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

YES 1.526 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

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

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

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

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

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

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

module Main where

import qualified Prelude

Haskell To QDPs

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963[label="xv401/EQ",fontsize=10,color="white",style="solid",shape="box"];338 -> 963[label="",style="solid", color="burlywood", weight=9];
963 -> 392[label="",style="solid", color="burlywood", weight=3];
964[label="xv401/GT",fontsize=10,color="white",style="solid",shape="box"];338 -> 964[label="",style="solid", color="burlywood", weight=9];
964 -> 393[label="",style="solid", color="burlywood", weight=3];
339[label="GT == xv401",fontsize=16,color="burlywood",shape="box"];965[label="xv401/LT",fontsize=10,color="white",style="solid",shape="box"];339 -> 965[label="",style="solid", color="burlywood", weight=9];
965 -> 394[label="",style="solid", color="burlywood", weight=3];
966[label="xv401/EQ",fontsize=10,color="white",style="solid",shape="box"];339 -> 966[label="",style="solid", color="burlywood", weight=9];
966 -> 395[label="",style="solid", color="burlywood", weight=3];
967[label="xv401/GT",fontsize=10,color="white",style="solid",shape="box"];339 -> 967[label="",style="solid", color="burlywood", weight=9];
967 -> 396[label="",style="solid", color="burlywood", weight=3];
340[label="(xv310,xv311,xv312) == xv401\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];968[label="xv401/(xv4010,xv4011,xv4012)",fontsize=10,color="white",style="solid",shape="box"];340 -> 968[label="",style="solid", color="burlywood", weight=9];
968 -> 397[label="",style="solid", color="burlywood", weight=3];
341[label="Left xv310 == xv401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];969[label="xv401/Left xv4010",fontsize=10,color="white",style="solid",shape="box"];341 -> 969[label="",style="solid", color="burlywood", weight=9];
969 -> 398[label="",style="solid", color="burlywood", weight=3];
970[label="xv401/Right xv4010",fontsize=10,color="white",style="solid",shape="box"];341 -> 970[label="",style="solid", color="burlywood", weight=9];
970 -> 399[label="",style="solid", color="burlywood", weight=3];
342[label="Right xv310 == xv401\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];971[label="xv401/Left xv4010",fontsize=10,color="white",style="solid",shape="box"];342 -> 971[label="",style="solid", color="burlywood", weight=9];
971 -> 400[label="",style="solid", color="burlywood", weight=3];
972[label="xv401/Right xv4010",fontsize=10,color="white",style="solid",shape="box"];342 -> 972[label="",style="solid", color="burlywood", weight=9];
972 -> 401[label="",style="solid", color="burlywood", weight=3];
343[label="False == xv401",fontsize=16,color="burlywood",shape="box"];973[label="xv401/False",fontsize=10,color="white",style="solid",shape="box"];343 -> 973[label="",style="solid", color="burlywood", weight=9];
973 -> 402[label="",style="solid", color="burlywood", weight=3];
974[label="xv401/True",fontsize=10,color="white",style="solid",shape="box"];343 -> 974[label="",style="solid", color="burlywood", weight=9];
974 -> 403[label="",style="solid", color="burlywood", weight=3];
344[label="True == xv401",fontsize=16,color="burlywood",shape="box"];975[label="xv401/False",fontsize=10,color="white",style="solid",shape="box"];344 -> 975[label="",style="solid", color="burlywood", weight=9];
975 -> 404[label="",style="solid", color="burlywood", weight=3];
976[label="xv401/True",fontsize=10,color="white",style="solid",shape="box"];344 -> 976[label="",style="solid", color="burlywood", weight=9];
976 -> 405[label="",style="solid", color="burlywood", weight=3];
345[label="primEqFloat xv31 xv401",fontsize=16,color="burlywood",shape="box"];977[label="xv31/Float xv310 xv311",fontsize=10,color="white",style="solid",shape="box"];345 -> 977[label="",style="solid", color="burlywood", weight=9];
977 -> 406[label="",style="solid", color="burlywood", weight=3];
346[label="primEqInt xv31 xv401",fontsize=16,color="burlywood",shape="triangle"];978[label="xv31/Pos xv310",fontsize=10,color="white",style="solid",shape="box"];346 -> 978[label="",style="solid", color="burlywood", weight=9];
978 -> 407[label="",style="solid", color="burlywood", weight=3];
979[label="xv31/Neg xv310",fontsize=10,color="white",style="solid",shape="box"];346 -> 979[label="",style="solid", color="burlywood", weight=9];
979 -> 408[label="",style="solid", color="burlywood", weight=3];
347[label="xv310 :% xv311 == xv401\n  Integral a",fontsize=16,color="burlywood",shape="box"];980[label="xv401/xv4010 :% xv4011",fontsize=10,color="white",style="solid",shape="box"];347 -> 980[label="",style="solid", color="burlywood", weight=9];
980 -> 409[label="",style="solid", color="burlywood", weight=3];
348[label="Integer xv310 == xv401",fontsize=16,color="burlywood",shape="box"];981[label="xv401/Integer xv4010",fontsize=10,color="white",style="solid",shape="box"];348 -> 981[label="",style="solid", color="burlywood", weight=9];
981 -> 410[label="",style="solid", color="burlywood", weight=3];
349[label="xv31\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];350[label="xv401\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];351[label="primEqDouble xv31 xv401",fontsize=16,color="burlywood",shape="box"];982[label="xv31/Double xv310 xv311",fontsize=10,color="white",style="solid",shape="box"];351 -> 982[label="",style="solid", color="burlywood", weight=9];
982 -> 411[label="",style="solid", color="burlywood", weight=3];
352[label="Nothing == xv401\n  Eq a",fontsize=16,color="burlywood",shape="box"];983[label="xv401/Nothing",fontsize=10,color="white",style="solid",shape="box"];352 -> 983[label="",style="solid", color="burlywood", weight=9];
983 -> 412[label="",style="solid", color="burlywood", weight=3];
984[label="xv401/Just xv4010",fontsize=10,color="white",style="solid",shape="box"];352 -> 984[label="",style="solid", color="burlywood", weight=9];
984 -> 413[label="",style="solid", color="burlywood", weight=3];
353[label="Just xv310 == xv401\n  Eq a",fontsize=16,color="burlywood",shape="box"];985[label="xv401/Nothing",fontsize=10,color="white",style="solid",shape="box"];353 -> 985[label="",style="solid", color="burlywood", weight=9];
985 -> 414[label="",style="solid", color="burlywood", weight=3];
986[label="xv401/Just xv4010",fontsize=10,color="white",style="solid",shape="box"];353 -> 986[label="",style="solid", color="burlywood", weight=9];
986 -> 415[label="",style="solid", color="burlywood", weight=3];
354[label="xv310 : xv311 == xv401\n  Eq a",fontsize=16,color="burlywood",shape="box"];987[label="xv401/xv4010 : xv4011",fontsize=10,color="white",style="solid",shape="box"];354 -> 987[label="",style="solid", color="burlywood", weight=9];
987 -> 416[label="",style="solid", color="burlywood", weight=3];
988[label="xv401/[]",fontsize=10,color="white",style="solid",shape="box"];354 -> 988[label="",style="solid", color="burlywood", weight=9];
988 -> 417[label="",style="solid", color="burlywood", weight=3];
355[label="[] == xv401\n  Eq a",fontsize=16,color="burlywood",shape="box"];989[label="xv401/xv4010 : xv4011",fontsize=10,color="white",style="solid",shape="box"];355 -> 989[label="",style="solid", color="burlywood", weight=9];
989 -> 418[label="",style="solid", color="burlywood", weight=3];
990[label="xv401/[]",fontsize=10,color="white",style="solid",shape="box"];355 -> 990[label="",style="solid", color="burlywood", weight=9];
990 -> 419[label="",style="solid", color="burlywood", weight=3];
356[label="primEqChar xv31 xv401",fontsize=16,color="burlywood",shape="box"];991[label="xv31/Char xv310",fontsize=10,color="white",style="solid",shape="box"];356 -> 991[label="",style="solid", color="burlywood", weight=9];
991 -> 420[label="",style="solid", color="burlywood", weight=3];
357[label="() == xv401",fontsize=16,color="burlywood",shape="box"];992[label="xv401/()",fontsize=10,color="white",style="solid",shape="box"];357 -> 992[label="",style="solid", color="burlywood", weight=9];
992 -> 421[label="",style="solid", color="burlywood", weight=3];
358[label="xv400",fontsize=16,color="green",shape="box"];359[label="xv30",fontsize=16,color="green",shape="box"];360[label="xv400\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];361[label="xv30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];362[label="xv400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];363[label="xv30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];364[label="xv400",fontsize=16,color="green",shape="box"];365[label="xv30",fontsize=16,color="green",shape="box"];366[label="xv400",fontsize=16,color="green",shape="box"];367[label="xv30",fontsize=16,color="green",shape="box"];368[label="xv400",fontsize=16,color="green",shape="box"];369[label="xv30",fontsize=16,color="green",shape="box"];370[label="xv400\n  Integral a",fontsize=16,color="green",shape="box"];371[label="xv30\n  Integral a",fontsize=16,color="green",shape="box"];372[label="xv400",fontsize=16,color="green",shape="box"];373[label="xv30",fontsize=16,color="green",shape="box"];374[label="xv30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];375[label="xv400\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];376[label="xv400",fontsize=16,color="green",shape="box"];377[label="xv30",fontsize=16,color="green",shape="box"];378[label="xv400\n  Eq a",fontsize=16,color="green",shape="box"];379[label="xv30\n  Eq a",fontsize=16,color="green",shape="box"];380[label="xv400\n  Eq a",fontsize=16,color="green",shape="box"];381[label="xv30\n  Eq a",fontsize=16,color="green",shape="box"];382[label="xv400",fontsize=16,color="green",shape="box"];383[label="xv30",fontsize=16,color="green",shape="box"];384[label="xv400",fontsize=16,color="green",shape="box"];385[label="xv30",fontsize=16,color="green",shape="box"];386[label="False",fontsize=16,color="green",shape="box"];387[label="xv32",fontsize=16,color="green",shape="box"];388[label="LT == LT",fontsize=16,color="black",shape="box"];388 -> 422[label="",style="solid", color="black", weight=3];
389[label="LT == EQ",fontsize=16,color="black",shape="box"];389 -> 423[label="",style="solid", color="black", weight=3];
390[label="LT == GT",fontsize=16,color="black",shape="box"];390 -> 424[label="",style="solid", color="black", weight=3];
391[label="EQ == LT",fontsize=16,color="black",shape="box"];391 -> 425[label="",style="solid", color="black", weight=3];
392[label="EQ == EQ",fontsize=16,color="black",shape="box"];392 -> 426[label="",style="solid", color="black", weight=3];
393[label="EQ == GT",fontsize=16,color="black",shape="box"];393 -> 427[label="",style="solid", color="black", weight=3];
394[label="GT == LT",fontsize=16,color="black",shape="box"];394 -> 428[label="",style="solid", color="black", weight=3];
395[label="GT == EQ",fontsize=16,color="black",shape="box"];395 -> 429[label="",style="solid", color="black", weight=3];
396[label="GT == GT",fontsize=16,color="black",shape="box"];396 -> 430[label="",style="solid", color="black", weight=3];
397[label="(xv310,xv311,xv312) == (xv4010,xv4011,xv4012)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];397 -> 431[label="",style="solid", color="black", weight=3];
398[label="Left xv310 == Left xv4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];398 -> 432[label="",style="solid", color="black", weight=3];
399[label="Left xv310 == Right xv4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];399 -> 433[label="",style="solid", color="black", weight=3];
400[label="Right xv310 == Left xv4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];400 -> 434[label="",style="solid", color="black", weight=3];
401[label="Right xv310 == Right xv4010\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];401 -> 435[label="",style="solid", color="black", weight=3];
402[label="False == False",fontsize=16,color="black",shape="box"];402 -> 436[label="",style="solid", color="black", weight=3];
403[label="False == True",fontsize=16,color="black",shape="box"];403 -> 437[label="",style="solid", color="black", weight=3];
404[label="True == False",fontsize=16,color="black",shape="box"];404 -> 438[label="",style="solid", color="black", weight=3];
405[label="True == True",fontsize=16,color="black",shape="box"];405 -> 439[label="",style="solid", color="black", weight=3];
406[label="primEqFloat (Float xv310 xv311) xv401",fontsize=16,color="burlywood",shape="box"];993[label="xv401/Float xv4010 xv4011",fontsize=10,color="white",style="solid",shape="box"];406 -> 993[label="",style="solid", color="burlywood", weight=9];
993 -> 440[label="",style="solid", color="burlywood", weight=3];
407[label="primEqInt (Pos xv310) xv401",fontsize=16,color="burlywood",shape="box"];994[label="xv310/Succ xv3100",fontsize=10,color="white",style="solid",shape="box"];407 -> 994[label="",style="solid", color="burlywood", weight=9];
994 -> 441[label="",style="solid", color="burlywood", weight=3];
995[label="xv310/Zero",fontsize=10,color="white",style="solid",shape="box"];407 -> 995[label="",style="solid", color="burlywood", weight=9];
995 -> 442[label="",style="solid", color="burlywood", weight=3];
408[label="primEqInt (Neg xv310) xv401",fontsize=16,color="burlywood",shape="box"];996[label="xv310/Succ xv3100",fontsize=10,color="white",style="solid",shape="box"];408 -> 996[label="",style="solid", color="burlywood", weight=9];
996 -> 443[label="",style="solid", color="burlywood", weight=3];
997[label="xv310/Zero",fontsize=10,color="white",style="solid",shape="box"];408 -> 997[label="",style="solid", color="burlywood", weight=9];
997 -> 444[label="",style="solid", color="burlywood", weight=3];
409[label="xv310 :% xv311 == xv4010 :% xv4011\n  Integral a",fontsize=16,color="black",shape="box"];409 -> 445[label="",style="solid", color="black", weight=3];
410[label="Integer xv310 == Integer xv4010",fontsize=16,color="black",shape="box"];410 -> 446[label="",style="solid", color="black", weight=3];
411[label="primEqDouble (Double xv310 xv311) xv401",fontsize=16,color="burlywood",shape="box"];998[label="xv401/Double xv4010 xv4011",fontsize=10,color="white",style="solid",shape="box"];411 -> 998[label="",style="solid", color="burlywood", weight=9];
998 -> 447[label="",style="solid", color="burlywood", weight=3];
412[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];412 -> 448[label="",style="solid", color="black", weight=3];
413[label="Nothing == Just xv4010\n  Eq a",fontsize=16,color="black",shape="box"];413 -> 449[label="",style="solid", color="black", weight=3];
414[label="Just xv310 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];414 -> 450[label="",style="solid", color="black", weight=3];
415[label="Just xv310 == Just xv4010\n  Eq a",fontsize=16,color="black",shape="box"];415 -> 451[label="",style="solid", color="black", weight=3];
416[label="xv310 : xv311 == xv4010 : xv4011\n  Eq a",fontsize=16,color="black",shape="box"];416 -> 452[label="",style="solid", color="black", weight=3];
417[label="xv310 : xv311 == []\n  Eq a",fontsize=16,color="black",shape="box"];417 -> 453[label="",style="solid", color="black", weight=3];
418[label="[] == xv4010 : xv4011\n  Eq a",fontsize=16,color="black",shape="box"];418 -> 454[label="",style="solid", color="black", weight=3];
419[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];419 -> 455[label="",style="solid", color="black", weight=3];
420[label="primEqChar (Char xv310) xv401",fontsize=16,color="burlywood",shape="box"];999[label="xv401/Char xv4010",fontsize=10,color="white",style="solid",shape="box"];420 -> 999[label="",style="solid", color="burlywood", weight=9];
999 -> 456[label="",style="solid", color="burlywood", weight=3];
421[label="() == ()",fontsize=16,color="black",shape="box"];421 -> 457[label="",style="solid", color="black", weight=3];
422[label="True",fontsize=16,color="green",shape="box"];423[label="False",fontsize=16,color="green",shape="box"];424[label="False",fontsize=16,color="green",shape="box"];425[label="False",fontsize=16,color="green",shape="box"];426[label="True",fontsize=16,color="green",shape="box"];427[label="False",fontsize=16,color="green",shape="box"];428[label="False",fontsize=16,color="green",shape="box"];429[label="False",fontsize=16,color="green",shape="box"];430[label="True",fontsize=16,color="green",shape="box"];431 -> 302[label="",style="dashed", color="red", weight=0];
431[label="xv310 == xv4010 && xv311 == xv4011 && xv312 == xv4012\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];431 -> 458[label="",style="dashed", color="magenta", weight=3];
431 -> 459[label="",style="dashed", color="magenta", weight=3];
432[label="xv310 == xv4010\n  Eq a",fontsize=16,color="blue",shape="box"];1001[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1001[label="",style="solid", color="blue", weight=9];
1001 -> 460[label="",style="solid", color="blue", weight=3];
1002[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1002[label="",style="solid", color="blue", weight=9];
1002 -> 461[label="",style="solid", color="blue", weight=3];
1003[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1003[label="",style="solid", color="blue", weight=9];
1003 -> 462[label="",style="solid", color="blue", weight=3];
1004[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1004[label="",style="solid", color="blue", weight=9];
1004 -> 463[label="",style="solid", color="blue", weight=3];
1005[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1005[label="",style="solid", color="blue", weight=9];
1005 -> 464[label="",style="solid", color="blue", weight=3];
1006[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1006[label="",style="solid", color="blue", weight=9];
1006 -> 465[label="",style="solid", color="blue", weight=3];
1007[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1007[label="",style="solid", color="blue", weight=9];
1007 -> 466[label="",style="solid", color="blue", weight=3];
1008[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1008[label="",style="solid", color="blue", weight=9];
1008 -> 467[label="",style="solid", color="blue", weight=3];
1009[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1009[label="",style="solid", color="blue", weight=9];
1009 -> 468[label="",style="solid", color="blue", weight=3];
1010[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1010[label="",style="solid", color="blue", weight=9];
1010 -> 469[label="",style="solid", color="blue", weight=3];
1011[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1011[label="",style="solid", color="blue", weight=9];
1011 -> 470[label="",style="solid", color="blue", weight=3];
1012[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1012[label="",style="solid", color="blue", weight=9];
1012 -> 471[label="",style="solid", color="blue", weight=3];
1013[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1013[label="",style="solid", color="blue", weight=9];
1013 -> 472[label="",style="solid", color="blue", weight=3];
1014[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];432 -> 1014[label="",style="solid", color="blue", weight=9];
1014 -> 473[label="",style="solid", color="blue", weight=3];
433[label="False",fontsize=16,color="green",shape="box"];434[label="False",fontsize=16,color="green",shape="box"];435[label="xv310 == xv4010\n  Eq a",fontsize=16,color="blue",shape="box"];1015[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1015[label="",style="solid", color="blue", weight=9];
1015 -> 474[label="",style="solid", color="blue", weight=3];
1016[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1016[label="",style="solid", color="blue", weight=9];
1016 -> 475[label="",style="solid", color="blue", weight=3];
1017[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1017[label="",style="solid", color="blue", weight=9];
1017 -> 476[label="",style="solid", color="blue", weight=3];
1018[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1018[label="",style="solid", color="blue", weight=9];
1018 -> 477[label="",style="solid", color="blue", weight=3];
1019[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1019[label="",style="solid", color="blue", weight=9];
1019 -> 478[label="",style="solid", color="blue", weight=3];
1020[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1020[label="",style="solid", color="blue", weight=9];
1020 -> 479[label="",style="solid", color="blue", weight=3];
1021[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1021[label="",style="solid", color="blue", weight=9];
1021 -> 480[label="",style="solid", color="blue", weight=3];
1022[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1022[label="",style="solid", color="blue", weight=9];
1022 -> 481[label="",style="solid", color="blue", weight=3];
1023[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1023[label="",style="solid", color="blue", weight=9];
1023 -> 482[label="",style="solid", color="blue", weight=3];
1024[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1024[label="",style="solid", color="blue", weight=9];
1024 -> 483[label="",style="solid", color="blue", weight=3];
1025[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];435 -> 1025[label="",style="solid", color="blue", weight=9];
1025 -> 484[label="",style="solid", color="blue", weight=3];
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687[label="xv4010",fontsize=16,color="green",shape="box"];688[label="xv310",fontsize=16,color="green",shape="box"];689[label="xv4010\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];690[label="xv310\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];691[label="xv4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];692[label="xv310\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];693[label="xv4010",fontsize=16,color="green",shape="box"];694[label="xv310",fontsize=16,color="green",shape="box"];695[label="xv4010",fontsize=16,color="green",shape="box"];696[label="xv310",fontsize=16,color="green",shape="box"];697[label="xv4010",fontsize=16,color="green",shape="box"];698[label="xv310",fontsize=16,color="green",shape="box"];699[label="xv4010\n  Integral a",fontsize=16,color="green",shape="box"];700[label="xv310\n  Integral a",fontsize=16,color="green",shape="box"];701[label="xv4010",fontsize=16,color="green",shape="box"];702[label="xv310",fontsize=16,color="green",shape="box"];703[label="xv310\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];704[label="xv4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];705[label="xv4010",fontsize=16,color="green",shape="box"];706[label="xv310",fontsize=16,color="green",shape="box"];707[label="xv4010\n  Eq a",fontsize=16,color="green",shape="box"];708[label="xv310\n  Eq a",fontsize=16,color="green",shape="box"];709[label="xv4010\n  Eq a",fontsize=16,color="green",shape="box"];710[label="xv310\n  Eq a",fontsize=16,color="green",shape="box"];711[label="xv4010",fontsize=16,color="green",shape="box"];712[label="xv310",fontsize=16,color="green",shape="box"];713[label="xv4010",fontsize=16,color="green",shape="box"];714[label="xv310",fontsize=16,color="green",shape="box"];715[label="primMulInt xv311 xv4011",fontsize=16,color="burlywood",shape="box"];1241[label="xv311/Pos xv3110",fontsize=10,color="white",style="solid",shape="box"];715 -> 1241[label="",style="solid", color="burlywood", weight=9];
1241 -> 830[label="",style="solid", color="burlywood", weight=3];
1242[label="xv311/Neg xv3110",fontsize=10,color="white",style="solid",shape="box"];715 -> 1242[label="",style="solid", color="burlywood", weight=9];
1242 -> 831[label="",style="solid", color="burlywood", weight=3];
716[label="xv4010",fontsize=16,color="green",shape="box"];717[label="xv310",fontsize=16,color="green",shape="box"];718 -> 518[label="",style="dashed", color="red", weight=0];
718[label="primEqNat xv3100 xv40100",fontsize=16,color="magenta"];718 -> 832[label="",style="dashed", color="magenta", weight=3];
718 -> 833[label="",style="dashed", color="magenta", weight=3];
719[label="False",fontsize=16,color="green",shape="box"];720[label="False",fontsize=16,color="green",shape="box"];721[label="True",fontsize=16,color="green",shape="box"];722[label="False",fontsize=16,color="green",shape="box"];723[label="True",fontsize=16,color="green",shape="box"];724 -> 518[label="",style="dashed", color="red", weight=0];
724[label="primEqNat xv3100 xv40100",fontsize=16,color="magenta"];724 -> 834[label="",style="dashed", color="magenta", weight=3];
724 -> 835[label="",style="dashed", color="magenta", weight=3];
725[label="False",fontsize=16,color="green",shape="box"];726[label="False",fontsize=16,color="green",shape="box"];727[label="True",fontsize=16,color="green",shape="box"];728[label="False",fontsize=16,color="green",shape="box"];729[label="True",fontsize=16,color="green",shape="box"];730[label="xv4011",fontsize=16,color="green",shape="box"];731[label="xv311",fontsize=16,color="green",shape="box"];732[label="xv4011",fontsize=16,color="green",shape="box"];733[label="xv311",fontsize=16,color="green",shape="box"];734[label="xv4010",fontsize=16,color="green",shape="box"];735[label="xv310",fontsize=16,color="green",shape="box"];736[label="xv4010",fontsize=16,color="green",shape="box"];737[label="xv310",fontsize=16,color="green",shape="box"];738[label="xv4011",fontsize=16,color="green",shape="box"];739[label="xv311",fontsize=16,color="green",shape="box"];740[label="xv4010",fontsize=16,color="green",shape="box"];741[label="xv310",fontsize=16,color="green",shape="box"];742[label="xv4010",fontsize=16,color="green",shape="box"];743[label="xv310",fontsize=16,color="green",shape="box"];744[label="xv4010\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];745[label="xv310\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];746[label="xv4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];747[label="xv310\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];748[label="xv4010",fontsize=16,color="green",shape="box"];749[label="xv310",fontsize=16,color="green",shape="box"];750[label="xv4010",fontsize=16,color="green",shape="box"];751[label="xv310",fontsize=16,color="green",shape="box"];752[label="xv4010",fontsize=16,color="green",shape="box"];753[label="xv310",fontsize=16,color="green",shape="box"];754[label="xv4010\n  Integral a",fontsize=16,color="green",shape="box"];755[label="xv310\n  Integral a",fontsize=16,color="green",shape="box"];756[label="xv4010",fontsize=16,color="green",shape="box"];757[label="xv310",fontsize=16,color="green",shape="box"];758[label="xv310\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];759[label="xv4010\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];760[label="xv4010",fontsize=16,color="green",shape="box"];761[label="xv310",fontsize=16,color="green",shape="box"];762[label="xv4010\n  Eq a",fontsize=16,color="green",shape="box"];763[label="xv310\n  Eq a",fontsize=16,color="green",shape="box"];764[label="xv4010\n  Eq a",fontsize=16,color="green",shape="box"];765[label="xv310\n  Eq a",fontsize=16,color="green",shape="box"];766[label="xv4010",fontsize=16,color="green",shape="box"];767[label="xv310",fontsize=16,color="green",shape="box"];768[label="xv4010",fontsize=16,color="green",shape="box"];769[label="xv310",fontsize=16,color="green",shape="box"];770[label="primEqNat (Succ xv3100) (Succ xv40100)",fontsize=16,color="black",shape="box"];770 -> 836[label="",style="solid", color="black", weight=3];
771[label="primEqNat (Succ xv3100) Zero",fontsize=16,color="black",shape="box"];771 -> 837[label="",style="solid", color="black", weight=3];
772[label="primEqNat Zero (Succ xv40100)",fontsize=16,color="black",shape="box"];772 -> 838[label="",style="solid", color="black", weight=3];
773[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];773 -> 839[label="",style="solid", color="black", weight=3];
774[label="xv4012",fontsize=16,color="green",shape="box"];775[label="xv312",fontsize=16,color="green",shape="box"];776[label="xv4012\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];777[label="xv312\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];778[label="xv4012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];779[label="xv312\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];780[label="xv4012",fontsize=16,color="green",shape="box"];781[label="xv312",fontsize=16,color="green",shape="box"];782[label="xv4012",fontsize=16,color="green",shape="box"];783[label="xv312",fontsize=16,color="green",shape="box"];784[label="xv4012",fontsize=16,color="green",shape="box"];785[label="xv312",fontsize=16,color="green",shape="box"];786[label="xv4012\n  Integral a",fontsize=16,color="green",shape="box"];787[label="xv312\n  Integral a",fontsize=16,color="green",shape="box"];788[label="xv4012",fontsize=16,color="green",shape="box"];789[label="xv312",fontsize=16,color="green",shape="box"];790[label="xv312\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];791[label="xv4012\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];792[label="xv4012",fontsize=16,color="green",shape="box"];793[label="xv312",fontsize=16,color="green",shape="box"];794[label="xv4012\n  Eq a",fontsize=16,color="green",shape="box"];795[label="xv312\n  Eq a",fontsize=16,color="green",shape="box"];796[label="xv4012\n  Eq a",fontsize=16,color="green",shape="box"];797[label="xv312\n  Eq a",fontsize=16,color="green",shape="box"];798[label="xv4012",fontsize=16,color="green",shape="box"];799[label="xv312",fontsize=16,color="green",shape="box"];800[label="xv4012",fontsize=16,color="green",shape="box"];801[label="xv312",fontsize=16,color="green",shape="box"];802[label="xv4011",fontsize=16,color="green",shape="box"];803[label="xv311",fontsize=16,color="green",shape="box"];804[label="xv4011\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];805[label="xv311\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];806[label="xv4011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];807[label="xv311\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];808[label="xv4011",fontsize=16,color="green",shape="box"];809[label="xv311",fontsize=16,color="green",shape="box"];810[label="xv4011",fontsize=16,color="green",shape="box"];811[label="xv311",fontsize=16,color="green",shape="box"];812[label="xv4011",fontsize=16,color="green",shape="box"];813[label="xv311",fontsize=16,color="green",shape="box"];814[label="xv4011\n  Integral a",fontsize=16,color="green",shape="box"];815[label="xv311\n  Integral a",fontsize=16,color="green",shape="box"];816[label="xv4011",fontsize=16,color="green",shape="box"];817[label="xv311",fontsize=16,color="green",shape="box"];818[label="xv311\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];819[label="xv4011\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];820[label="xv4011",fontsize=16,color="green",shape="box"];821[label="xv311",fontsize=16,color="green",shape="box"];822[label="xv4011\n  Eq a",fontsize=16,color="green",shape="box"];823[label="xv311\n  Eq a",fontsize=16,color="green",shape="box"];824[label="xv4011\n  Eq a",fontsize=16,color="green",shape="box"];825[label="xv311\n  Eq a",fontsize=16,color="green",shape="box"];826[label="xv4011",fontsize=16,color="green",shape="box"];827[label="xv311",fontsize=16,color="green",shape="box"];828[label="xv4011",fontsize=16,color="green",shape="box"];829[label="xv311",fontsize=16,color="green",shape="box"];830[label="primMulInt (Pos xv3110) xv4011",fontsize=16,color="burlywood",shape="box"];1245[label="xv4011/Pos xv40110",fontsize=10,color="white",style="solid",shape="box"];830 -> 1245[label="",style="solid", color="burlywood", weight=9];
1245 -> 840[label="",style="solid", color="burlywood", weight=3];
1246[label="xv4011/Neg xv40110",fontsize=10,color="white",style="solid",shape="box"];830 -> 1246[label="",style="solid", color="burlywood", weight=9];
1246 -> 841[label="",style="solid", color="burlywood", weight=3];
831[label="primMulInt (Neg xv3110) xv4011",fontsize=16,color="burlywood",shape="box"];1247[label="xv4011/Pos xv40110",fontsize=10,color="white",style="solid",shape="box"];831 -> 1247[label="",style="solid", color="burlywood", weight=9];
1247 -> 842[label="",style="solid", color="burlywood", weight=3];
1248[label="xv4011/Neg xv40110",fontsize=10,color="white",style="solid",shape="box"];831 -> 1248[label="",style="solid", color="burlywood", weight=9];
1248 -> 843[label="",style="solid", color="burlywood", weight=3];
832[label="xv3100",fontsize=16,color="green",shape="box"];833[label="xv40100",fontsize=16,color="green",shape="box"];834[label="xv3100",fontsize=16,color="green",shape="box"];835[label="xv40100",fontsize=16,color="green",shape="box"];836 -> 518[label="",style="dashed", color="red", weight=0];
836[label="primEqNat xv3100 xv40100",fontsize=16,color="magenta"];836 -> 844[label="",style="dashed", color="magenta", weight=3];
836 -> 845[label="",style="dashed", color="magenta", weight=3];
837[label="False",fontsize=16,color="green",shape="box"];838[label="False",fontsize=16,color="green",shape="box"];839[label="True",fontsize=16,color="green",shape="box"];840[label="primMulInt (Pos xv3110) (Pos xv40110)",fontsize=16,color="black",shape="box"];840 -> 846[label="",style="solid", color="black", weight=3];
841[label="primMulInt (Pos xv3110) (Neg xv40110)",fontsize=16,color="black",shape="box"];841 -> 847[label="",style="solid", color="black", weight=3];
842[label="primMulInt (Neg xv3110) (Pos xv40110)",fontsize=16,color="black",shape="box"];842 -> 848[label="",style="solid", color="black", weight=3];
843[label="primMulInt (Neg xv3110) (Neg xv40110)",fontsize=16,color="black",shape="box"];843 -> 849[label="",style="solid", color="black", weight=3];
844[label="xv3100",fontsize=16,color="green",shape="box"];845[label="xv40100",fontsize=16,color="green",shape="box"];846[label="Pos (primMulNat xv3110 xv40110)",fontsize=16,color="green",shape="box"];846 -> 850[label="",style="dashed", color="green", weight=3];
847[label="Neg (primMulNat xv3110 xv40110)",fontsize=16,color="green",shape="box"];847 -> 851[label="",style="dashed", color="green", weight=3];
848[label="Neg (primMulNat xv3110 xv40110)",fontsize=16,color="green",shape="box"];848 -> 852[label="",style="dashed", color="green", weight=3];
849[label="Pos (primMulNat xv3110 xv40110)",fontsize=16,color="green",shape="box"];849 -> 853[label="",style="dashed", color="green", weight=3];
850[label="primMulNat xv3110 xv40110",fontsize=16,color="burlywood",shape="triangle"];1250[label="xv3110/Succ xv31100",fontsize=10,color="white",style="solid",shape="box"];850 -> 1250[label="",style="solid", color="burlywood", weight=9];
1250 -> 854[label="",style="solid", color="burlywood", weight=3];
1251[label="xv3110/Zero",fontsize=10,color="white",style="solid",shape="box"];850 -> 1251[label="",style="solid", color="burlywood", weight=9];
1251 -> 855[label="",style="solid", color="burlywood", weight=3];
851 -> 850[label="",style="dashed", color="red", weight=0];
851[label="primMulNat xv3110 xv40110",fontsize=16,color="magenta"];851 -> 856[label="",style="dashed", color="magenta", weight=3];
852 -> 850[label="",style="dashed", color="red", weight=0];
852[label="primMulNat xv3110 xv40110",fontsize=16,color="magenta"];852 -> 857[label="",style="dashed", color="magenta", weight=3];
853 -> 850[label="",style="dashed", color="red", weight=0];
853[label="primMulNat xv3110 xv40110",fontsize=16,color="magenta"];853 -> 858[label="",style="dashed", color="magenta", weight=3];
853 -> 859[label="",style="dashed", color="magenta", weight=3];
854[label="primMulNat (Succ xv31100) xv40110",fontsize=16,color="burlywood",shape="box"];1255[label="xv40110/Succ xv401100",fontsize=10,color="white",style="solid",shape="box"];854 -> 1255[label="",style="solid", color="burlywood", weight=9];
1255 -> 860[label="",style="solid", color="burlywood", weight=3];
1256[label="xv40110/Zero",fontsize=10,color="white",style="solid",shape="box"];854 -> 1256[label="",style="solid", color="burlywood", weight=9];
1256 -> 861[label="",style="solid", color="burlywood", weight=3];
855[label="primMulNat Zero xv40110",fontsize=16,color="burlywood",shape="box"];1257[label="xv40110/Succ xv401100",fontsize=10,color="white",style="solid",shape="box"];855 -> 1257[label="",style="solid", color="burlywood", weight=9];
1257 -> 862[label="",style="solid", color="burlywood", weight=3];
1258[label="xv40110/Zero",fontsize=10,color="white",style="solid",shape="box"];855 -> 1258[label="",style="solid", color="burlywood", weight=9];
1258 -> 863[label="",style="solid", color="burlywood", weight=3];
856[label="xv40110",fontsize=16,color="green",shape="box"];857[label="xv3110",fontsize=16,color="green",shape="box"];858[label="xv40110",fontsize=16,color="green",shape="box"];859[label="xv3110",fontsize=16,color="green",shape="box"];860[label="primMulNat (Succ xv31100) (Succ xv401100)",fontsize=16,color="black",shape="box"];860 -> 864[label="",style="solid", color="black", weight=3];
861[label="primMulNat (Succ xv31100) Zero",fontsize=16,color="black",shape="box"];861 -> 865[label="",style="solid", color="black", weight=3];
862[label="primMulNat Zero (Succ xv401100)",fontsize=16,color="black",shape="box"];862 -> 866[label="",style="solid", color="black", weight=3];
863[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];863 -> 867[label="",style="solid", color="black", weight=3];
864 -> 868[label="",style="dashed", color="red", weight=0];
864[label="primPlusNat (primMulNat xv31100 (Succ xv401100)) (Succ xv401100)",fontsize=16,color="magenta"];864 -> 869[label="",style="dashed", color="magenta", weight=3];
865[label="Zero",fontsize=16,color="green",shape="box"];866[label="Zero",fontsize=16,color="green",shape="box"];867[label="Zero",fontsize=16,color="green",shape="box"];869 -> 850[label="",style="dashed", color="red", weight=0];
869[label="primMulNat xv31100 (Succ xv401100)",fontsize=16,color="magenta"];869 -> 870[label="",style="dashed", color="magenta", weight=3];
869 -> 871[label="",style="dashed", color="magenta", weight=3];
868[label="primPlusNat xv33 (Succ xv401100)",fontsize=16,color="burlywood",shape="triangle"];1261[label="xv33/Succ xv330",fontsize=10,color="white",style="solid",shape="box"];868 -> 1261[label="",style="solid", color="burlywood", weight=9];
1261 -> 872[label="",style="solid", color="burlywood", weight=3];
1262[label="xv33/Zero",fontsize=10,color="white",style="solid",shape="box"];868 -> 1262[label="",style="solid", color="burlywood", weight=9];
1262 -> 873[label="",style="solid", color="burlywood", weight=3];
870[label="Succ xv401100",fontsize=16,color="green",shape="box"];871[label="xv31100",fontsize=16,color="green",shape="box"];872[label="primPlusNat (Succ xv330) (Succ xv401100)",fontsize=16,color="black",shape="box"];872 -> 874[label="",style="solid", color="black", weight=3];
873[label="primPlusNat Zero (Succ xv401100)",fontsize=16,color="black",shape="box"];873 -> 875[label="",style="solid", color="black", weight=3];
874[label="Succ (Succ (primPlusNat xv330 xv401100))",fontsize=16,color="green",shape="box"];874 -> 876[label="",style="dashed", color="green", weight=3];
875[label="Succ xv401100",fontsize=16,color="green",shape="box"];876[label="primPlusNat xv330 xv401100",fontsize=16,color="burlywood",shape="triangle"];1263[label="xv330/Succ xv3300",fontsize=10,color="white",style="solid",shape="box"];876 -> 1263[label="",style="solid", color="burlywood", weight=9];
1263 -> 877[label="",style="solid", color="burlywood", weight=3];
1264[label="xv330/Zero",fontsize=10,color="white",style="solid",shape="box"];876 -> 1264[label="",style="solid", color="burlywood", weight=9];
1264 -> 878[label="",style="solid", color="burlywood", weight=3];
877[label="primPlusNat (Succ xv3300) xv401100",fontsize=16,color="burlywood",shape="box"];1265[label="xv401100/Succ xv4011000",fontsize=10,color="white",style="solid",shape="box"];877 -> 1265[label="",style="solid", color="burlywood", weight=9];
1265 -> 879[label="",style="solid", color="burlywood", weight=3];
1266[label="xv401100/Zero",fontsize=10,color="white",style="solid",shape="box"];877 -> 1266[label="",style="solid", color="burlywood", weight=9];
1266 -> 880[label="",style="solid", color="burlywood", weight=3];
878[label="primPlusNat Zero xv401100",fontsize=16,color="burlywood",shape="box"];1267[label="xv401100/Succ xv4011000",fontsize=10,color="white",style="solid",shape="box"];878 -> 1267[label="",style="solid", color="burlywood", weight=9];
1267 -> 881[label="",style="solid", color="burlywood", weight=3];
1268[label="xv401100/Zero",fontsize=10,color="white",style="solid",shape="box"];878 -> 1268[label="",style="solid", color="burlywood", weight=9];
1268 -> 882[label="",style="solid", color="burlywood", weight=3];
879[label="primPlusNat (Succ xv3300) (Succ xv4011000)",fontsize=16,color="black",shape="box"];879 -> 883[label="",style="solid", color="black", weight=3];
880[label="primPlusNat (Succ xv3300) Zero",fontsize=16,color="black",shape="box"];880 -> 884[label="",style="solid", color="black", weight=3];
881[label="primPlusNat Zero (Succ xv4011000)",fontsize=16,color="black",shape="box"];881 -> 885[label="",style="solid", color="black", weight=3];
882[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];882 -> 886[label="",style="solid", color="black", weight=3];
883[label="Succ (Succ (primPlusNat xv3300 xv4011000))",fontsize=16,color="green",shape="box"];883 -> 887[label="",style="dashed", color="green", weight=3];
884[label="Succ xv3300",fontsize=16,color="green",shape="box"];885[label="Succ xv4011000",fontsize=16,color="green",shape="box"];886[label="Zero",fontsize=16,color="green",shape="box"];887 -> 876[label="",style="dashed", color="red", weight=0];
887[label="primPlusNat xv3300 xv4011000",fontsize=16,color="magenta"];887 -> 888[label="",style="dashed", color="magenta", weight=3];
887 -> 889[label="",style="dashed", color="magenta", weight=3];
888[label="xv3300",fontsize=16,color="green",shape="box"];889[label="xv4011000",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(xv3300), Succ(xv4011000)) → new_primPlusNat(xv3300, xv4011000)

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(xv3300), Succ(xv4011000)) → new_primPlusNat(xv3300, xv4011000)
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(xv31100), Succ(xv401100)) → new_primMulNat(xv31100, Succ(xv401100))

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

new_primMulNat(Succ(xv31100), Succ(xv401100)) → new_primMulNat(xv31100, Succ(xv401100))
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(xv3100), Succ(xv40100)) → new_primEqNat(xv3100, xv40100)

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

new_primEqNat(Succ(xv3100), Succ(xv40100)) → new_primEqNat(xv3100, xv40100)
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_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(app(ty_Either, bac), bad))) → new_esEs0(xv310, xv4010, bac, bad)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(app(ty_Either, bf), bg)) → new_esEs0(xv312, xv4012, bf, bg)
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(ty_Maybe, bag))) → new_esEs2(xv310, xv4010, bag)
new_esEs2(Just(xv310), Just(xv4010), app(app(app(ty_@3, hh), baa), bab)) → new_esEs(xv310, xv4010, hh, baa, bab)
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(ty_[], bcb)) → new_esEs3(xv310, xv4010, bcb)
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(ty_[], bdd), bcf) → new_esEs3(xv30, xv400, bdd)
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_Either, bcg), bch), bcf) → new_esEs0(xv30, xv400, bcg, bch)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(ty_[], df)), cg)) → new_esEs3(xv311, xv4011, df)
new_esEs0(Right(xv310), Right(xv4010), gc, app(app(ty_@2, ha), hb)) → new_esEs1(xv310, xv4010, ha, hb)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(ty_Maybe, de), cg) → new_esEs2(xv311, xv4011, de)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(app(ty_Either, eb), ec)), bb), cg)) → new_esEs0(xv310, xv4010, eb, ec)
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(app(ty_Either, bbe), bbf))) → new_esEs0(xv310, xv4010, bbe, bbf)
new_esEs2(Just(xv310), Just(xv4010), app(ty_Maybe, bag)) → new_esEs2(xv310, xv4010, bag)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(app(app(ty_@3, cd), ce), cf)), cg)) → new_esEs(xv311, xv4011, cd, ce, cf)
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(ty_Maybe, bdc), bcf) → new_esEs2(xv30, xv400, bdc)
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs(xv310, xv4010, bbb, bbc, bbd)
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), bba) → new_esEs3(xv311, xv4011, bba)
new_esEs0(Right(xv310), Right(xv4010), gc, app(app(ty_Either, gg), gh)) → new_esEs0(xv310, xv4010, gg, gh)
new_esEs0(Left(xv310), Left(xv4010), app(ty_Maybe, ga), fc) → new_esEs2(xv310, xv4010, ga)
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(ty_[], bcb))) → new_esEs3(xv310, xv4010, bcb)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(ty_Maybe, de)), cg)) → new_esEs2(xv311, xv4011, de)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(app(ty_@2, dc), dd)), cg)) → new_esEs1(xv311, xv4011, dc, dd)
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), he, app(app(ty_@2, hf), hg)) → new_esEs1(xv31, xv401, hf, hg)
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(app(app(ty_@3, hh), baa), bab))) → new_esEs(xv310, xv4010, hh, baa, bab)
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(ty_Maybe, ga)), fc)) → new_esEs2(xv310, xv4010, ga)
new_esEs0(Left(xv310), Left(xv4010), app(ty_[], gb), fc) → new_esEs3(xv310, xv4010, gb)
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(app(ty_Either, fd), ff)), fc)) → new_esEs0(xv310, xv4010, fd, ff)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(ty_[], cc)) → new_esEs3(xv312, xv4012, cc)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(app(ty_Either, bf), bg))) → new_esEs0(xv312, xv4012, bf, bg)
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(app(app(ty_@3, eh), fa), fb)), fc)) → new_esEs(xv310, xv4010, eh, fa, fb)
new_esEs2(Just(xv310), Just(xv4010), app(app(ty_Either, bac), bad)) → new_esEs0(xv310, xv4010, bac, bad)
new_esEs0(Left(xv310), Left(xv4010), app(app(app(ty_@3, eh), fa), fb), fc) → new_esEs(xv310, xv4010, eh, fa, fb)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(app(ty_@2, ed), ee), bb, cg) → new_esEs1(xv310, xv4010, ed, ee)
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(app(ty_Either, bbe), bbf)) → new_esEs0(xv310, xv4010, bbe, bbf)
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(app(ty_Either, gg), gh))) → new_esEs0(xv310, xv4010, gg, gh)
new_esEs2(Just(xv310), Just(xv4010), app(ty_[], bah)) → new_esEs3(xv310, xv4010, bah)
new_esEs0(Left(xv310), Left(xv4010), app(app(ty_@2, fg), fh), fc) → new_esEs1(xv310, xv4010, fg, fh)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(ty_[], eg), bb, cg) → new_esEs3(xv310, xv4010, eg)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(app(ty_Either, eb), ec), bb, cg) → new_esEs0(xv310, xv4010, eb, ec)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(app(ty_@2, dc), dd), cg) → new_esEs1(xv311, xv4011, dc, dd)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(ty_[], cc))) → new_esEs3(xv312, xv4012, cc)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(app(ty_Either, da), db)), cg)) → new_esEs0(xv311, xv4011, da, db)
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(app(ty_@2, bbg), bbh))) → new_esEs1(xv310, xv4010, bbg, bbh)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(ty_Maybe, ef), bb, cg) → new_esEs2(xv310, xv4010, ef)
new_esEs0(Right(xv310), Right(xv4010), gc, app(app(app(ty_@3, gd), ge), gf)) → new_esEs(xv310, xv4010, gd, ge, gf)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(ty_Maybe, cb)) → new_esEs2(xv312, xv4012, cb)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(ty_[], eg)), bb), cg)) → new_esEs3(xv310, xv4010, eg)
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], bba)) → new_esEs3(xv311, xv4011, bba)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(app(app(ty_@3, dg), dh), ea), bb, cg) → new_esEs(xv310, xv4010, dg, dh, ea)
new_esEs0(Left(xv310), Left(xv4010), app(app(ty_Either, fd), ff), fc) → new_esEs0(xv310, xv4010, fd, ff)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(app(ty_@2, bh), ca)) → new_esEs1(xv312, xv4012, bh, ca)
new_esEs2(Just(xv310), Just(xv4010), app(app(ty_@2, bae), baf)) → new_esEs1(xv310, xv4010, bae, baf)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(app(app(ty_@3, dg), dh), ea)), bb), cg)) → new_esEs(xv310, xv4010, dg, dh, ea)
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(app(ty_@2, ha), hb))) → new_esEs1(xv310, xv4010, ha, hb)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(ty_Maybe, cb))) → new_esEs2(xv312, xv4012, cb)
new_esEs0(Right(xv310), Right(xv4010), gc, app(ty_Maybe, hc)) → new_esEs2(xv310, xv4010, hc)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(app(ty_Either, da), db), cg) → new_esEs0(xv311, xv4011, da, db)
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(app(ty_@2, bbg), bbh)) → new_esEs1(xv310, xv4010, bbg, bbh)
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(app(ty_@2, bae), baf))) → new_esEs1(xv310, xv4010, bae, baf)
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(ty_[], gb)), fc)) → new_esEs3(xv310, xv4010, gb)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(app(app(ty_@3, cd), ce), cf), cg) → new_esEs(xv311, xv4011, cd, ce, cf)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(app(app(ty_@3, bc), bd), be))) → new_esEs(xv312, xv4012, bc, bd, be)
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(ty_[], hd))) → new_esEs3(xv310, xv4010, hd)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(app(ty_@2, ed), ee)), bb), cg)) → new_esEs1(xv310, xv4010, ed, ee)
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_@2, bda), bdb), bcf) → new_esEs1(xv30, xv400, bda, bdb)
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(ty_Maybe, hc))) → new_esEs2(xv310, xv4010, hc)
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(app(ty_@2, fg), fh)), fc)) → new_esEs1(xv310, xv4010, fg, fh)
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(app(app(ty_@3, bbb), bbc), bbd))) → new_esEs(xv310, xv4010, bbb, bbc, bbd)
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(ty_Maybe, bca))) → new_esEs2(xv310, xv4010, bca)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(ty_Maybe, ef)), bb), cg)) → new_esEs2(xv310, xv4010, ef)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(ty_[], df), cg) → new_esEs3(xv311, xv4011, df)
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(ty_[], bah))) → new_esEs3(xv310, xv4010, bah)
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(app(ty_@2, bh), ca))) → new_esEs1(xv312, xv4012, bh, ca)
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(ty_Maybe, bca)) → new_esEs2(xv310, xv4010, bca)
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(app(app(ty_@3, gd), ge), gf))) → new_esEs(xv310, xv4010, gd, ge, gf)
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(app(app(ty_@3, bcc), bcd), bce), bcf) → new_esEs(xv30, xv400, bcc, bcd, bce)
new_esEs0(Right(xv310), Right(xv4010), gc, app(ty_[], hd)) → new_esEs3(xv310, xv4010, hd)
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(app(app(ty_@3, bc), bd), be)) → new_esEs(xv312, xv4012, bc, bd, be)

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

new_esEs2(Just(xv310), Just(xv4010), app(app(ty_@2, bae), baf)) → new_esEs1(xv310, xv4010, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(Just(xv310), Just(xv4010), app(app(app(ty_@3, hh), baa), bab)) → new_esEs(xv310, xv4010, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Just(xv310), Just(xv4010), app(ty_Maybe, bag)) → new_esEs2(xv310, xv4010, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(app(ty_@2, bbg), bbh)) → new_esEs1(xv310, xv4010, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs(xv310, xv4010, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(Just(xv310), Just(xv4010), app(ty_[], bah)) → new_esEs3(xv310, xv4010, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(Just(xv310), Just(xv4010), app(app(ty_Either, bac), bad)) → new_esEs0(xv310, xv4010, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(ty_Maybe, bca)) → new_esEs2(xv310, xv4010, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(app(ty_Either, bbe), bbf)) → new_esEs0(xv310, xv4010, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(xv310), Right(xv4010), gc, app(app(ty_@2, ha), hb)) → new_esEs1(xv310, xv4010, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(Left(xv310), Left(xv4010), app(app(ty_@2, fg), fh), fc) → new_esEs1(xv310, xv4010, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Left(xv310), Left(xv4010), app(app(app(ty_@3, eh), fa), fb), fc) → new_esEs(xv310, xv4010, eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Right(xv310), Right(xv4010), gc, app(app(app(ty_@3, gd), ge), gf)) → new_esEs(xv310, xv4010, gd, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(Left(xv310), Left(xv4010), app(ty_Maybe, ga), fc) → new_esEs2(xv310, xv4010, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xv310), Right(xv4010), gc, app(ty_Maybe, hc)) → new_esEs2(xv310, xv4010, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Left(xv310), Left(xv4010), app(ty_[], gb), fc) → new_esEs3(xv310, xv4010, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xv310), Right(xv4010), gc, app(ty_[], hd)) → new_esEs3(xv310, xv4010, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Right(xv310), Right(xv4010), gc, app(app(ty_Either, gg), gh)) → new_esEs0(xv310, xv4010, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(Left(xv310), Left(xv4010), app(app(ty_Either, fd), ff), fc) → new_esEs0(xv310, xv4010, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(app(ty_@2, ed), ee), bb, cg) → new_esEs1(xv310, xv4010, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(app(ty_@2, dc), dd), cg) → new_esEs1(xv311, xv4011, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(app(ty_@2, bh), ca)) → new_esEs1(xv312, xv4012, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), he, app(app(ty_@2, hf), hg)) → new_esEs1(xv31, xv401, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(app(ty_@2, dc), dd)), cg)) → new_esEs1(xv311, xv4011, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(app(ty_@2, bbg), bbh))) → new_esEs1(xv310, xv4010, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(app(ty_@2, ha), hb))) → new_esEs1(xv310, xv4010, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(app(ty_@2, bae), baf))) → new_esEs1(xv310, xv4010, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_@2, bda), bdb), bcf) → new_esEs1(xv30, xv400, bda, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(app(ty_@2, ed), ee)), bb), cg)) → new_esEs1(xv310, xv4010, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(app(ty_@2, fg), fh)), fc)) → new_esEs1(xv310, xv4010, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(app(ty_@2, bh), ca))) → new_esEs1(xv312, xv4012, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(app(app(ty_@3, dg), dh), ea), bb, cg) → new_esEs(xv310, xv4010, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(app(app(ty_@3, cd), ce), cf), cg) → new_esEs(xv311, xv4011, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(app(app(ty_@3, bc), bd), be)) → new_esEs(xv312, xv4012, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(app(app(ty_@3, cd), ce), cf)), cg)) → new_esEs(xv311, xv4011, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(app(app(ty_@3, hh), baa), bab))) → new_esEs(xv310, xv4010, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(app(app(ty_@3, eh), fa), fb)), fc)) → new_esEs(xv310, xv4010, eh, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(app(app(ty_@3, dg), dh), ea)), bb), cg)) → new_esEs(xv310, xv4010, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(app(app(ty_@3, bc), bd), be))) → new_esEs(xv312, xv4012, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(app(app(ty_@3, bbb), bbc), bbd))) → new_esEs(xv310, xv4010, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(app(app(ty_@3, gd), ge), gf))) → new_esEs(xv310, xv4010, gd, ge, gf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(app(app(ty_@3, bcc), bcd), bce), bcf) → new_esEs(xv30, xv400, bcc, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(ty_Maybe, de), cg) → new_esEs2(xv311, xv4011, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(ty_Maybe, ef), bb, cg) → new_esEs2(xv310, xv4010, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(ty_Maybe, cb)) → new_esEs2(xv312, xv4012, cb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(ty_[], cc)) → new_esEs3(xv312, xv4012, cc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(ty_[], eg), bb, cg) → new_esEs3(xv310, xv4010, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(ty_[], df), cg) → new_esEs3(xv311, xv4011, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, bb, app(app(ty_Either, bf), bg)) → new_esEs0(xv312, xv4012, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), app(app(ty_Either, eb), ec), bb, cg) → new_esEs0(xv310, xv4010, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xv310, xv311, xv312), @3(xv4010, xv4011, xv4012), ba, app(app(ty_Either, da), db), cg) → new_esEs0(xv311, xv4011, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(ty_Maybe, bag))) → new_esEs2(xv310, xv4010, bag)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(ty_Maybe, bdc), bcf) → new_esEs2(xv30, xv400, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(ty_Maybe, de)), cg)) → new_esEs2(xv311, xv4011, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(ty_Maybe, ga)), fc)) → new_esEs2(xv310, xv4010, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(ty_Maybe, cb))) → new_esEs2(xv312, xv4012, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(ty_Maybe, hc))) → new_esEs2(xv310, xv4010, hc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(ty_Maybe, bca))) → new_esEs2(xv310, xv4010, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(ty_Maybe, ef)), bb), cg)) → new_esEs2(xv310, xv4010, ef)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), app(ty_[], bcb)) → new_esEs3(xv310, xv4010, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(:(xv310, xv311), :(xv4010, xv4011), bba) → new_esEs3(xv311, xv4011, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(ty_[], bdd), bcf) → new_esEs3(xv30, xv400, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(ty_[], df)), cg)) → new_esEs3(xv311, xv4011, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(ty_[], bcb))) → new_esEs3(xv310, xv4010, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(ty_[], cc))) → new_esEs3(xv312, xv4012, cc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(ty_[], eg)), bb), cg)) → new_esEs3(xv310, xv4010, eg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], bba)) → new_esEs3(xv311, xv4011, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(ty_[], gb)), fc)) → new_esEs3(xv310, xv4010, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(ty_[], hd))) → new_esEs3(xv310, xv4010, hd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(ty_[], bah))) → new_esEs3(xv310, xv4010, bah)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, Just(xv310)), @2(xv400, Just(xv4010)), he, app(ty_Maybe, app(app(ty_Either, bac), bad))) → new_esEs0(xv310, xv4010, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, xv31), @2(xv400, xv401), app(app(ty_Either, bcg), bch), bcf) → new_esEs0(xv30, xv400, bcg, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, app(app(ty_Either, eb), ec)), bb), cg)) → new_esEs0(xv310, xv4010, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, :(xv310, xv311)), @2(xv400, :(xv4010, xv4011)), he, app(ty_[], app(app(ty_Either, bbe), bbf))) → new_esEs0(xv310, xv4010, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, Left(xv310)), @2(xv400, Left(xv4010)), he, app(app(ty_Either, app(app(ty_Either, fd), ff)), fc)) → new_esEs0(xv310, xv4010, fd, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), bb), app(app(ty_Either, bf), bg))) → new_esEs0(xv312, xv4012, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, Right(xv310)), @2(xv400, Right(xv4010)), he, app(app(ty_Either, gc), app(app(ty_Either, gg), gh))) → new_esEs0(xv310, xv4010, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, @3(xv310, xv311, xv312)), @2(xv400, @3(xv4010, xv4011, xv4012)), he, app(app(app(ty_@3, ba), app(app(ty_Either, da), db)), cg)) → new_esEs0(xv311, xv4011, da, db)
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_foldr(xv3, :(xv40, xv41), ba, bb) → new_foldr(xv3, xv41, ba, bb)

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

new_foldr(xv3, :(xv40, xv41), ba, bb) → new_foldr(xv3, xv41, ba, bb)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4