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

YES 1.762 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

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

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

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

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

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)

lookup0 k x y xys True = lookup k xys

lookup1 k x y xys True = Just y

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

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

          ↳ Narrow

mainModule Main

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

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
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1030 -> 5[label="",style="solid", color="burlywood", weight=3];
1031[label="yu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1031[label="",style="solid", color="burlywood", weight=9];
1031 -> 6[label="",style="solid", color="burlywood", weight=3];
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1032 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup yu3 []\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookup yu3 ((yu400,yu401) : yu41)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 yu3 []\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="lookup2 yu3 ((yu400,yu401) : yu41)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 yu3 yu400 yu401 yu41 (yu3 == yu400)\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1033[label="yu3/(yu30,yu31)",fontsize=10,color="white",style="solid",shape="box"];11 -> 1033[label="",style="solid", color="burlywood", weight=9];
1033 -> 12[label="",style="solid", color="burlywood", weight=3];
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1034 -> 13[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 (yu30,yu31) (yu4000,yu4001) yu401 yu41 ((yu30,yu31) == (yu4000,yu4001))\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14 -> 97[label="",style="dashed", color="red", weight=0];
14[label="lookup1 (yu30,yu31) (yu4000,yu4001) yu401 yu41 (yu30 == yu4000 && yu31 == yu4001)\n  Eq a  Eq b",fontsize=16,color="magenta"];14 -> 98[label="",style="dashed", color="magenta", weight=3];
14 -> 99[label="",style="dashed", color="magenta", weight=3];
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14 -> 103[label="",style="dashed", color="magenta", weight=3];
14 -> 104[label="",style="dashed", color="magenta", weight=3];
98[label="yu41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];99[label="yu4001\n  Eq a",fontsize=16,color="green",shape="box"];100[label="yu401",fontsize=16,color="green",shape="box"];101[label="yu31\n  Eq a",fontsize=16,color="green",shape="box"];102[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];103 -> 355[label="",style="dashed", color="red", weight=0];
103[label="yu30 == yu4000 && yu31 == yu4001\n  Eq a  Eq b",fontsize=16,color="magenta"];103 -> 356[label="",style="dashed", color="magenta", weight=3];
103 -> 357[label="",style="dashed", color="magenta", weight=3];
104[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];97[label="lookup1 (yu28,yu29) (yu30,yu31) yu32 yu33 yu34\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1037[label="yu34/False",fontsize=10,color="white",style="solid",shape="box"];97 -> 1037[label="",style="solid", color="burlywood", weight=9];
1037 -> 130[label="",style="solid", color="burlywood", weight=3];
1038[label="yu34/True",fontsize=10,color="white",style="solid",shape="box"];97 -> 1038[label="",style="solid", color="burlywood", weight=9];
1038 -> 131[label="",style="solid", color="burlywood", weight=3];
356[label="yu31 == yu4001\n  Eq a",fontsize=16,color="blue",shape="box"];1039[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1039[label="",style="solid", color="blue", weight=9];
1039 -> 360[label="",style="solid", color="blue", weight=3];
1040[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1040[label="",style="solid", color="blue", weight=9];
1040 -> 361[label="",style="solid", color="blue", weight=3];
1041[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1041[label="",style="solid", color="blue", weight=9];
1041 -> 362[label="",style="solid", color="blue", weight=3];
1042[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1042[label="",style="solid", color="blue", weight=9];
1042 -> 363[label="",style="solid", color="blue", weight=3];
1043[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1043[label="",style="solid", color="blue", weight=9];
1043 -> 364[label="",style="solid", color="blue", weight=3];
1044[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1044[label="",style="solid", color="blue", weight=9];
1044 -> 365[label="",style="solid", color="blue", weight=3];
1045[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1045[label="",style="solid", color="blue", weight=9];
1045 -> 366[label="",style="solid", color="blue", weight=3];
1046[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1046[label="",style="solid", color="blue", weight=9];
1046 -> 367[label="",style="solid", color="blue", weight=3];
1047[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1047[label="",style="solid", color="blue", weight=9];
1047 -> 368[label="",style="solid", color="blue", weight=3];
1048[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1048[label="",style="solid", color="blue", weight=9];
1048 -> 369[label="",style="solid", color="blue", weight=3];
1049[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1049[label="",style="solid", color="blue", weight=9];
1049 -> 370[label="",style="solid", color="blue", weight=3];
1050[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1050[label="",style="solid", color="blue", weight=9];
1050 -> 371[label="",style="solid", color="blue", weight=3];
1051[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1051[label="",style="solid", color="blue", weight=9];
1051 -> 372[label="",style="solid", color="blue", weight=3];
1052[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];356 -> 1052[label="",style="solid", color="blue", weight=9];
1052 -> 373[label="",style="solid", color="blue", weight=3];
357[label="yu30 == yu4000\n  Eq a",fontsize=16,color="blue",shape="box"];1053[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1053[label="",style="solid", color="blue", weight=9];
1053 -> 374[label="",style="solid", color="blue", weight=3];
1054[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1054[label="",style="solid", color="blue", weight=9];
1054 -> 375[label="",style="solid", color="blue", weight=3];
1055[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1055[label="",style="solid", color="blue", weight=9];
1055 -> 376[label="",style="solid", color="blue", weight=3];
1056[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1056[label="",style="solid", color="blue", weight=9];
1056 -> 377[label="",style="solid", color="blue", weight=3];
1057[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1057[label="",style="solid", color="blue", weight=9];
1057 -> 378[label="",style="solid", color="blue", weight=3];
1058[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1058[label="",style="solid", color="blue", weight=9];
1058 -> 379[label="",style="solid", color="blue", weight=3];
1059[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1059[label="",style="solid", color="blue", weight=9];
1059 -> 380[label="",style="solid", color="blue", weight=3];
1060[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1060[label="",style="solid", color="blue", weight=9];
1060 -> 381[label="",style="solid", color="blue", weight=3];
1061[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1061[label="",style="solid", color="blue", weight=9];
1061 -> 382[label="",style="solid", color="blue", weight=3];
1062[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1062[label="",style="solid", color="blue", weight=9];
1062 -> 383[label="",style="solid", color="blue", weight=3];
1063[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1063[label="",style="solid", color="blue", weight=9];
1063 -> 384[label="",style="solid", color="blue", weight=3];
1064[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1064[label="",style="solid", color="blue", weight=9];
1064 -> 385[label="",style="solid", color="blue", weight=3];
1065[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1065[label="",style="solid", color="blue", weight=9];
1065 -> 386[label="",style="solid", color="blue", weight=3];
1066[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];357 -> 1066[label="",style="solid", color="blue", weight=9];
1066 -> 387[label="",style="solid", color="blue", weight=3];
355[label="yu46 && yu47",fontsize=16,color="burlywood",shape="triangle"];1067[label="yu46/False",fontsize=10,color="white",style="solid",shape="box"];355 -> 1067[label="",style="solid", color="burlywood", weight=9];
1067 -> 388[label="",style="solid", color="burlywood", weight=3];
1068[label="yu46/True",fontsize=10,color="white",style="solid",shape="box"];355 -> 1068[label="",style="solid", color="burlywood", weight=9];
1068 -> 389[label="",style="solid", color="burlywood", weight=3];
130[label="lookup1 (yu28,yu29) (yu30,yu31) yu32 yu33 False\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];130 -> 148[label="",style="solid", color="black", weight=3];
131[label="lookup1 (yu28,yu29) (yu30,yu31) yu32 yu33 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];131 -> 149[label="",style="solid", color="black", weight=3];
360[label="yu31 == yu4001\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1069[label="yu31/(yu310,yu311)",fontsize=10,color="white",style="solid",shape="box"];360 -> 1069[label="",style="solid", color="burlywood", weight=9];
1069 -> 390[label="",style="solid", color="burlywood", weight=3];
361[label="yu31 == yu4001",fontsize=16,color="black",shape="triangle"];361 -> 391[label="",style="solid", color="black", weight=3];
362[label="yu31 == yu4001",fontsize=16,color="burlywood",shape="triangle"];1070[label="yu31/False",fontsize=10,color="white",style="solid",shape="box"];362 -> 1070[label="",style="solid", color="burlywood", weight=9];
1070 -> 392[label="",style="solid", color="burlywood", weight=3];
1071[label="yu31/True",fontsize=10,color="white",style="solid",shape="box"];362 -> 1071[label="",style="solid", color="burlywood", weight=9];
1071 -> 393[label="",style="solid", color="burlywood", weight=3];
363[label="yu31 == yu4001",fontsize=16,color="black",shape="triangle"];363 -> 394[label="",style="solid", color="black", weight=3];
364[label="yu31 == yu4001\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];1072[label="yu31/Left yu310",fontsize=10,color="white",style="solid",shape="box"];364 -> 1072[label="",style="solid", color="burlywood", weight=9];
1072 -> 395[label="",style="solid", color="burlywood", weight=3];
1073[label="yu31/Right yu310",fontsize=10,color="white",style="solid",shape="box"];364 -> 1073[label="",style="solid", color="burlywood", weight=9];
1073 -> 396[label="",style="solid", color="burlywood", weight=3];
365[label="yu31 == yu4001\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1074[label="yu31/yu310 : yu311",fontsize=10,color="white",style="solid",shape="box"];365 -> 1074[label="",style="solid", color="burlywood", weight=9];
1074 -> 397[label="",style="solid", color="burlywood", weight=3];
1075[label="yu31/[]",fontsize=10,color="white",style="solid",shape="box"];365 -> 1075[label="",style="solid", color="burlywood", weight=9];
1075 -> 398[label="",style="solid", color="burlywood", weight=3];
366[label="yu31 == yu4001",fontsize=16,color="burlywood",shape="triangle"];1076[label="yu31/LT",fontsize=10,color="white",style="solid",shape="box"];366 -> 1076[label="",style="solid", color="burlywood", weight=9];
1076 -> 399[label="",style="solid", color="burlywood", weight=3];
1077[label="yu31/EQ",fontsize=10,color="white",style="solid",shape="box"];366 -> 1077[label="",style="solid", color="burlywood", weight=9];
1077 -> 400[label="",style="solid", color="burlywood", weight=3];
1078[label="yu31/GT",fontsize=10,color="white",style="solid",shape="box"];366 -> 1078[label="",style="solid", color="burlywood", weight=9];
1078 -> 401[label="",style="solid", color="burlywood", weight=3];
367[label="yu31 == yu4001",fontsize=16,color="black",shape="triangle"];367 -> 402[label="",style="solid", color="black", weight=3];
368[label="yu31 == yu4001\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];1079[label="yu31/(yu310,yu311,yu312)",fontsize=10,color="white",style="solid",shape="box"];368 -> 1079[label="",style="solid", color="burlywood", weight=9];
1079 -> 403[label="",style="solid", color="burlywood", weight=3];
369[label="yu31 == yu4001\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];1080[label="yu31/yu310 :% yu311",fontsize=10,color="white",style="solid",shape="box"];369 -> 1080[label="",style="solid", color="burlywood", weight=9];
1080 -> 404[label="",style="solid", color="burlywood", weight=3];
370[label="yu31 == yu4001",fontsize=16,color="burlywood",shape="triangle"];1081[label="yu31/Integer yu310",fontsize=10,color="white",style="solid",shape="box"];370 -> 1081[label="",style="solid", color="burlywood", weight=9];
1081 -> 405[label="",style="solid", color="burlywood", weight=3];
371[label="yu31 == yu4001",fontsize=16,color="black",shape="triangle"];371 -> 406[label="",style="solid", color="black", weight=3];
372[label="yu31 == yu4001\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1082[label="yu31/Nothing",fontsize=10,color="white",style="solid",shape="box"];372 -> 1082[label="",style="solid", color="burlywood", weight=9];
1082 -> 407[label="",style="solid", color="burlywood", weight=3];
1083[label="yu31/Just yu310",fontsize=10,color="white",style="solid",shape="box"];372 -> 1083[label="",style="solid", color="burlywood", weight=9];
1083 -> 408[label="",style="solid", color="burlywood", weight=3];
373[label="yu31 == yu4001",fontsize=16,color="burlywood",shape="triangle"];1084[label="yu31/()",fontsize=10,color="white",style="solid",shape="box"];373 -> 1084[label="",style="solid", color="burlywood", weight=9];
1084 -> 409[label="",style="solid", color="burlywood", weight=3];
374 -> 360[label="",style="dashed", color="red", weight=0];
374[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="magenta"];374 -> 410[label="",style="dashed", color="magenta", weight=3];
374 -> 411[label="",style="dashed", color="magenta", weight=3];
375 -> 361[label="",style="dashed", color="red", weight=0];
375[label="yu30 == yu4000",fontsize=16,color="magenta"];375 -> 412[label="",style="dashed", color="magenta", weight=3];
375 -> 413[label="",style="dashed", color="magenta", weight=3];
376 -> 362[label="",style="dashed", color="red", weight=0];
376[label="yu30 == yu4000",fontsize=16,color="magenta"];376 -> 414[label="",style="dashed", color="magenta", weight=3];
376 -> 415[label="",style="dashed", color="magenta", weight=3];
377 -> 363[label="",style="dashed", color="red", weight=0];
377[label="yu30 == yu4000",fontsize=16,color="magenta"];377 -> 416[label="",style="dashed", color="magenta", weight=3];
377 -> 417[label="",style="dashed", color="magenta", weight=3];
378 -> 364[label="",style="dashed", color="red", weight=0];
378[label="yu30 == yu4000\n  Eq a  Eq b",fontsize=16,color="magenta"];378 -> 418[label="",style="dashed", color="magenta", weight=3];
378 -> 419[label="",style="dashed", color="magenta", weight=3];
379 -> 365[label="",style="dashed", color="red", weight=0];
379[label="yu30 == yu4000\n  Eq a",fontsize=16,color="magenta"];379 -> 420[label="",style="dashed", color="magenta", weight=3];
379 -> 421[label="",style="dashed", color="magenta", weight=3];
380 -> 366[label="",style="dashed", color="red", weight=0];
380[label="yu30 == yu4000",fontsize=16,color="magenta"];380 -> 422[label="",style="dashed", color="magenta", weight=3];
380 -> 423[label="",style="dashed", color="magenta", weight=3];
381 -> 367[label="",style="dashed", color="red", weight=0];
381[label="yu30 == yu4000",fontsize=16,color="magenta"];381 -> 424[label="",style="dashed", color="magenta", weight=3];
381 -> 425[label="",style="dashed", color="magenta", weight=3];
382 -> 368[label="",style="dashed", color="red", weight=0];
382[label="yu30 == yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];382 -> 426[label="",style="dashed", color="magenta", weight=3];
382 -> 427[label="",style="dashed", color="magenta", weight=3];
383 -> 369[label="",style="dashed", color="red", weight=0];
383[label="yu30 == yu4000\n  Integral a",fontsize=16,color="magenta"];383 -> 428[label="",style="dashed", color="magenta", weight=3];
383 -> 429[label="",style="dashed", color="magenta", weight=3];
384 -> 370[label="",style="dashed", color="red", weight=0];
384[label="yu30 == yu4000",fontsize=16,color="magenta"];384 -> 430[label="",style="dashed", color="magenta", weight=3];
384 -> 431[label="",style="dashed", color="magenta", weight=3];
385 -> 371[label="",style="dashed", color="red", weight=0];
385[label="yu30 == yu4000",fontsize=16,color="magenta"];385 -> 432[label="",style="dashed", color="magenta", weight=3];
385 -> 433[label="",style="dashed", color="magenta", weight=3];
386 -> 372[label="",style="dashed", color="red", weight=0];
386[label="yu30 == yu4000\n  Eq a",fontsize=16,color="magenta"];386 -> 434[label="",style="dashed", color="magenta", weight=3];
386 -> 435[label="",style="dashed", color="magenta", weight=3];
387 -> 373[label="",style="dashed", color="red", weight=0];
387[label="yu30 == yu4000",fontsize=16,color="magenta"];387 -> 436[label="",style="dashed", color="magenta", weight=3];
387 -> 437[label="",style="dashed", color="magenta", weight=3];
388[label="False && yu47",fontsize=16,color="black",shape="box"];388 -> 438[label="",style="solid", color="black", weight=3];
389[label="True && yu47",fontsize=16,color="black",shape="box"];389 -> 439[label="",style="solid", color="black", weight=3];
148[label="lookup0 (yu28,yu29) (yu30,yu31) yu32 yu33 otherwise\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];148 -> 172[label="",style="solid", color="black", weight=3];
149[label="Just yu32",fontsize=16,color="green",shape="box"];390[label="(yu310,yu311) == yu4001\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1099[label="yu4001/(yu40010,yu40011)",fontsize=10,color="white",style="solid",shape="box"];390 -> 1099[label="",style="solid", color="burlywood", weight=9];
1099 -> 440[label="",style="solid", color="burlywood", weight=3];
391[label="primEqChar yu31 yu4001",fontsize=16,color="burlywood",shape="box"];1100[label="yu31/Char yu310",fontsize=10,color="white",style="solid",shape="box"];391 -> 1100[label="",style="solid", color="burlywood", weight=9];
1100 -> 441[label="",style="solid", color="burlywood", weight=3];
392[label="False == yu4001",fontsize=16,color="burlywood",shape="box"];1101[label="yu4001/False",fontsize=10,color="white",style="solid",shape="box"];392 -> 1101[label="",style="solid", color="burlywood", weight=9];
1101 -> 442[label="",style="solid", color="burlywood", weight=3];
1102[label="yu4001/True",fontsize=10,color="white",style="solid",shape="box"];392 -> 1102[label="",style="solid", color="burlywood", weight=9];
1102 -> 443[label="",style="solid", color="burlywood", weight=3];
393[label="True == yu4001",fontsize=16,color="burlywood",shape="box"];1103[label="yu4001/False",fontsize=10,color="white",style="solid",shape="box"];393 -> 1103[label="",style="solid", color="burlywood", weight=9];
1103 -> 444[label="",style="solid", color="burlywood", weight=3];
1104[label="yu4001/True",fontsize=10,color="white",style="solid",shape="box"];393 -> 1104[label="",style="solid", color="burlywood", weight=9];
1104 -> 445[label="",style="solid", color="burlywood", weight=3];
394[label="primEqFloat yu31 yu4001",fontsize=16,color="burlywood",shape="box"];1105[label="yu31/Float yu310 yu311",fontsize=10,color="white",style="solid",shape="box"];394 -> 1105[label="",style="solid", color="burlywood", weight=9];
1105 -> 446[label="",style="solid", color="burlywood", weight=3];
395[label="Left yu310 == yu4001\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1106[label="yu4001/Left yu40010",fontsize=10,color="white",style="solid",shape="box"];395 -> 1106[label="",style="solid", color="burlywood", weight=9];
1106 -> 447[label="",style="solid", color="burlywood", weight=3];
1107[label="yu4001/Right yu40010",fontsize=10,color="white",style="solid",shape="box"];395 -> 1107[label="",style="solid", color="burlywood", weight=9];
1107 -> 448[label="",style="solid", color="burlywood", weight=3];
396[label="Right yu310 == yu4001\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1108[label="yu4001/Left yu40010",fontsize=10,color="white",style="solid",shape="box"];396 -> 1108[label="",style="solid", color="burlywood", weight=9];
1108 -> 449[label="",style="solid", color="burlywood", weight=3];
1109[label="yu4001/Right yu40010",fontsize=10,color="white",style="solid",shape="box"];396 -> 1109[label="",style="solid", color="burlywood", weight=9];
1109 -> 450[label="",style="solid", color="burlywood", weight=3];
397[label="yu310 : yu311 == yu4001\n  Eq a",fontsize=16,color="burlywood",shape="box"];1110[label="yu4001/yu40010 : yu40011",fontsize=10,color="white",style="solid",shape="box"];397 -> 1110[label="",style="solid", color="burlywood", weight=9];
1110 -> 451[label="",style="solid", color="burlywood", weight=3];
1111[label="yu4001/[]",fontsize=10,color="white",style="solid",shape="box"];397 -> 1111[label="",style="solid", color="burlywood", weight=9];
1111 -> 452[label="",style="solid", color="burlywood", weight=3];
398[label="[] == yu4001\n  Eq a",fontsize=16,color="burlywood",shape="box"];1112[label="yu4001/yu40010 : yu40011",fontsize=10,color="white",style="solid",shape="box"];398 -> 1112[label="",style="solid", color="burlywood", weight=9];
1112 -> 453[label="",style="solid", color="burlywood", weight=3];
1113[label="yu4001/[]",fontsize=10,color="white",style="solid",shape="box"];398 -> 1113[label="",style="solid", color="burlywood", weight=9];
1113 -> 454[label="",style="solid", color="burlywood", weight=3];
399[label="LT == yu4001",fontsize=16,color="burlywood",shape="box"];1114[label="yu4001/LT",fontsize=10,color="white",style="solid",shape="box"];399 -> 1114[label="",style="solid", color="burlywood", weight=9];
1114 -> 455[label="",style="solid", color="burlywood", weight=3];
1115[label="yu4001/EQ",fontsize=10,color="white",style="solid",shape="box"];399 -> 1115[label="",style="solid", color="burlywood", weight=9];
1115 -> 456[label="",style="solid", color="burlywood", weight=3];
1116[label="yu4001/GT",fontsize=10,color="white",style="solid",shape="box"];399 -> 1116[label="",style="solid", color="burlywood", weight=9];
1116 -> 457[label="",style="solid", color="burlywood", weight=3];
400[label="EQ == yu4001",fontsize=16,color="burlywood",shape="box"];1117[label="yu4001/LT",fontsize=10,color="white",style="solid",shape="box"];400 -> 1117[label="",style="solid", color="burlywood", weight=9];
1117 -> 458[label="",style="solid", color="burlywood", weight=3];
1118[label="yu4001/EQ",fontsize=10,color="white",style="solid",shape="box"];400 -> 1118[label="",style="solid", color="burlywood", weight=9];
1118 -> 459[label="",style="solid", color="burlywood", weight=3];
1119[label="yu4001/GT",fontsize=10,color="white",style="solid",shape="box"];400 -> 1119[label="",style="solid", color="burlywood", weight=9];
1119 -> 460[label="",style="solid", color="burlywood", weight=3];
401[label="GT == yu4001",fontsize=16,color="burlywood",shape="box"];1120[label="yu4001/LT",fontsize=10,color="white",style="solid",shape="box"];401 -> 1120[label="",style="solid", color="burlywood", weight=9];
1120 -> 461[label="",style="solid", color="burlywood", weight=3];
1121[label="yu4001/EQ",fontsize=10,color="white",style="solid",shape="box"];401 -> 1121[label="",style="solid", color="burlywood", weight=9];
1121 -> 462[label="",style="solid", color="burlywood", weight=3];
1122[label="yu4001/GT",fontsize=10,color="white",style="solid",shape="box"];401 -> 1122[label="",style="solid", color="burlywood", weight=9];
1122 -> 463[label="",style="solid", color="burlywood", weight=3];
402[label="primEqDouble yu31 yu4001",fontsize=16,color="burlywood",shape="box"];1123[label="yu31/Double yu310 yu311",fontsize=10,color="white",style="solid",shape="box"];402 -> 1123[label="",style="solid", color="burlywood", weight=9];
1123 -> 464[label="",style="solid", color="burlywood", weight=3];
403[label="(yu310,yu311,yu312) == yu4001\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1124[label="yu4001/(yu40010,yu40011,yu40012)",fontsize=10,color="white",style="solid",shape="box"];403 -> 1124[label="",style="solid", color="burlywood", weight=9];
1124 -> 465[label="",style="solid", color="burlywood", weight=3];
404[label="yu310 :% yu311 == yu4001\n  Integral a",fontsize=16,color="burlywood",shape="box"];1125[label="yu4001/yu40010 :% yu40011",fontsize=10,color="white",style="solid",shape="box"];404 -> 1125[label="",style="solid", color="burlywood", weight=9];
1125 -> 466[label="",style="solid", color="burlywood", weight=3];
405[label="Integer yu310 == yu4001",fontsize=16,color="burlywood",shape="box"];1126[label="yu4001/Integer yu40010",fontsize=10,color="white",style="solid",shape="box"];405 -> 1126[label="",style="solid", color="burlywood", weight=9];
1126 -> 467[label="",style="solid", color="burlywood", weight=3];
406[label="primEqInt yu31 yu4001",fontsize=16,color="burlywood",shape="triangle"];1127[label="yu31/Pos yu310",fontsize=10,color="white",style="solid",shape="box"];406 -> 1127[label="",style="solid", color="burlywood", weight=9];
1127 -> 468[label="",style="solid", color="burlywood", weight=3];
1128[label="yu31/Neg yu310",fontsize=10,color="white",style="solid",shape="box"];406 -> 1128[label="",style="solid", color="burlywood", weight=9];
1128 -> 469[label="",style="solid", color="burlywood", weight=3];
407[label="Nothing == yu4001\n  Eq a",fontsize=16,color="burlywood",shape="box"];1129[label="yu4001/Nothing",fontsize=10,color="white",style="solid",shape="box"];407 -> 1129[label="",style="solid", color="burlywood", weight=9];
1129 -> 470[label="",style="solid", color="burlywood", weight=3];
1130[label="yu4001/Just yu40010",fontsize=10,color="white",style="solid",shape="box"];407 -> 1130[label="",style="solid", color="burlywood", weight=9];
1130 -> 471[label="",style="solid", color="burlywood", weight=3];
408[label="Just yu310 == yu4001\n  Eq a",fontsize=16,color="burlywood",shape="box"];1131[label="yu4001/Nothing",fontsize=10,color="white",style="solid",shape="box"];408 -> 1131[label="",style="solid", color="burlywood", weight=9];
1131 -> 472[label="",style="solid", color="burlywood", weight=3];
1132[label="yu4001/Just yu40010",fontsize=10,color="white",style="solid",shape="box"];408 -> 1132[label="",style="solid", color="burlywood", weight=9];
1132 -> 473[label="",style="solid", color="burlywood", weight=3];
409[label="() == yu4001",fontsize=16,color="burlywood",shape="box"];1133[label="yu4001/()",fontsize=10,color="white",style="solid",shape="box"];409 -> 1133[label="",style="solid", color="burlywood", weight=9];
1133 -> 474[label="",style="solid", color="burlywood", weight=3];
410[label="yu4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];411[label="yu30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];412[label="yu4000",fontsize=16,color="green",shape="box"];413[label="yu30",fontsize=16,color="green",shape="box"];414[label="yu4000",fontsize=16,color="green",shape="box"];415[label="yu30",fontsize=16,color="green",shape="box"];416[label="yu4000",fontsize=16,color="green",shape="box"];417[label="yu30",fontsize=16,color="green",shape="box"];418[label="yu4000\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];419[label="yu30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];420[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];421[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];422[label="yu4000",fontsize=16,color="green",shape="box"];423[label="yu30",fontsize=16,color="green",shape="box"];424[label="yu4000",fontsize=16,color="green",shape="box"];425[label="yu30",fontsize=16,color="green",shape="box"];426[label="yu4000\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];427[label="yu30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];428[label="yu4000\n  Integral a",fontsize=16,color="green",shape="box"];429[label="yu30\n  Integral a",fontsize=16,color="green",shape="box"];430[label="yu4000",fontsize=16,color="green",shape="box"];431[label="yu30",fontsize=16,color="green",shape="box"];432[label="yu4000",fontsize=16,color="green",shape="box"];433[label="yu30",fontsize=16,color="green",shape="box"];434[label="yu4000\n  Eq a",fontsize=16,color="green",shape="box"];435[label="yu30\n  Eq a",fontsize=16,color="green",shape="box"];436[label="yu4000",fontsize=16,color="green",shape="box"];437[label="yu30",fontsize=16,color="green",shape="box"];438[label="False",fontsize=16,color="green",shape="box"];439[label="yu47",fontsize=16,color="green",shape="box"];172[label="lookup0 (yu28,yu29) (yu30,yu31) yu32 yu33 True\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];172 -> 222[label="",style="solid", color="black", weight=3];
440[label="(yu310,yu311) == (yu40010,yu40011)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];440 -> 475[label="",style="solid", color="black", weight=3];
441[label="primEqChar (Char yu310) yu4001",fontsize=16,color="burlywood",shape="box"];1134[label="yu4001/Char yu40010",fontsize=10,color="white",style="solid",shape="box"];441 -> 1134[label="",style="solid", color="burlywood", weight=9];
1134 -> 476[label="",style="solid", color="burlywood", weight=3];
442[label="False == False",fontsize=16,color="black",shape="box"];442 -> 477[label="",style="solid", color="black", weight=3];
443[label="False == True",fontsize=16,color="black",shape="box"];443 -> 478[label="",style="solid", color="black", weight=3];
444[label="True == False",fontsize=16,color="black",shape="box"];444 -> 479[label="",style="solid", color="black", weight=3];
445[label="True == True",fontsize=16,color="black",shape="box"];445 -> 480[label="",style="solid", color="black", weight=3];
446[label="primEqFloat (Float yu310 yu311) yu4001",fontsize=16,color="burlywood",shape="box"];1135[label="yu4001/Float yu40010 yu40011",fontsize=10,color="white",style="solid",shape="box"];446 -> 1135[label="",style="solid", color="burlywood", weight=9];
1135 -> 481[label="",style="solid", color="burlywood", weight=3];
447[label="Left yu310 == Left yu40010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];447 -> 482[label="",style="solid", color="black", weight=3];
448[label="Left yu310 == Right yu40010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];448 -> 483[label="",style="solid", color="black", weight=3];
449[label="Right yu310 == Left yu40010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];449 -> 484[label="",style="solid", color="black", weight=3];
450[label="Right yu310 == Right yu40010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];450 -> 485[label="",style="solid", color="black", weight=3];
451[label="yu310 : yu311 == yu40010 : yu40011\n  Eq a",fontsize=16,color="black",shape="box"];451 -> 486[label="",style="solid", color="black", weight=3];
452[label="yu310 : yu311 == []\n  Eq a",fontsize=16,color="black",shape="box"];452 -> 487[label="",style="solid", color="black", weight=3];
453[label="[] == yu40010 : yu40011\n  Eq a",fontsize=16,color="black",shape="box"];453 -> 488[label="",style="solid", color="black", weight=3];
454[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];454 -> 489[label="",style="solid", color="black", weight=3];
455[label="LT == LT",fontsize=16,color="black",shape="box"];455 -> 490[label="",style="solid", color="black", weight=3];
456[label="LT == EQ",fontsize=16,color="black",shape="box"];456 -> 491[label="",style="solid", color="black", weight=3];
457[label="LT == GT",fontsize=16,color="black",shape="box"];457 -> 492[label="",style="solid", color="black", weight=3];
458[label="EQ == LT",fontsize=16,color="black",shape="box"];458 -> 493[label="",style="solid", color="black", weight=3];
459[label="EQ == EQ",fontsize=16,color="black",shape="box"];459 -> 494[label="",style="solid", color="black", weight=3];
460[label="EQ == GT",fontsize=16,color="black",shape="box"];460 -> 495[label="",style="solid", color="black", weight=3];
461[label="GT == LT",fontsize=16,color="black",shape="box"];461 -> 496[label="",style="solid", color="black", weight=3];
462[label="GT == EQ",fontsize=16,color="black",shape="box"];462 -> 497[label="",style="solid", color="black", weight=3];
463[label="GT == GT",fontsize=16,color="black",shape="box"];463 -> 498[label="",style="solid", color="black", weight=3];
464[label="primEqDouble (Double yu310 yu311) yu4001",fontsize=16,color="burlywood",shape="box"];1136[label="yu4001/Double yu40010 yu40011",fontsize=10,color="white",style="solid",shape="box"];464 -> 1136[label="",style="solid", color="burlywood", weight=9];
1136 -> 499[label="",style="solid", color="burlywood", weight=3];
465[label="(yu310,yu311,yu312) == (yu40010,yu40011,yu40012)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];465 -> 500[label="",style="solid", color="black", weight=3];
466[label="yu310 :% yu311 == yu40010 :% yu40011\n  Integral a",fontsize=16,color="black",shape="box"];466 -> 501[label="",style="solid", color="black", weight=3];
467[label="Integer yu310 == Integer yu40010",fontsize=16,color="black",shape="box"];467 -> 502[label="",style="solid", color="black", weight=3];
468[label="primEqInt (Pos yu310) yu4001",fontsize=16,color="burlywood",shape="box"];1137[label="yu310/Succ yu3100",fontsize=10,color="white",style="solid",shape="box"];468 -> 1137[label="",style="solid", color="burlywood", weight=9];
1137 -> 503[label="",style="solid", color="burlywood", weight=3];
1138[label="yu310/Zero",fontsize=10,color="white",style="solid",shape="box"];468 -> 1138[label="",style="solid", color="burlywood", weight=9];
1138 -> 504[label="",style="solid", color="burlywood", weight=3];
469[label="primEqInt (Neg yu310) yu4001",fontsize=16,color="burlywood",shape="box"];1139[label="yu310/Succ yu3100",fontsize=10,color="white",style="solid",shape="box"];469 -> 1139[label="",style="solid", color="burlywood", weight=9];
1139 -> 505[label="",style="solid", color="burlywood", weight=3];
1140[label="yu310/Zero",fontsize=10,color="white",style="solid",shape="box"];469 -> 1140[label="",style="solid", color="burlywood", weight=9];
1140 -> 506[label="",style="solid", color="burlywood", weight=3];
470[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];470 -> 507[label="",style="solid", color="black", weight=3];
471[label="Nothing == Just yu40010\n  Eq a",fontsize=16,color="black",shape="box"];471 -> 508[label="",style="solid", color="black", weight=3];
472[label="Just yu310 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];472 -> 509[label="",style="solid", color="black", weight=3];
473[label="Just yu310 == Just yu40010\n  Eq a",fontsize=16,color="black",shape="box"];473 -> 510[label="",style="solid", color="black", weight=3];
474[label="() == ()",fontsize=16,color="black",shape="box"];474 -> 511[label="",style="solid", color="black", weight=3];
222 -> 4[label="",style="dashed", color="red", weight=0];
222[label="lookup (yu28,yu29) yu33\n  Eq a  Eq b",fontsize=16,color="magenta"];222 -> 288[label="",style="dashed", color="magenta", weight=3];
222 -> 289[label="",style="dashed", color="magenta", weight=3];
475 -> 355[label="",style="dashed", color="red", weight=0];
475[label="yu310 == yu40010 && yu311 == yu40011\n  Eq a  Eq b",fontsize=16,color="magenta"];475 -> 512[label="",style="dashed", color="magenta", weight=3];
475 -> 513[label="",style="dashed", color="magenta", weight=3];
476[label="primEqChar (Char yu310) (Char yu40010)",fontsize=16,color="black",shape="box"];476 -> 514[label="",style="solid", color="black", weight=3];
477[label="True",fontsize=16,color="green",shape="box"];478[label="False",fontsize=16,color="green",shape="box"];479[label="False",fontsize=16,color="green",shape="box"];480[label="True",fontsize=16,color="green",shape="box"];481[label="primEqFloat (Float yu310 yu311) (Float yu40010 yu40011)",fontsize=16,color="black",shape="box"];481 -> 515[label="",style="solid", color="black", weight=3];
482[label="yu310 == yu40010\n  Eq a",fontsize=16,color="blue",shape="box"];1143[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1143[label="",style="solid", color="blue", weight=9];
1143 -> 516[label="",style="solid", color="blue", weight=3];
1144[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1144[label="",style="solid", color="blue", weight=9];
1144 -> 517[label="",style="solid", color="blue", weight=3];
1145[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1145[label="",style="solid", color="blue", weight=9];
1145 -> 518[label="",style="solid", color="blue", weight=3];
1146[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1146[label="",style="solid", color="blue", weight=9];
1146 -> 519[label="",style="solid", color="blue", weight=3];
1147[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1147[label="",style="solid", color="blue", weight=9];
1147 -> 520[label="",style="solid", color="blue", weight=3];
1148[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1148[label="",style="solid", color="blue", weight=9];
1148 -> 521[label="",style="solid", color="blue", weight=3];
1149[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1149[label="",style="solid", color="blue", weight=9];
1149 -> 522[label="",style="solid", color="blue", weight=3];
1150[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1150[label="",style="solid", color="blue", weight=9];
1150 -> 523[label="",style="solid", color="blue", weight=3];
1151[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1151[label="",style="solid", color="blue", weight=9];
1151 -> 524[label="",style="solid", color="blue", weight=3];
1152[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1152[label="",style="solid", color="blue", weight=9];
1152 -> 525[label="",style="solid", color="blue", weight=3];
1153[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1153[label="",style="solid", color="blue", weight=9];
1153 -> 526[label="",style="solid", color="blue", weight=3];
1154[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1154[label="",style="solid", color="blue", weight=9];
1154 -> 527[label="",style="solid", color="blue", weight=3];
1155[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1155[label="",style="solid", color="blue", weight=9];
1155 -> 528[label="",style="solid", color="blue", weight=3];
1156[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];482 -> 1156[label="",style="solid", color="blue", weight=9];
1156 -> 529[label="",style="solid", color="blue", weight=3];
483[label="False",fontsize=16,color="green",shape="box"];484[label="False",fontsize=16,color="green",shape="box"];485[label="yu310 == yu40010\n  Eq a",fontsize=16,color="blue",shape="box"];1157[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];485 -> 1157[label="",style="solid", color="blue", weight=9];
1157 -> 530[label="",style="solid", color="blue", weight=3];
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1159[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];485 -> 1159[label="",style="solid", color="blue", weight=9];
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1164[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];485 -> 1164[label="",style="solid", color="blue", weight=9];
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1168[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];485 -> 1168[label="",style="solid", color="blue", weight=9];
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1208[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];512 -> 1208[label="",style="solid", color="blue", weight=9];
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1212[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];513 -> 1212[label="",style="solid", color="blue", weight=9];
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1213[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];513 -> 1213[label="",style="solid", color="blue", weight=9];
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1218[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];513 -> 1218[label="",style="solid", color="blue", weight=9];
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1220[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];513 -> 1220[label="",style="solid", color="blue", weight=9];
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909[label="False",fontsize=16,color="green",shape="box"];910[label="False",fontsize=16,color="green",shape="box"];911[label="True",fontsize=16,color="green",shape="box"];912[label="False",fontsize=16,color="green",shape="box"];913[label="True",fontsize=16,color="green",shape="box"];914 -> 514[label="",style="dashed", color="red", weight=0];
914[label="primEqNat yu3100 yu400100",fontsize=16,color="magenta"];914 -> 980[label="",style="dashed", color="magenta", weight=3];
914 -> 981[label="",style="dashed", color="magenta", weight=3];
915[label="False",fontsize=16,color="green",shape="box"];916[label="False",fontsize=16,color="green",shape="box"];917[label="True",fontsize=16,color="green",shape="box"];918[label="primMulInt (Pos yu3110) yu40011",fontsize=16,color="burlywood",shape="box"];1445[label="yu40011/Pos yu400110",fontsize=10,color="white",style="solid",shape="box"];918 -> 1445[label="",style="solid", color="burlywood", weight=9];
1445 -> 982[label="",style="solid", color="burlywood", weight=3];
1446[label="yu40011/Neg yu400110",fontsize=10,color="white",style="solid",shape="box"];918 -> 1446[label="",style="solid", color="burlywood", weight=9];
1446 -> 983[label="",style="solid", color="burlywood", weight=3];
919[label="primMulInt (Neg yu3110) yu40011",fontsize=16,color="burlywood",shape="box"];1447[label="yu40011/Pos yu400110",fontsize=10,color="white",style="solid",shape="box"];919 -> 1447[label="",style="solid", color="burlywood", weight=9];
1447 -> 984[label="",style="solid", color="burlywood", weight=3];
1448[label="yu40011/Neg yu400110",fontsize=10,color="white",style="solid",shape="box"];919 -> 1448[label="",style="solid", color="burlywood", weight=9];
1448 -> 985[label="",style="solid", color="burlywood", weight=3];
920[label="yu40012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];921[label="yu312\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];922[label="yu40012",fontsize=16,color="green",shape="box"];923[label="yu312",fontsize=16,color="green",shape="box"];924[label="yu40012",fontsize=16,color="green",shape="box"];925[label="yu312",fontsize=16,color="green",shape="box"];926[label="yu40012",fontsize=16,color="green",shape="box"];927[label="yu312",fontsize=16,color="green",shape="box"];928[label="yu40012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];929[label="yu312\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];930[label="yu40012\n  Eq a",fontsize=16,color="green",shape="box"];931[label="yu312\n  Eq a",fontsize=16,color="green",shape="box"];932[label="yu40012",fontsize=16,color="green",shape="box"];933[label="yu312",fontsize=16,color="green",shape="box"];934[label="yu40012",fontsize=16,color="green",shape="box"];935[label="yu312",fontsize=16,color="green",shape="box"];936[label="yu40012\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];937[label="yu312\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];938[label="yu40012\n  Integral a",fontsize=16,color="green",shape="box"];939[label="yu312\n  Integral a",fontsize=16,color="green",shape="box"];940[label="yu40012",fontsize=16,color="green",shape="box"];941[label="yu312",fontsize=16,color="green",shape="box"];942[label="yu40012",fontsize=16,color="green",shape="box"];943[label="yu312",fontsize=16,color="green",shape="box"];944[label="yu40012\n  Eq a",fontsize=16,color="green",shape="box"];945[label="yu312\n  Eq a",fontsize=16,color="green",shape="box"];946[label="yu40012",fontsize=16,color="green",shape="box"];947[label="yu312",fontsize=16,color="green",shape="box"];948[label="yu40011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];949[label="yu311\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];950[label="yu40011",fontsize=16,color="green",shape="box"];951[label="yu311",fontsize=16,color="green",shape="box"];952[label="yu40011",fontsize=16,color="green",shape="box"];953[label="yu311",fontsize=16,color="green",shape="box"];954[label="yu40011",fontsize=16,color="green",shape="box"];955[label="yu311",fontsize=16,color="green",shape="box"];956[label="yu40011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];957[label="yu311\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];958[label="yu40011\n  Eq a",fontsize=16,color="green",shape="box"];959[label="yu311\n  Eq a",fontsize=16,color="green",shape="box"];960[label="yu40011",fontsize=16,color="green",shape="box"];961[label="yu311",fontsize=16,color="green",shape="box"];962[label="yu40011",fontsize=16,color="green",shape="box"];963[label="yu311",fontsize=16,color="green",shape="box"];964[label="yu40011\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];965[label="yu311\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];966[label="yu40011\n  Integral a",fontsize=16,color="green",shape="box"];967[label="yu311\n  Integral a",fontsize=16,color="green",shape="box"];968[label="yu40011",fontsize=16,color="green",shape="box"];969[label="yu311",fontsize=16,color="green",shape="box"];970[label="yu40011",fontsize=16,color="green",shape="box"];971[label="yu311",fontsize=16,color="green",shape="box"];972[label="yu40011\n  Eq a",fontsize=16,color="green",shape="box"];973[label="yu311\n  Eq a",fontsize=16,color="green",shape="box"];974[label="yu40011",fontsize=16,color="green",shape="box"];975[label="yu311",fontsize=16,color="green",shape="box"];976[label="yu3100",fontsize=16,color="green",shape="box"];977[label="yu400100",fontsize=16,color="green",shape="box"];978[label="yu3100",fontsize=16,color="green",shape="box"];979[label="yu400100",fontsize=16,color="green",shape="box"];980[label="yu3100",fontsize=16,color="green",shape="box"];981[label="yu400100",fontsize=16,color="green",shape="box"];982[label="primMulInt (Pos yu3110) (Pos yu400110)",fontsize=16,color="black",shape="box"];982 -> 986[label="",style="solid", color="black", weight=3];
983[label="primMulInt (Pos yu3110) (Neg yu400110)",fontsize=16,color="black",shape="box"];983 -> 987[label="",style="solid", color="black", weight=3];
984[label="primMulInt (Neg yu3110) (Pos yu400110)",fontsize=16,color="black",shape="box"];984 -> 988[label="",style="solid", color="black", weight=3];
985[label="primMulInt (Neg yu3110) (Neg yu400110)",fontsize=16,color="black",shape="box"];985 -> 989[label="",style="solid", color="black", weight=3];
986[label="Pos (primMulNat yu3110 yu400110)",fontsize=16,color="green",shape="box"];986 -> 990[label="",style="dashed", color="green", weight=3];
987[label="Neg (primMulNat yu3110 yu400110)",fontsize=16,color="green",shape="box"];987 -> 991[label="",style="dashed", color="green", weight=3];
988[label="Neg (primMulNat yu3110 yu400110)",fontsize=16,color="green",shape="box"];988 -> 992[label="",style="dashed", color="green", weight=3];
989[label="Pos (primMulNat yu3110 yu400110)",fontsize=16,color="green",shape="box"];989 -> 993[label="",style="dashed", color="green", weight=3];
990[label="primMulNat yu3110 yu400110",fontsize=16,color="burlywood",shape="triangle"];1449[label="yu3110/Succ yu31100",fontsize=10,color="white",style="solid",shape="box"];990 -> 1449[label="",style="solid", color="burlywood", weight=9];
1449 -> 994[label="",style="solid", color="burlywood", weight=3];
1450[label="yu3110/Zero",fontsize=10,color="white",style="solid",shape="box"];990 -> 1450[label="",style="solid", color="burlywood", weight=9];
1450 -> 995[label="",style="solid", color="burlywood", weight=3];
991 -> 990[label="",style="dashed", color="red", weight=0];
991[label="primMulNat yu3110 yu400110",fontsize=16,color="magenta"];991 -> 996[label="",style="dashed", color="magenta", weight=3];
992 -> 990[label="",style="dashed", color="red", weight=0];
992[label="primMulNat yu3110 yu400110",fontsize=16,color="magenta"];992 -> 997[label="",style="dashed", color="magenta", weight=3];
993 -> 990[label="",style="dashed", color="red", weight=0];
993[label="primMulNat yu3110 yu400110",fontsize=16,color="magenta"];993 -> 998[label="",style="dashed", color="magenta", weight=3];
993 -> 999[label="",style="dashed", color="magenta", weight=3];
994[label="primMulNat (Succ yu31100) yu400110",fontsize=16,color="burlywood",shape="box"];1454[label="yu400110/Succ yu4001100",fontsize=10,color="white",style="solid",shape="box"];994 -> 1454[label="",style="solid", color="burlywood", weight=9];
1454 -> 1000[label="",style="solid", color="burlywood", weight=3];
1455[label="yu400110/Zero",fontsize=10,color="white",style="solid",shape="box"];994 -> 1455[label="",style="solid", color="burlywood", weight=9];
1455 -> 1001[label="",style="solid", color="burlywood", weight=3];
995[label="primMulNat Zero yu400110",fontsize=16,color="burlywood",shape="box"];1456[label="yu400110/Succ yu4001100",fontsize=10,color="white",style="solid",shape="box"];995 -> 1456[label="",style="solid", color="burlywood", weight=9];
1456 -> 1002[label="",style="solid", color="burlywood", weight=3];
1457[label="yu400110/Zero",fontsize=10,color="white",style="solid",shape="box"];995 -> 1457[label="",style="solid", color="burlywood", weight=9];
1457 -> 1003[label="",style="solid", color="burlywood", weight=3];
996[label="yu400110",fontsize=16,color="green",shape="box"];997[label="yu3110",fontsize=16,color="green",shape="box"];998[label="yu400110",fontsize=16,color="green",shape="box"];999[label="yu3110",fontsize=16,color="green",shape="box"];1000[label="primMulNat (Succ yu31100) (Succ yu4001100)",fontsize=16,color="black",shape="box"];1000 -> 1004[label="",style="solid", color="black", weight=3];
1001[label="primMulNat (Succ yu31100) Zero",fontsize=16,color="black",shape="box"];1001 -> 1005[label="",style="solid", color="black", weight=3];
1002[label="primMulNat Zero (Succ yu4001100)",fontsize=16,color="black",shape="box"];1002 -> 1006[label="",style="solid", color="black", weight=3];
1003[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];1003 -> 1007[label="",style="solid", color="black", weight=3];
1004 -> 1008[label="",style="dashed", color="red", weight=0];
1004[label="primPlusNat (primMulNat yu31100 (Succ yu4001100)) (Succ yu4001100)",fontsize=16,color="magenta"];1004 -> 1009[label="",style="dashed", color="magenta", weight=3];
1005[label="Zero",fontsize=16,color="green",shape="box"];1006[label="Zero",fontsize=16,color="green",shape="box"];1007[label="Zero",fontsize=16,color="green",shape="box"];1009 -> 990[label="",style="dashed", color="red", weight=0];
1009[label="primMulNat yu31100 (Succ yu4001100)",fontsize=16,color="magenta"];1009 -> 1010[label="",style="dashed", color="magenta", weight=3];
1009 -> 1011[label="",style="dashed", color="magenta", weight=3];
1008[label="primPlusNat yu48 (Succ yu4001100)",fontsize=16,color="burlywood",shape="triangle"];1460[label="yu48/Succ yu480",fontsize=10,color="white",style="solid",shape="box"];1008 -> 1460[label="",style="solid", color="burlywood", weight=9];
1460 -> 1012[label="",style="solid", color="burlywood", weight=3];
1461[label="yu48/Zero",fontsize=10,color="white",style="solid",shape="box"];1008 -> 1461[label="",style="solid", color="burlywood", weight=9];
1461 -> 1013[label="",style="solid", color="burlywood", weight=3];
1010[label="Succ yu4001100",fontsize=16,color="green",shape="box"];1011[label="yu31100",fontsize=16,color="green",shape="box"];1012[label="primPlusNat (Succ yu480) (Succ yu4001100)",fontsize=16,color="black",shape="box"];1012 -> 1014[label="",style="solid", color="black", weight=3];
1013[label="primPlusNat Zero (Succ yu4001100)",fontsize=16,color="black",shape="box"];1013 -> 1015[label="",style="solid", color="black", weight=3];
1014[label="Succ (Succ (primPlusNat yu480 yu4001100))",fontsize=16,color="green",shape="box"];1014 -> 1016[label="",style="dashed", color="green", weight=3];
1015[label="Succ yu4001100",fontsize=16,color="green",shape="box"];1016[label="primPlusNat yu480 yu4001100",fontsize=16,color="burlywood",shape="triangle"];1462[label="yu480/Succ yu4800",fontsize=10,color="white",style="solid",shape="box"];1016 -> 1462[label="",style="solid", color="burlywood", weight=9];
1462 -> 1017[label="",style="solid", color="burlywood", weight=3];
1463[label="yu480/Zero",fontsize=10,color="white",style="solid",shape="box"];1016 -> 1463[label="",style="solid", color="burlywood", weight=9];
1463 -> 1018[label="",style="solid", color="burlywood", weight=3];
1017[label="primPlusNat (Succ yu4800) yu4001100",fontsize=16,color="burlywood",shape="box"];1464[label="yu4001100/Succ yu40011000",fontsize=10,color="white",style="solid",shape="box"];1017 -> 1464[label="",style="solid", color="burlywood", weight=9];
1464 -> 1019[label="",style="solid", color="burlywood", weight=3];
1465[label="yu4001100/Zero",fontsize=10,color="white",style="solid",shape="box"];1017 -> 1465[label="",style="solid", color="burlywood", weight=9];
1465 -> 1020[label="",style="solid", color="burlywood", weight=3];
1018[label="primPlusNat Zero yu4001100",fontsize=16,color="burlywood",shape="box"];1466[label="yu4001100/Succ yu40011000",fontsize=10,color="white",style="solid",shape="box"];1018 -> 1466[label="",style="solid", color="burlywood", weight=9];
1466 -> 1021[label="",style="solid", color="burlywood", weight=3];
1467[label="yu4001100/Zero",fontsize=10,color="white",style="solid",shape="box"];1018 -> 1467[label="",style="solid", color="burlywood", weight=9];
1467 -> 1022[label="",style="solid", color="burlywood", weight=3];
1019[label="primPlusNat (Succ yu4800) (Succ yu40011000)",fontsize=16,color="black",shape="box"];1019 -> 1023[label="",style="solid", color="black", weight=3];
1020[label="primPlusNat (Succ yu4800) Zero",fontsize=16,color="black",shape="box"];1020 -> 1024[label="",style="solid", color="black", weight=3];
1021[label="primPlusNat Zero (Succ yu40011000)",fontsize=16,color="black",shape="box"];1021 -> 1025[label="",style="solid", color="black", weight=3];
1022[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1022 -> 1026[label="",style="solid", color="black", weight=3];
1023[label="Succ (Succ (primPlusNat yu4800 yu40011000))",fontsize=16,color="green",shape="box"];1023 -> 1027[label="",style="dashed", color="green", weight=3];
1024[label="Succ yu4800",fontsize=16,color="green",shape="box"];1025[label="Succ yu40011000",fontsize=16,color="green",shape="box"];1026[label="Zero",fontsize=16,color="green",shape="box"];1027 -> 1016[label="",style="dashed", color="red", weight=0];
1027[label="primPlusNat yu4800 yu40011000",fontsize=16,color="magenta"];1027 -> 1028[label="",style="dashed", color="magenta", weight=3];
1027 -> 1029[label="",style="dashed", color="magenta", weight=3];
1028[label="yu40011000",fontsize=16,color="green",shape="box"];1029[label="yu4800",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(yu4800), Succ(yu40011000)) → new_primPlusNat(yu4800, yu40011000)

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

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

new_primPlusNat(Succ(yu4800), Succ(yu40011000)) → new_primPlusNat(yu4800, yu40011000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(yu31100), Succ(yu4001100)) → new_primMulNat(yu31100, Succ(yu4001100))

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

new_primMulNat(Succ(yu31100), Succ(yu4001100)) → new_primMulNat(yu31100, Succ(yu4001100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(yu3100), Succ(yu400100)) → new_primEqNat(yu3100, yu400100)

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

new_primEqNat(Succ(yu3100), Succ(yu400100)) → new_primEqNat(yu3100, yu400100)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(app(ty_@2, cc), cd), ce) → new_esEs(yu310, yu40010, cc, cd)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(app(app(ty_@3, bcg), bch), bda), hf, bbb) → new_esEs2(yu310, yu40010, bcg, bch, bda)
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_@2, gd), ge)) → new_esEs(yu310, yu40010, gd, ge)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(ty_Maybe, bca), bbb) → new_esEs3(yu311, yu40011, bca)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(ty_Maybe, de), ce) → new_esEs3(yu310, yu40010, de)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(ty_[], da), ce) → new_esEs1(yu310, yu40010, da)
new_esEs3(Just(yu310), Just(yu40010), app(app(ty_Either, bde), bdf)) → new_esEs0(yu310, yu40010, bde, bdf)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(ty_Maybe, bag)) → new_esEs3(yu312, yu40012, bag)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(app(ty_Either, bcd), bce), hf, bbb) → new_esEs0(yu310, yu40010, bcd, bce)
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), gc) → new_esEs1(yu311, yu40011, gc)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(ty_[], bbe), bbb) → new_esEs1(yu311, yu40011, bbe)
new_esEs0(Left(yu310), Left(yu40010), app(ty_Maybe, eg), dh) → new_esEs3(yu310, yu40010, eg)
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(ty_[], gh)) → new_esEs1(yu310, yu40010, gh)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(app(ty_Either, bd), be)) → new_esEs0(yu311, yu40011, bd, be)
new_esEs0(Left(yu310), Left(yu40010), app(app(app(ty_@3, ed), ee), ef), dh) → new_esEs2(yu310, yu40010, ed, ee, ef)
new_esEs0(Left(yu310), Left(yu40010), app(app(ty_Either, ea), eb), dh) → new_esEs0(yu310, yu40010, ea, eb)
new_esEs0(Left(yu310), Left(yu40010), app(app(ty_@2, df), dg), dh) → new_esEs(yu310, yu40010, df, dg)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(ty_Maybe, cb)) → new_esEs3(yu311, yu40011, cb)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(app(ty_Either, cf), cg), ce) → new_esEs0(yu310, yu40010, cf, cg)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(app(app(ty_@3, bg), bh), ca)) → new_esEs2(yu311, yu40011, bg, bh, ca)
new_esEs0(Right(yu310), Right(yu40010), eh, app(app(ty_Either, fc), fd)) → new_esEs0(yu310, yu40010, fc, fd)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(ty_[], bf)) → new_esEs1(yu311, yu40011, bf)
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_Either, gf), gg)) → new_esEs0(yu310, yu40010, gf, gg)
new_esEs0(Right(yu310), Right(yu40010), eh, app(ty_[], ff)) → new_esEs1(yu310, yu40010, ff)
new_esEs0(Left(yu310), Left(yu40010), app(ty_[], ec), dh) → new_esEs1(yu310, yu40010, ec)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_esEs2(yu311, yu40011, bbf, bbg, bbh)
new_esEs0(Right(yu310), Right(yu40010), eh, app(app(app(ty_@3, fg), fh), ga)) → new_esEs2(yu310, yu40010, fg, fh, ga)
new_esEs3(Just(yu310), Just(yu40010), app(app(app(ty_@3, bdh), bea), beb)) → new_esEs2(yu310, yu40010, bdh, bea, beb)
new_esEs3(Just(yu310), Just(yu40010), app(ty_Maybe, bec)) → new_esEs3(yu310, yu40010, bec)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(ty_Maybe, bdb), hf, bbb) → new_esEs3(yu310, yu40010, bdb)
new_esEs3(Just(yu310), Just(yu40010), app(app(ty_@2, bdc), bdd)) → new_esEs(yu310, yu40010, bdc, bdd)
new_esEs0(Right(yu310), Right(yu40010), eh, app(ty_Maybe, gb)) → new_esEs3(yu310, yu40010, gb)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(app(ty_@2, bb), bc)) → new_esEs(yu311, yu40011, bb, bc)
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(app(app(ty_@3, db), dc), dd), ce) → new_esEs2(yu310, yu40010, db, dc, dd)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(ty_[], bac)) → new_esEs1(yu312, yu40012, bac)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(app(ty_@2, bah), bba), bbb) → new_esEs(yu311, yu40011, bah, bba)
new_esEs3(Just(yu310), Just(yu40010), app(ty_[], bdg)) → new_esEs1(yu310, yu40010, bdg)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(app(ty_@2, bcb), bcc), hf, bbb) → new_esEs(yu310, yu40010, bcb, bcc)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(app(ty_Either, bbc), bbd), bbb) → new_esEs0(yu311, yu40011, bbc, bbd)
new_esEs0(Right(yu310), Right(yu40010), eh, app(app(ty_@2, fa), fb)) → new_esEs(yu310, yu40010, fa, fb)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(app(ty_@2, hg), hh)) → new_esEs(yu312, yu40012, hg, hh)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(ty_[], bcf), hf, bbb) → new_esEs1(yu310, yu40010, bcf)
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(app(app(ty_@3, ha), hb), hc)) → new_esEs2(yu310, yu40010, ha, hb, hc)
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(ty_Maybe, hd)) → new_esEs3(yu310, yu40010, hd)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(app(ty_Either, baa), bab)) → new_esEs0(yu312, yu40012, baa, bab)
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(app(app(ty_@3, bad), bae), baf)) → new_esEs2(yu312, yu40012, bad, bae, baf)

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

new_esEs3(Just(yu310), Just(yu40010), app(app(ty_@2, bdc), bdd)) → new_esEs(yu310, yu40010, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(yu310), Just(yu40010), app(app(app(ty_@3, bdh), bea), beb)) → new_esEs2(yu310, yu40010, bdh, bea, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(yu310), Just(yu40010), app(ty_[], bdg)) → new_esEs1(yu310, yu40010, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_@2, gd), ge)) → new_esEs(yu310, yu40010, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(app(app(ty_@3, ha), hb), hc)) → new_esEs2(yu310, yu40010, ha, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(yu310), Just(yu40010), app(ty_Maybe, bec)) → new_esEs3(yu310, yu40010, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(yu310), Just(yu40010), app(app(ty_Either, bde), bdf)) → new_esEs0(yu310, yu40010, bde, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(ty_Maybe, hd)) → new_esEs3(yu310, yu40010, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(app(ty_Either, gf), gg)) → new_esEs0(yu310, yu40010, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(app(ty_@2, cc), cd), ce) → new_esEs(yu310, yu40010, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(app(ty_@2, bb), bc)) → new_esEs(yu311, yu40011, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(app(app(ty_@3, bg), bh), ca)) → new_esEs2(yu311, yu40011, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(app(app(ty_@3, db), dc), dd), ce) → new_esEs2(yu310, yu40010, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(ty_[], da), ce) → new_esEs1(yu310, yu40010, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(ty_[], bf)) → new_esEs1(yu311, yu40011, bf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(ty_Maybe, de), ce) → new_esEs3(yu310, yu40010, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(ty_Maybe, cb)) → new_esEs3(yu311, yu40011, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), ba, app(app(ty_Either, bd), be)) → new_esEs0(yu311, yu40011, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(yu310, yu311), @2(yu40010, yu40011), app(app(ty_Either, cf), cg), ce) → new_esEs0(yu310, yu40010, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(app(ty_@2, bah), bba), bbb) → new_esEs(yu311, yu40011, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(app(ty_@2, bcb), bcc), hf, bbb) → new_esEs(yu310, yu40010, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(app(ty_@2, hg), hh)) → new_esEs(yu312, yu40012, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(Left(yu310), Left(yu40010), app(app(ty_@2, df), dg), dh) → new_esEs(yu310, yu40010, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(yu310), Right(yu40010), eh, app(app(ty_@2, fa), fb)) → new_esEs(yu310, yu40010, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(app(app(ty_@3, bcg), bch), bda), hf, bbb) → new_esEs2(yu310, yu40010, bcg, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_esEs2(yu311, yu40011, bbf, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(app(app(ty_@3, bad), bae), baf)) → new_esEs2(yu312, yu40012, bad, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(ty_[], bbe), bbb) → new_esEs1(yu311, yu40011, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(ty_[], bac)) → new_esEs1(yu312, yu40012, bac)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(ty_[], bcf), hf, bbb) → new_esEs1(yu310, yu40010, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(ty_Maybe, bca), bbb) → new_esEs3(yu311, yu40011, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(ty_Maybe, bag)) → new_esEs3(yu312, yu40012, bag)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(ty_Maybe, bdb), hf, bbb) → new_esEs3(yu310, yu40010, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), app(app(ty_Either, bcd), bce), hf, bbb) → new_esEs0(yu310, yu40010, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, app(app(ty_Either, bbc), bbd), bbb) → new_esEs0(yu311, yu40011, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), he, hf, app(app(ty_Either, baa), bab)) → new_esEs0(yu312, yu40012, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(Left(yu310), Left(yu40010), app(app(app(ty_@3, ed), ee), ef), dh) → new_esEs2(yu310, yu40010, ed, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Right(yu310), Right(yu40010), eh, app(app(app(ty_@3, fg), fh), ga)) → new_esEs2(yu310, yu40010, fg, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), gc) → new_esEs1(yu311, yu40011, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs1(:(yu310, yu311), :(yu40010, yu40011), app(ty_[], gh)) → new_esEs1(yu310, yu40010, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(yu310), Right(yu40010), eh, app(ty_[], ff)) → new_esEs1(yu310, yu40010, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Left(yu310), Left(yu40010), app(ty_[], ec), dh) → new_esEs1(yu310, yu40010, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Left(yu310), Left(yu40010), app(ty_Maybe, eg), dh) → new_esEs3(yu310, yu40010, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(yu310), Right(yu40010), eh, app(ty_Maybe, gb)) → new_esEs3(yu310, yu40010, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Left(yu310), Left(yu40010), app(app(ty_Either, ea), eb), dh) → new_esEs0(yu310, yu40010, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(yu310), Right(yu40010), eh, app(app(ty_Either, fc), fd)) → new_esEs0(yu310, yu40010, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_lookup1(yu28, yu29, yu30, yu31, yu32, yu33, False, ba, bb, bc) → new_lookup(@2(yu28, yu29), yu33, ba, bb, bc)
new_lookup(@2(yu30, yu31), :(@2(@2(yu4000, yu4001), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu31, yu4000, yu4001, yu401, yu41, new_asAs(new_esEs5(yu30, yu4000, be), new_esEs4(yu31, yu4001, bf)), bd, be, bf)

The TRS R consists of the following rules:

new_esEs23(yu310, yu40010, ty_@0) → new_esEs20(yu310, yu40010)
new_esEs23(yu310, yu40010, app(app(ty_Either, hc), hd)) → new_esEs12(yu310, yu40010, hc, hd)
new_esEs12(Right(yu310), Right(yu40010), de, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs15(yu310, yu40010, bhb, bhc, bhd)
new_primPlusNat1(Succ(yu4800), Succ(yu40011000)) → Succ(Succ(new_primPlusNat1(yu4800, yu40011000)))
new_primEqInt(Neg(Succ(yu3100)), Pos(yu40010)) → False
new_primEqInt(Pos(Succ(yu3100)), Neg(yu40010)) → False
new_esEs26(yu311, yu40011, app(app(ty_Either, bda), bdb)) → new_esEs12(yu311, yu40011, bda, bdb)
new_esEs12(Right(yu310), Right(yu40010), de, ty_Double) → new_esEs14(yu310, yu40010)
new_esEs22(yu311, yu40011, ty_@0) → new_esEs20(yu311, yu40011)
new_esEs22(yu311, yu40011, app(ty_[], gc)) → new_esEs6(yu311, yu40011, gc)
new_esEs12(Right(yu310), Right(yu40010), de, ty_Integer) → new_esEs17(yu310, yu40010)
new_esEs26(yu311, yu40011, app(ty_Ratio, bdg)) → new_esEs16(yu311, yu40011, bdg)
new_esEs7(yu310, yu40010, ty_Integer) → new_esEs17(yu310, yu40010)
new_esEs26(yu311, yu40011, ty_Double) → new_esEs14(yu311, yu40011)
new_esEs12(Right(yu310), Right(yu40010), de, app(ty_Ratio, bhe)) → new_esEs16(yu310, yu40010, bhe)
new_esEs19(Just(yu310), Just(yu40010), ty_Char) → new_esEs9(yu310, yu40010)
new_primEqInt(Neg(Zero), Pos(Succ(yu400100))) → False
new_esEs6(:(yu310, yu311), :(yu40010, yu40011), bg) → new_asAs(new_esEs7(yu310, yu40010, bg), new_esEs6(yu311, yu40011, bg))
new_primEqInt(Pos(Zero), Neg(Succ(yu400100))) → False
new_esEs4(yu31, yu4001, ty_Int) → new_esEs18(yu31, yu4001)
new_esEs12(Left(yu310), Left(yu40010), app(ty_Ratio, bgc), df) → new_esEs16(yu310, yu40010, bgc)
new_esEs7(yu310, yu40010, ty_Float) → new_esEs11(yu310, yu40010)
new_esEs26(yu311, yu40011, app(ty_Maybe, bdh)) → new_esEs19(yu311, yu40011, bdh)
new_esEs23(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs21(yu312, yu40012, app(ty_Maybe, ff)) → new_esEs19(yu312, yu40012, ff)
new_primMulNat0(Zero, Zero) → Zero
new_esEs27(yu310, yu40010, app(ty_Ratio, bfa)) → new_esEs16(yu310, yu40010, bfa)
new_esEs19(Just(yu310), Just(yu40010), app(app(ty_Either, bbg), bbh)) → new_esEs12(yu310, yu40010, bbg, bbh)
new_esEs12(Left(yu310), Left(yu40010), ty_@0, df) → new_esEs20(yu310, yu40010)
new_esEs12(Right(yu310), Right(yu40010), de, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs23(yu310, yu40010, ty_Float) → new_esEs11(yu310, yu40010)
new_esEs22(yu311, yu40011, ty_Char) → new_esEs9(yu311, yu40011)
new_esEs21(yu312, yu40012, app(app(ty_Either, ef), eg)) → new_esEs12(yu312, yu40012, ef, eg)
new_primPlusNat0(Zero, yu4001100) → Succ(yu4001100)
new_esEs22(yu311, yu40011, ty_Float) → new_esEs11(yu311, yu40011)
new_esEs21(yu312, yu40012, ty_@0) → new_esEs20(yu312, yu40012)
new_esEs19(Just(yu310), Just(yu40010), ty_Ordering) → new_esEs13(yu310, yu40010)
new_esEs13(EQ, EQ) → True
new_esEs26(yu311, yu40011, ty_Int) → new_esEs18(yu311, yu40011)
new_esEs5(yu30, yu4000, ty_Float) → new_esEs11(yu30, yu4000)
new_esEs19(Just(yu310), Just(yu40010), ty_@0) → new_esEs20(yu310, yu40010)
new_sr(Neg(yu3110), Pos(yu400110)) → Neg(new_primMulNat0(yu3110, yu400110))
new_sr(Pos(yu3110), Neg(yu400110)) → Neg(new_primMulNat0(yu3110, yu400110))
new_esEs27(yu310, yu40010, app(app(ty_@2, bea), beb)) → new_esEs8(yu310, yu40010, bea, beb)
new_esEs23(yu310, yu40010, app(ty_Maybe, bab)) → new_esEs19(yu310, yu40010, bab)
new_esEs19(Just(yu310), Just(yu40010), ty_Bool) → new_esEs10(yu310, yu40010)
new_esEs5(yu30, yu4000, app(app(ty_Either, bae), baf)) → new_esEs12(yu30, yu4000, bae, baf)
new_esEs22(yu311, yu40011, ty_Bool) → new_esEs10(yu311, yu40011)
new_esEs4(yu31, yu4001, ty_@0) → new_esEs20(yu31, yu4001)
new_esEs5(yu30, yu4000, app(ty_Ratio, bbc)) → new_esEs16(yu30, yu4000, bbc)
new_esEs12(Left(yu310), Right(yu40010), de, df) → False
new_esEs12(Right(yu310), Left(yu40010), de, df) → False
new_esEs12(Left(yu310), Left(yu40010), app(app(ty_@2, bfc), bfd), df) → new_esEs8(yu310, yu40010, bfc, bfd)
new_esEs19(Just(yu310), Nothing, ec) → False
new_esEs19(Nothing, Just(yu40010), ec) → False
new_esEs4(yu31, yu4001, ty_Float) → new_esEs11(yu31, yu4001)
new_esEs27(yu310, yu40010, ty_Bool) → new_esEs10(yu310, yu40010)
new_esEs7(yu310, yu40010, app(app(ty_Either, cb), cc)) → new_esEs12(yu310, yu40010, cb, cc)
new_esEs25(yu310, yu40010, ty_Integer) → new_esEs17(yu310, yu40010)
new_esEs19(Nothing, Nothing, ec) → True
new_esEs27(yu310, yu40010, app(app(ty_Either, bec), bed)) → new_esEs12(yu310, yu40010, bec, bed)
new_esEs10(True, True) → True
new_esEs7(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs13(GT, GT) → True
new_esEs12(Right(yu310), Right(yu40010), de, ty_Bool) → new_esEs10(yu310, yu40010)
new_esEs27(yu310, yu40010, ty_Double) → new_esEs14(yu310, yu40010)
new_esEs19(Just(yu310), Just(yu40010), app(app(ty_@2, bbe), bbf)) → new_esEs8(yu310, yu40010, bbe, bbf)
new_esEs12(Left(yu310), Left(yu40010), app(app(ty_Either, bfe), bff), df) → new_esEs12(yu310, yu40010, bfe, bff)
new_esEs12(Left(yu310), Left(yu40010), app(ty_Maybe, bgd), df) → new_esEs19(yu310, yu40010, bgd)
new_primEqNat0(Zero, Succ(yu400100)) → False
new_primEqNat0(Succ(yu3100), Zero) → False
new_esEs17(Integer(yu310), Integer(yu40010)) → new_primEqInt(yu310, yu40010)
new_esEs5(yu30, yu4000, app(ty_[], bag)) → new_esEs6(yu30, yu4000, bag)
new_esEs21(yu312, yu40012, app(app(ty_@2, ed), ee)) → new_esEs8(yu312, yu40012, ed, ee)
new_esEs12(Right(yu310), Right(yu40010), de, app(ty_Maybe, bhf)) → new_esEs19(yu310, yu40010, bhf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs22(yu311, yu40011, ty_Double) → new_esEs14(yu311, yu40011)
new_esEs26(yu311, yu40011, ty_Bool) → new_esEs10(yu311, yu40011)
new_esEs13(EQ, LT) → False
new_esEs13(LT, EQ) → False
new_esEs27(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs26(yu311, yu40011, app(app(ty_@2, bcg), bch)) → new_esEs8(yu311, yu40011, bcg, bch)
new_esEs27(yu310, yu40010, ty_Float) → new_esEs11(yu310, yu40010)
new_esEs20(@0, @0) → True
new_esEs22(yu311, yu40011, ty_Ordering) → new_esEs13(yu311, yu40011)
new_esEs5(yu30, yu4000, ty_Ordering) → new_esEs13(yu30, yu4000)
new_esEs21(yu312, yu40012, ty_Ordering) → new_esEs13(yu312, yu40012)
new_esEs15(@3(yu310, yu311, yu312), @3(yu40010, yu40011, yu40012), dg, dh, ea) → new_asAs(new_esEs23(yu310, yu40010, dg), new_asAs(new_esEs22(yu311, yu40011, dh), new_esEs21(yu312, yu40012, ea)))
new_esEs12(Left(yu310), Left(yu40010), ty_Bool, df) → new_esEs10(yu310, yu40010)
new_esEs4(yu31, yu4001, ty_Char) → new_esEs9(yu31, yu4001)
new_esEs5(yu30, yu4000, ty_@0) → new_esEs20(yu30, yu4000)
new_esEs4(yu31, yu4001, ty_Double) → new_esEs14(yu31, yu4001)
new_esEs4(yu31, yu4001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs15(yu31, yu4001, dg, dh, ea)
new_esEs21(yu312, yu40012, ty_Int) → new_esEs18(yu312, yu40012)
new_esEs23(yu310, yu40010, app(app(ty_@2, ha), hb)) → new_esEs8(yu310, yu40010, ha, hb)
new_esEs18(yu31, yu4001) → new_primEqInt(yu31, yu4001)
new_esEs6([], :(yu40010, yu40011), bg) → False
new_esEs6(:(yu310, yu311), [], bg) → False
new_esEs7(yu310, yu40010, app(ty_Maybe, db)) → new_esEs19(yu310, yu40010, db)
new_esEs23(yu310, yu40010, ty_Double) → new_esEs14(yu310, yu40010)
new_esEs7(yu310, yu40010, app(ty_[], cd)) → new_esEs6(yu310, yu40010, cd)
new_esEs19(Just(yu310), Just(yu40010), app(ty_[], bca)) → new_esEs6(yu310, yu40010, bca)
new_esEs21(yu312, yu40012, ty_Char) → new_esEs9(yu312, yu40012)
new_esEs23(yu310, yu40010, app(ty_Ratio, baa)) → new_esEs16(yu310, yu40010, baa)
new_esEs19(Just(yu310), Just(yu40010), app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs15(yu310, yu40010, bcb, bcc, bcd)
new_esEs22(yu311, yu40011, app(ty_Ratio, gg)) → new_esEs16(yu311, yu40011, gg)
new_esEs8(@2(yu310, yu311), @2(yu40010, yu40011), dc, dd) → new_asAs(new_esEs27(yu310, yu40010, dc), new_esEs26(yu311, yu40011, dd))
new_esEs7(yu310, yu40010, ty_Ordering) → new_esEs13(yu310, yu40010)
new_esEs21(yu312, yu40012, ty_Integer) → new_esEs17(yu312, yu40012)
new_esEs22(yu311, yu40011, app(app(app(ty_@3, gd), ge), gf)) → new_esEs15(yu311, yu40011, gd, ge, gf)
new_esEs4(yu31, yu4001, app(ty_[], bg)) → new_esEs6(yu31, yu4001, bg)
new_esEs26(yu311, yu40011, app(ty_[], bdc)) → new_esEs6(yu311, yu40011, bdc)
new_sr(Neg(yu3110), Neg(yu400110)) → Pos(new_primMulNat0(yu3110, yu400110))
new_esEs27(yu310, yu40010, ty_Ordering) → new_esEs13(yu310, yu40010)
new_esEs12(Left(yu310), Left(yu40010), ty_Char, df) → new_esEs9(yu310, yu40010)
new_sr(Pos(yu3110), Pos(yu400110)) → Pos(new_primMulNat0(yu3110, yu400110))
new_asAs(False, yu47) → False
new_esEs22(yu311, yu40011, ty_Int) → new_esEs18(yu311, yu40011)
new_primEqNat0(Zero, Zero) → True
new_esEs22(yu311, yu40011, app(app(ty_Either, ga), gb)) → new_esEs12(yu311, yu40011, ga, gb)
new_primMulNat0(Zero, Succ(yu4001100)) → Zero
new_primMulNat0(Succ(yu31100), Zero) → Zero
new_esEs13(GT, EQ) → False
new_esEs13(EQ, GT) → False
new_esEs4(yu31, yu4001, ty_Bool) → new_esEs10(yu31, yu4001)
new_esEs12(Right(yu310), Right(yu40010), de, ty_Float) → new_esEs11(yu310, yu40010)
new_esEs13(GT, LT) → False
new_esEs13(LT, GT) → False
new_esEs19(Just(yu310), Just(yu40010), ty_Float) → new_esEs11(yu310, yu40010)
new_esEs14(Double(yu310, yu311), Double(yu40010, yu40011)) → new_esEs18(new_sr(yu310, yu40010), new_sr(yu311, yu40011))
new_esEs19(Just(yu310), Just(yu40010), ty_Integer) → new_esEs17(yu310, yu40010)
new_esEs5(yu30, yu4000, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs15(yu30, yu4000, bah, bba, bbb)
new_esEs12(Left(yu310), Left(yu40010), ty_Integer, df) → new_esEs17(yu310, yu40010)
new_esEs24(yu311, yu40011, ty_Integer) → new_esEs17(yu311, yu40011)
new_esEs4(yu31, yu4001, ty_Integer) → new_esEs17(yu31, yu4001)
new_esEs12(Left(yu310), Left(yu40010), ty_Float, df) → new_esEs11(yu310, yu40010)
new_esEs16(:%(yu310, yu311), :%(yu40010, yu40011), eb) → new_asAs(new_esEs25(yu310, yu40010, eb), new_esEs24(yu311, yu40011, eb))
new_esEs7(yu310, yu40010, ty_Bool) → new_esEs10(yu310, yu40010)
new_esEs23(yu310, yu40010, ty_Char) → new_esEs9(yu310, yu40010)
new_esEs7(yu310, yu40010, app(app(ty_@2, bh), ca)) → new_esEs8(yu310, yu40010, bh, ca)
new_esEs5(yu30, yu4000, ty_Char) → new_esEs9(yu30, yu4000)
new_esEs27(yu310, yu40010, ty_@0) → new_esEs20(yu310, yu40010)
new_primPlusNat0(Succ(yu480), yu4001100) → Succ(Succ(new_primPlusNat1(yu480, yu4001100)))
new_esEs7(yu310, yu40010, ty_Double) → new_esEs14(yu310, yu40010)
new_esEs23(yu310, yu40010, ty_Bool) → new_esEs10(yu310, yu40010)
new_esEs12(Right(yu310), Right(yu40010), de, app(ty_[], bha)) → new_esEs6(yu310, yu40010, bha)
new_esEs26(yu311, yu40011, ty_Float) → new_esEs11(yu311, yu40011)
new_esEs21(yu312, yu40012, app(ty_Ratio, fd)) → new_esEs16(yu312, yu40012, fd)
new_esEs12(Left(yu310), Left(yu40010), ty_Int, df) → new_esEs18(yu310, yu40010)
new_esEs4(yu31, yu4001, app(app(ty_Either, de), df)) → new_esEs12(yu31, yu4001, de, df)
new_primEqInt(Neg(Succ(yu3100)), Neg(Succ(yu400100))) → new_primEqNat0(yu3100, yu400100)
new_esEs22(yu311, yu40011, app(ty_Maybe, gh)) → new_esEs19(yu311, yu40011, gh)
new_esEs23(yu310, yu40010, app(ty_[], he)) → new_esEs6(yu310, yu40010, he)
new_esEs6([], [], bg) → True
new_esEs12(Left(yu310), Left(yu40010), ty_Double, df) → new_esEs14(yu310, yu40010)
new_primPlusNat1(Zero, Succ(yu40011000)) → Succ(yu40011000)
new_primPlusNat1(Succ(yu4800), Zero) → Succ(yu4800)
new_esEs23(yu310, yu40010, app(app(app(ty_@3, hf), hg), hh)) → new_esEs15(yu310, yu40010, hf, hg, hh)
new_esEs19(Just(yu310), Just(yu40010), ty_Int) → new_esEs18(yu310, yu40010)
new_esEs5(yu30, yu4000, ty_Int) → new_esEs18(yu30, yu4000)
new_esEs26(yu311, yu40011, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs15(yu311, yu40011, bdd, bde, bdf)
new_esEs4(yu31, yu4001, ty_Ordering) → new_esEs13(yu31, yu4001)
new_esEs25(yu310, yu40010, ty_Int) → new_esEs18(yu310, yu40010)
new_esEs21(yu312, yu40012, ty_Double) → new_esEs14(yu312, yu40012)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs12(Right(yu310), Right(yu40010), de, app(app(ty_Either, bgg), bgh)) → new_esEs12(yu310, yu40010, bgg, bgh)
new_esEs12(Right(yu310), Right(yu40010), de, ty_@0) → new_esEs20(yu310, yu40010)
new_esEs22(yu311, yu40011, ty_Integer) → new_esEs17(yu311, yu40011)
new_esEs4(yu31, yu4001, app(app(ty_@2, dc), dd)) → new_esEs8(yu31, yu4001, dc, dd)
new_esEs19(Just(yu310), Just(yu40010), ty_Double) → new_esEs14(yu310, yu40010)
new_primEqInt(Neg(Zero), Neg(Succ(yu400100))) → False
new_primEqInt(Neg(Succ(yu3100)), Neg(Zero)) → False
new_esEs21(yu312, yu40012, app(ty_[], eh)) → new_esEs6(yu312, yu40012, eh)
new_esEs12(Right(yu310), Right(yu40010), de, ty_Ordering) → new_esEs13(yu310, yu40010)
new_esEs26(yu311, yu40011, ty_Char) → new_esEs9(yu311, yu40011)
new_esEs21(yu312, yu40012, ty_Float) → new_esEs11(yu312, yu40012)
new_esEs5(yu30, yu4000, ty_Double) → new_esEs14(yu30, yu4000)
new_esEs19(Just(yu310), Just(yu40010), app(ty_Maybe, bcf)) → new_esEs19(yu310, yu40010, bcf)
new_esEs9(Char(yu310), Char(yu40010)) → new_primEqNat0(yu310, yu40010)
new_esEs23(yu310, yu40010, ty_Integer) → new_esEs17(yu310, yu40010)
new_esEs10(False, False) → True
new_esEs5(yu30, yu4000, app(app(ty_@2, bac), bad)) → new_esEs8(yu30, yu4000, bac, bad)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs7(yu310, yu40010, ty_Char) → new_esEs9(yu310, yu40010)
new_esEs5(yu30, yu4000, ty_Integer) → new_esEs17(yu30, yu4000)
new_esEs21(yu312, yu40012, app(app(app(ty_@3, fa), fb), fc)) → new_esEs15(yu312, yu40012, fa, fb, fc)
new_esEs27(yu310, yu40010, app(ty_[], bee)) → new_esEs6(yu310, yu40010, bee)
new_asAs(True, yu47) → yu47
new_esEs7(yu310, yu40010, ty_@0) → new_esEs20(yu310, yu40010)
new_primMulNat0(Succ(yu31100), Succ(yu4001100)) → new_primPlusNat0(new_primMulNat0(yu31100, Succ(yu4001100)), yu4001100)
new_esEs12(Right(yu310), Right(yu40010), de, app(app(ty_@2, bge), bgf)) → new_esEs8(yu310, yu40010, bge, bgf)
new_esEs22(yu311, yu40011, app(app(ty_@2, fg), fh)) → new_esEs8(yu311, yu40011, fg, fh)
new_esEs10(True, False) → False
new_esEs10(False, True) → False
new_esEs26(yu311, yu40011, ty_Integer) → new_esEs17(yu311, yu40011)
new_esEs13(LT, LT) → True
new_primEqInt(Pos(Succ(yu3100)), Pos(Succ(yu400100))) → new_primEqNat0(yu3100, yu400100)
new_esEs19(Just(yu310), Just(yu40010), app(ty_Ratio, bce)) → new_esEs16(yu310, yu40010, bce)
new_esEs5(yu30, yu4000, ty_Bool) → new_esEs10(yu30, yu4000)
new_esEs4(yu31, yu4001, app(ty_Maybe, ec)) → new_esEs19(yu31, yu4001, ec)
new_esEs11(Float(yu310, yu311), Float(yu40010, yu40011)) → new_esEs18(new_sr(yu310, yu40010), new_sr(yu311, yu40011))
new_esEs7(yu310, yu40010, app(app(app(ty_@3, ce), cf), cg)) → new_esEs15(yu310, yu40010, ce, cf, cg)
new_esEs27(yu310, yu40010, app(ty_Maybe, bfb)) → new_esEs19(yu310, yu40010, bfb)
new_esEs27(yu310, yu40010, app(app(app(ty_@3, bef), beg), beh)) → new_esEs15(yu310, yu40010, bef, beg, beh)
new_esEs12(Left(yu310), Left(yu40010), app(ty_[], bfg), df) → new_esEs6(yu310, yu40010, bfg)
new_esEs24(yu311, yu40011, ty_Int) → new_esEs18(yu311, yu40011)
new_primEqNat0(Succ(yu3100), Succ(yu400100)) → new_primEqNat0(yu3100, yu400100)
new_esEs5(yu30, yu4000, app(ty_Maybe, bbd)) → new_esEs19(yu30, yu4000, bbd)
new_esEs27(yu310, yu40010, ty_Integer) → new_esEs17(yu310, yu40010)
new_esEs26(yu311, yu40011, ty_@0) → new_esEs20(yu311, yu40011)
new_esEs21(yu312, yu40012, ty_Bool) → new_esEs10(yu312, yu40012)
new_esEs12(Left(yu310), Left(yu40010), ty_Ordering, df) → new_esEs13(yu310, yu40010)
new_esEs7(yu310, yu40010, app(ty_Ratio, da)) → new_esEs16(yu310, yu40010, da)
new_esEs4(yu31, yu4001, app(ty_Ratio, eb)) → new_esEs16(yu31, yu4001, eb)
new_esEs26(yu311, yu40011, ty_Ordering) → new_esEs13(yu311, yu40011)
new_primEqInt(Pos(Succ(yu3100)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yu400100))) → False
new_esEs12(Left(yu310), Left(yu40010), app(app(app(ty_@3, bfh), bga), bgb), df) → new_esEs15(yu310, yu40010, bfh, bga, bgb)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs12(Right(yu310), Right(yu40010), de, ty_Char) → new_esEs9(yu310, yu40010)
new_esEs27(yu310, yu40010, ty_Char) → new_esEs9(yu310, yu40010)
new_esEs23(yu310, yu40010, ty_Ordering) → new_esEs13(yu310, yu40010)

The set Q consists of the following terms:

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

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

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

new_lookup1(yu28, yu29, yu30, yu31, yu32, yu33, False, ba, bb, bc) → new_lookup(@2(yu28, yu29), yu33, ba, bb, bc)
The graph contains the following edges 6 >= 2, 8 >= 3, 9 >= 4, 10 >= 5
new_lookup(@2(yu30, yu31), :(@2(@2(yu4000, yu4001), yu401), yu41), bd, be, bf) → new_lookup1(yu30, yu31, yu4000, yu4001, yu401, yu41, new_asAs(new_esEs5(yu30, yu4000, be), new_esEs4(yu31, yu4001, bf)), bd, be, bf)
The graph contains the following edges 1 > 1, 1 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 8, 4 >= 9, 5 >= 10

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