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

YES 1.891 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] _	=	True
isPrefixOf	_ []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] vw	=	True
isPrefixOf	vx []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule List

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

module List where

import qualified Maybe
import qualified Prelude

isPrefixOf :: Eq a => [a] -> [a] -> Bool

isPrefixOf	[] vw	=	True
isPrefixOf	vx []	=	False
isPrefixOf	(x : xs) (y : ys)	=	x == y && isPrefixOf xs ys

isSuffixOf :: Eq a => [a] -> [a] -> Bool

isSuffixOf

x y

reverse x `isPrefixOf` reverse y

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

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346[label="xy35\n  Eq a",fontsize=16,color="green",shape="box"];347[label="xy3410\n  Eq a",fontsize=16,color="green",shape="box"];348 -> 614[label="",style="dashed", color="red", weight=0];
348[label="xy32 == xy350 && isPrefixOf xy31 xy351\n  Eq a",fontsize=16,color="magenta"];348 -> 615[label="",style="dashed", color="magenta", weight=3];
348 -> 616[label="",style="dashed", color="magenta", weight=3];
349[label="False",fontsize=16,color="green",shape="box"];615[label="xy32 == xy350\n  Eq a",fontsize=16,color="blue",shape="box"];1327[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1327[label="",style="solid", color="blue", weight=9];
1327 -> 632[label="",style="solid", color="blue", weight=3];
1328[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1328[label="",style="solid", color="blue", weight=9];
1328 -> 633[label="",style="solid", color="blue", weight=3];
1329[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1329[label="",style="solid", color="blue", weight=9];
1329 -> 634[label="",style="solid", color="blue", weight=3];
1330[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1330[label="",style="solid", color="blue", weight=9];
1330 -> 635[label="",style="solid", color="blue", weight=3];
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1332[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1332[label="",style="solid", color="blue", weight=9];
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1333[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1333[label="",style="solid", color="blue", weight=9];
1333 -> 638[label="",style="solid", color="blue", weight=3];
1334[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1334[label="",style="solid", color="blue", weight=9];
1334 -> 639[label="",style="solid", color="blue", weight=3];
1335[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1335[label="",style="solid", color="blue", weight=9];
1335 -> 640[label="",style="solid", color="blue", weight=3];
1336[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1336[label="",style="solid", color="blue", weight=9];
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1337[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];615 -> 1337[label="",style="solid", color="blue", weight=9];
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1341 -> 646[label="",style="solid", color="burlywood", weight=3];
1342[label="xy31/[]",fontsize=10,color="white",style="solid",shape="box"];616 -> 1342[label="",style="solid", color="burlywood", weight=9];
1342 -> 647[label="",style="solid", color="burlywood", weight=3];
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1343 -> 648[label="",style="solid", color="burlywood", weight=3];
1344[label="xy49/True",fontsize=10,color="white",style="solid",shape="box"];614 -> 1344[label="",style="solid", color="burlywood", weight=9];
1344 -> 649[label="",style="solid", color="burlywood", weight=3];
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1345 -> 650[label="",style="solid", color="burlywood", weight=3];
1346[label="xy32/Right xy320",fontsize=10,color="white",style="solid",shape="box"];632 -> 1346[label="",style="solid", color="burlywood", weight=9];
1346 -> 651[label="",style="solid", color="burlywood", weight=3];
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634[label="xy32 == xy350",fontsize=16,color="burlywood",shape="triangle"];1347[label="xy32/()",fontsize=10,color="white",style="solid",shape="box"];634 -> 1347[label="",style="solid", color="burlywood", weight=9];
1347 -> 653[label="",style="solid", color="burlywood", weight=3];
635[label="xy32 == xy350\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];1348[label="xy32/(xy320,xy321,xy322)",fontsize=10,color="white",style="solid",shape="box"];635 -> 1348[label="",style="solid", color="burlywood", weight=9];
1348 -> 654[label="",style="solid", color="burlywood", weight=3];
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1349 -> 655[label="",style="solid", color="burlywood", weight=3];
1350[label="xy32/EQ",fontsize=10,color="white",style="solid",shape="box"];636 -> 1350[label="",style="solid", color="burlywood", weight=9];
1350 -> 656[label="",style="solid", color="burlywood", weight=3];
1351[label="xy32/GT",fontsize=10,color="white",style="solid",shape="box"];636 -> 1351[label="",style="solid", color="burlywood", weight=9];
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1352 -> 659[label="",style="solid", color="burlywood", weight=3];
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1353 -> 661[label="",style="solid", color="burlywood", weight=3];
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642[label="xy32 == xy350",fontsize=16,color="burlywood",shape="triangle"];1354[label="xy32/Integer xy320",fontsize=10,color="white",style="solid",shape="box"];642 -> 1354[label="",style="solid", color="burlywood", weight=9];
1354 -> 663[label="",style="solid", color="burlywood", weight=3];
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1355 -> 664[label="",style="solid", color="burlywood", weight=3];
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1356 -> 665[label="",style="solid", color="burlywood", weight=3];
644[label="xy32 == xy350",fontsize=16,color="burlywood",shape="triangle"];1357[label="xy32/False",fontsize=10,color="white",style="solid",shape="box"];644 -> 1357[label="",style="solid", color="burlywood", weight=9];
1357 -> 666[label="",style="solid", color="burlywood", weight=3];
1358[label="xy32/True",fontsize=10,color="white",style="solid",shape="box"];644 -> 1358[label="",style="solid", color="burlywood", weight=9];
1358 -> 667[label="",style="solid", color="burlywood", weight=3];
645[label="xy32 == xy350\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];1359[label="xy32/Nothing",fontsize=10,color="white",style="solid",shape="box"];645 -> 1359[label="",style="solid", color="burlywood", weight=9];
1359 -> 668[label="",style="solid", color="burlywood", weight=3];
1360[label="xy32/Just xy320",fontsize=10,color="white",style="solid",shape="box"];645 -> 1360[label="",style="solid", color="burlywood", weight=9];
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1361 -> 670[label="",style="solid", color="burlywood", weight=3];
1362[label="xy351/[]",fontsize=10,color="white",style="solid",shape="box"];646 -> 1362[label="",style="solid", color="burlywood", weight=9];
1362 -> 671[label="",style="solid", color="burlywood", weight=3];
647[label="isPrefixOf [] xy351\n  Eq a",fontsize=16,color="black",shape="box"];647 -> 672[label="",style="solid", color="black", weight=3];
648[label="False && xy61",fontsize=16,color="black",shape="box"];648 -> 673[label="",style="solid", color="black", weight=3];
649[label="True && xy61",fontsize=16,color="black",shape="box"];649 -> 674[label="",style="solid", color="black", weight=3];
650[label="Left xy320 == xy350\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1363[label="xy350/Left xy3500",fontsize=10,color="white",style="solid",shape="box"];650 -> 1363[label="",style="solid", color="burlywood", weight=9];
1363 -> 675[label="",style="solid", color="burlywood", weight=3];
1364[label="xy350/Right xy3500",fontsize=10,color="white",style="solid",shape="box"];650 -> 1364[label="",style="solid", color="burlywood", weight=9];
1364 -> 676[label="",style="solid", color="burlywood", weight=3];
651[label="Right xy320 == xy350\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1365[label="xy350/Left xy3500",fontsize=10,color="white",style="solid",shape="box"];651 -> 1365[label="",style="solid", color="burlywood", weight=9];
1365 -> 677[label="",style="solid", color="burlywood", weight=3];
1366[label="xy350/Right xy3500",fontsize=10,color="white",style="solid",shape="box"];651 -> 1366[label="",style="solid", color="burlywood", weight=9];
1366 -> 678[label="",style="solid", color="burlywood", weight=3];
652[label="primEqChar xy32 xy350",fontsize=16,color="burlywood",shape="box"];1367[label="xy32/Char xy320",fontsize=10,color="white",style="solid",shape="box"];652 -> 1367[label="",style="solid", color="burlywood", weight=9];
1367 -> 679[label="",style="solid", color="burlywood", weight=3];
653[label="() == xy350",fontsize=16,color="burlywood",shape="box"];1368[label="xy350/()",fontsize=10,color="white",style="solid",shape="box"];653 -> 1368[label="",style="solid", color="burlywood", weight=9];
1368 -> 680[label="",style="solid", color="burlywood", weight=3];
654[label="(xy320,xy321,xy322) == xy350\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1369[label="xy350/(xy3500,xy3501,xy3502)",fontsize=10,color="white",style="solid",shape="box"];654 -> 1369[label="",style="solid", color="burlywood", weight=9];
1369 -> 681[label="",style="solid", color="burlywood", weight=3];
655[label="LT == xy350",fontsize=16,color="burlywood",shape="box"];1370[label="xy350/LT",fontsize=10,color="white",style="solid",shape="box"];655 -> 1370[label="",style="solid", color="burlywood", weight=9];
1370 -> 682[label="",style="solid", color="burlywood", weight=3];
1371[label="xy350/EQ",fontsize=10,color="white",style="solid",shape="box"];655 -> 1371[label="",style="solid", color="burlywood", weight=9];
1371 -> 683[label="",style="solid", color="burlywood", weight=3];
1372[label="xy350/GT",fontsize=10,color="white",style="solid",shape="box"];655 -> 1372[label="",style="solid", color="burlywood", weight=9];
1372 -> 684[label="",style="solid", color="burlywood", weight=3];
656[label="EQ == xy350",fontsize=16,color="burlywood",shape="box"];1373[label="xy350/LT",fontsize=10,color="white",style="solid",shape="box"];656 -> 1373[label="",style="solid", color="burlywood", weight=9];
1373 -> 685[label="",style="solid", color="burlywood", weight=3];
1374[label="xy350/EQ",fontsize=10,color="white",style="solid",shape="box"];656 -> 1374[label="",style="solid", color="burlywood", weight=9];
1374 -> 686[label="",style="solid", color="burlywood", weight=3];
1375[label="xy350/GT",fontsize=10,color="white",style="solid",shape="box"];656 -> 1375[label="",style="solid", color="burlywood", weight=9];
1375 -> 687[label="",style="solid", color="burlywood", weight=3];
657[label="GT == xy350",fontsize=16,color="burlywood",shape="box"];1376[label="xy350/LT",fontsize=10,color="white",style="solid",shape="box"];657 -> 1376[label="",style="solid", color="burlywood", weight=9];
1376 -> 688[label="",style="solid", color="burlywood", weight=3];
1377[label="xy350/EQ",fontsize=10,color="white",style="solid",shape="box"];657 -> 1377[label="",style="solid", color="burlywood", weight=9];
1377 -> 689[label="",style="solid", color="burlywood", weight=3];
1378[label="xy350/GT",fontsize=10,color="white",style="solid",shape="box"];657 -> 1378[label="",style="solid", color="burlywood", weight=9];
1378 -> 690[label="",style="solid", color="burlywood", weight=3];
658[label="primEqFloat xy32 xy350",fontsize=16,color="burlywood",shape="box"];1379[label="xy32/Float xy320 xy321",fontsize=10,color="white",style="solid",shape="box"];658 -> 1379[label="",style="solid", color="burlywood", weight=9];
1379 -> 691[label="",style="solid", color="burlywood", weight=3];
659[label="xy320 :% xy321 == xy350\n  Integral a",fontsize=16,color="burlywood",shape="box"];1380[label="xy350/xy3500 :% xy3501",fontsize=10,color="white",style="solid",shape="box"];659 -> 1380[label="",style="solid", color="burlywood", weight=9];
1380 -> 692[label="",style="solid", color="burlywood", weight=3];
660[label="primEqDouble xy32 xy350",fontsize=16,color="burlywood",shape="box"];1381[label="xy32/Double xy320 xy321",fontsize=10,color="white",style="solid",shape="box"];660 -> 1381[label="",style="solid", color="burlywood", weight=9];
1381 -> 693[label="",style="solid", color="burlywood", weight=3];
661[label="(xy320,xy321) == xy350\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1382[label="xy350/(xy3500,xy3501)",fontsize=10,color="white",style="solid",shape="box"];661 -> 1382[label="",style="solid", color="burlywood", weight=9];
1382 -> 694[label="",style="solid", color="burlywood", weight=3];
662[label="primEqInt xy32 xy350",fontsize=16,color="burlywood",shape="triangle"];1383[label="xy32/Pos xy320",fontsize=10,color="white",style="solid",shape="box"];662 -> 1383[label="",style="solid", color="burlywood", weight=9];
1383 -> 695[label="",style="solid", color="burlywood", weight=3];
1384[label="xy32/Neg xy320",fontsize=10,color="white",style="solid",shape="box"];662 -> 1384[label="",style="solid", color="burlywood", weight=9];
1384 -> 696[label="",style="solid", color="burlywood", weight=3];
663[label="Integer xy320 == xy350",fontsize=16,color="burlywood",shape="box"];1385[label="xy350/Integer xy3500",fontsize=10,color="white",style="solid",shape="box"];663 -> 1385[label="",style="solid", color="burlywood", weight=9];
1385 -> 697[label="",style="solid", color="burlywood", weight=3];
664[label="xy320 : xy321 == xy350\n  Eq a",fontsize=16,color="burlywood",shape="box"];1386[label="xy350/xy3500 : xy3501",fontsize=10,color="white",style="solid",shape="box"];664 -> 1386[label="",style="solid", color="burlywood", weight=9];
1386 -> 698[label="",style="solid", color="burlywood", weight=3];
1387[label="xy350/[]",fontsize=10,color="white",style="solid",shape="box"];664 -> 1387[label="",style="solid", color="burlywood", weight=9];
1387 -> 699[label="",style="solid", color="burlywood", weight=3];
665[label="[] == xy350\n  Eq a",fontsize=16,color="burlywood",shape="box"];1388[label="xy350/xy3500 : xy3501",fontsize=10,color="white",style="solid",shape="box"];665 -> 1388[label="",style="solid", color="burlywood", weight=9];
1388 -> 700[label="",style="solid", color="burlywood", weight=3];
1389[label="xy350/[]",fontsize=10,color="white",style="solid",shape="box"];665 -> 1389[label="",style="solid", color="burlywood", weight=9];
1389 -> 701[label="",style="solid", color="burlywood", weight=3];
666[label="False == xy350",fontsize=16,color="burlywood",shape="box"];1390[label="xy350/False",fontsize=10,color="white",style="solid",shape="box"];666 -> 1390[label="",style="solid", color="burlywood", weight=9];
1390 -> 702[label="",style="solid", color="burlywood", weight=3];
1391[label="xy350/True",fontsize=10,color="white",style="solid",shape="box"];666 -> 1391[label="",style="solid", color="burlywood", weight=9];
1391 -> 703[label="",style="solid", color="burlywood", weight=3];
667[label="True == xy350",fontsize=16,color="burlywood",shape="box"];1392[label="xy350/False",fontsize=10,color="white",style="solid",shape="box"];667 -> 1392[label="",style="solid", color="burlywood", weight=9];
1392 -> 704[label="",style="solid", color="burlywood", weight=3];
1393[label="xy350/True",fontsize=10,color="white",style="solid",shape="box"];667 -> 1393[label="",style="solid", color="burlywood", weight=9];
1393 -> 705[label="",style="solid", color="burlywood", weight=3];
668[label="Nothing == xy350\n  Eq a",fontsize=16,color="burlywood",shape="box"];1394[label="xy350/Nothing",fontsize=10,color="white",style="solid",shape="box"];668 -> 1394[label="",style="solid", color="burlywood", weight=9];
1394 -> 706[label="",style="solid", color="burlywood", weight=3];
1395[label="xy350/Just xy3500",fontsize=10,color="white",style="solid",shape="box"];668 -> 1395[label="",style="solid", color="burlywood", weight=9];
1395 -> 707[label="",style="solid", color="burlywood", weight=3];
669[label="Just xy320 == xy350\n  Eq a",fontsize=16,color="burlywood",shape="box"];1396[label="xy350/Nothing",fontsize=10,color="white",style="solid",shape="box"];669 -> 1396[label="",style="solid", color="burlywood", weight=9];
1396 -> 708[label="",style="solid", color="burlywood", weight=3];
1397[label="xy350/Just xy3500",fontsize=10,color="white",style="solid",shape="box"];669 -> 1397[label="",style="solid", color="burlywood", weight=9];
1397 -> 709[label="",style="solid", color="burlywood", weight=3];
670[label="isPrefixOf (xy310 : xy311) (xy3510 : xy3511)\n  Eq a",fontsize=16,color="black",shape="box"];670 -> 710[label="",style="solid", color="black", weight=3];
671[label="isPrefixOf (xy310 : xy311) []\n  Eq a",fontsize=16,color="black",shape="box"];671 -> 711[label="",style="solid", color="black", weight=3];
672[label="True",fontsize=16,color="green",shape="box"];673[label="False",fontsize=16,color="green",shape="box"];674[label="xy61",fontsize=16,color="green",shape="box"];675[label="Left xy320 == Left xy3500\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];675 -> 712[label="",style="solid", color="black", weight=3];
676[label="Left xy320 == Right xy3500\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];676 -> 713[label="",style="solid", color="black", weight=3];
677[label="Right xy320 == Left xy3500\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];677 -> 714[label="",style="solid", color="black", weight=3];
678[label="Right xy320 == Right xy3500\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];678 -> 715[label="",style="solid", color="black", weight=3];
679[label="primEqChar (Char xy320) xy350",fontsize=16,color="burlywood",shape="box"];1398[label="xy350/Char xy3500",fontsize=10,color="white",style="solid",shape="box"];679 -> 1398[label="",style="solid", color="burlywood", weight=9];
1398 -> 716[label="",style="solid", color="burlywood", weight=3];
680[label="() == ()",fontsize=16,color="black",shape="box"];680 -> 717[label="",style="solid", color="black", weight=3];
681[label="(xy320,xy321,xy322) == (xy3500,xy3501,xy3502)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];681 -> 718[label="",style="solid", color="black", weight=3];
682[label="LT == LT",fontsize=16,color="black",shape="box"];682 -> 719[label="",style="solid", color="black", weight=3];
683[label="LT == EQ",fontsize=16,color="black",shape="box"];683 -> 720[label="",style="solid", color="black", weight=3];
684[label="LT == GT",fontsize=16,color="black",shape="box"];684 -> 721[label="",style="solid", color="black", weight=3];
685[label="EQ == LT",fontsize=16,color="black",shape="box"];685 -> 722[label="",style="solid", color="black", weight=3];
686[label="EQ == EQ",fontsize=16,color="black",shape="box"];686 -> 723[label="",style="solid", color="black", weight=3];
687[label="EQ == GT",fontsize=16,color="black",shape="box"];687 -> 724[label="",style="solid", color="black", weight=3];
688[label="GT == LT",fontsize=16,color="black",shape="box"];688 -> 725[label="",style="solid", color="black", weight=3];
689[label="GT == EQ",fontsize=16,color="black",shape="box"];689 -> 726[label="",style="solid", color="black", weight=3];
690[label="GT == GT",fontsize=16,color="black",shape="box"];690 -> 727[label="",style="solid", color="black", weight=3];
691[label="primEqFloat (Float xy320 xy321) xy350",fontsize=16,color="burlywood",shape="box"];1399[label="xy350/Float xy3500 xy3501",fontsize=10,color="white",style="solid",shape="box"];691 -> 1399[label="",style="solid", color="burlywood", weight=9];
1399 -> 728[label="",style="solid", color="burlywood", weight=3];
692[label="xy320 :% xy321 == xy3500 :% xy3501\n  Integral a",fontsize=16,color="black",shape="box"];692 -> 729[label="",style="solid", color="black", weight=3];
693[label="primEqDouble (Double xy320 xy321) xy350",fontsize=16,color="burlywood",shape="box"];1400[label="xy350/Double xy3500 xy3501",fontsize=10,color="white",style="solid",shape="box"];693 -> 1400[label="",style="solid", color="burlywood", weight=9];
1400 -> 730[label="",style="solid", color="burlywood", weight=3];
694[label="(xy320,xy321) == (xy3500,xy3501)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];694 -> 731[label="",style="solid", color="black", weight=3];
695[label="primEqInt (Pos xy320) xy350",fontsize=16,color="burlywood",shape="box"];1401[label="xy320/Succ xy3200",fontsize=10,color="white",style="solid",shape="box"];695 -> 1401[label="",style="solid", color="burlywood", weight=9];
1401 -> 732[label="",style="solid", color="burlywood", weight=3];
1402[label="xy320/Zero",fontsize=10,color="white",style="solid",shape="box"];695 -> 1402[label="",style="solid", color="burlywood", weight=9];
1402 -> 733[label="",style="solid", color="burlywood", weight=3];
696[label="primEqInt (Neg xy320) xy350",fontsize=16,color="burlywood",shape="box"];1403[label="xy320/Succ xy3200",fontsize=10,color="white",style="solid",shape="box"];696 -> 1403[label="",style="solid", color="burlywood", weight=9];
1403 -> 734[label="",style="solid", color="burlywood", weight=3];
1404[label="xy320/Zero",fontsize=10,color="white",style="solid",shape="box"];696 -> 1404[label="",style="solid", color="burlywood", weight=9];
1404 -> 735[label="",style="solid", color="burlywood", weight=3];
697[label="Integer xy320 == Integer xy3500",fontsize=16,color="black",shape="box"];697 -> 736[label="",style="solid", color="black", weight=3];
698[label="xy320 : xy321 == xy3500 : xy3501\n  Eq a",fontsize=16,color="black",shape="box"];698 -> 737[label="",style="solid", color="black", weight=3];
699[label="xy320 : xy321 == []\n  Eq a",fontsize=16,color="black",shape="box"];699 -> 738[label="",style="solid", color="black", weight=3];
700[label="[] == xy3500 : xy3501\n  Eq a",fontsize=16,color="black",shape="box"];700 -> 739[label="",style="solid", color="black", weight=3];
701[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];701 -> 740[label="",style="solid", color="black", weight=3];
702[label="False == False",fontsize=16,color="black",shape="box"];702 -> 741[label="",style="solid", color="black", weight=3];
703[label="False == True",fontsize=16,color="black",shape="box"];703 -> 742[label="",style="solid", color="black", weight=3];
704[label="True == False",fontsize=16,color="black",shape="box"];704 -> 743[label="",style="solid", color="black", weight=3];
705[label="True == True",fontsize=16,color="black",shape="box"];705 -> 744[label="",style="solid", color="black", weight=3];
706[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];706 -> 745[label="",style="solid", color="black", weight=3];
707[label="Nothing == Just xy3500\n  Eq a",fontsize=16,color="black",shape="box"];707 -> 746[label="",style="solid", color="black", weight=3];
708[label="Just xy320 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];708 -> 747[label="",style="solid", color="black", weight=3];
709[label="Just xy320 == Just xy3500\n  Eq a",fontsize=16,color="black",shape="box"];709 -> 748[label="",style="solid", color="black", weight=3];
710 -> 614[label="",style="dashed", color="red", weight=0];
710[label="xy310 == xy3510 && isPrefixOf xy311 xy3511\n  Eq a",fontsize=16,color="magenta"];710 -> 749[label="",style="dashed", color="magenta", weight=3];
710 -> 750[label="",style="dashed", color="magenta", weight=3];
711[label="False",fontsize=16,color="green",shape="box"];712[label="xy320 == xy3500\n  Eq a",fontsize=16,color="blue",shape="box"];1406[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1406[label="",style="solid", color="blue", weight=9];
1406 -> 751[label="",style="solid", color="blue", weight=3];
1407[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1407[label="",style="solid", color="blue", weight=9];
1407 -> 752[label="",style="solid", color="blue", weight=3];
1408[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1408[label="",style="solid", color="blue", weight=9];
1408 -> 753[label="",style="solid", color="blue", weight=3];
1409[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1409[label="",style="solid", color="blue", weight=9];
1409 -> 754[label="",style="solid", color="blue", weight=3];
1410[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1410[label="",style="solid", color="blue", weight=9];
1410 -> 755[label="",style="solid", color="blue", weight=3];
1411[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1411[label="",style="solid", color="blue", weight=9];
1411 -> 756[label="",style="solid", color="blue", weight=3];
1412[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1412[label="",style="solid", color="blue", weight=9];
1412 -> 757[label="",style="solid", color="blue", weight=3];
1413[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1413[label="",style="solid", color="blue", weight=9];
1413 -> 758[label="",style="solid", color="blue", weight=3];
1414[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1414[label="",style="solid", color="blue", weight=9];
1414 -> 759[label="",style="solid", color="blue", weight=3];
1415[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1415[label="",style="solid", color="blue", weight=9];
1415 -> 760[label="",style="solid", color="blue", weight=3];
1416[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1416[label="",style="solid", color="blue", weight=9];
1416 -> 761[label="",style="solid", color="blue", weight=3];
1417[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1417[label="",style="solid", color="blue", weight=9];
1417 -> 762[label="",style="solid", color="blue", weight=3];
1418[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1418[label="",style="solid", color="blue", weight=9];
1418 -> 763[label="",style="solid", color="blue", weight=3];
1419[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];712 -> 1419[label="",style="solid", color="blue", weight=9];
1419 -> 764[label="",style="solid", color="blue", weight=3];
713[label="False",fontsize=16,color="green",shape="box"];714[label="False",fontsize=16,color="green",shape="box"];715[label="xy320 == xy3500\n  Eq a",fontsize=16,color="blue",shape="box"];1420[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1420[label="",style="solid", color="blue", weight=9];
1420 -> 765[label="",style="solid", color="blue", weight=3];
1421[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1421[label="",style="solid", color="blue", weight=9];
1421 -> 766[label="",style="solid", color="blue", weight=3];
1422[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1422[label="",style="solid", color="blue", weight=9];
1422 -> 767[label="",style="solid", color="blue", weight=3];
1423[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1423[label="",style="solid", color="blue", weight=9];
1423 -> 768[label="",style="solid", color="blue", weight=3];
1424[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1424[label="",style="solid", color="blue", weight=9];
1424 -> 769[label="",style="solid", color="blue", weight=3];
1425[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1425[label="",style="solid", color="blue", weight=9];
1425 -> 770[label="",style="solid", color="blue", weight=3];
1426[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1426[label="",style="solid", color="blue", weight=9];
1426 -> 771[label="",style="solid", color="blue", weight=3];
1427[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1427[label="",style="solid", color="blue", weight=9];
1427 -> 772[label="",style="solid", color="blue", weight=3];
1428[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1428[label="",style="solid", color="blue", weight=9];
1428 -> 773[label="",style="solid", color="blue", weight=3];
1429[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1429[label="",style="solid", color="blue", weight=9];
1429 -> 774[label="",style="solid", color="blue", weight=3];
1430[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1430[label="",style="solid", color="blue", weight=9];
1430 -> 775[label="",style="solid", color="blue", weight=3];
1431[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1431[label="",style="solid", color="blue", weight=9];
1431 -> 776[label="",style="solid", color="blue", weight=3];
1432[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1432[label="",style="solid", color="blue", weight=9];
1432 -> 777[label="",style="solid", color="blue", weight=3];
1433[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];715 -> 1433[label="",style="solid", color="blue", weight=9];
1433 -> 778[label="",style="solid", color="blue", weight=3];
716[label="primEqChar (Char xy320) (Char xy3500)",fontsize=16,color="black",shape="box"];716 -> 779[label="",style="solid", color="black", weight=3];
717[label="True",fontsize=16,color="green",shape="box"];718 -> 614[label="",style="dashed", color="red", weight=0];
718[label="xy320 == xy3500 && xy321 == xy3501 && xy322 == xy3502\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];718 -> 780[label="",style="dashed", color="magenta", weight=3];
718 -> 781[label="",style="dashed", color="magenta", weight=3];
719[label="True",fontsize=16,color="green",shape="box"];720[label="False",fontsize=16,color="green",shape="box"];721[label="False",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[label="False",fontsize=16,color="green",shape="box"];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="primEqFloat (Float xy320 xy321) (Float xy3500 xy3501)",fontsize=16,color="black",shape="box"];728 -> 782[label="",style="solid", color="black", weight=3];
729 -> 614[label="",style="dashed", color="red", weight=0];
729[label="xy320 == xy3500 && xy321 == xy3501\n  Integral a",fontsize=16,color="magenta"];729 -> 783[label="",style="dashed", color="magenta", weight=3];
729 -> 784[label="",style="dashed", color="magenta", weight=3];
730[label="primEqDouble (Double xy320 xy321) (Double xy3500 xy3501)",fontsize=16,color="black",shape="box"];730 -> 785[label="",style="solid", color="black", weight=3];
731 -> 614[label="",style="dashed", color="red", weight=0];
731[label="xy320 == xy3500 && xy321 == xy3501\n  Eq a  Eq b",fontsize=16,color="magenta"];731 -> 786[label="",style="dashed", color="magenta", weight=3];
731 -> 787[label="",style="dashed", color="magenta", weight=3];
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1538[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];786 -> 1538[label="",style="solid", color="blue", weight=9];
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1548[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];787 -> 1548[label="",style="solid", color="blue", weight=9];
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1550[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];787 -> 1550[label="",style="solid", color="blue", weight=9];
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1551[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];787 -> 1551[label="",style="solid", color="blue", weight=9];
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1553[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];787 -> 1553[label="",style="solid", color="blue", weight=9];
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1562[label="xy3500/Zero",fontsize=10,color="white",style="solid",shape="box"];793 -> 1562[label="",style="solid", color="burlywood", weight=9];
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1576[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];798 -> 1576[label="",style="solid", color="blue", weight=9];
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1306[label="Succ (Succ (primPlusNat xy6200 xy3501000))",fontsize=16,color="green",shape="box"];1306 -> 1310[label="",style="dashed", color="green", weight=3];
1307[label="Succ xy6200",fontsize=16,color="green",shape="box"];1308[label="Succ xy3501000",fontsize=16,color="green",shape="box"];1309[label="Zero",fontsize=16,color="green",shape="box"];1310 -> 1299[label="",style="dashed", color="red", weight=0];
1310[label="primPlusNat xy6200 xy3501000",fontsize=16,color="magenta"];1310 -> 1311[label="",style="dashed", color="magenta", weight=3];
1310 -> 1312[label="",style="dashed", color="magenta", weight=3];
1311[label="xy6200",fontsize=16,color="green",shape="box"];1312[label="xy3501000",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(xy6200), Succ(xy3501000)) → new_primPlusNat(xy6200, xy3501000)

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(xy6200), Succ(xy3501000)) → new_primPlusNat(xy6200, xy3501000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(xy32100), Succ(xy350100)) → new_primMulNat(xy32100, Succ(xy350100))

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

new_primMulNat(Succ(xy32100), Succ(xy350100)) → new_primMulNat(xy32100, Succ(xy350100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(xy3200), Succ(xy35000)) → new_primEqNat(xy3200, xy35000)

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

new_primEqNat(Succ(xy3200), Succ(xy35000)) → new_primEqNat(xy3200, xy35000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(app(ty_@2, fh), ga), ea) → new_esEs1(xy321, xy3501, fh, ga)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(xy320, xy3500, hh, baa, bab)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(ty_Maybe, bbh)) → new_esEs3(xy321, xy3501, bbh)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(app(ty_Either, he), hf), hg) → new_esEs(xy320, xy3500, he, hf)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(ty_Maybe, eh), dh, ea) → new_esEs3(xy320, xy3500, eh)
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(ty_Maybe, bda)) → new_esEs3(xy320, xy3500, bda)
new_esEs3(Just(xy320), Just(xy3500), app(app(ty_@2, bdh), bea)) → new_esEs1(xy320, xy3500, bdh, bea)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(app(ty_Either, df), dg), dh, ea) → new_esEs(xy320, xy3500, df, dg)
new_esEs(Left(xy320), Left(xy3500), app(app(ty_@2, bg), bh), bc) → new_esEs1(xy320, xy3500, bg, bh)
new_esEs3(Just(xy320), Just(xy3500), app(ty_[], beb)) → new_esEs2(xy320, xy3500, beb)
new_esEs(Right(xy320), Right(xy3500), cc, app(ty_Maybe, de)) → new_esEs3(xy320, xy3500, de)
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(xy320, xy3500, bcc, bcd, bce)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(ty_[], eg), dh, ea) → new_esEs2(xy320, xy3500, eg)
new_esEs(Right(xy320), Right(xy3500), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(xy320, xy3500, cf, cg, da)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(app(ty_Either, gd), ge)) → new_esEs(xy322, xy3502, gd, ge)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(ty_Maybe, baf), hg) → new_esEs3(xy320, xy3500, baf)
new_esEs(Left(xy320), Left(xy3500), app(ty_[], ca), bc) → new_esEs2(xy320, xy3500, ca)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(ty_[], bae), hg) → new_esEs2(xy320, xy3500, bae)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(xy321, xy3501, fd, ff, fg)
new_esEs(Left(xy320), Left(xy3500), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(xy320, xy3500, bd, be, bf)
new_esEs3(Just(xy320), Just(xy3500), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(xy320, xy3500, bde, bdf, bdg)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(ty_Maybe, gc), ea) → new_esEs3(xy321, xy3501, gc)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(ty_[], bbg)) → new_esEs2(xy321, xy3501, bbg)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(ty_Maybe, hd)) → new_esEs3(xy322, xy3502, hd)
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(app(ty_Either, bca), bcb)) → new_esEs(xy320, xy3500, bca, bcb)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(app(ty_@2, bbe), bbf)) → new_esEs1(xy321, xy3501, bbe, bbf)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(app(ty_@2, ha), hb)) → new_esEs1(xy322, xy3502, ha, hb)
new_esEs(Right(xy320), Right(xy3500), cc, app(ty_[], dd)) → new_esEs2(xy320, xy3500, dd)
new_esEs(Right(xy320), Right(xy3500), cc, app(app(ty_Either, cd), ce)) → new_esEs(xy320, xy3500, cd, ce)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(ty_[], gb), ea) → new_esEs2(xy321, xy3501, gb)
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(app(ty_@2, bcf), bcg)) → new_esEs1(xy320, xy3500, bcf, bcg)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(xy322, xy3502, gf, gg, gh)
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), bdb) → new_esEs2(xy321, xy3501, bdb)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(app(ty_@2, bac), bad), hg) → new_esEs1(xy320, xy3500, bac, bad)
new_esEs3(Just(xy320), Just(xy3500), app(ty_Maybe, bec)) → new_esEs3(xy320, xy3500, bec)
new_esEs(Left(xy320), Left(xy3500), app(ty_Maybe, cb), bc) → new_esEs3(xy320, xy3500, cb)
new_esEs3(Just(xy320), Just(xy3500), app(app(ty_Either, bdc), bdd)) → new_esEs(xy320, xy3500, bdc, bdd)
new_esEs(Right(xy320), Right(xy3500), cc, app(app(ty_@2, db), dc)) → new_esEs1(xy320, xy3500, db, dc)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(ty_[], hc)) → new_esEs2(xy322, xy3502, hc)
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(ty_[], bch)) → new_esEs2(xy320, xy3500, bch)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(app(ty_@2, ee), ef), dh, ea) → new_esEs1(xy320, xy3500, ee, ef)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(app(ty_Either, fb), fc), ea) → new_esEs(xy321, xy3501, fb, fc)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(app(ty_Either, bah), bba)) → new_esEs(xy321, xy3501, bah, bba)
new_esEs(Left(xy320), Left(xy3500), app(app(ty_Either, ba), bb), bc) → new_esEs(xy320, xy3500, ba, bb)
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(xy320, xy3500, eb, ec, ed)
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(xy321, xy3501, bbb, bbc, bbd)

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

new_esEs3(Just(xy320), Just(xy3500), app(app(ty_@2, bdh), bea)) → new_esEs1(xy320, xy3500, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(xy320), Just(xy3500), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(xy320, xy3500, bde, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(app(ty_@2, bcf), bcg)) → new_esEs1(xy320, xy3500, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(xy320, xy3500, bcc, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(xy320), Just(xy3500), app(ty_Maybe, bec)) → new_esEs3(xy320, xy3500, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(ty_Maybe, bda)) → new_esEs3(xy320, xy3500, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xy320), Just(xy3500), app(ty_[], beb)) → new_esEs2(xy320, xy3500, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xy320), Just(xy3500), app(app(ty_Either, bdc), bdd)) → new_esEs(xy320, xy3500, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(app(ty_Either, bca), bcb)) → new_esEs(xy320, xy3500, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(app(ty_@2, fh), ga), ea) → new_esEs1(xy321, xy3501, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(app(ty_@2, ha), hb)) → new_esEs1(xy322, xy3502, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(app(ty_@2, ee), ef), dh, ea) → new_esEs1(xy320, xy3500, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(app(ty_@2, bbe), bbf)) → new_esEs1(xy321, xy3501, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(app(ty_@2, bac), bad), hg) → new_esEs1(xy320, xy3500, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Left(xy320), Left(xy3500), app(app(ty_@2, bg), bh), bc) → new_esEs1(xy320, xy3500, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Right(xy320), Right(xy3500), cc, app(app(ty_@2, db), dc)) → new_esEs1(xy320, xy3500, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(xy321, xy3501, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(xy322, xy3502, gf, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(xy320, xy3500, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(ty_Maybe, eh), dh, ea) → new_esEs3(xy320, xy3500, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(ty_Maybe, gc), ea) → new_esEs3(xy321, xy3501, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(ty_Maybe, hd)) → new_esEs3(xy322, xy3502, hd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(ty_[], eg), dh, ea) → new_esEs2(xy320, xy3500, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(ty_[], gb), ea) → new_esEs2(xy321, xy3501, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(ty_[], hc)) → new_esEs2(xy322, xy3502, hc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), app(app(ty_Either, df), dg), dh, ea) → new_esEs(xy320, xy3500, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, dh, app(app(ty_Either, gd), ge)) → new_esEs(xy322, xy3502, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xy320, xy321, xy322), @3(xy3500, xy3501, xy3502), fa, app(app(ty_Either, fb), fc), ea) → new_esEs(xy321, xy3501, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(xy320, xy3500, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(xy321, xy3501, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(ty_Maybe, bbh)) → new_esEs3(xy321, xy3501, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(ty_Maybe, baf), hg) → new_esEs3(xy320, xy3500, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(ty_[], bae), hg) → new_esEs2(xy320, xy3500, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(ty_[], bbg)) → new_esEs2(xy321, xy3501, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), app(app(ty_Either, he), hf), hg) → new_esEs(xy320, xy3500, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xy320, xy321), @2(xy3500, xy3501), bag, app(app(ty_Either, bah), bba)) → new_esEs(xy321, xy3501, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Right(xy320), Right(xy3500), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(xy320, xy3500, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(Left(xy320), Left(xy3500), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(xy320, xy3500, bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(Right(xy320), Right(xy3500), cc, app(ty_Maybe, de)) → new_esEs3(xy320, xy3500, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Left(xy320), Left(xy3500), app(ty_Maybe, cb), bc) → new_esEs3(xy320, xy3500, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Left(xy320), Left(xy3500), app(ty_[], ca), bc) → new_esEs2(xy320, xy3500, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Right(xy320), Right(xy3500), cc, app(ty_[], dd)) → new_esEs2(xy320, xy3500, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Right(xy320), Right(xy3500), cc, app(app(ty_Either, cd), ce)) → new_esEs(xy320, xy3500, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Left(xy320), Left(xy3500), app(app(ty_Either, ba), bb), bc) → new_esEs(xy320, xy3500, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), bdb) → new_esEs2(xy321, xy3501, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs2(:(xy320, xy321), :(xy3500, xy3501), app(ty_[], bch)) → new_esEs2(xy320, xy3500, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_isPrefixOf(:(xy310, xy311), :(xy3510, xy3511), ba) → new_isPrefixOf(xy311, xy3511, ba)

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

new_isPrefixOf(:(xy310, xy311), :(xy3510, xy3511), ba) → new_isPrefixOf(xy311, xy3511, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_isPrefixOf0(xy32, xy31, xy35, :(xy3410, xy3411), ba) → new_isPrefixOf0(xy32, xy31, new_flip(xy35, xy3410, ba), xy3411, ba)

The TRS R consists of the following rules:

new_flip(xy31, xy32, ba) → :(xy32, xy31)

The set Q consists of the following terms:

new_flip(x0, x1, 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_isPrefixOf0(xy32, xy31, xy35, :(xy3410, xy3411), ba) → new_isPrefixOf0(xy32, xy31, new_flip(xy35, xy3410, ba), xy3411, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 4 > 4, 5 >= 5

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_isPrefixOf1(xy31, xy32, :(xy330, xy331), xy34, ba) → new_isPrefixOf1(new_flip(xy31, xy32, ba), xy330, xy331, xy34, ba)

The TRS R consists of the following rules:

new_flip(xy31, xy32, ba) → :(xy32, xy31)

The set Q consists of the following terms:

new_flip(x0, x1, 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_isPrefixOf1(xy31, xy32, :(xy330, xy331), xy34, ba) → new_isPrefixOf1(new_flip(xy31, xy32, ba), xy330, xy331, xy34, ba)
The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5