H-Termination proof of ../tpdb/FP/full_haskell/Prelude_lookup

YES H-Termination proof of ../tpdb/FP/full_haskell/Prelude_lookup_4.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

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

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

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

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

lookup k [] = Nothing

lookup k ((x,y) : xys)

| k == x

= Just y

| otherwise

= lookup k xys

is transformed to

lookup k [] = lookup3 k []

lookup k ((x,y) : xys) = lookup2 k ((x,y) : xys)

lookup1 k x y xys True = Just y

lookup1 k x y xys False = lookup0 k x y xys otherwise

lookup0 k x y xys True = lookup k xys

lookup2 k ((x,y) : xys) = lookup1 k x y xys (k == x)

lookup3 k [] = Nothing

lookup3 xy xz = lookup2 xy xz

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

mainModule Main

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

module Main where

import qualified Prelude

Num Reduction:All numbers are transformed to thier corresponding representation with Succ, Pred and Zero.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

mainModule Main

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

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookup\n",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookup yu3\n",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookup yu3 yu4\n",fontsize=16,color="burlywood",shape="triangle"];945[label="yu4/yu40 : yu41",fontsize=10,color="white",style="solid",shape="box"];4 -> 945[label="",style="solid", color="burlywood", weight=9];
945 -> 5[label="",style="solid", color="burlywood", weight=3];
946[label="yu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 946[label="",style="solid", color="burlywood", weight=9];
946 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookup yu3 (yu40 : yu41)\n",fontsize=16,color="burlywood",shape="box"];947[label="yu40/(yu400,yu401)",fontsize=10,color="white",style="solid",shape="box"];5 -> 947[label="",style="solid", color="burlywood", weight=9];
947 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup yu3 []\n",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookup yu3 ((yu400,yu401) : yu41)\n",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 yu3 []\n",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="lookup2 yu3 ((yu400,yu401) : yu41)\n",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Nothing\n",fontsize=16,color="green",shape="box"];11[label="lookup1 yu3 yu400 yu401 yu41 (yu3 == yu400)\n",fontsize=16,color="burlywood",shape="box"];948[label="yu3/yu30 : yu31",fontsize=10,color="white",style="solid",shape="box"];11 -> 948[label="",style="solid", color="burlywood", weight=9];
948 -> 12[label="",style="solid", color="burlywood", weight=3];
949[label="yu3/[]",fontsize=10,color="white",style="solid",shape="box"];11 -> 949[label="",style="solid", color="burlywood", weight=9];
949 -> 13[label="",style="solid", color="burlywood", weight=3];
12[label="lookup1 (yu30 : yu31) yu400 yu401 yu41 (yu30 : yu31 == yu400)\n",fontsize=16,color="burlywood",shape="box"];950[label="yu400/yu4000 : yu4001",fontsize=10,color="white",style="solid",shape="box"];12 -> 950[label="",style="solid", color="burlywood", weight=9];
950 -> 14[label="",style="solid", color="burlywood", weight=3];
951[label="yu400/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 951[label="",style="solid", color="burlywood", weight=9];
951 -> 15[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 [] yu400 yu401 yu41 ([] == yu400)\n",fontsize=16,color="burlywood",shape="box"];952[label="yu400/yu4000 : yu4001",fontsize=10,color="white",style="solid",shape="box"];13 -> 952[label="",style="solid", color="burlywood", weight=9];
952 -> 16[label="",style="solid", color="burlywood", weight=3];
953[label="yu400/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 953[label="",style="solid", color="burlywood", weight=9];
953 -> 17[label="",style="solid", color="burlywood", weight=3];
14[label="lookup1 (yu30 : yu31) (yu4000 : yu4001) yu401 yu41 (yu30 : yu31 == yu4000 : yu4001)\n",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="lookup1 (yu30 : yu31) [] yu401 yu41 (yu30 : yu31 == [])\n",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="lookup1 [] (yu4000 : yu4001) yu401 yu41 ([] == yu4000 : yu4001)\n",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="lookup1 [] [] yu401 yu41 ([] == [])\n",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18 -> 111[label="",style="dashed", color="red", weight=0];
18[label="lookup1 (yu30 : yu31) (yu4000 : yu4001) yu401 yu41 (yu30 == yu4000 && yu31 == yu4001)\n",fontsize=16,color="magenta"];18 -> 112[label="",style="dashed", color="magenta", weight=3];
18 -> 113[label="",style="dashed", color="magenta", weight=3];
18 -> 114[label="",style="dashed", color="magenta", weight=3];
18 -> 115[label="",style="dashed", color="magenta", weight=3];
18 -> 116[label="",style="dashed", color="magenta", weight=3];
18 -> 117[label="",style="dashed", color="magenta", weight=3];
18 -> 118[label="",style="dashed", color="magenta", weight=3];
19[label="lookup1 (yu30 : yu31) [] yu401 yu41 False\n",fontsize=16,color="black",shape="box"];19 -> 30[label="",style="solid", color="black", weight=3];
20[label="lookup1 [] (yu4000 : yu4001) yu401 yu41 False\n",fontsize=16,color="black",shape="box"];20 -> 31[label="",style="solid", color="black", weight=3];
21[label="lookup1 [] [] yu401 yu41 True\n",fontsize=16,color="black",shape="box"];21 -> 32[label="",style="solid", color="black", weight=3];
112[label="yu4001\n",fontsize=16,color="green",shape="box"];113[label="yu4000\n",fontsize=16,color="green",shape="box"];114[label="yu401\n",fontsize=16,color="green",shape="box"];115[label="yu30\n",fontsize=16,color="green",shape="box"];116 -> 310[label="",style="dashed", color="red", weight=0];
116[label="yu30 == yu4000 && yu31 == yu4001\n",fontsize=16,color="magenta"];116 -> 311[label="",style="dashed", color="magenta", weight=3];
116 -> 312[label="",style="dashed", color="magenta", weight=3];
117[label="yu41\n",fontsize=16,color="green",shape="box"];118[label="yu31\n",fontsize=16,color="green",shape="box"];111[label="lookup1 (yu13 : yu14) (yu15 : yu16) yu17 yu18 yu20\n",fontsize=16,color="burlywood",shape="triangle"];956[label="yu20/False",fontsize=10,color="white",style="solid",shape="box"];111 -> 956[label="",style="solid", color="burlywood", weight=9];
956 -> 126[label="",style="solid", color="burlywood", weight=3];
957[label="yu20/True",fontsize=10,color="white",style="solid",shape="box"];111 -> 957[label="",style="solid", color="burlywood", weight=9];
957 -> 127[label="",style="solid", color="burlywood", weight=3];
30[label="lookup0 (yu30 : yu31) [] yu401 yu41 otherwise\n",fontsize=16,color="black",shape="box"];30 -> 49[label="",style="solid", color="black", weight=3];
31[label="lookup0 [] (yu4000 : yu4001) yu401 yu41 otherwise\n",fontsize=16,color="black",shape="box"];31 -> 50[label="",style="solid", color="black", weight=3];
32[label="Just yu401\n",fontsize=16,color="green",shape="box"];311[label="yu31 == yu4001\n",fontsize=16,color="burlywood",shape="triangle"];958[label="yu31/yu310 : yu311",fontsize=10,color="white",style="solid",shape="box"];311 -> 958[label="",style="solid", color="burlywood", weight=9];
958 -> 315[label="",style="solid", color="burlywood", weight=3];
959[label="yu31/[]",fontsize=10,color="white",style="solid",shape="box"];311 -> 959[label="",style="solid", color="burlywood", weight=9];
959 -> 316[label="",style="solid", color="burlywood", weight=3];
312[label="yu30 == yu4000\n",fontsize=16,color="blue",shape="box"];960[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 960[label="",style="solid", color="blue", weight=9];
960 -> 317[label="",style="solid", color="blue", weight=3];
961[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 961[label="",style="solid", color="blue", weight=9];
961 -> 318[label="",style="solid", color="blue", weight=3];
962[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 962[label="",style="solid", color="blue", weight=9];
962 -> 319[label="",style="solid", color="blue", weight=3];
963[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 963[label="",style="solid", color="blue", weight=9];
963 -> 320[label="",style="solid", color="blue", weight=3];
964[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 964[label="",style="solid", color="blue", weight=9];
964 -> 321[label="",style="solid", color="blue", weight=3];
965[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 965[label="",style="solid", color="blue", weight=9];
965 -> 322[label="",style="solid", color="blue", weight=3];
966[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 966[label="",style="solid", color="blue", weight=9];
966 -> 323[label="",style="solid", color="blue", weight=3];
967[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 967[label="",style="solid", color="blue", weight=9];
967 -> 324[label="",style="solid", color="blue", weight=3];
968[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 968[label="",style="solid", color="blue", weight=9];
968 -> 325[label="",style="solid", color="blue", weight=3];
969[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 969[label="",style="solid", color="blue", weight=9];
969 -> 326[label="",style="solid", color="blue", weight=3];
970[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 970[label="",style="solid", color="blue", weight=9];
970 -> 327[label="",style="solid", color="blue", weight=3];
971[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 971[label="",style="solid", color="blue", weight=9];
971 -> 328[label="",style="solid", color="blue", weight=3];
972[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 972[label="",style="solid", color="blue", weight=9];
972 -> 329[label="",style="solid", color="blue", weight=3];
973[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];312 -> 973[label="",style="solid", color="blue", weight=9];
973 -> 330[label="",style="solid", color="blue", weight=3];
310[label="yu32 && yu33\n",fontsize=16,color="burlywood",shape="triangle"];974[label="yu32/False",fontsize=10,color="white",style="solid",shape="box"];310 -> 974[label="",style="solid", color="burlywood", weight=9];
974 -> 331[label="",style="solid", color="burlywood", weight=3];
975[label="yu32/True",fontsize=10,color="white",style="solid",shape="box"];310 -> 975[label="",style="solid", color="burlywood", weight=9];
975 -> 332[label="",style="solid", color="burlywood", weight=3];
126[label="lookup1 (yu13 : yu14) (yu15 : yu16) yu17 yu18 False\n",fontsize=16,color="black",shape="box"];126 -> 148[label="",style="solid", color="black", weight=3];
127[label="lookup1 (yu13 : yu14) (yu15 : yu16) yu17 yu18 True\n",fontsize=16,color="black",shape="box"];127 -> 149[label="",style="solid", color="black", weight=3];
49[label="lookup0 (yu30 : yu31) [] yu401 yu41 True\n",fontsize=16,color="black",shape="box"];49 -> 73[label="",style="solid", color="black", weight=3];
50[label="lookup0 [] (yu4000 : yu4001) yu401 yu41 True\n",fontsize=16,color="black",shape="box"];50 -> 74[label="",style="solid", color="black", weight=3];
315[label="yu310 : yu311 == yu4001\n",fontsize=16,color="burlywood",shape="box"];976[label="yu4001/yu40010 : yu40011",fontsize=10,color="white",style="solid",shape="box"];315 -> 976[label="",style="solid", color="burlywood", weight=9];
976 -> 333[label="",style="solid", color="burlywood", weight=3];
977[label="yu4001/[]",fontsize=10,color="white",style="solid",shape="box"];315 -> 977[label="",style="solid", color="burlywood", weight=9];
977 -> 334[label="",style="solid", color="burlywood", weight=3];
316[label="[] == yu4001\n",fontsize=16,color="burlywood",shape="box"];978[label="yu4001/yu40010 : yu40011",fontsize=10,color="white",style="solid",shape="box"];316 -> 978[label="",style="solid", color="burlywood", weight=9];
978 -> 335[label="",style="solid", color="burlywood", weight=3];
979[label="yu4001/[]",fontsize=10,color="white",style="solid",shape="box"];316 -> 979[label="",style="solid", color="burlywood", weight=9];
979 -> 336[label="",style="solid", color="burlywood", weight=3];
317[label="yu30 == yu4000\n",fontsize=16,color="black",shape="triangle"];317 -> 337[label="",style="solid", color="black", weight=3];
318[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];980[label="yu30/(yu300,yu301)",fontsize=10,color="white",style="solid",shape="box"];318 -> 980[label="",style="solid", color="burlywood", weight=9];
980 -> 338[label="",style="solid", color="burlywood", weight=3];
319[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];981[label="yu30/(yu300,yu301,yu302)",fontsize=10,color="white",style="solid",shape="box"];319 -> 981[label="",style="solid", color="burlywood", weight=9];
981 -> 339[label="",style="solid", color="burlywood", weight=3];
320[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];982[label="yu30/Left yu300",fontsize=10,color="white",style="solid",shape="box"];320 -> 982[label="",style="solid", color="burlywood", weight=9];
982 -> 340[label="",style="solid", color="burlywood", weight=3];
983[label="yu30/Right yu300",fontsize=10,color="white",style="solid",shape="box"];320 -> 983[label="",style="solid", color="burlywood", weight=9];
983 -> 341[label="",style="solid", color="burlywood", weight=3];
321[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];984[label="yu30/Integer yu300",fontsize=10,color="white",style="solid",shape="box"];321 -> 984[label="",style="solid", color="burlywood", weight=9];
984 -> 342[label="",style="solid", color="burlywood", weight=3];
322[label="yu30 == yu4000\n",fontsize=16,color="black",shape="triangle"];322 -> 343[label="",style="solid", color="black", weight=3];
323[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];985[label="yu30/False",fontsize=10,color="white",style="solid",shape="box"];323 -> 985[label="",style="solid", color="burlywood", weight=9];
985 -> 344[label="",style="solid", color="burlywood", weight=3];
986[label="yu30/True",fontsize=10,color="white",style="solid",shape="box"];323 -> 986[label="",style="solid", color="burlywood", weight=9];
986 -> 345[label="",style="solid", color="burlywood", weight=3];
324[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];987[label="yu30/LT",fontsize=10,color="white",style="solid",shape="box"];324 -> 987[label="",style="solid", color="burlywood", weight=9];
987 -> 346[label="",style="solid", color="burlywood", weight=3];
988[label="yu30/EQ",fontsize=10,color="white",style="solid",shape="box"];324 -> 988[label="",style="solid", color="burlywood", weight=9];
988 -> 347[label="",style="solid", color="burlywood", weight=3];
989[label="yu30/GT",fontsize=10,color="white",style="solid",shape="box"];324 -> 989[label="",style="solid", color="burlywood", weight=9];
989 -> 348[label="",style="solid", color="burlywood", weight=3];
325 -> 311[label="",style="dashed", color="red", weight=0];
325[label="yu30 == yu4000\n",fontsize=16,color="magenta"];325 -> 349[label="",style="dashed", color="magenta", weight=3];
325 -> 350[label="",style="dashed", color="magenta", weight=3];
326[label="yu30 == yu4000\n",fontsize=16,color="black",shape="triangle"];326 -> 351[label="",style="solid", color="black", weight=3];
327[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];991[label="yu30/()",fontsize=10,color="white",style="solid",shape="box"];327 -> 991[label="",style="solid", color="burlywood", weight=9];
991 -> 352[label="",style="solid", color="burlywood", weight=3];
328[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];992[label="yu30/yu300 :% yu301",fontsize=10,color="white",style="solid",shape="box"];328 -> 992[label="",style="solid", color="burlywood", weight=9];
992 -> 353[label="",style="solid", color="burlywood", weight=3];
329[label="yu30 == yu4000\n",fontsize=16,color="burlywood",shape="triangle"];993[label="yu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];329 -> 993[label="",style="solid", color="burlywood", weight=9];
993 -> 354[label="",style="solid", color="burlywood", weight=3];
994[label="yu30/Just yu300",fontsize=10,color="white",style="solid",shape="box"];329 -> 994[label="",style="solid", color="burlywood", weight=9];
994 -> 355[label="",style="solid", color="burlywood", weight=3];
330[label="yu30 == yu4000\n",fontsize=16,color="black",shape="triangle"];330 -> 356[label="",style="solid", color="black", weight=3];
331[label="False && yu33\n",fontsize=16,color="black",shape="box"];331 -> 357[label="",style="solid", color="black", weight=3];
332[label="True && yu33\n",fontsize=16,color="black",shape="box"];332 -> 358[label="",style="solid", color="black", weight=3];
148[label="lookup0 (yu13 : yu14) (yu15 : yu16) yu17 yu18 otherwise\n",fontsize=16,color="black",shape="box"];148 -> 172[label="",style="solid", color="black", weight=3];
149[label="Just yu17\n",fontsize=16,color="green",shape="box"];73 -> 4[label="",style="dashed", color="red", weight=0];
73[label="lookup (yu30 : yu31) yu41\n",fontsize=16,color="magenta"];73 -> 144[label="",style="dashed", color="magenta", weight=3];
73 -> 145[label="",style="dashed", color="magenta", weight=3];
74 -> 4[label="",style="dashed", color="red", weight=0];
74[label="lookup [] yu41\n",fontsize=16,color="magenta"];74 -> 146[label="",style="dashed", color="magenta", weight=3];
74 -> 147[label="",style="dashed", color="magenta", weight=3];
333[label="yu310 : yu311 == yu40010 : yu40011\n",fontsize=16,color="black",shape="box"];333 -> 359[label="",style="solid", color="black", weight=3];
334[label="yu310 : yu311 == []\n",fontsize=16,color="black",shape="box"];334 -> 360[label="",style="solid", color="black", weight=3];
335[label="[] == yu40010 : yu40011\n",fontsize=16,color="black",shape="box"];335 -> 361[label="",style="solid", color="black", weight=3];
336[label="[] == []\n",fontsize=16,color="black",shape="box"];336 -> 362[label="",style="solid", color="black", weight=3];
337[label="primEqFloat yu30 yu4000\n",fontsize=16,color="burlywood",shape="box"];997[label="yu30/Float yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];337 -> 997[label="",style="solid", color="burlywood", weight=9];
997 -> 363[label="",style="solid", color="burlywood", weight=3];
338[label="(yu300,yu301) == yu4000\n",fontsize=16,color="burlywood",shape="box"];998[label="yu4000/(yu40000,yu40001)",fontsize=10,color="white",style="solid",shape="box"];338 -> 998[label="",style="solid", color="burlywood", weight=9];
998 -> 364[label="",style="solid", color="burlywood", weight=3];
339[label="(yu300,yu301,yu302) == yu4000\n",fontsize=16,color="burlywood",shape="box"];999[label="yu4000/(yu40000,yu40001,yu40002)",fontsize=10,color="white",style="solid",shape="box"];339 -> 999[label="",style="solid", color="burlywood", weight=9];
999 -> 365[label="",style="solid", color="burlywood", weight=3];
340[label="Left yu300 == yu4000\n",fontsize=16,color="burlywood",shape="box"];1000[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];340 -> 1000[label="",style="solid", color="burlywood", weight=9];
1000 -> 366[label="",style="solid", color="burlywood", weight=3];
1001[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];340 -> 1001[label="",style="solid", color="burlywood", weight=9];
1001 -> 367[label="",style="solid", color="burlywood", weight=3];
341[label="Right yu300 == yu4000\n",fontsize=16,color="burlywood",shape="box"];1002[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];341 -> 1002[label="",style="solid", color="burlywood", weight=9];
1002 -> 368[label="",style="solid", color="burlywood", weight=3];
1003[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];341 -> 1003[label="",style="solid", color="burlywood", weight=9];
1003 -> 369[label="",style="solid", color="burlywood", weight=3];
342[label="Integer yu300 == yu4000\n",fontsize=16,color="burlywood",shape="box"];1004[label="yu4000/Integer yu40000",fontsize=10,color="white",style="solid",shape="box"];342 -> 1004[label="",style="solid", color="burlywood", weight=9];
1004 -> 370[label="",style="solid", color="burlywood", weight=3];
343[label="primEqDouble yu30 yu4000\n",fontsize=16,color="burlywood",shape="box"];1005[label="yu30/Double yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];343 -> 1005[label="",style="solid", color="burlywood", weight=9];
1005 -> 371[label="",style="solid", color="burlywood", weight=3];
344[label="False == yu4000\n",fontsize=16,color="burlywood",shape="box"];1006[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];344 -> 1006[label="",style="solid", color="burlywood", weight=9];
1006 -> 372[label="",style="solid", color="burlywood", weight=3];
1007[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];344 -> 1007[label="",style="solid", color="burlywood", weight=9];
1007 -> 373[label="",style="solid", color="burlywood", weight=3];
345[label="True == yu4000\n",fontsize=16,color="burlywood",shape="box"];1008[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];345 -> 1008[label="",style="solid", color="burlywood", weight=9];
1008 -> 374[label="",style="solid", color="burlywood", weight=3];
1009[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];345 -> 1009[label="",style="solid", color="burlywood", weight=9];
1009 -> 375[label="",style="solid", color="burlywood", weight=3];
346[label="LT == yu4000\n",fontsize=16,color="burlywood",shape="box"];1010[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];346 -> 1010[label="",style="solid", color="burlywood", weight=9];
1010 -> 376[label="",style="solid", color="burlywood", weight=3];
1011[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];346 -> 1011[label="",style="solid", color="burlywood", weight=9];
1011 -> 377[label="",style="solid", color="burlywood", weight=3];
1012[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];346 -> 1012[label="",style="solid", color="burlywood", weight=9];
1012 -> 378[label="",style="solid", color="burlywood", weight=3];
347[label="EQ == yu4000\n",fontsize=16,color="burlywood",shape="box"];1013[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];347 -> 1013[label="",style="solid", color="burlywood", weight=9];
1013 -> 379[label="",style="solid", color="burlywood", weight=3];
1014[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];347 -> 1014[label="",style="solid", color="burlywood", weight=9];
1014 -> 380[label="",style="solid", color="burlywood", weight=3];
1015[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];347 -> 1015[label="",style="solid", color="burlywood", weight=9];
1015 -> 381[label="",style="solid", color="burlywood", weight=3];
348[label="GT == yu4000\n",fontsize=16,color="burlywood",shape="box"];1016[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];348 -> 1016[label="",style="solid", color="burlywood", weight=9];
1016 -> 382[label="",style="solid", color="burlywood", weight=3];
1017[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];348 -> 1017[label="",style="solid", color="burlywood", weight=9];
1017 -> 383[label="",style="solid", color="burlywood", weight=3];
1018[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];348 -> 1018[label="",style="solid", color="burlywood", weight=9];
1018 -> 384[label="",style="solid", color="burlywood", weight=3];
349[label="yu30\n",fontsize=16,color="green",shape="box"];350[label="yu4000\n",fontsize=16,color="green",shape="box"];351[label="primEqChar yu30 yu4000\n",fontsize=16,color="burlywood",shape="box"];1019[label="yu30/Char yu300",fontsize=10,color="white",style="solid",shape="box"];351 -> 1019[label="",style="solid", color="burlywood", weight=9];
1019 -> 385[label="",style="solid", color="burlywood", weight=3];
352[label="() == yu4000\n",fontsize=16,color="burlywood",shape="box"];1020[label="yu4000/()",fontsize=10,color="white",style="solid",shape="box"];352 -> 1020[label="",style="solid", color="burlywood", weight=9];
1020 -> 386[label="",style="solid", color="burlywood", weight=3];
353[label="yu300 :% yu301 == yu4000\n",fontsize=16,color="burlywood",shape="box"];1021[label="yu4000/yu40000 :% yu40001",fontsize=10,color="white",style="solid",shape="box"];353 -> 1021[label="",style="solid", color="burlywood", weight=9];
1021 -> 387[label="",style="solid", color="burlywood", weight=3];
354[label="Nothing == yu4000\n",fontsize=16,color="burlywood",shape="box"];1022[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];354 -> 1022[label="",style="solid", color="burlywood", weight=9];
1022 -> 388[label="",style="solid", color="burlywood", weight=3];
1023[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];354 -> 1023[label="",style="solid", color="burlywood", weight=9];
1023 -> 389[label="",style="solid", color="burlywood", weight=3];
355[label="Just yu300 == yu4000\n",fontsize=16,color="burlywood",shape="box"];1024[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];355 -> 1024[label="",style="solid", color="burlywood", weight=9];
1024 -> 390[label="",style="solid", color="burlywood", weight=3];
1025[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];355 -> 1025[label="",style="solid", color="burlywood", weight=9];
1025 -> 391[label="",style="solid", color="burlywood", weight=3];
356[label="primEqInt yu30 yu4000\n",fontsize=16,color="burlywood",shape="triangle"];1026[label="yu30/Pos yu300",fontsize=10,color="white",style="solid",shape="box"];356 -> 1026[label="",style="solid", color="burlywood", weight=9];
1026 -> 392[label="",style="solid", color="burlywood", weight=3];
1027[label="yu30/Neg yu300",fontsize=10,color="white",style="solid",shape="box"];356 -> 1027[label="",style="solid", color="burlywood", weight=9];
1027 -> 393[label="",style="solid", color="burlywood", weight=3];
357[label="False\n",fontsize=16,color="green",shape="box"];358[label="yu33\n",fontsize=16,color="green",shape="box"];172[label="lookup0 (yu13 : yu14) (yu15 : yu16) yu17 yu18 True\n",fontsize=16,color="black",shape="box"];172 -> 222[label="",style="solid", color="black", weight=3];
144[label="yu30 : yu31\n",fontsize=16,color="green",shape="box"];145[label="yu41\n",fontsize=16,color="green",shape="box"];146[label="[]\n",fontsize=16,color="green",shape="box"];147[label="yu41\n",fontsize=16,color="green",shape="box"];359 -> 310[label="",style="dashed", color="red", weight=0];
359[label="yu310 == yu40010 && yu311 == yu40011\n",fontsize=16,color="magenta"];359 -> 394[label="",style="dashed", color="magenta", weight=3];
359 -> 395[label="",style="dashed", color="magenta", weight=3];
360[label="False\n",fontsize=16,color="green",shape="box"];361[label="False\n",fontsize=16,color="green",shape="box"];362[label="True\n",fontsize=16,color="green",shape="box"];363[label="primEqFloat (Float yu300 yu301) yu4000\n",fontsize=16,color="burlywood",shape="box"];1029[label="yu4000/Float yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];363 -> 1029[label="",style="solid", color="burlywood", weight=9];
1029 -> 396[label="",style="solid", color="burlywood", weight=3];
364[label="(yu300,yu301) == (yu40000,yu40001)\n",fontsize=16,color="black",shape="box"];364 -> 397[label="",style="solid", color="black", weight=3];
365[label="(yu300,yu301,yu302) == (yu40000,yu40001,yu40002)\n",fontsize=16,color="black",shape="box"];365 -> 398[label="",style="solid", color="black", weight=3];
366[label="Left yu300 == Left yu40000\n",fontsize=16,color="black",shape="box"];366 -> 399[label="",style="solid", color="black", weight=3];
367[label="Left yu300 == Right yu40000\n",fontsize=16,color="black",shape="box"];367 -> 400[label="",style="solid", color="black", weight=3];
368[label="Right yu300 == Left yu40000\n",fontsize=16,color="black",shape="box"];368 -> 401[label="",style="solid", color="black", weight=3];
369[label="Right yu300 == Right yu40000\n",fontsize=16,color="black",shape="box"];369 -> 402[label="",style="solid", color="black", weight=3];
370[label="Integer yu300 == Integer yu40000\n",fontsize=16,color="black",shape="box"];370 -> 403[label="",style="solid", color="black", weight=3];
371[label="primEqDouble (Double yu300 yu301) yu4000\n",fontsize=16,color="burlywood",shape="box"];1030[label="yu4000/Double yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];371 -> 1030[label="",style="solid", color="burlywood", weight=9];
1030 -> 404[label="",style="solid", color="burlywood", weight=3];
372[label="False == False\n",fontsize=16,color="black",shape="box"];372 -> 405[label="",style="solid", color="black", weight=3];
373[label="False == True\n",fontsize=16,color="black",shape="box"];373 -> 406[label="",style="solid", color="black", weight=3];
374[label="True == False\n",fontsize=16,color="black",shape="box"];374 -> 407[label="",style="solid", color="black", weight=3];
375[label="True == True\n",fontsize=16,color="black",shape="box"];375 -> 408[label="",style="solid", color="black", weight=3];
376[label="LT == LT\n",fontsize=16,color="black",shape="box"];376 -> 409[label="",style="solid", color="black", weight=3];
377[label="LT == EQ\n",fontsize=16,color="black",shape="box"];377 -> 410[label="",style="solid", color="black", weight=3];
378[label="LT == GT\n",fontsize=16,color="black",shape="box"];378 -> 411[label="",style="solid", color="black", weight=3];
379[label="EQ == LT\n",fontsize=16,color="black",shape="box"];379 -> 412[label="",style="solid", color="black", weight=3];
380[label="EQ == EQ\n",fontsize=16,color="black",shape="box"];380 -> 413[label="",style="solid", color="black", weight=3];
381[label="EQ == GT\n",fontsize=16,color="black",shape="box"];381 -> 414[label="",style="solid", color="black", weight=3];
382[label="GT == LT\n",fontsize=16,color="black",shape="box"];382 -> 415[label="",style="solid", color="black", weight=3];
383[label="GT == EQ\n",fontsize=16,color="black",shape="box"];383 -> 416[label="",style="solid", color="black", weight=3];
384[label="GT == GT\n",fontsize=16,color="black",shape="box"];384 -> 417[label="",style="solid", color="black", weight=3];
385[label="primEqChar (Char yu300) yu4000\n",fontsize=16,color="burlywood",shape="box"];1031[label="yu4000/Char yu40000",fontsize=10,color="white",style="solid",shape="box"];385 -> 1031[label="",style="solid", color="burlywood", weight=9];
1031 -> 418[label="",style="solid", color="burlywood", weight=3];
386[label="() == ()\n",fontsize=16,color="black",shape="box"];386 -> 419[label="",style="solid", color="black", weight=3];
387[label="yu300 :% yu301 == yu40000 :% yu40001\n",fontsize=16,color="black",shape="box"];387 -> 420[label="",style="solid", color="black", weight=3];
388[label="Nothing == Nothing\n",fontsize=16,color="black",shape="box"];388 -> 421[label="",style="solid", color="black", weight=3];
389[label="Nothing == Just yu40000\n",fontsize=16,color="black",shape="box"];389 -> 422[label="",style="solid", color="black", weight=3];
390[label="Just yu300 == Nothing\n",fontsize=16,color="black",shape="box"];390 -> 423[label="",style="solid", color="black", weight=3];
391[label="Just yu300 == Just yu40000\n",fontsize=16,color="black",shape="box"];391 -> 424[label="",style="solid", color="black", weight=3];
392[label="primEqInt (Pos yu300) yu4000\n",fontsize=16,color="burlywood",shape="box"];1032[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];392 -> 1032[label="",style="solid", color="burlywood", weight=9];
1032 -> 425[label="",style="solid", color="burlywood", weight=3];
1033[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];392 -> 1033[label="",style="solid", color="burlywood", weight=9];
1033 -> 426[label="",style="solid", color="burlywood", weight=3];
393[label="primEqInt (Neg yu300) yu4000\n",fontsize=16,color="burlywood",shape="box"];1034[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];393 -> 1034[label="",style="solid", color="burlywood", weight=9];
1034 -> 427[label="",style="solid", color="burlywood", weight=3];
1035[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];393 -> 1035[label="",style="solid", color="burlywood", weight=9];
1035 -> 428[label="",style="solid", color="burlywood", weight=3];
222 -> 4[label="",style="dashed", color="red", weight=0];
222[label="lookup (yu13 : yu14) yu18\n",fontsize=16,color="magenta"];222 -> 288[label="",style="dashed", color="magenta", weight=3];
222 -> 289[label="",style="dashed", color="magenta", weight=3];
394 -> 311[label="",style="dashed", color="red", weight=0];
394[label="yu311 == yu40011\n",fontsize=16,color="magenta"];394 -> 429[label="",style="dashed", color="magenta", weight=3];
394 -> 430[label="",style="dashed", color="magenta", weight=3];
395[label="yu310 == yu40010\n",fontsize=16,color="blue",shape="box"];1038[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1038[label="",style="solid", color="blue", weight=9];
1038 -> 431[label="",style="solid", color="blue", weight=3];
1039[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1039[label="",style="solid", color="blue", weight=9];
1039 -> 432[label="",style="solid", color="blue", weight=3];
1040[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1040[label="",style="solid", color="blue", weight=9];
1040 -> 433[label="",style="solid", color="blue", weight=3];
1041[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1041[label="",style="solid", color="blue", weight=9];
1041 -> 434[label="",style="solid", color="blue", weight=3];
1042[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1042[label="",style="solid", color="blue", weight=9];
1042 -> 435[label="",style="solid", color="blue", weight=3];
1043[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1043[label="",style="solid", color="blue", weight=9];
1043 -> 436[label="",style="solid", color="blue", weight=3];
1044[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1044[label="",style="solid", color="blue", weight=9];
1044 -> 437[label="",style="solid", color="blue", weight=3];
1045[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1045[label="",style="solid", color="blue", weight=9];
1045 -> 438[label="",style="solid", color="blue", weight=3];
1046[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1046[label="",style="solid", color="blue", weight=9];
1046 -> 439[label="",style="solid", color="blue", weight=3];
1047[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1047[label="",style="solid", color="blue", weight=9];
1047 -> 440[label="",style="solid", color="blue", weight=3];
1048[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1048[label="",style="solid", color="blue", weight=9];
1048 -> 441[label="",style="solid", color="blue", weight=3];
1049[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1049[label="",style="solid", color="blue", weight=9];
1049 -> 442[label="",style="solid", color="blue", weight=3];
1050[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1050[label="",style="solid", color="blue", weight=9];
1050 -> 443[label="",style="solid", color="blue", weight=3];
1051[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];395 -> 1051[label="",style="solid", color="blue", weight=9];
1051 -> 444[label="",style="solid", color="blue", weight=3];
396[label="primEqFloat (Float yu300 yu301) (Float yu40000 yu40001)\n",fontsize=16,color="black",shape="box"];396 -> 445[label="",style="solid", color="black", weight=3];
397 -> 310[label="",style="dashed", color="red", weight=0];
397[label="yu300 == yu40000 && yu301 == yu40001\n",fontsize=16,color="magenta"];397 -> 446[label="",style="dashed", color="magenta", weight=3];
397 -> 447[label="",style="dashed", color="magenta", weight=3];
398 -> 310[label="",style="dashed", color="red", weight=0];
398[label="yu300 == yu40000 && yu301 == yu40001 && yu302 == yu40002\n",fontsize=16,color="magenta"];398 -> 448[label="",style="dashed", color="magenta", weight=3];
398 -> 449[label="",style="dashed", color="magenta", weight=3];
399[label="yu300 == yu40000\n",fontsize=16,color="blue",shape="box"];1054[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1054[label="",style="solid", color="blue", weight=9];
1054 -> 450[label="",style="solid", color="blue", weight=3];
1055[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1055[label="",style="solid", color="blue", weight=9];
1055 -> 451[label="",style="solid", color="blue", weight=3];
1056[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1056[label="",style="solid", color="blue", weight=9];
1056 -> 452[label="",style="solid", color="blue", weight=3];
1057[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1057[label="",style="solid", color="blue", weight=9];
1057 -> 453[label="",style="solid", color="blue", weight=3];
1058[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1058[label="",style="solid", color="blue", weight=9];
1058 -> 454[label="",style="solid", color="blue", weight=3];
1059[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1059[label="",style="solid", color="blue", weight=9];
1059 -> 455[label="",style="solid", color="blue", weight=3];
1060[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1060[label="",style="solid", color="blue", weight=9];
1060 -> 456[label="",style="solid", color="blue", weight=3];
1061[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1061[label="",style="solid", color="blue", weight=9];
1061 -> 457[label="",style="solid", color="blue", weight=3];
1062[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1062[label="",style="solid", color="blue", weight=9];
1062 -> 458[label="",style="solid", color="blue", weight=3];
1063[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1063[label="",style="solid", color="blue", weight=9];
1063 -> 459[label="",style="solid", color="blue", weight=3];
1064[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1064[label="",style="solid", color="blue", weight=9];
1064 -> 460[label="",style="solid", color="blue", weight=3];
1065[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1065[label="",style="solid", color="blue", weight=9];
1065 -> 461[label="",style="solid", color="blue", weight=3];
1066[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1066[label="",style="solid", color="blue", weight=9];
1066 -> 462[label="",style="solid", color="blue", weight=3];
1067[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];399 -> 1067[label="",style="solid", color="blue", weight=9];
1067 -> 463[label="",style="solid", color="blue", weight=3];
400[label="False\n",fontsize=16,color="green",shape="box"];401[label="False\n",fontsize=16,color="green",shape="box"];402[label="yu300 == yu40000\n",fontsize=16,color="blue",shape="box"];1068[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1068[label="",style="solid", color="blue", weight=9];
1068 -> 464[label="",style="solid", color="blue", weight=3];
1069[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1069[label="",style="solid", color="blue", weight=9];
1069 -> 465[label="",style="solid", color="blue", weight=3];
1070[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1070[label="",style="solid", color="blue", weight=9];
1070 -> 466[label="",style="solid", color="blue", weight=3];
1071[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1071[label="",style="solid", color="blue", weight=9];
1071 -> 467[label="",style="solid", color="blue", weight=3];
1072[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1072[label="",style="solid", color="blue", weight=9];
1072 -> 468[label="",style="solid", color="blue", weight=3];
1073[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1073[label="",style="solid", color="blue", weight=9];
1073 -> 469[label="",style="solid", color="blue", weight=3];
1074[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1074[label="",style="solid", color="blue", weight=9];
1074 -> 470[label="",style="solid", color="blue", weight=3];
1075[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1075[label="",style="solid", color="blue", weight=9];
1075 -> 471[label="",style="solid", color="blue", weight=3];
1076[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1076[label="",style="solid", color="blue", weight=9];
1076 -> 472[label="",style="solid", color="blue", weight=3];
1077[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1077[label="",style="solid", color="blue", weight=9];
1077 -> 473[label="",style="solid", color="blue", weight=3];
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1079[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];402 -> 1079[label="",style="solid", color="blue", weight=9];
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403 -> 356[label="",style="dashed", color="red", weight=0];
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1086[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1086[label="",style="solid", color="blue", weight=9];
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1088[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1088[label="",style="solid", color="blue", weight=9];
1088 -> 488[label="",style="solid", color="blue", weight=3];
1089[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1089[label="",style="solid", color="blue", weight=9];
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1090[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1090[label="",style="solid", color="blue", weight=9];
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1091[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1091[label="",style="solid", color="blue", weight=9];
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1092[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1092[label="",style="solid", color="blue", weight=9];
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1093[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1093[label="",style="solid", color="blue", weight=9];
1093 -> 493[label="",style="solid", color="blue", weight=3];
1094[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1094[label="",style="solid", color="blue", weight=9];
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1095[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1095[label="",style="solid", color="blue", weight=9];
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1097[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];424 -> 1097[label="",style="solid", color="blue", weight=9];
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1101[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];426 -> 1101[label="",style="solid", color="burlywood", weight=9];
1101 -> 501[label="",style="solid", color="burlywood", weight=3];
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1103[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];427 -> 1103[label="",style="solid", color="burlywood", weight=9];
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431 -> 507[label="",style="dashed", color="magenta", weight=3];
432 -> 318[label="",style="dashed", color="red", weight=0];
432[label="yu310 == yu40010\n",fontsize=16,color="magenta"];432 -> 508[label="",style="dashed", color="magenta", weight=3];
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433 -> 319[label="",style="dashed", color="red", weight=0];
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435 -> 321[label="",style="dashed", color="red", weight=0];
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436 -> 322[label="",style="dashed", color="red", weight=0];
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445 -> 330[label="",style="dashed", color="red", weight=0];
445[label="yu300 * yu40000 == yu301 * yu40001\n",fontsize=16,color="magenta"];445 -> 534[label="",style="dashed", color="magenta", weight=3];
445 -> 535[label="",style="dashed", color="magenta", weight=3];
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1121 -> 536[label="",style="solid", color="blue", weight=3];
1122[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1122[label="",style="solid", color="blue", weight=9];
1122 -> 537[label="",style="solid", color="blue", weight=3];
1123[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1123[label="",style="solid", color="blue", weight=9];
1123 -> 538[label="",style="solid", color="blue", weight=3];
1124[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1124[label="",style="solid", color="blue", weight=9];
1124 -> 539[label="",style="solid", color="blue", weight=3];
1125[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1125[label="",style="solid", color="blue", weight=9];
1125 -> 540[label="",style="solid", color="blue", weight=3];
1126[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1126[label="",style="solid", color="blue", weight=9];
1126 -> 541[label="",style="solid", color="blue", weight=3];
1127[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1127[label="",style="solid", color="blue", weight=9];
1127 -> 542[label="",style="solid", color="blue", weight=3];
1128[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1128[label="",style="solid", color="blue", weight=9];
1128 -> 543[label="",style="solid", color="blue", weight=3];
1129[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1129[label="",style="solid", color="blue", weight=9];
1129 -> 544[label="",style="solid", color="blue", weight=3];
1130[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1130[label="",style="solid", color="blue", weight=9];
1130 -> 545[label="",style="solid", color="blue", weight=3];
1131[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1131[label="",style="solid", color="blue", weight=9];
1131 -> 546[label="",style="solid", color="blue", weight=3];
1132[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1132[label="",style="solid", color="blue", weight=9];
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1134[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];446 -> 1134[label="",style="solid", color="blue", weight=9];
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1138[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1138[label="",style="solid", color="blue", weight=9];
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1139[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1139[label="",style="solid", color="blue", weight=9];
1139 -> 554[label="",style="solid", color="blue", weight=3];
1140[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1140[label="",style="solid", color="blue", weight=9];
1140 -> 555[label="",style="solid", color="blue", weight=3];
1141[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1141[label="",style="solid", color="blue", weight=9];
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1142[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1142[label="",style="solid", color="blue", weight=9];
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1143[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1143[label="",style="solid", color="blue", weight=9];
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1144[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1144[label="",style="solid", color="blue", weight=9];
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1145[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];447 -> 1145[label="",style="solid", color="blue", weight=9];
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1154[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];449 -> 1154[label="",style="solid", color="blue", weight=9];
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1155[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];449 -> 1155[label="",style="solid", color="blue", weight=9];
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1156[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];449 -> 1156[label="",style="solid", color="blue", weight=9];
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1157[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];449 -> 1157[label="",style="solid", color="blue", weight=9];
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1159[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];449 -> 1159[label="",style="solid", color="blue", weight=9];
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673[label="primEqInt (Pos (Succ yu3000)) (Pos Zero)\n",fontsize=16,color="black",shape="box"];673 -> 814[label="",style="solid", color="black", weight=3];
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676[label="primEqInt (Pos Zero) (Pos Zero)\n",fontsize=16,color="black",shape="box"];676 -> 816[label="",style="solid", color="black", weight=3];
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678[label="primEqInt (Pos Zero) (Neg Zero)\n",fontsize=16,color="black",shape="box"];678 -> 818[label="",style="solid", color="black", weight=3];
679[label="False\n",fontsize=16,color="green",shape="box"];680[label="primEqInt (Neg (Succ yu3000)) (Neg (Succ yu400000))\n",fontsize=16,color="black",shape="box"];680 -> 819[label="",style="solid", color="black", weight=3];
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683[label="primEqInt (Neg Zero) (Pos Zero)\n",fontsize=16,color="black",shape="box"];683 -> 822[label="",style="solid", color="black", weight=3];
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685[label="primEqInt (Neg Zero) (Neg Zero)\n",fontsize=16,color="black",shape="box"];685 -> 824[label="",style="solid", color="black", weight=3];
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896[label="Neg (primMulNat yu3000 yu400000)\n",fontsize=16,color="green",shape="box"];896 -> 904[label="",style="dashed", color="green", weight=3];
897[label="Neg (primMulNat yu3000 yu400000)\n",fontsize=16,color="green",shape="box"];897 -> 905[label="",style="dashed", color="green", weight=3];
898[label="Pos (primMulNat yu3000 yu400000)\n",fontsize=16,color="green",shape="box"];898 -> 906[label="",style="dashed", color="green", weight=3];
899 -> 813[label="",style="dashed", color="red", weight=0];
899[label="primEqNat yu30000 yu4000000\n",fontsize=16,color="magenta"];899 -> 907[label="",style="dashed", color="magenta", weight=3];
899 -> 908[label="",style="dashed", color="magenta", weight=3];
900[label="False\n",fontsize=16,color="green",shape="box"];901[label="False\n",fontsize=16,color="green",shape="box"];902[label="True\n",fontsize=16,color="green",shape="box"];903[label="primMulNat yu3000 yu400000\n",fontsize=16,color="burlywood",shape="triangle"];1343[label="yu3000/Succ yu30000",fontsize=10,color="white",style="solid",shape="box"];903 -> 1343[label="",style="solid", color="burlywood", weight=9];
1343 -> 909[label="",style="solid", color="burlywood", weight=3];
1344[label="yu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];903 -> 1344[label="",style="solid", color="burlywood", weight=9];
1344 -> 910[label="",style="solid", color="burlywood", weight=3];
904 -> 903[label="",style="dashed", color="red", weight=0];
904[label="primMulNat yu3000 yu400000\n",fontsize=16,color="magenta"];904 -> 911[label="",style="dashed", color="magenta", weight=3];
905 -> 903[label="",style="dashed", color="red", weight=0];
905[label="primMulNat yu3000 yu400000\n",fontsize=16,color="magenta"];905 -> 912[label="",style="dashed", color="magenta", weight=3];
906 -> 903[label="",style="dashed", color="red", weight=0];
906[label="primMulNat yu3000 yu400000\n",fontsize=16,color="magenta"];906 -> 913[label="",style="dashed", color="magenta", weight=3];
906 -> 914[label="",style="dashed", color="magenta", weight=3];
907[label="yu30000\n",fontsize=16,color="green",shape="box"];908[label="yu4000000\n",fontsize=16,color="green",shape="box"];909[label="primMulNat (Succ yu30000) yu400000\n",fontsize=16,color="burlywood",shape="box"];1348[label="yu400000/Succ yu4000000",fontsize=10,color="white",style="solid",shape="box"];909 -> 1348[label="",style="solid", color="burlywood", weight=9];
1348 -> 915[label="",style="solid", color="burlywood", weight=3];
1349[label="yu400000/Zero",fontsize=10,color="white",style="solid",shape="box"];909 -> 1349[label="",style="solid", color="burlywood", weight=9];
1349 -> 916[label="",style="solid", color="burlywood", weight=3];
910[label="primMulNat Zero yu400000\n",fontsize=16,color="burlywood",shape="box"];1350[label="yu400000/Succ yu4000000",fontsize=10,color="white",style="solid",shape="box"];910 -> 1350[label="",style="solid", color="burlywood", weight=9];
1350 -> 917[label="",style="solid", color="burlywood", weight=3];
1351[label="yu400000/Zero",fontsize=10,color="white",style="solid",shape="box"];910 -> 1351[label="",style="solid", color="burlywood", weight=9];
1351 -> 918[label="",style="solid", color="burlywood", weight=3];
911[label="yu400000\n",fontsize=16,color="green",shape="box"];912[label="yu3000\n",fontsize=16,color="green",shape="box"];913[label="yu3000\n",fontsize=16,color="green",shape="box"];914[label="yu400000\n",fontsize=16,color="green",shape="box"];915[label="primMulNat (Succ yu30000) (Succ yu4000000)\n",fontsize=16,color="black",shape="box"];915 -> 919[label="",style="solid", color="black", weight=3];
916[label="primMulNat (Succ yu30000) Zero\n",fontsize=16,color="black",shape="box"];916 -> 920[label="",style="solid", color="black", weight=3];
917[label="primMulNat Zero (Succ yu4000000)\n",fontsize=16,color="black",shape="box"];917 -> 921[label="",style="solid", color="black", weight=3];
918[label="primMulNat Zero Zero\n",fontsize=16,color="black",shape="box"];918 -> 922[label="",style="solid", color="black", weight=3];
919 -> 923[label="",style="dashed", color="red", weight=0];
919[label="primPlusNat (primMulNat yu30000 (Succ yu4000000)) (Succ yu4000000)\n",fontsize=16,color="magenta"];919 -> 924[label="",style="dashed", color="magenta", weight=3];
920[label="Zero\n",fontsize=16,color="green",shape="box"];921[label="Zero\n",fontsize=16,color="green",shape="box"];922[label="Zero\n",fontsize=16,color="green",shape="box"];924 -> 903[label="",style="dashed", color="red", weight=0];
924[label="primMulNat yu30000 (Succ yu4000000)\n",fontsize=16,color="magenta"];924 -> 925[label="",style="dashed", color="magenta", weight=3];
924 -> 926[label="",style="dashed", color="magenta", weight=3];
923[label="primPlusNat yu34 (Succ yu4000000)\n",fontsize=16,color="burlywood",shape="triangle"];1354[label="yu34/Succ yu340",fontsize=10,color="white",style="solid",shape="box"];923 -> 1354[label="",style="solid", color="burlywood", weight=9];
1354 -> 927[label="",style="solid", color="burlywood", weight=3];
1355[label="yu34/Zero",fontsize=10,color="white",style="solid",shape="box"];923 -> 1355[label="",style="solid", color="burlywood", weight=9];
1355 -> 928[label="",style="solid", color="burlywood", weight=3];
925[label="yu30000\n",fontsize=16,color="green",shape="box"];926[label="Succ yu4000000\n",fontsize=16,color="green",shape="box"];927[label="primPlusNat (Succ yu340) (Succ yu4000000)\n",fontsize=16,color="black",shape="box"];927 -> 929[label="",style="solid", color="black", weight=3];
928[label="primPlusNat Zero (Succ yu4000000)\n",fontsize=16,color="black",shape="box"];928 -> 930[label="",style="solid", color="black", weight=3];
929[label="Succ (Succ (primPlusNat yu340 yu4000000))\n",fontsize=16,color="green",shape="box"];929 -> 931[label="",style="dashed", color="green", weight=3];
930[label="Succ yu4000000\n",fontsize=16,color="green",shape="box"];931[label="primPlusNat yu340 yu4000000\n",fontsize=16,color="burlywood",shape="triangle"];1356[label="yu340/Succ yu3400",fontsize=10,color="white",style="solid",shape="box"];931 -> 1356[label="",style="solid", color="burlywood", weight=9];
1356 -> 932[label="",style="solid", color="burlywood", weight=3];
1357[label="yu340/Zero",fontsize=10,color="white",style="solid",shape="box"];931 -> 1357[label="",style="solid", color="burlywood", weight=9];
1357 -> 933[label="",style="solid", color="burlywood", weight=3];
932[label="primPlusNat (Succ yu3400) yu4000000\n",fontsize=16,color="burlywood",shape="box"];1358[label="yu4000000/Succ yu40000000",fontsize=10,color="white",style="solid",shape="box"];932 -> 1358[label="",style="solid", color="burlywood", weight=9];
1358 -> 934[label="",style="solid", color="burlywood", weight=3];
1359[label="yu4000000/Zero",fontsize=10,color="white",style="solid",shape="box"];932 -> 1359[label="",style="solid", color="burlywood", weight=9];
1359 -> 935[label="",style="solid", color="burlywood", weight=3];
933[label="primPlusNat Zero yu4000000\n",fontsize=16,color="burlywood",shape="box"];1360[label="yu4000000/Succ yu40000000",fontsize=10,color="white",style="solid",shape="box"];933 -> 1360[label="",style="solid", color="burlywood", weight=9];
1360 -> 936[label="",style="solid", color="burlywood", weight=3];
1361[label="yu4000000/Zero",fontsize=10,color="white",style="solid",shape="box"];933 -> 1361[label="",style="solid", color="burlywood", weight=9];
1361 -> 937[label="",style="solid", color="burlywood", weight=3];
934[label="primPlusNat (Succ yu3400) (Succ yu40000000)\n",fontsize=16,color="black",shape="box"];934 -> 938[label="",style="solid", color="black", weight=3];
935[label="primPlusNat (Succ yu3400) Zero\n",fontsize=16,color="black",shape="box"];935 -> 939[label="",style="solid", color="black", weight=3];
936[label="primPlusNat Zero (Succ yu40000000)\n",fontsize=16,color="black",shape="box"];936 -> 940[label="",style="solid", color="black", weight=3];
937[label="primPlusNat Zero Zero\n",fontsize=16,color="black",shape="box"];937 -> 941[label="",style="solid", color="black", weight=3];
938[label="Succ (Succ (primPlusNat yu3400 yu40000000))\n",fontsize=16,color="green",shape="box"];938 -> 942[label="",style="dashed", color="green", weight=3];
939[label="Succ yu3400\n",fontsize=16,color="green",shape="box"];940[label="Succ yu40000000\n",fontsize=16,color="green",shape="box"];941[label="Zero\n",fontsize=16,color="green",shape="box"];942 -> 931[label="",style="dashed", color="red", weight=0];
942[label="primPlusNat yu3400 yu40000000\n",fontsize=16,color="magenta"];942 -> 943[label="",style="dashed", color="magenta", weight=3];
942 -> 944[label="",style="dashed", color="magenta", weight=3];
943[label="yu40000000\n",fontsize=16,color="green",shape="box"];944[label="yu3400\n",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_primMulNat(Succ(yu30000), Succ(yu4000000)) → new_primMulNat(yu30000, Succ(yu4000000))

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_primMulNat(Succ(yu30000), Succ(yu4000000)) → new_primMulNat(yu30000, Succ(yu4000000))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_primPlusNat(Succ(yu3400), Succ(yu40000000)) → new_primPlusNat(yu3400, yu40000000)

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

new_primPlusNat(Succ(yu3400), Succ(yu40000000)) → new_primPlusNat(yu3400, yu40000000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                  ↳ QDP

                  ↳ QDP

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

new_lookup(:(yu30, yu31), :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup1(yu30, yu31, yu4000, yu4001, yu401, yu41, new_asAs(new_esEs5(yu30, yu4000, bc), new_esEs4(yu31, yu4001, bc)), bb, bc)
new_lookup(:(yu30, yu31), :(@2([], yu401), yu41), bb, bc) → new_lookup(:(yu30, yu31), yu41, bb, bc)
new_lookup1(yu13, yu14, yu15, yu16, yu17, yu18, False, h, ba) → new_lookup(:(yu13, yu14), yu18, h, ba)
new_lookup([], :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup([], yu41, bb, bc)

The TRS R consists of the following rules:

new_esEs7(Just(yu300), Just(yu40000), app(ty_Maybe, cf)) → new_esEs7(yu300, yu40000, cf)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs14(yu30, yu4000)
new_esEs21(yu310, yu40010, ty_Double) → new_esEs13(yu310, yu40010)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs7(Nothing, Just(yu40000), bd) → False
new_esEs7(Just(yu300), Nothing, bd) → False
new_esEs5(yu30, yu4000, app(app(app(ty_@3, ga), gb), gc)) → new_esEs10(yu30, yu4000, ga, gb, gc)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs12(yu30, yu4000)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs10(yu301, yu40001, bcf, bcg, bch)
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_esEs21(yu310, yu40010, app(app(ty_Either, ec), cg)) → new_esEs11(yu310, yu40010, ec, cg)
new_esEs23(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs10(yu300, yu40000, bbd, bbe, bbf)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs7(Just(yu300), Just(yu40000), ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs7(Just(yu300), Just(yu40000), ty_Double) → new_esEs13(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, ea), cg) → new_esEs17(yu300, yu40000, ea)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, cg) → new_esEs15(yu300, yu40000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs14(yu302, yu40002)
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_Ratio, fd)) → new_esEs17(yu300, yu40000, fd)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs13(yu301, yu40001)
new_esEs4(:(yu310, yu311), :(yu40010, yu40011), bc) → new_asAs(new_esEs21(yu310, yu40010, bc), new_esEs4(yu311, yu40011, bc))
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_[], fc)) → new_esEs4(yu300, yu40000, fc)
new_esEs26(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs23(yu301, yu40001, app(app(app(ty_@3, bab), bac), bad)) → new_esEs10(yu301, yu40001, bab, bac, bad)
new_esEs26(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs23(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_sr(Neg(yu3000), Pos(yu400000)) → Neg(new_primMulNat0(yu3000, yu400000))
new_sr(Pos(yu3000), Neg(yu400000)) → Neg(new_primMulNat0(yu3000, yu400000))
new_esEs5(yu30, yu4000, app(ty_Ratio, ge)) → new_esEs17(yu30, yu4000, ge)
new_esEs19(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_esEs5(yu30, yu4000, app(ty_[], gd)) → new_esEs4(yu30, yu4000, gd)
new_esEs13(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs18(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs20(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(ty_Either, fa), fb)) → new_esEs11(yu300, yu40000, fa, fb)
new_esEs23(yu301, yu40001, app(app(ty_@2, hh), baa)) → new_esEs9(yu301, yu40001, hh, baa)
new_esEs7(Just(yu300), Just(yu40000), app(app(ty_@2, be), bf)) → new_esEs9(yu300, yu40000, be, bf)
new_esEs23(yu301, yu40001, ty_Double) → new_esEs13(yu301, yu40001)
new_esEs21(yu310, yu40010, app(ty_Maybe, bd)) → new_esEs7(yu310, yu40010, bd)
new_esEs23(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs12(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs13(yu302, yu40002)
new_esEs26(yu300, yu40000, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, df), dg), cg) → new_esEs11(yu300, yu40000, df, dg)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, cg) → new_esEs13(yu300, yu40000)
new_primEqNat0(Zero, Succ(yu4000000)) → False
new_primEqNat0(Succ(yu30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(yu301, yu40001, app(ty_Ratio, bdd)) → new_esEs17(yu301, yu40001, bdd)
new_esEs24(yu300, yu40000, app(ty_[], bca)) → new_esEs4(yu300, yu40000, bca)
new_esEs5(yu30, yu4000, app(ty_Maybe, bd)) → new_esEs7(yu30, yu4000, bd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs15(Char(yu300), Char(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, gh), ha), hb)) → new_esEs10(yu302, yu40002, gh, ha, hb)
new_esEs26(yu300, yu40000, app(app(ty_Either, bec), bed)) → new_esEs11(yu300, yu40000, bec, bed)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(app(ty_@3, ef), eg), eh)) → new_esEs10(yu300, yu40000, ef, eg, eh)
new_esEs5(yu30, yu4000, app(app(ty_@2, fg), fh)) → new_esEs9(yu30, yu4000, fg, fh)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs8(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs6(yu30, yu4000)
new_esEs26(yu300, yu40000, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Char) → new_esEs15(yu300, yu40000)
new_primPlusNat1(Succ(yu340), yu4000000) → Succ(Succ(new_primPlusNat0(yu340, yu4000000)))
new_esEs26(yu300, yu40000, app(ty_Ratio, bef)) → new_esEs17(yu300, yu40000, bef)
new_esEs24(yu300, yu40000, app(ty_Maybe, bcc)) → new_esEs7(yu300, yu40000, bcc)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs12(yu302, yu40002)
new_esEs14(EQ, EQ) → True
new_esEs23(yu301, yu40001, app(ty_Maybe, bba)) → new_esEs7(yu301, yu40001, bba)
new_esEs14(LT, EQ) → False
new_esEs14(EQ, LT) → False
new_esEs23(yu301, yu40001, app(ty_Ratio, bah)) → new_esEs17(yu301, yu40001, bah)
new_esEs23(yu301, yu40001, app(app(ty_Either, bae), baf)) → new_esEs11(yu301, yu40001, bae, baf)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs6(yu302, yu40002)
new_esEs7(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs6(True, True) → True
new_esEs18(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_esEs7(Just(yu300), Just(yu40000), app(app(ty_Either, cb), cc)) → new_esEs11(yu300, yu40000, cb, cc)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs7(Just(yu300), Just(yu40000), ty_Char) → new_esEs15(yu300, yu40000)
new_esEs7(Just(yu300), Just(yu40000), app(ty_[], cd)) → new_esEs4(yu300, yu40000, cd)
new_esEs25(yu301, yu40001, app(ty_Maybe, bde)) → new_esEs7(yu301, yu40001, bde)
new_esEs17(:%(yu300, yu301), :%(yu40000, yu40001), ge) → new_asAs(new_esEs20(yu300, yu40000, ge), new_esEs19(yu301, yu40001, ge))
new_esEs7(Just(yu300), Just(yu40000), ty_Float) → new_esEs8(yu300, yu40000)
new_esEs14(EQ, GT) → False
new_esEs14(GT, EQ) → False
new_esEs21(yu310, yu40010, app(app(ty_@2, fg), fh)) → new_esEs9(yu310, yu40010, fg, fh)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs15(yu30, yu4000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, cg) → new_esEs6(yu300, yu40000)
new_esEs9(@2(yu300, yu301), @2(yu40000, yu40001), fg, fh) → new_asAs(new_esEs26(yu300, yu40000, fg), new_esEs25(yu301, yu40001, fh))
new_sr(Neg(yu3000), Neg(yu400000)) → Pos(new_primMulNat0(yu3000, yu400000))
new_esEs21(yu310, yu40010, app(ty_[], gd)) → new_esEs4(yu310, yu40010, gd)
new_esEs22(yu302, yu40002, app(app(ty_@2, gf), gg)) → new_esEs9(yu302, yu40002, gf, gg)
new_asAs(False, yu33) → False
new_sr(Pos(yu3000), Pos(yu400000)) → Pos(new_primMulNat0(yu3000, yu400000))
new_esEs23(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs18(yu302, yu40002)
new_primEqNat0(Zero, Zero) → True
new_esEs26(yu300, yu40000, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs23(yu301, yu40001, ty_Ordering) → new_esEs14(yu301, yu40001)
new_primMulNat0(Succ(yu30000), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000000)) → Zero
new_esEs24(yu300, yu40000, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_Bool) → new_esEs6(yu310, yu40010)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs5(yu30, yu4000, app(app(ty_Either, ec), cg)) → new_esEs11(yu30, yu4000, ec, cg)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_primMulNat0(Succ(yu30000), Succ(yu4000000)) → new_primPlusNat1(new_primMulNat0(yu30000, Succ(yu4000000)), yu4000000)
new_esEs26(yu300, yu40000, app(app(ty_@2, bdf), bdg)) → new_esEs9(yu300, yu40000, bdf, bdg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], dh), cg) → new_esEs4(yu300, yu40000, dh)
new_esEs26(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs26(yu300, yu40000, app(ty_Maybe, beg)) → new_esEs7(yu300, yu40000, beg)
new_esEs24(yu300, yu40000, app(ty_Ratio, bcb)) → new_esEs17(yu300, yu40000, bcb)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, dc), dd), de), cg) → new_esEs10(yu300, yu40000, dc, dd, de)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, cg) → new_esEs8(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_Maybe, ff)) → new_esEs7(yu300, yu40000, ff)
new_esEs14(LT, GT) → False
new_esEs14(GT, LT) → False
new_esEs16(@0, @0) → True
new_esEs14(GT, GT) → True
new_esEs22(yu302, yu40002, ty_Float) → new_esEs8(yu302, yu40002)
new_esEs26(yu300, yu40000, app(ty_[], bee)) → new_esEs4(yu300, yu40000, bee)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_@2, bcd), bce)) → new_esEs9(yu301, yu40001, bcd, bce)
new_esEs7(Just(yu300), Just(yu40000), ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Int) → new_esEs18(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs4([], [], bc) → True
new_esEs7(Just(yu300), Just(yu40000), ty_Int) → new_esEs18(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_@0) → new_esEs16(yu310, yu40010)
new_esEs7(Just(yu300), Just(yu40000), app(app(app(ty_@3, bg), bh), ca)) → new_esEs10(yu300, yu40000, bg, bh, ca)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, da), db), cg) → new_esEs9(yu300, yu40000, da, db)
new_esEs5(yu30, yu4000, ty_Int) → new_esEs18(yu30, yu4000)
new_esEs8(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs18(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs21(yu310, yu40010, ty_Char) → new_esEs15(yu310, yu40010)
new_esEs21(yu310, yu40010, ty_Ordering) → new_esEs14(yu310, yu40010)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs11(Left(yu300), Left(yu40000), ty_Int, cg) → new_esEs18(yu300, yu40000)
new_esEs19(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs7(Just(yu300), Just(yu40000), app(ty_Ratio, ce)) → new_esEs17(yu300, yu40000, ce)
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_esEs22(yu302, yu40002, app(ty_Ratio, hf)) → new_esEs17(yu302, yu40002, hf)
new_esEs24(yu300, yu40000, app(app(ty_@2, bbb), bbc)) → new_esEs9(yu300, yu40000, bbb, bbc)
new_primPlusNat1(Zero, yu4000000) → Succ(yu4000000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, cg) → new_esEs12(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_Double) → new_esEs13(yu30, yu4000)
new_esEs4([], :(yu40010, yu40011), bc) → False
new_esEs4(:(yu310, yu311), [], bc) → False
new_esEs5(yu30, yu4000, ty_Float) → new_esEs8(yu30, yu4000)
new_esEs21(yu310, yu40010, ty_Float) → new_esEs8(yu310, yu40010)
new_esEs23(yu301, yu40001, ty_Float) → new_esEs8(yu301, yu40001)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_Either, bda), bdb)) → new_esEs11(yu301, yu40001, bda, bdb)
new_primPlusNat0(Succ(yu3400), Succ(yu40000000)) → Succ(Succ(new_primPlusNat0(yu3400, yu40000000)))
new_esEs21(yu310, yu40010, app(app(app(ty_@3, ga), gb), gc)) → new_esEs10(yu310, yu40010, ga, gb, gc)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, cg) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(ty_@2, ed), ee)) → new_esEs9(yu300, yu40000, ed, ee)
new_esEs21(yu310, yu40010, app(ty_Ratio, ge)) → new_esEs17(yu310, yu40010, ge)
new_asAs(True, yu33) → yu33
new_esEs14(LT, LT) → True
new_esEs23(yu301, yu40001, ty_Bool) → new_esEs6(yu301, yu40001)
new_esEs22(yu302, yu40002, app(ty_[], he)) → new_esEs4(yu302, yu40002, he)
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs22(yu302, yu40002, app(app(ty_Either, hc), hd)) → new_esEs11(yu302, yu40002, hc, hd)
new_esEs6(True, False) → False
new_esEs6(False, True) → False
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs14(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs6(False, False) → True
new_esEs21(yu310, yu40010, ty_Integer) → new_esEs12(yu310, yu40010)
new_primEqNat0(Succ(yu30000), Succ(yu4000000)) → new_primEqNat0(yu30000, yu4000000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs6(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, cg) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs15(yu302, yu40002)
new_esEs24(yu300, yu40000, app(app(ty_Either, bbg), bbh)) → new_esEs11(yu300, yu40000, bbg, bbh)
new_esEs7(Nothing, Nothing, bd) → True
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, eb), cg) → new_esEs7(yu300, yu40000, eb)
new_esEs26(yu300, yu40000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs10(yu300, yu40000, bdh, bea, beb)
new_esEs10(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), ga, gb, gc) → new_asAs(new_esEs24(yu300, yu40000, ga), new_asAs(new_esEs23(yu301, yu40001, gb), new_esEs22(yu302, yu40002, gc)))
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(yu302, yu40002, app(ty_Maybe, hg)) → new_esEs7(yu302, yu40002, hg)
new_primPlusNat0(Zero, Succ(yu40000000)) → Succ(yu40000000)
new_primPlusNat0(Succ(yu3400), Zero) → Succ(yu3400)
new_esEs23(yu301, yu40001, app(ty_[], bag)) → new_esEs4(yu301, yu40001, bag)
new_esEs25(yu301, yu40001, app(ty_[], bdc)) → new_esEs4(yu301, yu40001, bdc)
new_esEs11(Right(yu300), Left(yu40000), ec, cg) → False
new_esEs11(Left(yu300), Right(yu40000), ec, cg) → False

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ UsableRulesProof

                        ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_lookup([], :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup([], yu41, bb, bc)

The TRS R consists of the following rules:

new_esEs7(Just(yu300), Just(yu40000), app(ty_Maybe, cf)) → new_esEs7(yu300, yu40000, cf)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs14(yu30, yu4000)
new_esEs21(yu310, yu40010, ty_Double) → new_esEs13(yu310, yu40010)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs7(Nothing, Just(yu40000), bd) → False
new_esEs7(Just(yu300), Nothing, bd) → False
new_esEs5(yu30, yu4000, app(app(app(ty_@3, ga), gb), gc)) → new_esEs10(yu30, yu4000, ga, gb, gc)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs12(yu30, yu4000)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs10(yu301, yu40001, bcf, bcg, bch)
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_esEs21(yu310, yu40010, app(app(ty_Either, ec), cg)) → new_esEs11(yu310, yu40010, ec, cg)
new_esEs23(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs10(yu300, yu40000, bbd, bbe, bbf)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs7(Just(yu300), Just(yu40000), ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs7(Just(yu300), Just(yu40000), ty_Double) → new_esEs13(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, ea), cg) → new_esEs17(yu300, yu40000, ea)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, cg) → new_esEs15(yu300, yu40000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs14(yu302, yu40002)
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_Ratio, fd)) → new_esEs17(yu300, yu40000, fd)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs13(yu301, yu40001)
new_esEs4(:(yu310, yu311), :(yu40010, yu40011), bc) → new_asAs(new_esEs21(yu310, yu40010, bc), new_esEs4(yu311, yu40011, bc))
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_[], fc)) → new_esEs4(yu300, yu40000, fc)
new_esEs26(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs23(yu301, yu40001, app(app(app(ty_@3, bab), bac), bad)) → new_esEs10(yu301, yu40001, bab, bac, bad)
new_esEs26(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs23(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_sr(Neg(yu3000), Pos(yu400000)) → Neg(new_primMulNat0(yu3000, yu400000))
new_sr(Pos(yu3000), Neg(yu400000)) → Neg(new_primMulNat0(yu3000, yu400000))
new_esEs5(yu30, yu4000, app(ty_Ratio, ge)) → new_esEs17(yu30, yu4000, ge)
new_esEs19(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_esEs5(yu30, yu4000, app(ty_[], gd)) → new_esEs4(yu30, yu4000, gd)
new_esEs13(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs18(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs20(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(ty_Either, fa), fb)) → new_esEs11(yu300, yu40000, fa, fb)
new_esEs23(yu301, yu40001, app(app(ty_@2, hh), baa)) → new_esEs9(yu301, yu40001, hh, baa)
new_esEs7(Just(yu300), Just(yu40000), app(app(ty_@2, be), bf)) → new_esEs9(yu300, yu40000, be, bf)
new_esEs23(yu301, yu40001, ty_Double) → new_esEs13(yu301, yu40001)
new_esEs21(yu310, yu40010, app(ty_Maybe, bd)) → new_esEs7(yu310, yu40010, bd)
new_esEs23(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs12(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs13(yu302, yu40002)
new_esEs26(yu300, yu40000, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, df), dg), cg) → new_esEs11(yu300, yu40000, df, dg)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, cg) → new_esEs13(yu300, yu40000)
new_primEqNat0(Zero, Succ(yu4000000)) → False
new_primEqNat0(Succ(yu30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(yu301, yu40001, app(ty_Ratio, bdd)) → new_esEs17(yu301, yu40001, bdd)
new_esEs24(yu300, yu40000, app(ty_[], bca)) → new_esEs4(yu300, yu40000, bca)
new_esEs5(yu30, yu4000, app(ty_Maybe, bd)) → new_esEs7(yu30, yu4000, bd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs15(Char(yu300), Char(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, gh), ha), hb)) → new_esEs10(yu302, yu40002, gh, ha, hb)
new_esEs26(yu300, yu40000, app(app(ty_Either, bec), bed)) → new_esEs11(yu300, yu40000, bec, bed)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(app(ty_@3, ef), eg), eh)) → new_esEs10(yu300, yu40000, ef, eg, eh)
new_esEs5(yu30, yu4000, app(app(ty_@2, fg), fh)) → new_esEs9(yu30, yu4000, fg, fh)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs8(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs6(yu30, yu4000)
new_esEs26(yu300, yu40000, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Char) → new_esEs15(yu300, yu40000)
new_primPlusNat1(Succ(yu340), yu4000000) → Succ(Succ(new_primPlusNat0(yu340, yu4000000)))
new_esEs26(yu300, yu40000, app(ty_Ratio, bef)) → new_esEs17(yu300, yu40000, bef)
new_esEs24(yu300, yu40000, app(ty_Maybe, bcc)) → new_esEs7(yu300, yu40000, bcc)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs12(yu302, yu40002)
new_esEs14(EQ, EQ) → True
new_esEs23(yu301, yu40001, app(ty_Maybe, bba)) → new_esEs7(yu301, yu40001, bba)
new_esEs14(LT, EQ) → False
new_esEs14(EQ, LT) → False
new_esEs23(yu301, yu40001, app(ty_Ratio, bah)) → new_esEs17(yu301, yu40001, bah)
new_esEs23(yu301, yu40001, app(app(ty_Either, bae), baf)) → new_esEs11(yu301, yu40001, bae, baf)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs6(yu302, yu40002)
new_esEs7(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs6(True, True) → True
new_esEs18(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_esEs7(Just(yu300), Just(yu40000), app(app(ty_Either, cb), cc)) → new_esEs11(yu300, yu40000, cb, cc)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs7(Just(yu300), Just(yu40000), ty_Char) → new_esEs15(yu300, yu40000)
new_esEs7(Just(yu300), Just(yu40000), app(ty_[], cd)) → new_esEs4(yu300, yu40000, cd)
new_esEs25(yu301, yu40001, app(ty_Maybe, bde)) → new_esEs7(yu301, yu40001, bde)
new_esEs17(:%(yu300, yu301), :%(yu40000, yu40001), ge) → new_asAs(new_esEs20(yu300, yu40000, ge), new_esEs19(yu301, yu40001, ge))
new_esEs7(Just(yu300), Just(yu40000), ty_Float) → new_esEs8(yu300, yu40000)
new_esEs14(EQ, GT) → False
new_esEs14(GT, EQ) → False
new_esEs21(yu310, yu40010, app(app(ty_@2, fg), fh)) → new_esEs9(yu310, yu40010, fg, fh)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs15(yu30, yu4000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, cg) → new_esEs6(yu300, yu40000)
new_esEs9(@2(yu300, yu301), @2(yu40000, yu40001), fg, fh) → new_asAs(new_esEs26(yu300, yu40000, fg), new_esEs25(yu301, yu40001, fh))
new_sr(Neg(yu3000), Neg(yu400000)) → Pos(new_primMulNat0(yu3000, yu400000))
new_esEs21(yu310, yu40010, app(ty_[], gd)) → new_esEs4(yu310, yu40010, gd)
new_esEs22(yu302, yu40002, app(app(ty_@2, gf), gg)) → new_esEs9(yu302, yu40002, gf, gg)
new_asAs(False, yu33) → False
new_sr(Pos(yu3000), Pos(yu400000)) → Pos(new_primMulNat0(yu3000, yu400000))
new_esEs23(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs18(yu302, yu40002)
new_primEqNat0(Zero, Zero) → True
new_esEs26(yu300, yu40000, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs23(yu301, yu40001, ty_Ordering) → new_esEs14(yu301, yu40001)
new_primMulNat0(Succ(yu30000), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000000)) → Zero
new_esEs24(yu300, yu40000, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_Bool) → new_esEs6(yu310, yu40010)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs5(yu30, yu4000, app(app(ty_Either, ec), cg)) → new_esEs11(yu30, yu4000, ec, cg)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_primMulNat0(Succ(yu30000), Succ(yu4000000)) → new_primPlusNat1(new_primMulNat0(yu30000, Succ(yu4000000)), yu4000000)
new_esEs26(yu300, yu40000, app(app(ty_@2, bdf), bdg)) → new_esEs9(yu300, yu40000, bdf, bdg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], dh), cg) → new_esEs4(yu300, yu40000, dh)
new_esEs26(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs26(yu300, yu40000, app(ty_Maybe, beg)) → new_esEs7(yu300, yu40000, beg)
new_esEs24(yu300, yu40000, app(ty_Ratio, bcb)) → new_esEs17(yu300, yu40000, bcb)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, dc), dd), de), cg) → new_esEs10(yu300, yu40000, dc, dd, de)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, cg) → new_esEs8(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_Maybe, ff)) → new_esEs7(yu300, yu40000, ff)
new_esEs14(LT, GT) → False
new_esEs14(GT, LT) → False
new_esEs16(@0, @0) → True
new_esEs14(GT, GT) → True
new_esEs22(yu302, yu40002, ty_Float) → new_esEs8(yu302, yu40002)
new_esEs26(yu300, yu40000, app(ty_[], bee)) → new_esEs4(yu300, yu40000, bee)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_@2, bcd), bce)) → new_esEs9(yu301, yu40001, bcd, bce)
new_esEs7(Just(yu300), Just(yu40000), ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Int) → new_esEs18(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs4([], [], bc) → True
new_esEs7(Just(yu300), Just(yu40000), ty_Int) → new_esEs18(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_@0) → new_esEs16(yu310, yu40010)
new_esEs7(Just(yu300), Just(yu40000), app(app(app(ty_@3, bg), bh), ca)) → new_esEs10(yu300, yu40000, bg, bh, ca)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, da), db), cg) → new_esEs9(yu300, yu40000, da, db)
new_esEs5(yu30, yu4000, ty_Int) → new_esEs18(yu30, yu4000)
new_esEs8(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs18(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs21(yu310, yu40010, ty_Char) → new_esEs15(yu310, yu40010)
new_esEs21(yu310, yu40010, ty_Ordering) → new_esEs14(yu310, yu40010)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs11(Left(yu300), Left(yu40000), ty_Int, cg) → new_esEs18(yu300, yu40000)
new_esEs19(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs7(Just(yu300), Just(yu40000), app(ty_Ratio, ce)) → new_esEs17(yu300, yu40000, ce)
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_esEs22(yu302, yu40002, app(ty_Ratio, hf)) → new_esEs17(yu302, yu40002, hf)
new_esEs24(yu300, yu40000, app(app(ty_@2, bbb), bbc)) → new_esEs9(yu300, yu40000, bbb, bbc)
new_primPlusNat1(Zero, yu4000000) → Succ(yu4000000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, cg) → new_esEs12(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_Double) → new_esEs13(yu30, yu4000)
new_esEs4([], :(yu40010, yu40011), bc) → False
new_esEs4(:(yu310, yu311), [], bc) → False
new_esEs5(yu30, yu4000, ty_Float) → new_esEs8(yu30, yu4000)
new_esEs21(yu310, yu40010, ty_Float) → new_esEs8(yu310, yu40010)
new_esEs23(yu301, yu40001, ty_Float) → new_esEs8(yu301, yu40001)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_Either, bda), bdb)) → new_esEs11(yu301, yu40001, bda, bdb)
new_primPlusNat0(Succ(yu3400), Succ(yu40000000)) → Succ(Succ(new_primPlusNat0(yu3400, yu40000000)))
new_esEs21(yu310, yu40010, app(app(app(ty_@3, ga), gb), gc)) → new_esEs10(yu310, yu40010, ga, gb, gc)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, cg) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(ty_@2, ed), ee)) → new_esEs9(yu300, yu40000, ed, ee)
new_esEs21(yu310, yu40010, app(ty_Ratio, ge)) → new_esEs17(yu310, yu40010, ge)
new_asAs(True, yu33) → yu33
new_esEs14(LT, LT) → True
new_esEs23(yu301, yu40001, ty_Bool) → new_esEs6(yu301, yu40001)
new_esEs22(yu302, yu40002, app(ty_[], he)) → new_esEs4(yu302, yu40002, he)
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs22(yu302, yu40002, app(app(ty_Either, hc), hd)) → new_esEs11(yu302, yu40002, hc, hd)
new_esEs6(True, False) → False
new_esEs6(False, True) → False
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs14(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs6(False, False) → True
new_esEs21(yu310, yu40010, ty_Integer) → new_esEs12(yu310, yu40010)
new_primEqNat0(Succ(yu30000), Succ(yu4000000)) → new_primEqNat0(yu30000, yu4000000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs6(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, cg) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs15(yu302, yu40002)
new_esEs24(yu300, yu40000, app(app(ty_Either, bbg), bbh)) → new_esEs11(yu300, yu40000, bbg, bbh)
new_esEs7(Nothing, Nothing, bd) → True
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, eb), cg) → new_esEs7(yu300, yu40000, eb)
new_esEs26(yu300, yu40000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs10(yu300, yu40000, bdh, bea, beb)
new_esEs10(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), ga, gb, gc) → new_asAs(new_esEs24(yu300, yu40000, ga), new_asAs(new_esEs23(yu301, yu40001, gb), new_esEs22(yu302, yu40002, gc)))
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(yu302, yu40002, app(ty_Maybe, hg)) → new_esEs7(yu302, yu40002, hg)
new_primPlusNat0(Zero, Succ(yu40000000)) → Succ(yu40000000)
new_primPlusNat0(Succ(yu3400), Zero) → Succ(yu3400)
new_esEs23(yu301, yu40001, app(ty_[], bag)) → new_esEs4(yu301, yu40001, bag)
new_esEs25(yu301, yu40001, app(ty_[], bdc)) → new_esEs4(yu301, yu40001, bdc)
new_esEs11(Right(yu300), Left(yu40000), ec, cg) → False
new_esEs11(Left(yu300), Right(yu40000), ec, cg) → False

The set Q consists of the following terms:

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

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

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

                        ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_lookup([], :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup([], yu41, bb, bc)

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

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

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_esEs21(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Char, x2)
new_esEs4([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs14(GT, EQ)
new_esEs14(EQ, GT)
new_esEs5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs22(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs21(x0, x1, ty_Float)
new_esEs11(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs5(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Ordering)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs11(Left(x0), Left(x1), ty_Int, x2)
new_esEs11(Right(x0), Right(x1), x2, ty_Int)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs11(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs11(Right(x0), Right(x1), x2, ty_Char)
new_esEs11(Left(x0), Left(x1), ty_@0, x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(@0, @0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs5(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(GT, LT)
new_esEs14(LT, GT)
new_esEs20(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_esEs24(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, ty_Int)
new_esEs11(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs11(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs26(x0, x1, ty_Int)
new_esEs11(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqNat0(Zero, Zero)
new_esEs4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(False, False)
new_esEs21(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Float)
new_asAs(False, x0)
new_esEs11(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Zero)
new_esEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, ty_Integer)
new_esEs11(Right(x0), Right(x1), x2, ty_Double)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_sr(Neg(x0), Neg(x1))
new_esEs23(x0, x1, ty_Float)
new_esEs5(x0, x1, ty_Integer)
new_esEs11(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs11(Left(x0), Left(x1), ty_Double, x2)
new_esEs11(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs11(Left(x0), Left(x1), ty_Bool, x2)
new_primPlusNat1(Zero, x0)
new_esEs22(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs25(x0, x1, ty_Int)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs25(x0, x1, ty_Ordering)
new_esEs11(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(LT, EQ)
new_esEs14(EQ, LT)
new_esEs11(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Int)
new_esEs14(GT, GT)
new_esEs21(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4([], :(x0, x1), x2)
new_esEs11(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_sr(Pos(x0), Pos(x1))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs14(EQ, EQ)
new_esEs24(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat0(Zero, Zero)
new_esEs5(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs14(LT, LT)
new_esEs6(True, True)
new_primPlusNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Int)
new_esEs11(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(Float(x0, x1), Float(x2, x3))
new_esEs25(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs7(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Nothing, Nothing, x0)
new_esEs6(False, True)
new_esEs6(True, False)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs15(Char(x0), Char(x1))
new_esEs12(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs11(Right(x0), Left(x1), x2, x3)
new_esEs11(Left(x0), Right(x1), x2, x3)
new_esEs25(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Char)
new_esEs11(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs11(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs18(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                          ↳ UsableRulesProof

                            ↳ QDP

                              ↳ QReductionProof

                                ↳ QDP

                                  ↳ QDPSizeChangeProof

                        ↳ QDP

                  ↳ QDP

                  ↳ QDP

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

new_lookup([], :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup([], yu41, bb, bc)

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

new_lookup([], :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup([], yu41, bb, bc)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ DependencyGraphProof

                      ↳ AND

                        ↳ QDP

                        ↳ QDP

                          ↳ QDPSizeChangeProof

                  ↳ QDP

                  ↳ QDP

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

new_lookup(:(yu30, yu31), :(@2([], yu401), yu41), bb, bc) → new_lookup(:(yu30, yu31), yu41, bb, bc)
new_lookup(:(yu30, yu31), :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup1(yu30, yu31, yu4000, yu4001, yu401, yu41, new_asAs(new_esEs5(yu30, yu4000, bc), new_esEs4(yu31, yu4001, bc)), bb, bc)
new_lookup1(yu13, yu14, yu15, yu16, yu17, yu18, False, h, ba) → new_lookup(:(yu13, yu14), yu18, h, ba)

The TRS R consists of the following rules:

new_esEs7(Just(yu300), Just(yu40000), app(ty_Maybe, cf)) → new_esEs7(yu300, yu40000, cf)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs14(yu30, yu4000)
new_esEs21(yu310, yu40010, ty_Double) → new_esEs13(yu310, yu40010)
new_esEs25(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) → False
new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) → False
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs7(Nothing, Just(yu40000), bd) → False
new_esEs7(Just(yu300), Nothing, bd) → False
new_esEs5(yu30, yu4000, app(app(app(ty_@3, ga), gb), gc)) → new_esEs10(yu30, yu4000, ga, gb, gc)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs12(yu30, yu4000)
new_esEs25(yu301, yu40001, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs10(yu301, yu40001, bcf, bcg, bch)
new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) → False
new_esEs21(yu310, yu40010, app(app(ty_Either, ec), cg)) → new_esEs11(yu310, yu40010, ec, cg)
new_esEs23(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs24(yu300, yu40000, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs10(yu300, yu40000, bbd, bbe, bbf)
new_esEs22(yu302, yu40002, ty_@0) → new_esEs16(yu302, yu40002)
new_esEs7(Just(yu300), Just(yu40000), ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs7(Just(yu300), Just(yu40000), ty_Double) → new_esEs13(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(ty_Ratio, ea), cg) → new_esEs17(yu300, yu40000, ea)
new_esEs11(Left(yu300), Left(yu40000), ty_Char, cg) → new_esEs15(yu300, yu40000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs7(Just(yu300), Just(yu40000), ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Ordering) → new_esEs14(yu302, yu40002)
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_Ratio, fd)) → new_esEs17(yu300, yu40000, fd)
new_esEs25(yu301, yu40001, ty_Double) → new_esEs13(yu301, yu40001)
new_esEs4(:(yu310, yu311), :(yu40010, yu40011), bc) → new_asAs(new_esEs21(yu310, yu40010, bc), new_esEs4(yu311, yu40011, bc))
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_[], fc)) → new_esEs4(yu300, yu40000, fc)
new_esEs26(yu300, yu40000, ty_Char) → new_esEs15(yu300, yu40000)
new_esEs23(yu301, yu40001, app(app(app(ty_@3, bab), bac), bad)) → new_esEs10(yu301, yu40001, bab, bac, bad)
new_esEs26(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs23(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_sr(Neg(yu3000), Pos(yu400000)) → Neg(new_primMulNat0(yu3000, yu400000))
new_sr(Pos(yu3000), Neg(yu400000)) → Neg(new_primMulNat0(yu3000, yu400000))
new_esEs5(yu30, yu4000, app(ty_Ratio, ge)) → new_esEs17(yu30, yu4000, ge)
new_esEs19(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_esEs5(yu30, yu4000, app(ty_[], gd)) → new_esEs4(yu30, yu4000, gd)
new_esEs13(Double(yu300, yu301), Double(yu40000, yu40001)) → new_esEs18(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs20(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(ty_Either, fa), fb)) → new_esEs11(yu300, yu40000, fa, fb)
new_esEs23(yu301, yu40001, app(app(ty_@2, hh), baa)) → new_esEs9(yu301, yu40001, hh, baa)
new_esEs7(Just(yu300), Just(yu40000), app(app(ty_@2, be), bf)) → new_esEs9(yu300, yu40000, be, bf)
new_esEs23(yu301, yu40001, ty_Double) → new_esEs13(yu301, yu40001)
new_esEs21(yu310, yu40010, app(ty_Maybe, bd)) → new_esEs7(yu310, yu40010, bd)
new_esEs23(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs12(Integer(yu300), Integer(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Double) → new_esEs13(yu302, yu40002)
new_esEs26(yu300, yu40000, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_Either, df), dg), cg) → new_esEs11(yu300, yu40000, df, dg)
new_esEs11(Left(yu300), Left(yu40000), ty_Double, cg) → new_esEs13(yu300, yu40000)
new_primEqNat0(Zero, Succ(yu4000000)) → False
new_primEqNat0(Succ(yu30000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(yu301, yu40001, app(ty_Ratio, bdd)) → new_esEs17(yu301, yu40001, bdd)
new_esEs24(yu300, yu40000, app(ty_[], bca)) → new_esEs4(yu300, yu40000, bca)
new_esEs5(yu30, yu4000, app(ty_Maybe, bd)) → new_esEs7(yu30, yu4000, bd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs15(Char(yu300), Char(yu40000)) → new_primEqInt(yu300, yu40000)
new_esEs22(yu302, yu40002, app(app(app(ty_@3, gh), ha), hb)) → new_esEs10(yu302, yu40002, gh, ha, hb)
new_esEs26(yu300, yu40000, app(app(ty_Either, bec), bed)) → new_esEs11(yu300, yu40000, bec, bed)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(app(ty_@3, ef), eg), eh)) → new_esEs10(yu300, yu40000, ef, eg, eh)
new_esEs5(yu30, yu4000, app(app(ty_@2, fg), fh)) → new_esEs9(yu30, yu4000, fg, fh)
new_esEs25(yu301, yu40001, ty_Float) → new_esEs8(yu301, yu40001)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs6(yu30, yu4000)
new_esEs26(yu300, yu40000, ty_Ordering) → new_esEs14(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Char) → new_esEs15(yu300, yu40000)
new_primPlusNat1(Succ(yu340), yu4000000) → Succ(Succ(new_primPlusNat0(yu340, yu4000000)))
new_esEs26(yu300, yu40000, app(ty_Ratio, bef)) → new_esEs17(yu300, yu40000, bef)
new_esEs24(yu300, yu40000, app(ty_Maybe, bcc)) → new_esEs7(yu300, yu40000, bcc)
new_esEs22(yu302, yu40002, ty_Integer) → new_esEs12(yu302, yu40002)
new_esEs14(EQ, EQ) → True
new_esEs23(yu301, yu40001, app(ty_Maybe, bba)) → new_esEs7(yu301, yu40001, bba)
new_esEs14(LT, EQ) → False
new_esEs14(EQ, LT) → False
new_esEs23(yu301, yu40001, app(ty_Ratio, bah)) → new_esEs17(yu301, yu40001, bah)
new_esEs23(yu301, yu40001, app(app(ty_Either, bae), baf)) → new_esEs11(yu301, yu40001, bae, baf)
new_esEs22(yu302, yu40002, ty_Bool) → new_esEs6(yu302, yu40002)
new_esEs7(Just(yu300), Just(yu40000), ty_@0) → new_esEs16(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs6(True, True) → True
new_esEs18(yu30, yu4000) → new_primEqInt(yu30, yu4000)
new_esEs7(Just(yu300), Just(yu40000), app(app(ty_Either, cb), cc)) → new_esEs11(yu300, yu40000, cb, cc)
new_esEs24(yu300, yu40000, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs16(yu30, yu4000)
new_esEs7(Just(yu300), Just(yu40000), ty_Char) → new_esEs15(yu300, yu40000)
new_esEs7(Just(yu300), Just(yu40000), app(ty_[], cd)) → new_esEs4(yu300, yu40000, cd)
new_esEs25(yu301, yu40001, app(ty_Maybe, bde)) → new_esEs7(yu301, yu40001, bde)
new_esEs17(:%(yu300, yu301), :%(yu40000, yu40001), ge) → new_asAs(new_esEs20(yu300, yu40000, ge), new_esEs19(yu301, yu40001, ge))
new_esEs7(Just(yu300), Just(yu40000), ty_Float) → new_esEs8(yu300, yu40000)
new_esEs14(EQ, GT) → False
new_esEs14(GT, EQ) → False
new_esEs21(yu310, yu40010, app(app(ty_@2, fg), fh)) → new_esEs9(yu310, yu40010, fg, fh)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs15(yu30, yu4000)
new_esEs11(Left(yu300), Left(yu40000), ty_Bool, cg) → new_esEs6(yu300, yu40000)
new_esEs9(@2(yu300, yu301), @2(yu40000, yu40001), fg, fh) → new_asAs(new_esEs26(yu300, yu40000, fg), new_esEs25(yu301, yu40001, fh))
new_sr(Neg(yu3000), Neg(yu400000)) → Pos(new_primMulNat0(yu3000, yu400000))
new_esEs21(yu310, yu40010, app(ty_[], gd)) → new_esEs4(yu310, yu40010, gd)
new_esEs22(yu302, yu40002, app(app(ty_@2, gf), gg)) → new_esEs9(yu302, yu40002, gf, gg)
new_asAs(False, yu33) → False
new_sr(Pos(yu3000), Pos(yu400000)) → Pos(new_primMulNat0(yu3000, yu400000))
new_esEs23(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_esEs22(yu302, yu40002, ty_Int) → new_esEs18(yu302, yu40002)
new_primEqNat0(Zero, Zero) → True
new_esEs26(yu300, yu40000, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs23(yu301, yu40001, ty_Ordering) → new_esEs14(yu301, yu40001)
new_primMulNat0(Succ(yu30000), Zero) → Zero
new_primMulNat0(Zero, Succ(yu4000000)) → Zero
new_esEs24(yu300, yu40000, ty_Double) → new_esEs13(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_Bool) → new_esEs6(yu310, yu40010)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Bool) → new_esEs6(yu300, yu40000)
new_esEs5(yu30, yu4000, app(app(ty_Either, ec), cg)) → new_esEs11(yu30, yu4000, ec, cg)
new_esEs25(yu301, yu40001, ty_@0) → new_esEs16(yu301, yu40001)
new_primMulNat0(Succ(yu30000), Succ(yu4000000)) → new_primPlusNat1(new_primMulNat0(yu30000, Succ(yu4000000)), yu4000000)
new_esEs26(yu300, yu40000, app(app(ty_@2, bdf), bdg)) → new_esEs9(yu300, yu40000, bdf, bdg)
new_esEs11(Left(yu300), Left(yu40000), app(ty_[], dh), cg) → new_esEs4(yu300, yu40000, dh)
new_esEs26(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs26(yu300, yu40000, app(ty_Maybe, beg)) → new_esEs7(yu300, yu40000, beg)
new_esEs24(yu300, yu40000, app(ty_Ratio, bcb)) → new_esEs17(yu300, yu40000, bcb)
new_esEs11(Left(yu300), Left(yu40000), app(app(app(ty_@3, dc), dd), de), cg) → new_esEs10(yu300, yu40000, dc, dd, de)
new_esEs11(Left(yu300), Left(yu40000), ty_Float, cg) → new_esEs8(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(ty_Maybe, ff)) → new_esEs7(yu300, yu40000, ff)
new_esEs14(LT, GT) → False
new_esEs14(GT, LT) → False
new_esEs16(@0, @0) → True
new_esEs14(GT, GT) → True
new_esEs22(yu302, yu40002, ty_Float) → new_esEs8(yu302, yu40002)
new_esEs26(yu300, yu40000, app(ty_[], bee)) → new_esEs4(yu300, yu40000, bee)
new_esEs20(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_@2, bcd), bce)) → new_esEs9(yu301, yu40001, bcd, bce)
new_esEs7(Just(yu300), Just(yu40000), ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs26(yu300, yu40000, ty_Integer) → new_esEs12(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Int) → new_esEs18(yu300, yu40000)
new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs4([], [], bc) → True
new_esEs7(Just(yu300), Just(yu40000), ty_Int) → new_esEs18(yu300, yu40000)
new_esEs21(yu310, yu40010, ty_@0) → new_esEs16(yu310, yu40010)
new_esEs7(Just(yu300), Just(yu40000), app(app(app(ty_@3, bg), bh), ca)) → new_esEs10(yu300, yu40000, bg, bh, ca)
new_esEs25(yu301, yu40001, ty_Char) → new_esEs15(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), app(app(ty_@2, da), db), cg) → new_esEs9(yu300, yu40000, da, db)
new_esEs5(yu30, yu4000, ty_Int) → new_esEs18(yu30, yu4000)
new_esEs8(Float(yu300, yu301), Float(yu40000, yu40001)) → new_esEs18(new_sr(yu300, yu40000), new_sr(yu301, yu40001))
new_esEs21(yu310, yu40010, ty_Char) → new_esEs15(yu310, yu40010)
new_esEs21(yu310, yu40010, ty_Ordering) → new_esEs14(yu310, yu40010)
new_esEs25(yu301, yu40001, ty_Int) → new_esEs18(yu301, yu40001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs11(Left(yu300), Left(yu40000), ty_Int, cg) → new_esEs18(yu300, yu40000)
new_esEs19(yu301, yu40001, ty_Integer) → new_esEs12(yu301, yu40001)
new_esEs7(Just(yu300), Just(yu40000), app(ty_Ratio, ce)) → new_esEs17(yu300, yu40000, ce)
new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) → False
new_esEs22(yu302, yu40002, app(ty_Ratio, hf)) → new_esEs17(yu302, yu40002, hf)
new_esEs24(yu300, yu40000, app(app(ty_@2, bbb), bbc)) → new_esEs9(yu300, yu40000, bbb, bbc)
new_primPlusNat1(Zero, yu4000000) → Succ(yu4000000)
new_esEs11(Left(yu300), Left(yu40000), ty_Integer, cg) → new_esEs12(yu300, yu40000)
new_esEs5(yu30, yu4000, ty_Double) → new_esEs13(yu30, yu4000)
new_esEs4([], :(yu40010, yu40011), bc) → False
new_esEs4(:(yu310, yu311), [], bc) → False
new_esEs5(yu30, yu4000, ty_Float) → new_esEs8(yu30, yu4000)
new_esEs21(yu310, yu40010, ty_Float) → new_esEs8(yu310, yu40010)
new_esEs23(yu301, yu40001, ty_Float) → new_esEs8(yu301, yu40001)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, app(app(ty_Either, bda), bdb)) → new_esEs11(yu301, yu40001, bda, bdb)
new_primPlusNat0(Succ(yu3400), Succ(yu40000000)) → Succ(Succ(new_primPlusNat0(yu3400, yu40000000)))
new_esEs21(yu310, yu40010, app(app(app(ty_@3, ga), gb), gc)) → new_esEs10(yu310, yu40010, ga, gb, gc)
new_esEs11(Right(yu300), Right(yu40000), ec, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs11(Left(yu300), Left(yu40000), ty_@0, cg) → new_esEs16(yu300, yu40000)
new_esEs24(yu300, yu40000, ty_Float) → new_esEs8(yu300, yu40000)
new_esEs11(Right(yu300), Right(yu40000), ec, app(app(ty_@2, ed), ee)) → new_esEs9(yu300, yu40000, ed, ee)
new_esEs21(yu310, yu40010, app(ty_Ratio, ge)) → new_esEs17(yu310, yu40010, ge)
new_asAs(True, yu33) → yu33
new_esEs14(LT, LT) → True
new_esEs23(yu301, yu40001, ty_Bool) → new_esEs6(yu301, yu40001)
new_esEs22(yu302, yu40002, app(ty_[], he)) → new_esEs4(yu302, yu40002, he)
new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) → new_primEqNat0(yu3000, yu400000)
new_esEs22(yu302, yu40002, app(app(ty_Either, hc), hd)) → new_esEs11(yu302, yu40002, hc, hd)
new_esEs6(True, False) → False
new_esEs6(False, True) → False
new_esEs25(yu301, yu40001, ty_Ordering) → new_esEs14(yu301, yu40001)
new_esEs24(yu300, yu40000, ty_Int) → new_esEs18(yu300, yu40000)
new_esEs6(False, False) → True
new_esEs21(yu310, yu40010, ty_Integer) → new_esEs12(yu310, yu40010)
new_primEqNat0(Succ(yu30000), Succ(yu4000000)) → new_primEqNat0(yu30000, yu4000000)
new_esEs24(yu300, yu40000, ty_@0) → new_esEs16(yu300, yu40000)
new_esEs25(yu301, yu40001, ty_Bool) → new_esEs6(yu301, yu40001)
new_esEs11(Left(yu300), Left(yu40000), ty_Ordering, cg) → new_esEs14(yu300, yu40000)
new_esEs22(yu302, yu40002, ty_Char) → new_esEs15(yu302, yu40002)
new_esEs24(yu300, yu40000, app(app(ty_Either, bbg), bbh)) → new_esEs11(yu300, yu40000, bbg, bbh)
new_esEs7(Nothing, Nothing, bd) → True
new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) → False
new_esEs11(Left(yu300), Left(yu40000), app(ty_Maybe, eb), cg) → new_esEs7(yu300, yu40000, eb)
new_esEs26(yu300, yu40000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs10(yu300, yu40000, bdh, bea, beb)
new_esEs10(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), ga, gb, gc) → new_asAs(new_esEs24(yu300, yu40000, ga), new_asAs(new_esEs23(yu301, yu40001, gb), new_esEs22(yu302, yu40002, gc)))
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(yu302, yu40002, app(ty_Maybe, hg)) → new_esEs7(yu302, yu40002, hg)
new_primPlusNat0(Zero, Succ(yu40000000)) → Succ(yu40000000)
new_primPlusNat0(Succ(yu3400), Zero) → Succ(yu3400)
new_esEs23(yu301, yu40001, app(ty_[], bag)) → new_esEs4(yu301, yu40001, bag)
new_esEs25(yu301, yu40001, app(ty_[], bdc)) → new_esEs4(yu301, yu40001, bdc)
new_esEs11(Right(yu300), Left(yu40000), ec, cg) → False
new_esEs11(Left(yu300), Right(yu40000), ec, cg) → False

The set Q consists of the following terms:

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

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

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

new_lookup1(yu13, yu14, yu15, yu16, yu17, yu18, False, h, ba) → new_lookup(:(yu13, yu14), yu18, h, ba)
The graph contains the following edges 6 >= 2, 8 >= 3, 9 >= 4
new_lookup(:(yu30, yu31), :(@2([], yu401), yu41), bb, bc) → new_lookup(:(yu30, yu31), yu41, bb, bc)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
new_lookup(:(yu30, yu31), :(@2(:(yu4000, yu4001), yu401), yu41), bb, bc) → new_lookup1(yu30, yu31, yu4000, yu4001, yu401, yu41, new_asAs(new_esEs5(yu30, yu4000, bc), new_esEs4(yu31, yu4001, bc)), bb, bc)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 8, 4 >= 9

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

                  ↳ QDP

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

new_esEs3(Just(yu300), Just(yu40000), app(app(ty_@2, bcc), bcd)) → new_esEs0(yu300, yu40000, bcc, bcd)
new_esEs2(Left(yu300), Left(yu40000), app(ty_[], bah), bg) → new_esEs(yu300, yu40000, bah)
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_@2, ba), bb)) → new_esEs0(yu310, yu40010, ba, bb)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(app(app(ty_@3, ga), gb), gc), be) → new_esEs1(yu301, yu40001, ga, gb, gc)
new_esEs2(Right(yu300), Right(yu40000), bf, app(ty_[], bca)) → new_esEs(yu300, yu40000, bca)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(app(ty_Either, fb), fc)) → new_esEs2(yu302, yu40002, fb, fc)
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_@2, baa), bab), bg) → new_esEs0(yu300, yu40000, baa, bab)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, he), hf), bd, be) → new_esEs2(yu300, yu40000, he, hf)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, ea), eb), bb) → new_esEs2(yu300, yu40000, ea, eb)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(ty_Maybe, gg), be) → new_esEs3(yu301, yu40001, gg)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(app(app(ty_@3, cd), ce), cf)) → new_esEs1(yu301, yu40001, cd, ce, cf)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(app(app(ty_@3, eg), eh), fa)) → new_esEs1(yu302, yu40002, eg, eh, fa)
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_Either, baf), bag), bg) → new_esEs2(yu300, yu40000, baf, bag)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(app(ty_@2, ee), ef)) → new_esEs0(yu302, yu40002, ee, ef)
new_esEs3(Just(yu300), Just(yu40000), app(app(ty_Either, bch), bda)) → new_esEs2(yu300, yu40000, bch, bda)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(app(ty_Either, gd), ge), be) → new_esEs2(yu301, yu40001, gd, ge)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, gh), ha), bd, be) → new_esEs0(yu300, yu40000, gh, ha)
new_esEs2(Right(yu300), Right(yu40000), bf, app(app(ty_@2, bbb), bbc)) → new_esEs0(yu300, yu40000, bbb, bbc)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(ty_[], db)) → new_esEs(yu301, yu40001, db)
new_esEs2(Right(yu300), Right(yu40000), bf, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs1(yu300, yu40000, bbd, bbe, bbf)
new_esEs3(Just(yu300), Just(yu40000), app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs1(yu300, yu40000, bce, bcf, bcg)
new_esEs3(Just(yu300), Just(yu40000), app(ty_[], bdb)) → new_esEs(yu300, yu40000, bdb)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, hb), hc), hd), bd, be) → new_esEs1(yu300, yu40000, hb, hc, hd)
new_esEs(:(yu310, yu311), :(yu40010, yu40011), h) → new_esEs(yu311, yu40011, h)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(ty_Maybe, ff)) → new_esEs3(yu302, yu40002, ff)
new_esEs2(Left(yu300), Left(yu40000), app(app(app(ty_@3, bac), bad), bae), bg) → new_esEs1(yu300, yu40000, bac, bad, bae)
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(yu310, yu40010, bc, bd, be)
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_Either, bf), bg)) → new_esEs2(yu310, yu40010, bf, bg)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(ty_Maybe, dc)) → new_esEs3(yu301, yu40001, dc)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(app(ty_Either, cg), da)) → new_esEs2(yu301, yu40001, cg, da)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, ed), bb) → new_esEs3(yu300, yu40000, ed)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, hh), bd, be) → new_esEs3(yu300, yu40000, hh)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], hg), bd, be) → new_esEs(yu300, yu40000, hg)
new_esEs2(Right(yu300), Right(yu40000), bf, app(app(ty_Either, bbg), bbh)) → new_esEs2(yu300, yu40000, bbg, bbh)
new_esEs3(Just(yu300), Just(yu40000), app(ty_Maybe, bdc)) → new_esEs3(yu300, yu40000, bdc)
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(ty_Maybe, ca)) → new_esEs3(yu310, yu40010, ca)
new_esEs2(Right(yu300), Right(yu40000), bf, app(ty_Maybe, bcb)) → new_esEs3(yu300, yu40000, bcb)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, dd), de), bb) → new_esEs0(yu300, yu40000, dd, de)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], ec), bb) → new_esEs(yu300, yu40000, ec)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, df), dg), dh), bb) → new_esEs1(yu300, yu40000, df, dg, dh)
new_esEs2(Left(yu300), Left(yu40000), app(ty_Maybe, bba), bg) → new_esEs3(yu300, yu40000, bba)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(app(ty_@2, fg), fh), be) → new_esEs0(yu301, yu40001, fg, fh)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(ty_[], fd)) → new_esEs(yu302, yu40002, fd)
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(app(ty_@2, cb), cc)) → new_esEs0(yu301, yu40001, cb, cc)
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(ty_[], gf), be) → new_esEs(yu301, yu40001, gf)
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(ty_[], bh)) → new_esEs(yu310, yu40010, bh)

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

new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(ty_Maybe, ca)) → new_esEs3(yu310, yu40010, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_Either, bf), bg)) → new_esEs2(yu310, yu40010, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(yu310, yu40010, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_@2, ba), bb)) → new_esEs0(yu310, yu40010, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(yu300), Just(yu40000), app(ty_Maybe, bdc)) → new_esEs3(yu300, yu40000, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(yu300), Just(yu40000), app(app(ty_Either, bch), bda)) → new_esEs2(yu300, yu40000, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(yu300), Just(yu40000), app(ty_[], bdb)) → new_esEs(yu300, yu40000, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(yu300), Just(yu40000), app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs1(yu300, yu40000, bce, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(yu300), Just(yu40000), app(app(ty_@2, bcc), bcd)) → new_esEs0(yu300, yu40000, bcc, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(ty_Maybe, dc)) → new_esEs3(yu301, yu40001, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, ed), bb) → new_esEs3(yu300, yu40000, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, ea), eb), bb) → new_esEs2(yu300, yu40000, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(app(ty_Either, cg), da)) → new_esEs2(yu301, yu40001, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(ty_[], db)) → new_esEs(yu301, yu40001, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], ec), bb) → new_esEs(yu300, yu40000, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(app(app(ty_@3, cd), ce), cf)) → new_esEs1(yu301, yu40001, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, df), dg), dh), bb) → new_esEs1(yu300, yu40000, df, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, dd), de), bb) → new_esEs0(yu300, yu40000, dd, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@2(yu300, yu301), @2(yu40000, yu40001), ba, app(app(ty_@2, cb), cc)) → new_esEs0(yu301, yu40001, cb, cc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(ty_Maybe, gg), be) → new_esEs3(yu301, yu40001, gg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(ty_Maybe, ff)) → new_esEs3(yu302, yu40002, ff)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, hh), bd, be) → new_esEs3(yu300, yu40000, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(yu300), Right(yu40000), bf, app(ty_Maybe, bcb)) → new_esEs3(yu300, yu40000, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(yu300), Left(yu40000), app(ty_Maybe, bba), bg) → new_esEs3(yu300, yu40000, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(:(yu310, yu311), :(yu40010, yu40011), h) → new_esEs(yu311, yu40011, h)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs(:(yu310, yu311), :(yu40010, yu40011), app(ty_[], bh)) → new_esEs(yu310, yu40010, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(app(ty_Either, fb), fc)) → new_esEs2(yu302, yu40002, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, he), hf), bd, be) → new_esEs2(yu300, yu40000, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(app(ty_Either, gd), ge), be) → new_esEs2(yu301, yu40001, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_Either, baf), bag), bg) → new_esEs2(yu300, yu40000, baf, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(yu300), Right(yu40000), bf, app(app(ty_Either, bbg), bbh)) → new_esEs2(yu300, yu40000, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], hg), bd, be) → new_esEs(yu300, yu40000, hg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(ty_[], fd)) → new_esEs(yu302, yu40002, fd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(ty_[], gf), be) → new_esEs(yu301, yu40001, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(Left(yu300), Left(yu40000), app(ty_[], bah), bg) → new_esEs(yu300, yu40000, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Right(yu300), Right(yu40000), bf, app(ty_[], bca)) → new_esEs(yu300, yu40000, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(app(app(ty_@3, ga), gb), gc), be) → new_esEs1(yu301, yu40001, ga, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(app(app(ty_@3, eg), eh), fa)) → new_esEs1(yu302, yu40002, eg, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, hb), hc), hd), bd, be) → new_esEs1(yu300, yu40000, hb, hc, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, bd, app(app(ty_@2, ee), ef)) → new_esEs0(yu302, yu40002, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, gh), ha), bd, be) → new_esEs0(yu300, yu40000, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), bc, app(app(ty_@2, fg), fh), be) → new_esEs0(yu301, yu40001, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(Right(yu300), Right(yu40000), bf, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs1(yu300, yu40000, bbd, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(Left(yu300), Left(yu40000), app(app(app(ty_@3, bac), bad), bae), bg) → new_esEs1(yu300, yu40000, bac, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Left(yu300), Left(yu40000), app(app(ty_@2, baa), bab), bg) → new_esEs0(yu300, yu40000, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Right(yu300), Right(yu40000), bf, app(app(ty_@2, bbb), bbc)) → new_esEs0(yu300, yu40000, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ NumRed

            ↳ HASKELL

              ↳ Narrow

                ↳ AND

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                  ↳ QDP

                    ↳ QDPSizeChangeProof

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

new_primEqNat(Succ(yu30000), Succ(yu4000000)) → new_primEqNat(yu30000, yu4000000)

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

new_primEqNat(Succ(yu30000), Succ(yu4000000)) → new_primEqNat(yu30000, yu4000000)
The graph contains the following edges 1 > 1, 2 > 2

lookup	k []	= lookup3 k []
lookup	k ((x,y) : xys)	= lookup2 k ((x,y) : xys)

lookup1	k x y xys True	= Just y
lookup1	k x y xys False	= lookup0 k x y xys otherwise