color="black", weight=3];
989[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];989 -> 993[label="",style="solid", color="black", weight=3];
990[label="Succ (Succ (primPlusNat xy3200 xy4001000))",fontsize=16,color="green",shape="box"];990 -> 994[label="",style="dashed", color="green", weight=3];
991[label="Succ xy3200",fontsize=16,color="green",shape="box"];992[label="Succ xy4001000",fontsize=16,color="green",shape="box"];993[label="Zero",fontsize=16,color="green",shape="box"];994 -> 983[label="",style="dashed", color="red", weight=0];
994[label="primPlusNat xy3200 xy4001000",fontsize=16,color="magenta"];994 -> 995[label="",style="dashed", color="magenta", weight=3];
994 -> 996[label="",style="dashed", color="magenta", weight=3];
995[label="xy3200",fontsize=16,color="green",shape="box"];996[label="xy4001000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_primPlusNat(Succ(xy3200), Succ(xy4001000)) → new_primPlusNat(xy3200, xy4001000)

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

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

new_primPlusNat(Succ(xy3200), Succ(xy4001000)) → new_primPlusNat(xy3200, xy4001000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_primMulNat(Succ(xy30100), Succ(xy400100)) → new_primMulNat(xy30100, Succ(xy400100))

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

new_primMulNat(Succ(xy30100), Succ(xy400100)) → new_primMulNat(xy30100, Succ(xy400100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_primEqNat(Succ(xy3000), Succ(xy40000)) → new_primEqNat(xy3000, xy40000)

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

new_primEqNat(Succ(xy3000), Succ(xy40000)) → new_primEqNat(xy3000, xy40000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(app(ty_@2, bbf), bbg), ca) → new_esEs1(xy301, xy4001, bbf, bbg)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(ty_Maybe, bbh), ca) → new_esEs2(xy301, xy4001, bbh)
new_esEs0(Left(xy300), Left(xy4000), app(ty_[], cc), bc) → new_esEs(xy300, xy4000, cc)
new_esEs2(Just(xy300), Just(xy4000), app(ty_[], ha)) → new_esEs(xy300, xy4000, ha)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(app(app(ty_@3, gf), gg), gh)) → new_esEs3(xy301, xy4001, gf, gg, gh)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs3(xy302, xy4002, bdb, bdc, bdd)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(ty_[], bcd)) → new_esEs(xy302, xy4002, bcd)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_Either, eg), eh), be) → new_esEs0(xy300, xy4000, eg, eh)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(app(ty_Either, ga), gb)) → new_esEs0(xy301, xy4001, ga, gb)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bae), baf), bh, ca) → new_esEs1(xy300, xy4000, bae, baf)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(xy310, xy4010, bg, bh, ca)
new_esEs0(Right(xy300), Right(xy4000), bb, app(app(ty_@2, dh), ea)) → new_esEs1(xy300, xy4000, dh, ea)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_[], bab), bh, ca) → new_esEs(xy300, xy4000, bab)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(ty_[], bbc), ca) → new_esEs(xy301, xy4001, bbc)
new_esEs0(Left(xy300), Left(xy4000), app(app(app(ty_@3, db), dc), dd), bc) → new_esEs3(xy300, xy4000, db, dc, dd)
new_esEs2(Just(xy300), Just(xy4000), app(ty_Maybe, hf)) → new_esEs2(xy300, xy4000, hf)
new_esEs0(Left(xy300), Left(xy4000), app(app(ty_Either, cd), ce), bc) → new_esEs0(xy300, xy4000, cd, ce)
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_@2, hd), he)) → new_esEs1(xy300, xy4000, hd, he)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(ty_[], fh)) → new_esEs(xy301, xy4001, fh)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_Maybe, bf)) → new_esEs2(xy310, xy4010, bf)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_Maybe, fc), be) → new_esEs2(xy300, xy4000, fc)
new_esEs0(Right(xy300), Right(xy4000), bb, app(app(app(ty_@3, ec), ed), ee)) → new_esEs3(xy300, xy4000, ec, ed, ee)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_[], ef), be) → new_esEs(xy300, xy4000, ef)
new_esEs0(Right(xy300), Right(xy4000), bb, app(app(ty_Either, df), dg)) → new_esEs0(xy300, xy4000, df, dg)
new_esEs0(Left(xy300), Left(xy4000), app(ty_Maybe, da), bc) → new_esEs2(xy300, xy4000, da)
new_esEs0(Right(xy300), Right(xy4000), bb, app(ty_Maybe, eb)) → new_esEs2(xy300, xy4000, eb)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(app(ty_@2, gc), gd)) → new_esEs1(xy301, xy4001, gc, gd)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_@2, bd), be)) → new_esEs1(xy310, xy4010, bd, be)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(app(app(ty_@3, bca), bcb), bcc), ca) → new_esEs3(xy301, xy4001, bca, bcb, bcc)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_Either, bb), bc)) → new_esEs0(xy310, xy4010, bb, bc)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), cb) → new_esEs(xy311, xy4011, cb)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(app(ty_@2, bcg), bch)) → new_esEs1(xy302, xy4002, bcg, bch)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(app(ty_@3, fd), ff), fg), be) → new_esEs3(xy300, xy4000, fd, ff, fg)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_@2, fa), fb), be) → new_esEs1(xy300, xy4000, fa, fb)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bag), bh, ca) → new_esEs2(xy300, xy4000, bag)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(ty_Maybe, bda)) → new_esEs2(xy302, xy4002, bda)
new_esEs0(Right(xy300), Right(xy4000), bb, app(ty_[], de)) → new_esEs(xy300, xy4000, de)
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(ty_Maybe, ge)) → new_esEs2(xy301, xy4001, ge)
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_Either, hb), hc)) → new_esEs0(xy300, xy4000, hb, hc)
new_esEs2(Just(xy300), Just(xy4000), app(app(app(ty_@3, hg), hh), baa)) → new_esEs3(xy300, xy4000, hg, hh, baa)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(app(ty_Either, bbd), bbe), ca) → new_esEs0(xy301, xy4001, bbd, bbe)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(app(ty_Either, bce), bcf)) → new_esEs0(xy302, xy4002, bce, bcf)
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_[], ba)) → new_esEs(xy310, xy4010, ba)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, bah), bba), bbb), bh, ca) → new_esEs3(xy300, xy4000, bah, bba, bbb)
new_esEs0(Left(xy300), Left(xy4000), app(app(ty_@2, cf), cg), bc) → new_esEs1(xy300, xy4000, cf, cg)
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bac), bad), bh, ca) → new_esEs0(xy300, xy4000, bac, bad)

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

new_esEs2(Just(xy300), Just(xy4000), app(app(app(ty_@3, hg), hh), baa)) → new_esEs3(xy300, xy4000, hg, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_Either, hb), hc)) → new_esEs0(xy300, xy4000, hb, hc)
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, bg), bh), ca)) → new_esEs3(xy310, xy4010, bg, bh, ca)
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_Either, bb), bc)) → new_esEs0(xy310, xy4010, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy300), Just(xy4000), app(ty_Maybe, hf)) → new_esEs2(xy300, xy4000, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_Maybe, bf)) → new_esEs2(xy310, xy4010, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Just(xy300), Just(xy4000), app(app(ty_@2, hd), he)) → new_esEs1(xy300, xy4000, hd, he)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xy300), Just(xy4000), app(ty_[], ha)) → new_esEs(xy300, xy4000, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(app(ty_@2, bd), be)) → new_esEs1(xy310, xy4010, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(app(app(ty_@3, gf), gg), gh)) → new_esEs3(xy301, xy4001, gf, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(app(ty_@3, fd), ff), fg), be) → new_esEs3(xy300, xy4000, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs3(xy302, xy4002, bdb, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(app(app(ty_@3, bca), bcb), bcc), ca) → new_esEs3(xy301, xy4001, bca, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, bah), bba), bbb), bh, ca) → new_esEs3(xy300, xy4000, bah, bba, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Left(xy300), Left(xy4000), app(app(app(ty_@3, db), dc), dd), bc) → new_esEs3(xy300, xy4000, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Right(xy300), Right(xy4000), bb, app(app(app(ty_@3, ec), ed), ee)) → new_esEs3(xy300, xy4000, ec, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_Either, eg), eh), be) → new_esEs0(xy300, xy4000, eg, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(app(ty_Either, ga), gb)) → new_esEs0(xy301, xy4001, ga, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_Maybe, fc), be) → new_esEs2(xy300, xy4000, fc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(ty_Maybe, ge)) → new_esEs2(xy301, xy4001, ge)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(app(ty_@2, gc), gd)) → new_esEs1(xy301, xy4001, gc, gd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(app(ty_@2, fa), fb), be) → new_esEs1(xy300, xy4000, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), bd, app(ty_[], fh)) → new_esEs(xy301, xy4001, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy300, xy301), @2(xy4000, xy4001), app(ty_[], ef), be) → new_esEs(xy300, xy4000, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(xy310, xy311), :(xy4010, xy4011), cb) → new_esEs(xy311, xy4011, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(:(xy310, xy311), :(xy4010, xy4011), app(ty_[], ba)) → new_esEs(xy310, xy4010, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(app(ty_Either, bbd), bbe), ca) → new_esEs0(xy301, xy4001, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(app(ty_Either, bce), bcf)) → new_esEs0(xy302, xy4002, bce, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bac), bad), bh, ca) → new_esEs0(xy300, xy4000, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Left(xy300), Left(xy4000), app(app(ty_Either, cd), ce), bc) → new_esEs0(xy300, xy4000, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(xy300), Right(xy4000), bb, app(app(ty_Either, df), dg)) → new_esEs0(xy300, xy4000, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(ty_Maybe, bbh), ca) → new_esEs2(xy301, xy4001, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(ty_Maybe, bda)) → new_esEs2(xy302, xy4002, bda)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bag), bh, ca) → new_esEs2(xy300, xy4000, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Left(xy300), Left(xy4000), app(ty_Maybe, da), bc) → new_esEs2(xy300, xy4000, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xy300), Right(xy4000), bb, app(ty_Maybe, eb)) → new_esEs2(xy300, xy4000, eb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(app(ty_@2, bbf), bbg), ca) → new_esEs1(xy301, xy4001, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bae), baf), bh, ca) → new_esEs1(xy300, xy4000, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(app(ty_@2, bcg), bch)) → new_esEs1(xy302, xy4002, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, bh, app(ty_[], bcd)) → new_esEs(xy302, xy4002, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), app(ty_[], bab), bh, ca) → new_esEs(xy300, xy4000, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), bg, app(ty_[], bbc), ca) → new_esEs(xy301, xy4001, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Right(xy300), Right(xy4000), bb, app(app(ty_@2, dh), ea)) → new_esEs1(xy300, xy4000, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(Left(xy300), Left(xy4000), app(app(ty_@2, cf), cg), bc) → new_esEs1(xy300, xy4000, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Left(xy300), Left(xy4000), app(ty_[], cc), bc) → new_esEs(xy300, xy4000, cc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xy300), Right(xy4000), bb, app(ty_[], de)) → new_esEs(xy300, xy4000, de)
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

                    ↳ DependencyGraphProof

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

new_deleteBy([], :(:(xy400, xy401), xy41), bb) → new_deleteBy([], xy41, bb)
new_deleteBy0(xy12, xy13, xy14, xy15, xy16, False, ba) → new_deleteBy(:(xy15, xy16), xy12, ba)
new_deleteBy(:(xy30, xy31), :([], xy41), bb) → new_deleteBy(:(xy30, xy31), xy41, bb)
new_deleteBy(:(xy30, xy31), :(:(xy400, xy401), xy41), bb) → new_deleteBy0(xy41, xy400, xy401, xy30, xy31, new_asAs(new_esEs4(xy30, xy400, bb), new_esEs5(xy31, xy401, bb)), bb)

The TRS R consists of the following rules:

new_esEs13(Right(xy300), Right(xy4000), bd, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs6(xy310, xy4010, app(ty_Maybe, bh)) → new_esEs16(xy310, xy4010, bh)
new_esEs6(xy310, xy4010, ty_Integer) → new_esEs10(xy310, xy4010)
new_esEs13(Left(xy300), Left(xy4000), app(ty_Maybe, bch), be) → new_esEs16(xy300, xy4000, bch)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Float) → new_esEs7(xy300, xy4000)
new_primPlusNat1(Succ(xy3200), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy3200, xy4001000)))
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, cf), cg)) → new_esEs13(xy300, xy4000, cf, cg)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_esEs21(xy301, xy4001, app(ty_Maybe, fh)) → new_esEs16(xy301, xy4001, fh)
new_esEs20(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_Float) → new_esEs7(xy310, xy4010)
new_esEs24(xy302, xy4002, ty_Char) → new_esEs9(xy302, xy4002)
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_esEs5([], [], bb) → True
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_Ratio, bec)) → new_esEs17(xy300, xy4000, bec)
new_esEs13(Left(xy300), Left(xy4000), app(app(ty_Either, bcd), bce), be) → new_esEs13(xy300, xy4000, bcd, bce)
new_esEs23(xy301, xy4001, app(app(ty_Either, hh), baa)) → new_esEs13(xy301, xy4001, hh, baa)
new_esEs6(xy310, xy4010, ty_Int) → new_esEs11(xy310, xy4010)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_[], bde)) → new_esEs5(xy300, xy4000, bde)
new_esEs24(xy302, xy4002, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs18(xy302, xy4002, bbh, bca, bcb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs5(:(xy310, xy311), :(xy4010, xy4011), bb) → new_asAs(new_esEs6(xy310, xy4010, bb), new_esEs5(xy311, xy4011, bb))
new_esEs16(Nothing, Nothing, bh) → True
new_esEs21(xy301, xy4001, app(ty_[], fb)) → new_esEs5(xy301, xy4001, fb)
new_esEs11(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(ty_@2, bdh), bea)) → new_esEs14(xy300, xy4000, bdh, bea)
new_esEs6(xy310, xy4010, ty_Ordering) → new_esEs8(xy310, xy4010)
new_esEs5([], :(xy4010, xy4011), bb) → False
new_esEs5(:(xy310, xy311), [], bb) → False
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs8(xy30, xy400)
new_esEs6(xy310, xy4010, app(app(ty_@2, bf), bg)) → new_esEs14(xy310, xy4010, bf, bg)
new_esEs22(xy300, xy4000, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs20(xy300, xy4000, app(app(ty_@2, ec), ed)) → new_esEs14(xy300, xy4000, ec, ed)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_esEs20(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs20(xy300, xy4000, app(ty_Maybe, ee)) → new_esEs16(xy300, xy4000, ee)
new_esEs13(Left(xy300), Left(xy4000), ty_Ordering, be) → new_esEs8(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs13(Left(xy300), Left(xy4000), ty_@0, be) → new_esEs12(xy300, xy4000)
new_esEs6(xy310, xy4010, app(app(ty_Either, bd), be)) → new_esEs13(xy310, xy4010, bd, be)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, dc)) → new_esEs16(xy300, xy4000, dc)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(app(ty_@3, bed), bee), bef)) → new_esEs18(xy300, xy4000, bed, bee, bef)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs13(Left(xy300), Left(xy4000), ty_Char, be) → new_esEs9(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, de), df), dg)) → new_esEs18(xy300, xy4000, de, df, dg)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs20(xy300, xy4000, app(app(ty_Either, ea), eb)) → new_esEs13(xy300, xy4000, ea, eb)
new_esEs12(@0, @0) → True
new_esEs6(xy310, xy4010, ty_Double) → new_esEs19(xy310, xy4010)
new_esEs22(xy300, xy4000, app(app(ty_Either, gf), gg)) → new_esEs13(xy300, xy4000, gf, gg)
new_esEs22(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs4(xy30, xy400, app(app(app(ty_@3, cb), cc), cd)) → new_esEs18(xy30, xy400, cb, cc, cd)
new_esEs24(xy302, xy4002, ty_Bool) → new_esEs15(xy302, xy4002)
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_esEs4(xy30, xy400, app(ty_[], bc)) → new_esEs5(xy30, xy400, bc)
new_esEs23(xy301, xy4001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs18(xy301, xy4001, baf, bag, bah)
new_esEs20(xy300, xy4000, app(ty_[], dh)) → new_esEs5(xy300, xy4000, dh)
new_esEs22(xy300, xy4000, app(app(ty_@2, gh), ha)) → new_esEs14(xy300, xy4000, gh, ha)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs13(Left(xy300), Left(xy4000), app(app(ty_@2, bcf), bcg), be) → new_esEs14(xy300, xy4000, bcf, bcg)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs9(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs21(xy301, xy4001, app(app(ty_@2, ff), fg)) → new_esEs14(xy301, xy4001, ff, fg)
new_esEs10(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_esEs23(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs14(@2(xy300, xy301), @2(xy4000, xy4001), bf, bg) → new_asAs(new_esEs20(xy300, xy4000, bf), new_esEs21(xy301, xy4001, bg))
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs24(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs24(xy302, xy4002, app(app(ty_@2, bbd), bbe)) → new_esEs14(xy302, xy4002, bbd, bbe)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs22(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs23(xy301, xy4001, app(ty_[], hg)) → new_esEs5(xy301, xy4001, hg)
new_esEs4(xy30, xy400, ty_Char) → new_esEs9(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs23(xy301, xy4001, app(ty_Ratio, bae)) → new_esEs17(xy301, xy4001, bae)
new_esEs22(xy300, xy4000, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs20(xy300, xy4000, app(ty_Ratio, ef)) → new_esEs17(xy300, xy4000, ef)
new_esEs13(Left(xy300), Left(xy4000), ty_Double, be) → new_esEs19(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Int) → new_esEs11(xy30, xy400)
new_esEs24(xy302, xy4002, ty_Int) → new_esEs11(xy302, xy4002)
new_esEs22(xy300, xy4000, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs4(xy30, xy400, app(ty_Ratio, ca)) → new_esEs17(xy30, xy400, ca)
new_esEs4(xy30, xy400, ty_Float) → new_esEs7(xy30, xy400)
new_esEs20(xy300, xy4000, ty_Float) → new_esEs7(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Char) → new_esEs9(xy301, xy4001)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs11(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs21(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), app(app(app(ty_@3, bdb), bdc), bdd), be) → new_esEs18(xy300, xy4000, bdb, bdc, bdd)
new_esEs22(xy300, xy4000, app(ty_[], ge)) → new_esEs5(xy300, xy4000, ge)
new_esEs8(LT, LT) → True
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs12(xy300, xy4000)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs21(xy301, xy4001, app(app(app(ty_@3, gb), gc), gd)) → new_esEs18(xy301, xy4001, gb, gc, gd)
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_asAs(False, xy31) → False
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs8(xy300, xy4000)
new_primEqNat0(Zero, Zero) → True
new_esEs20(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs7(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Ordering) → new_esEs8(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), ty_Integer, be) → new_esEs10(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_@0) → new_esEs12(xy310, xy4010)
new_esEs18(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cb, cc, cd) → new_asAs(new_esEs22(xy300, xy4000, cb), new_asAs(new_esEs23(xy301, xy4001, cc), new_esEs24(xy302, xy4002, cd)))
new_esEs24(xy302, xy4002, app(ty_Ratio, bbg)) → new_esEs17(xy302, xy4002, bbg)
new_esEs24(xy302, xy4002, app(ty_Maybe, bbf)) → new_esEs16(xy302, xy4002, bbf)
new_esEs13(Left(xy300), Left(xy4000), ty_Int, be) → new_esEs11(xy300, xy4000)
new_esEs6(xy310, xy4010, app(ty_Ratio, ca)) → new_esEs17(xy310, xy4010, ca)
new_esEs6(xy310, xy4010, ty_Bool) → new_esEs15(xy310, xy4010)
new_esEs13(Left(xy300), Left(xy4000), app(ty_[], bcc), be) → new_esEs5(xy300, xy4000, bcc)
new_esEs23(xy301, xy4001, ty_Char) → new_esEs9(xy301, xy4001)
new_esEs4(xy30, xy400, ty_@0) → new_esEs12(xy30, xy400)
new_esEs8(GT, GT) → True
new_esEs24(xy302, xy4002, app(ty_[], bba)) → new_esEs5(xy302, xy4002, bba)
new_primPlusNat0(Succ(xy320), xy400100) → Succ(Succ(new_primPlusNat1(xy320, xy400100)))
new_esEs24(xy302, xy4002, ty_Integer) → new_esEs10(xy302, xy4002)
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_Maybe, beb)) → new_esEs16(xy300, xy4000, beb)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs23(xy301, xy4001, ty_@0) → new_esEs12(xy301, xy4001)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs10(xy30, xy400)
new_esEs22(xy300, xy4000, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_Char) → new_esEs9(xy310, xy4010)
new_esEs23(xy301, xy4001, ty_Float) → new_esEs7(xy301, xy4001)
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs13(Right(xy300), Left(xy4000), bd, be) → False
new_esEs13(Left(xy300), Right(xy4000), bd, be) → False
new_esEs15(True, True) → True
new_esEs20(xy300, xy4000, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(ty_Either, bdf), bdg)) → new_esEs13(xy300, xy4000, bdf, bdg)
new_esEs23(xy301, xy4001, ty_Ordering) → new_esEs8(xy301, xy4001)
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy3200), Zero) → Succ(xy3200)
new_esEs23(xy301, xy4001, app(ty_Maybe, bad)) → new_esEs16(xy301, xy4001, bad)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs21(xy301, xy4001, ty_Float) → new_esEs7(xy301, xy4001)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, da), db)) → new_esEs14(xy300, xy4000, da, db)
new_esEs7(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs11(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(xy30, xy400, app(app(ty_Either, bd), be)) → new_esEs13(xy30, xy400, bd, be)
new_esEs16(Nothing, Just(xy4000), bh) → False
new_esEs16(Just(xy300), Nothing, bh) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_esEs13(Left(xy300), Left(xy4000), ty_Bool, be) → new_esEs15(xy300, xy4000)
new_esEs8(EQ, EQ) → True
new_esEs20(xy300, xy4000, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs24(xy302, xy4002, app(app(ty_Either, bbb), bbc)) → new_esEs13(xy302, xy4002, bbb, bbc)
new_esEs22(xy300, xy4000, app(ty_Ratio, hc)) → new_esEs17(xy300, xy4000, hc)
new_esEs9(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs11(xy300, xy4000)
new_esEs21(xy301, xy4001, app(app(ty_Either, fc), fd)) → new_esEs13(xy301, xy4001, fc, fd)
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], ce)) → new_esEs5(xy300, xy4000, ce)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs20(xy300, xy4000, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs21(xy301, xy4001, app(ty_Ratio, ga)) → new_esEs17(xy301, xy4001, ga)
new_asAs(True, xy31) → xy31
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs22(xy300, xy4000, app(ty_Maybe, hb)) → new_esEs16(xy300, xy4000, hb)
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), app(ty_Ratio, bda), be) → new_esEs17(xy300, xy4000, bda)
new_esEs22(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs20(xy300, xy4000, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs6(xy310, xy4010, app(app(app(ty_@3, cb), cc), cd)) → new_esEs18(xy310, xy4010, cb, cc, cd)
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_Maybe, bh)) → new_esEs16(xy30, xy400, bh)
new_esEs6(xy310, xy4010, app(ty_[], bc)) → new_esEs5(xy310, xy4010, bc)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, dd)) → new_esEs17(xy300, xy4000, dd)
new_esEs23(xy301, xy4001, app(app(ty_@2, bab), bac)) → new_esEs14(xy301, xy4001, bab, bac)
new_esEs24(xy302, xy4002, ty_Ordering) → new_esEs8(xy302, xy4002)
new_esEs24(xy302, xy4002, ty_Float) → new_esEs7(xy302, xy4002)
new_esEs23(xy301, xy4001, ty_Bool) → new_esEs15(xy301, xy4001)
new_esEs21(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs4(xy30, xy400, app(app(ty_@2, bf), bg)) → new_esEs14(xy30, xy400, bf, bg)
new_esEs13(Left(xy300), Left(xy4000), ty_Float, be) → new_esEs7(xy300, xy4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_esEs22(xy300, xy4000, ty_Float) → new_esEs7(xy300, xy4000)
new_esEs17(:%(xy300, xy301), :%(xy4000, xy4001), ca) → new_asAs(new_esEs25(xy300, xy4000, ca), new_esEs26(xy301, xy4001, ca))
new_esEs24(xy302, xy4002, ty_@0) → new_esEs12(xy302, xy4002)
new_esEs21(xy301, xy4001, ty_Bool) → new_esEs15(xy301, xy4001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs21(xy301, xy4001, ty_@0) → new_esEs12(xy301, xy4001)
new_esEs22(xy300, xy4000, app(app(app(ty_@3, hd), he), hf)) → new_esEs18(xy300, xy4000, hd, he, hf)
new_esEs20(xy300, xy4000, app(app(app(ty_@3, eg), eh), fa)) → new_esEs18(xy300, xy4000, eg, eh, fa)
new_esEs15(False, False) → True

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ QDPSizeChangeProof

                        ↳ QDP

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

new_deleteBy0(xy12, xy13, xy14, xy15, xy16, False, ba) → new_deleteBy(:(xy15, xy16), xy12, ba)
new_deleteBy(:(xy30, xy31), :([], xy41), bb) → new_deleteBy(:(xy30, xy31), xy41, bb)
new_deleteBy(:(xy30, xy31), :(:(xy400, xy401), xy41), bb) → new_deleteBy0(xy41, xy400, xy401, xy30, xy31, new_asAs(new_esEs4(xy30, xy400, bb), new_esEs5(xy31, xy401, bb)), bb)

The TRS R consists of the following rules:

new_esEs13(Right(xy300), Right(xy4000), bd, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs6(xy310, xy4010, app(ty_Maybe, bh)) → new_esEs16(xy310, xy4010, bh)
new_esEs6(xy310, xy4010, ty_Integer) → new_esEs10(xy310, xy4010)
new_esEs13(Left(xy300), Left(xy4000), app(ty_Maybe, bch), be) → new_esEs16(xy300, xy4000, bch)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Float) → new_esEs7(xy300, xy4000)
new_primPlusNat1(Succ(xy3200), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy3200, xy4001000)))
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, cf), cg)) → new_esEs13(xy300, xy4000, cf, cg)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_esEs21(xy301, xy4001, app(ty_Maybe, fh)) → new_esEs16(xy301, xy4001, fh)
new_esEs20(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_Float) → new_esEs7(xy310, xy4010)
new_esEs24(xy302, xy4002, ty_Char) → new_esEs9(xy302, xy4002)
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_esEs5([], [], bb) → True
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_Ratio, bec)) → new_esEs17(xy300, xy4000, bec)
new_esEs13(Left(xy300), Left(xy4000), app(app(ty_Either, bcd), bce), be) → new_esEs13(xy300, xy4000, bcd, bce)
new_esEs23(xy301, xy4001, app(app(ty_Either, hh), baa)) → new_esEs13(xy301, xy4001, hh, baa)
new_esEs6(xy310, xy4010, ty_Int) → new_esEs11(xy310, xy4010)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_[], bde)) → new_esEs5(xy300, xy4000, bde)
new_esEs24(xy302, xy4002, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs18(xy302, xy4002, bbh, bca, bcb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs5(:(xy310, xy311), :(xy4010, xy4011), bb) → new_asAs(new_esEs6(xy310, xy4010, bb), new_esEs5(xy311, xy4011, bb))
new_esEs16(Nothing, Nothing, bh) → True
new_esEs21(xy301, xy4001, app(ty_[], fb)) → new_esEs5(xy301, xy4001, fb)
new_esEs11(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(ty_@2, bdh), bea)) → new_esEs14(xy300, xy4000, bdh, bea)
new_esEs6(xy310, xy4010, ty_Ordering) → new_esEs8(xy310, xy4010)
new_esEs5([], :(xy4010, xy4011), bb) → False
new_esEs5(:(xy310, xy311), [], bb) → False
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs8(xy30, xy400)
new_esEs6(xy310, xy4010, app(app(ty_@2, bf), bg)) → new_esEs14(xy310, xy4010, bf, bg)
new_esEs22(xy300, xy4000, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs20(xy300, xy4000, app(app(ty_@2, ec), ed)) → new_esEs14(xy300, xy4000, ec, ed)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_esEs20(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs20(xy300, xy4000, app(ty_Maybe, ee)) → new_esEs16(xy300, xy4000, ee)
new_esEs13(Left(xy300), Left(xy4000), ty_Ordering, be) → new_esEs8(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs13(Left(xy300), Left(xy4000), ty_@0, be) → new_esEs12(xy300, xy4000)
new_esEs6(xy310, xy4010, app(app(ty_Either, bd), be)) → new_esEs13(xy310, xy4010, bd, be)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, dc)) → new_esEs16(xy300, xy4000, dc)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(app(ty_@3, bed), bee), bef)) → new_esEs18(xy300, xy4000, bed, bee, bef)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs13(Left(xy300), Left(xy4000), ty_Char, be) → new_esEs9(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, de), df), dg)) → new_esEs18(xy300, xy4000, de, df, dg)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs20(xy300, xy4000, app(app(ty_Either, ea), eb)) → new_esEs13(xy300, xy4000, ea, eb)
new_esEs12(@0, @0) → True
new_esEs6(xy310, xy4010, ty_Double) → new_esEs19(xy310, xy4010)
new_esEs22(xy300, xy4000, app(app(ty_Either, gf), gg)) → new_esEs13(xy300, xy4000, gf, gg)
new_esEs22(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs4(xy30, xy400, app(app(app(ty_@3, cb), cc), cd)) → new_esEs18(xy30, xy400, cb, cc, cd)
new_esEs24(xy302, xy4002, ty_Bool) → new_esEs15(xy302, xy4002)
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_esEs4(xy30, xy400, app(ty_[], bc)) → new_esEs5(xy30, xy400, bc)
new_esEs23(xy301, xy4001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs18(xy301, xy4001, baf, bag, bah)
new_esEs20(xy300, xy4000, app(ty_[], dh)) → new_esEs5(xy300, xy4000, dh)
new_esEs22(xy300, xy4000, app(app(ty_@2, gh), ha)) → new_esEs14(xy300, xy4000, gh, ha)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs13(Left(xy300), Left(xy4000), app(app(ty_@2, bcf), bcg), be) → new_esEs14(xy300, xy4000, bcf, bcg)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs9(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs21(xy301, xy4001, app(app(ty_@2, ff), fg)) → new_esEs14(xy301, xy4001, ff, fg)
new_esEs10(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_esEs23(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs14(@2(xy300, xy301), @2(xy4000, xy4001), bf, bg) → new_asAs(new_esEs20(xy300, xy4000, bf), new_esEs21(xy301, xy4001, bg))
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs24(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs24(xy302, xy4002, app(app(ty_@2, bbd), bbe)) → new_esEs14(xy302, xy4002, bbd, bbe)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs22(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs23(xy301, xy4001, app(ty_[], hg)) → new_esEs5(xy301, xy4001, hg)
new_esEs4(xy30, xy400, ty_Char) → new_esEs9(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs23(xy301, xy4001, app(ty_Ratio, bae)) → new_esEs17(xy301, xy4001, bae)
new_esEs22(xy300, xy4000, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs20(xy300, xy4000, app(ty_Ratio, ef)) → new_esEs17(xy300, xy4000, ef)
new_esEs13(Left(xy300), Left(xy4000), ty_Double, be) → new_esEs19(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Int) → new_esEs11(xy30, xy400)
new_esEs24(xy302, xy4002, ty_Int) → new_esEs11(xy302, xy4002)
new_esEs22(xy300, xy4000, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs4(xy30, xy400, app(ty_Ratio, ca)) → new_esEs17(xy30, xy400, ca)
new_esEs4(xy30, xy400, ty_Float) → new_esEs7(xy30, xy400)
new_esEs20(xy300, xy4000, ty_Float) → new_esEs7(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Char) → new_esEs9(xy301, xy4001)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs11(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs21(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), app(app(app(ty_@3, bdb), bdc), bdd), be) → new_esEs18(xy300, xy4000, bdb, bdc, bdd)
new_esEs22(xy300, xy4000, app(ty_[], ge)) → new_esEs5(xy300, xy4000, ge)
new_esEs8(LT, LT) → True
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs12(xy300, xy4000)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs21(xy301, xy4001, app(app(app(ty_@3, gb), gc), gd)) → new_esEs18(xy301, xy4001, gb, gc, gd)
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_asAs(False, xy31) → False
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs8(xy300, xy4000)
new_primEqNat0(Zero, Zero) → True
new_esEs20(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs7(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Ordering) → new_esEs8(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), ty_Integer, be) → new_esEs10(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_@0) → new_esEs12(xy310, xy4010)
new_esEs18(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cb, cc, cd) → new_asAs(new_esEs22(xy300, xy4000, cb), new_asAs(new_esEs23(xy301, xy4001, cc), new_esEs24(xy302, xy4002, cd)))
new_esEs24(xy302, xy4002, app(ty_Ratio, bbg)) → new_esEs17(xy302, xy4002, bbg)
new_esEs24(xy302, xy4002, app(ty_Maybe, bbf)) → new_esEs16(xy302, xy4002, bbf)
new_esEs13(Left(xy300), Left(xy4000), ty_Int, be) → new_esEs11(xy300, xy4000)
new_esEs6(xy310, xy4010, app(ty_Ratio, ca)) → new_esEs17(xy310, xy4010, ca)
new_esEs6(xy310, xy4010, ty_Bool) → new_esEs15(xy310, xy4010)
new_esEs13(Left(xy300), Left(xy4000), app(ty_[], bcc), be) → new_esEs5(xy300, xy4000, bcc)
new_esEs23(xy301, xy4001, ty_Char) → new_esEs9(xy301, xy4001)
new_esEs4(xy30, xy400, ty_@0) → new_esEs12(xy30, xy400)
new_esEs8(GT, GT) → True
new_esEs24(xy302, xy4002, app(ty_[], bba)) → new_esEs5(xy302, xy4002, bba)
new_primPlusNat0(Succ(xy320), xy400100) → Succ(Succ(new_primPlusNat1(xy320, xy400100)))
new_esEs24(xy302, xy4002, ty_Integer) → new_esEs10(xy302, xy4002)
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_Maybe, beb)) → new_esEs16(xy300, xy4000, beb)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs23(xy301, xy4001, ty_@0) → new_esEs12(xy301, xy4001)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs10(xy30, xy400)
new_esEs22(xy300, xy4000, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_Char) → new_esEs9(xy310, xy4010)
new_esEs23(xy301, xy4001, ty_Float) → new_esEs7(xy301, xy4001)
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs13(Right(xy300), Left(xy4000), bd, be) → False
new_esEs13(Left(xy300), Right(xy4000), bd, be) → False
new_esEs15(True, True) → True
new_esEs20(xy300, xy4000, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(ty_Either, bdf), bdg)) → new_esEs13(xy300, xy4000, bdf, bdg)
new_esEs23(xy301, xy4001, ty_Ordering) → new_esEs8(xy301, xy4001)
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy3200), Zero) → Succ(xy3200)
new_esEs23(xy301, xy4001, app(ty_Maybe, bad)) → new_esEs16(xy301, xy4001, bad)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs21(xy301, xy4001, ty_Float) → new_esEs7(xy301, xy4001)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, da), db)) → new_esEs14(xy300, xy4000, da, db)
new_esEs7(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs11(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(xy30, xy400, app(app(ty_Either, bd), be)) → new_esEs13(xy30, xy400, bd, be)
new_esEs16(Nothing, Just(xy4000), bh) → False
new_esEs16(Just(xy300), Nothing, bh) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_esEs13(Left(xy300), Left(xy4000), ty_Bool, be) → new_esEs15(xy300, xy4000)
new_esEs8(EQ, EQ) → True
new_esEs20(xy300, xy4000, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs24(xy302, xy4002, app(app(ty_Either, bbb), bbc)) → new_esEs13(xy302, xy4002, bbb, bbc)
new_esEs22(xy300, xy4000, app(ty_Ratio, hc)) → new_esEs17(xy300, xy4000, hc)
new_esEs9(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs11(xy300, xy4000)
new_esEs21(xy301, xy4001, app(app(ty_Either, fc), fd)) → new_esEs13(xy301, xy4001, fc, fd)
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], ce)) → new_esEs5(xy300, xy4000, ce)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs20(xy300, xy4000, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs21(xy301, xy4001, app(ty_Ratio, ga)) → new_esEs17(xy301, xy4001, ga)
new_asAs(True, xy31) → xy31
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs22(xy300, xy4000, app(ty_Maybe, hb)) → new_esEs16(xy300, xy4000, hb)
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), app(ty_Ratio, bda), be) → new_esEs17(xy300, xy4000, bda)
new_esEs22(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs20(xy300, xy4000, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs6(xy310, xy4010, app(app(app(ty_@3, cb), cc), cd)) → new_esEs18(xy310, xy4010, cb, cc, cd)
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_Maybe, bh)) → new_esEs16(xy30, xy400, bh)
new_esEs6(xy310, xy4010, app(ty_[], bc)) → new_esEs5(xy310, xy4010, bc)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, dd)) → new_esEs17(xy300, xy4000, dd)
new_esEs23(xy301, xy4001, app(app(ty_@2, bab), bac)) → new_esEs14(xy301, xy4001, bab, bac)
new_esEs24(xy302, xy4002, ty_Ordering) → new_esEs8(xy302, xy4002)
new_esEs24(xy302, xy4002, ty_Float) → new_esEs7(xy302, xy4002)
new_esEs23(xy301, xy4001, ty_Bool) → new_esEs15(xy301, xy4001)
new_esEs21(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs4(xy30, xy400, app(app(ty_@2, bf), bg)) → new_esEs14(xy30, xy400, bf, bg)
new_esEs13(Left(xy300), Left(xy4000), ty_Float, be) → new_esEs7(xy300, xy4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_esEs22(xy300, xy4000, ty_Float) → new_esEs7(xy300, xy4000)
new_esEs17(:%(xy300, xy301), :%(xy4000, xy4001), ca) → new_asAs(new_esEs25(xy300, xy4000, ca), new_esEs26(xy301, xy4001, ca))
new_esEs24(xy302, xy4002, ty_@0) → new_esEs12(xy302, xy4002)
new_esEs21(xy301, xy4001, ty_Bool) → new_esEs15(xy301, xy4001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs21(xy301, xy4001, ty_@0) → new_esEs12(xy301, xy4001)
new_esEs22(xy300, xy4000, app(app(app(ty_@3, hd), he), hf)) → new_esEs18(xy300, xy4000, hd, he, hf)
new_esEs20(xy300, xy4000, app(app(app(ty_@3, eg), eh), fa)) → new_esEs18(xy300, xy4000, eg, eh, fa)
new_esEs15(False, False) → True

The set Q consists of the following terms:

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

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

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

new_deleteBy(:(xy30, xy31), :([], xy41), bb) → new_deleteBy(:(xy30, xy31), xy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
new_deleteBy(:(xy30, xy31), :(:(xy400, xy401), xy41), bb) → new_deleteBy0(xy41, xy400, xy401, xy30, xy31, new_asAs(new_esEs4(xy30, xy400, bb), new_esEs5(xy31, xy401, bb)), bb)
The graph contains the following edges 2 > 1, 2 > 2, 2 > 3, 1 > 4, 1 > 5, 3 >= 7
new_deleteBy0(xy12, xy13, xy14, xy15, xy16, False, ba) → new_deleteBy(:(xy15, xy16), xy12, ba)
The graph contains the following edges 1 >= 2, 7 >= 3

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ UsableRulesProof

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

new_deleteBy([], :(:(xy400, xy401), xy41), bb) → new_deleteBy([], xy41, bb)

The TRS R consists of the following rules:

new_esEs13(Right(xy300), Right(xy4000), bd, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs6(xy310, xy4010, app(ty_Maybe, bh)) → new_esEs16(xy310, xy4010, bh)
new_esEs6(xy310, xy4010, ty_Integer) → new_esEs10(xy310, xy4010)
new_esEs13(Left(xy300), Left(xy4000), app(ty_Maybe, bch), be) → new_esEs16(xy300, xy4000, bch)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Float) → new_esEs7(xy300, xy4000)
new_primPlusNat1(Succ(xy3200), Succ(xy4001000)) → Succ(Succ(new_primPlusNat1(xy3200, xy4001000)))
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_Either, cf), cg)) → new_esEs13(xy300, xy4000, cf, cg)
new_primEqInt(Neg(Succ(xy3000)), Pos(xy4000)) → False
new_primEqInt(Pos(Succ(xy3000)), Neg(xy4000)) → False
new_esEs21(xy301, xy4001, app(ty_Maybe, fh)) → new_esEs16(xy301, xy4001, fh)
new_esEs20(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_Float) → new_esEs7(xy310, xy4010)
new_esEs24(xy302, xy4002, ty_Char) → new_esEs9(xy302, xy4002)
new_primEqInt(Neg(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xy40000))) → False
new_esEs5([], [], bb) → True
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_Ratio, bec)) → new_esEs17(xy300, xy4000, bec)
new_esEs13(Left(xy300), Left(xy4000), app(app(ty_Either, bcd), bce), be) → new_esEs13(xy300, xy4000, bcd, bce)
new_esEs23(xy301, xy4001, app(app(ty_Either, hh), baa)) → new_esEs13(xy301, xy4001, hh, baa)
new_esEs6(xy310, xy4010, ty_Int) → new_esEs11(xy310, xy4010)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_[], bde)) → new_esEs5(xy300, xy4000, bde)
new_esEs24(xy302, xy4002, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs18(xy302, xy4002, bbh, bca, bcb)
new_primMulNat0(Zero, Zero) → Zero
new_esEs5(:(xy310, xy311), :(xy4010, xy4011), bb) → new_asAs(new_esEs6(xy310, xy4010, bb), new_esEs5(xy311, xy4011, bb))
new_esEs16(Nothing, Nothing, bh) → True
new_esEs21(xy301, xy4001, app(ty_[], fb)) → new_esEs5(xy301, xy4001, fb)
new_esEs11(xy30, xy400) → new_primEqInt(xy30, xy400)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(ty_@2, bdh), bea)) → new_esEs14(xy300, xy4000, bdh, bea)
new_esEs6(xy310, xy4010, ty_Ordering) → new_esEs8(xy310, xy4010)
new_esEs5([], :(xy4010, xy4011), bb) → False
new_esEs5(:(xy310, xy311), [], bb) → False
new_esEs4(xy30, xy400, ty_Ordering) → new_esEs8(xy30, xy400)
new_esEs6(xy310, xy4010, app(app(ty_@2, bf), bg)) → new_esEs14(xy310, xy4010, bf, bg)
new_esEs22(xy300, xy4000, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs20(xy300, xy4000, app(app(ty_@2, ec), ed)) → new_esEs14(xy300, xy4000, ec, ed)
new_primPlusNat0(Zero, xy400100) → Succ(xy400100)
new_esEs20(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs20(xy300, xy4000, app(ty_Maybe, ee)) → new_esEs16(xy300, xy4000, ee)
new_esEs13(Left(xy300), Left(xy4000), ty_Ordering, be) → new_esEs8(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_sr(Pos(xy3010), Neg(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_sr(Neg(xy3010), Pos(xy40010)) → Neg(new_primMulNat0(xy3010, xy40010))
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs13(Left(xy300), Left(xy4000), ty_@0, be) → new_esEs12(xy300, xy4000)
new_esEs6(xy310, xy4010, app(app(ty_Either, bd), be)) → new_esEs13(xy310, xy4010, bd, be)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Maybe, dc)) → new_esEs16(xy300, xy4000, dc)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(app(ty_@3, bed), bee), bef)) → new_esEs18(xy300, xy4000, bed, bee, bef)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs13(Left(xy300), Left(xy4000), ty_Char, be) → new_esEs9(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Double) → new_esEs19(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), app(app(app(ty_@3, de), df), dg)) → new_esEs18(xy300, xy4000, de, df, dg)
new_esEs23(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs20(xy300, xy4000, app(app(ty_Either, ea), eb)) → new_esEs13(xy300, xy4000, ea, eb)
new_esEs12(@0, @0) → True
new_esEs6(xy310, xy4010, ty_Double) → new_esEs19(xy310, xy4010)
new_esEs22(xy300, xy4000, app(app(ty_Either, gf), gg)) → new_esEs13(xy300, xy4000, gf, gg)
new_esEs22(xy300, xy4000, ty_Integer) → new_esEs10(xy300, xy4000)
new_esEs4(xy30, xy400, app(app(app(ty_@3, cb), cc), cd)) → new_esEs18(xy30, xy400, cb, cc, cd)
new_esEs24(xy302, xy4002, ty_Bool) → new_esEs15(xy302, xy4002)
new_primEqNat0(Succ(xy3000), Zero) → False
new_primEqNat0(Zero, Succ(xy40000)) → False
new_esEs4(xy30, xy400, app(ty_[], bc)) → new_esEs5(xy30, xy400, bc)
new_esEs23(xy301, xy4001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs18(xy301, xy4001, baf, bag, bah)
new_esEs20(xy300, xy4000, app(ty_[], dh)) → new_esEs5(xy300, xy4000, dh)
new_esEs22(xy300, xy4000, app(app(ty_@2, gh), ha)) → new_esEs14(xy300, xy4000, gh, ha)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs13(Left(xy300), Left(xy4000), app(app(ty_@2, bcf), bcg), be) → new_esEs14(xy300, xy4000, bcf, bcg)
new_esEs16(Just(xy300), Just(xy4000), ty_Char) → new_esEs9(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs21(xy301, xy4001, app(app(ty_@2, ff), fg)) → new_esEs14(xy301, xy4001, ff, fg)
new_esEs10(Integer(xy300), Integer(xy4000)) → new_primEqInt(xy300, xy4000)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_esEs23(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs14(@2(xy300, xy301), @2(xy4000, xy4001), bf, bg) → new_asAs(new_esEs20(xy300, xy4000, bf), new_esEs21(xy301, xy4001, bg))
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs24(xy302, xy4002, ty_Double) → new_esEs19(xy302, xy4002)
new_esEs24(xy302, xy4002, app(app(ty_@2, bbd), bbe)) → new_esEs14(xy302, xy4002, bbd, bbe)
new_esEs26(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs22(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs23(xy301, xy4001, app(ty_[], hg)) → new_esEs5(xy301, xy4001, hg)
new_esEs4(xy30, xy400, ty_Char) → new_esEs9(xy30, xy400)
new_esEs16(Just(xy300), Just(xy4000), ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs23(xy301, xy4001, app(ty_Ratio, bae)) → new_esEs17(xy301, xy4001, bae)
new_esEs22(xy300, xy4000, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs20(xy300, xy4000, app(ty_Ratio, ef)) → new_esEs17(xy300, xy4000, ef)
new_esEs13(Left(xy300), Left(xy4000), ty_Double, be) → new_esEs19(xy300, xy4000)
new_esEs4(xy30, xy400, ty_Int) → new_esEs11(xy30, xy400)
new_esEs24(xy302, xy4002, ty_Int) → new_esEs11(xy302, xy4002)
new_esEs22(xy300, xy4000, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs4(xy30, xy400, app(ty_Ratio, ca)) → new_esEs17(xy30, xy400, ca)
new_esEs4(xy30, xy400, ty_Float) → new_esEs7(xy30, xy400)
new_esEs20(xy300, xy4000, ty_Float) → new_esEs7(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Char) → new_esEs9(xy301, xy4001)
new_esEs19(Double(xy300, xy301), Double(xy4000, xy4001)) → new_esEs11(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_esEs21(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), app(app(app(ty_@3, bdb), bdc), bdd), be) → new_esEs18(xy300, xy4000, bdb, bdc, bdd)
new_esEs22(xy300, xy4000, app(ty_[], ge)) → new_esEs5(xy300, xy4000, ge)
new_esEs8(LT, LT) → True
new_esEs16(Just(xy300), Just(xy4000), ty_@0) → new_esEs12(xy300, xy4000)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs23(xy301, xy4001, ty_Double) → new_esEs19(xy301, xy4001)
new_esEs21(xy301, xy4001, app(app(app(ty_@3, gb), gc), gd)) → new_esEs18(xy301, xy4001, gb, gc, gd)
new_sr(Neg(xy3010), Neg(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_asAs(False, xy31) → False
new_sr(Pos(xy3010), Pos(xy40010)) → Pos(new_primMulNat0(xy3010, xy40010))
new_esEs16(Just(xy300), Just(xy4000), ty_Ordering) → new_esEs8(xy300, xy4000)
new_primEqNat0(Zero, Zero) → True
new_esEs20(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_primMulNat0(Succ(xy30100), Zero) → Zero
new_primMulNat0(Zero, Succ(xy400100)) → Zero
new_esEs16(Just(xy300), Just(xy4000), ty_Float) → new_esEs7(xy300, xy4000)
new_esEs21(xy301, xy4001, ty_Ordering) → new_esEs8(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), ty_Integer, be) → new_esEs10(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_@0) → new_esEs12(xy310, xy4010)
new_esEs18(@3(xy300, xy301, xy302), @3(xy4000, xy4001, xy4002), cb, cc, cd) → new_asAs(new_esEs22(xy300, xy4000, cb), new_asAs(new_esEs23(xy301, xy4001, cc), new_esEs24(xy302, xy4002, cd)))
new_esEs24(xy302, xy4002, app(ty_Ratio, bbg)) → new_esEs17(xy302, xy4002, bbg)
new_esEs24(xy302, xy4002, app(ty_Maybe, bbf)) → new_esEs16(xy302, xy4002, bbf)
new_esEs13(Left(xy300), Left(xy4000), ty_Int, be) → new_esEs11(xy300, xy4000)
new_esEs6(xy310, xy4010, app(ty_Ratio, ca)) → new_esEs17(xy310, xy4010, ca)
new_esEs6(xy310, xy4010, ty_Bool) → new_esEs15(xy310, xy4010)
new_esEs13(Left(xy300), Left(xy4000), app(ty_[], bcc), be) → new_esEs5(xy300, xy4000, bcc)
new_esEs23(xy301, xy4001, ty_Char) → new_esEs9(xy301, xy4001)
new_esEs4(xy30, xy400, ty_@0) → new_esEs12(xy30, xy400)
new_esEs8(GT, GT) → True
new_esEs24(xy302, xy4002, app(ty_[], bba)) → new_esEs5(xy302, xy4002, bba)
new_primPlusNat0(Succ(xy320), xy400100) → Succ(Succ(new_primPlusNat1(xy320, xy400100)))
new_esEs24(xy302, xy4002, ty_Integer) → new_esEs10(xy302, xy4002)
new_esEs13(Right(xy300), Right(xy4000), bd, app(ty_Maybe, beb)) → new_esEs16(xy300, xy4000, beb)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_esEs23(xy301, xy4001, ty_@0) → new_esEs12(xy301, xy4001)
new_esEs4(xy30, xy400, ty_Integer) → new_esEs10(xy30, xy400)
new_esEs22(xy300, xy4000, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs6(xy310, xy4010, ty_Char) → new_esEs9(xy310, xy4010)
new_esEs23(xy301, xy4001, ty_Float) → new_esEs7(xy301, xy4001)
new_primEqInt(Neg(Succ(xy3000)), Neg(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs13(Right(xy300), Left(xy4000), bd, be) → False
new_esEs13(Left(xy300), Right(xy4000), bd, be) → False
new_esEs15(True, True) → True
new_esEs20(xy300, xy4000, ty_Ordering) → new_esEs8(xy300, xy4000)
new_esEs13(Right(xy300), Right(xy4000), bd, app(app(ty_Either, bdf), bdg)) → new_esEs13(xy300, xy4000, bdf, bdg)
new_esEs23(xy301, xy4001, ty_Ordering) → new_esEs8(xy301, xy4001)
new_primPlusNat1(Zero, Succ(xy4001000)) → Succ(xy4001000)
new_primPlusNat1(Succ(xy3200), Zero) → Succ(xy3200)
new_esEs23(xy301, xy4001, app(ty_Maybe, bad)) → new_esEs16(xy301, xy4001, bad)
new_esEs4(xy30, xy400, ty_Bool) → new_esEs15(xy30, xy400)
new_esEs21(xy301, xy4001, ty_Float) → new_esEs7(xy301, xy4001)
new_esEs16(Just(xy300), Just(xy4000), app(app(ty_@2, da), db)) → new_esEs14(xy300, xy4000, da, db)
new_esEs7(Float(xy300, xy301), Float(xy4000, xy4001)) → new_esEs11(new_sr(xy300, xy4000), new_sr(xy301, xy4001))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs4(xy30, xy400, app(app(ty_Either, bd), be)) → new_esEs13(xy30, xy400, bd, be)
new_esEs16(Nothing, Just(xy4000), bh) → False
new_esEs16(Just(xy300), Nothing, bh) → False
new_primEqInt(Neg(Zero), Neg(Succ(xy40000))) → False
new_primEqInt(Neg(Succ(xy3000)), Neg(Zero)) → False
new_esEs13(Left(xy300), Left(xy4000), ty_Bool, be) → new_esEs15(xy300, xy4000)
new_esEs8(EQ, EQ) → True
new_esEs20(xy300, xy4000, ty_Bool) → new_esEs15(xy300, xy4000)
new_esEs24(xy302, xy4002, app(app(ty_Either, bbb), bbc)) → new_esEs13(xy302, xy4002, bbb, bbc)
new_esEs22(xy300, xy4000, app(ty_Ratio, hc)) → new_esEs17(xy300, xy4000, hc)
new_esEs9(Char(xy300), Char(xy4000)) → new_primEqNat0(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Int) → new_esEs11(xy300, xy4000)
new_esEs21(xy301, xy4001, app(app(ty_Either, fc), fd)) → new_esEs13(xy301, xy4001, fc, fd)
new_esEs16(Just(xy300), Just(xy4000), app(ty_[], ce)) → new_esEs5(xy300, xy4000, ce)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs20(xy300, xy4000, ty_Char) → new_esEs9(xy300, xy4000)
new_esEs21(xy301, xy4001, app(ty_Ratio, ga)) → new_esEs17(xy301, xy4001, ga)
new_asAs(True, xy31) → xy31
new_esEs13(Right(xy300), Right(xy4000), bd, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs16(Just(xy300), Just(xy4000), ty_Double) → new_esEs19(xy300, xy4000)
new_esEs25(xy300, xy4000, ty_Int) → new_esEs11(xy300, xy4000)
new_esEs22(xy300, xy4000, app(ty_Maybe, hb)) → new_esEs16(xy300, xy4000, hb)
new_primMulNat0(Succ(xy30100), Succ(xy400100)) → new_primPlusNat0(new_primMulNat0(xy30100, Succ(xy400100)), xy400100)
new_primEqInt(Pos(Succ(xy3000)), Pos(Succ(xy40000))) → new_primEqNat0(xy3000, xy40000)
new_esEs26(xy301, xy4001, ty_Integer) → new_esEs10(xy301, xy4001)
new_esEs13(Left(xy300), Left(xy4000), app(ty_Ratio, bda), be) → new_esEs17(xy300, xy4000, bda)
new_esEs22(xy300, xy4000, ty_Double) → new_esEs19(xy300, xy4000)
new_esEs20(xy300, xy4000, ty_@0) → new_esEs12(xy300, xy4000)
new_esEs6(xy310, xy4010, app(app(app(ty_@3, cb), cc), cd)) → new_esEs18(xy310, xy4010, cb, cc, cd)
new_primEqNat0(Succ(xy3000), Succ(xy40000)) → new_primEqNat0(xy3000, xy40000)
new_esEs4(xy30, xy400, app(ty_Maybe, bh)) → new_esEs16(xy30, xy400, bh)
new_esEs6(xy310, xy4010, app(ty_[], bc)) → new_esEs5(xy310, xy4010, bc)
new_esEs16(Just(xy300), Just(xy4000), app(ty_Ratio, dd)) → new_esEs17(xy300, xy4000, dd)
new_esEs23(xy301, xy4001, app(app(ty_@2, bab), bac)) → new_esEs14(xy301, xy4001, bab, bac)
new_esEs24(xy302, xy4002, ty_Ordering) → new_esEs8(xy302, xy4002)
new_esEs24(xy302, xy4002, ty_Float) → new_esEs7(xy302, xy4002)
new_esEs23(xy301, xy4001, ty_Bool) → new_esEs15(xy301, xy4001)
new_esEs21(xy301, xy4001, ty_Int) → new_esEs11(xy301, xy4001)
new_esEs4(xy30, xy400, app(app(ty_@2, bf), bg)) → new_esEs14(xy30, xy400, bf, bg)
new_esEs13(Left(xy300), Left(xy4000), ty_Float, be) → new_esEs7(xy300, xy4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(xy40000))) → False
new_primEqInt(Pos(Succ(xy3000)), Pos(Zero)) → False
new_esEs22(xy300, xy4000, ty_Float) → new_esEs7(xy300, xy4000)
new_esEs17(:%(xy300, xy301), :%(xy4000, xy4001), ca) → new_asAs(new_esEs25(xy300, xy4000, ca), new_esEs26(xy301, xy4001, ca))
new_esEs24(xy302, xy4002, ty_@0) → new_esEs12(xy302, xy4002)
new_esEs21(xy301, xy4001, ty_Bool) → new_esEs15(xy301, xy4001)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs21(xy301, xy4001, ty_@0) → new_esEs12(xy301, xy4001)
new_esEs22(xy300, xy4000, app(app(app(ty_@3, hd), he), hf)) → new_esEs18(xy300, xy4000, hd, he, hf)
new_esEs20(xy300, xy4000, app(app(app(ty_@3, eg), eh), fa)) → new_esEs18(xy300, xy4000, eg, eh, fa)
new_esEs15(False, False) → True

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

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

new_deleteBy([], :(:(xy400, xy401), xy41), bb) → new_deleteBy([], xy41, bb)

R is empty.
The set Q consists of the following terms:

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

                                ↳ QDP

                                  ↳ QDPSizeChangeProof

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

new_deleteBy([], :(:(xy400, xy401), xy41), bb) → new_deleteBy([], xy41, bb)

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

new_deleteBy([], :(:(xy400, xy401), xy41), bb) → new_deleteBy([], xy41, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3

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