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

YES 1.9040000000000001 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 a, Eq b) => [Either b a] -> [Either b a] -> Bool) :: (Eq b, Eq a) => [Either b a] -> [Either 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 a, Eq b) => [Either a b] -> [Either a b] -> Bool) :: (Eq a, Eq b) => [Either a b] -> [Either 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

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 a, Eq b) => [Either a b] -> [Either 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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1265 -> 570[label="",style="solid", color="burlywood", weight=3];
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1266 -> 571[label="",style="solid", color="burlywood", weight=3];
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1268 -> 574[label="",style="solid", color="burlywood", weight=3];
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1278 -> 586[label="",style="solid", color="burlywood", weight=3];
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565[label="xy23 == xy260",fontsize=16,color="burlywood",shape="triangle"];1279[label="xy23/Integer xy230",fontsize=10,color="white",style="solid",shape="box"];565 -> 1279[label="",style="solid", color="burlywood", weight=9];
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1282 -> 591[label="",style="solid", color="burlywood", weight=3];
1283[label="xy23/Right xy230",fontsize=10,color="white",style="solid",shape="box"];567 -> 1283[label="",style="solid", color="burlywood", weight=9];
1283 -> 592[label="",style="solid", color="burlywood", weight=3];
568[label="xy23 == xy260",fontsize=16,color="black",shape="triangle"];568 -> 593[label="",style="solid", color="black", weight=3];
569[label="False && xy50",fontsize=16,color="black",shape="box"];569 -> 594[label="",style="solid", color="black", weight=3];
570[label="True && xy50",fontsize=16,color="black",shape="box"];570 -> 595[label="",style="solid", color="black", weight=3];
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573[label="True",fontsize=16,color="green",shape="box"];574[label="(xy230,xy231,xy232) == xy260\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];1284[label="xy260/(xy2600,xy2601,xy2602)",fontsize=10,color="white",style="solid",shape="box"];574 -> 1284[label="",style="solid", color="burlywood", weight=9];
1284 -> 598[label="",style="solid", color="burlywood", weight=3];
575[label="xy230 : xy231 == xy260\n  Eq a",fontsize=16,color="burlywood",shape="box"];1285[label="xy260/xy2600 : xy2601",fontsize=10,color="white",style="solid",shape="box"];575 -> 1285[label="",style="solid", color="burlywood", weight=9];
1285 -> 599[label="",style="solid", color="burlywood", weight=3];
1286[label="xy260/[]",fontsize=10,color="white",style="solid",shape="box"];575 -> 1286[label="",style="solid", color="burlywood", weight=9];
1286 -> 600[label="",style="solid", color="burlywood", weight=3];
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1287 -> 601[label="",style="solid", color="burlywood", weight=3];
1288[label="xy260/[]",fontsize=10,color="white",style="solid",shape="box"];576 -> 1288[label="",style="solid", color="burlywood", weight=9];
1288 -> 602[label="",style="solid", color="burlywood", weight=3];
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1289 -> 603[label="",style="solid", color="burlywood", weight=3];
578[label="primEqFloat xy23 xy260",fontsize=16,color="burlywood",shape="box"];1290[label="xy23/Float xy230 xy231",fontsize=10,color="white",style="solid",shape="box"];578 -> 1290[label="",style="solid", color="burlywood", weight=9];
1290 -> 604[label="",style="solid", color="burlywood", weight=3];
579[label="LT == xy260",fontsize=16,color="burlywood",shape="box"];1291[label="xy260/LT",fontsize=10,color="white",style="solid",shape="box"];579 -> 1291[label="",style="solid", color="burlywood", weight=9];
1291 -> 605[label="",style="solid", color="burlywood", weight=3];
1292[label="xy260/EQ",fontsize=10,color="white",style="solid",shape="box"];579 -> 1292[label="",style="solid", color="burlywood", weight=9];
1292 -> 606[label="",style="solid", color="burlywood", weight=3];
1293[label="xy260/GT",fontsize=10,color="white",style="solid",shape="box"];579 -> 1293[label="",style="solid", color="burlywood", weight=9];
1293 -> 607[label="",style="solid", color="burlywood", weight=3];
580[label="EQ == xy260",fontsize=16,color="burlywood",shape="box"];1294[label="xy260/LT",fontsize=10,color="white",style="solid",shape="box"];580 -> 1294[label="",style="solid", color="burlywood", weight=9];
1294 -> 608[label="",style="solid", color="burlywood", weight=3];
1295[label="xy260/EQ",fontsize=10,color="white",style="solid",shape="box"];580 -> 1295[label="",style="solid", color="burlywood", weight=9];
1295 -> 609[label="",style="solid", color="burlywood", weight=3];
1296[label="xy260/GT",fontsize=10,color="white",style="solid",shape="box"];580 -> 1296[label="",style="solid", color="burlywood", weight=9];
1296 -> 610[label="",style="solid", color="burlywood", weight=3];
581[label="GT == xy260",fontsize=16,color="burlywood",shape="box"];1297[label="xy260/LT",fontsize=10,color="white",style="solid",shape="box"];581 -> 1297[label="",style="solid", color="burlywood", weight=9];
1297 -> 611[label="",style="solid", color="burlywood", weight=3];
1298[label="xy260/EQ",fontsize=10,color="white",style="solid",shape="box"];581 -> 1298[label="",style="solid", color="burlywood", weight=9];
1298 -> 612[label="",style="solid", color="burlywood", weight=3];
1299[label="xy260/GT",fontsize=10,color="white",style="solid",shape="box"];581 -> 1299[label="",style="solid", color="burlywood", weight=9];
1299 -> 613[label="",style="solid", color="burlywood", weight=3];
582[label="Nothing == xy260\n  Eq a",fontsize=16,color="burlywood",shape="box"];1300[label="xy260/Nothing",fontsize=10,color="white",style="solid",shape="box"];582 -> 1300[label="",style="solid", color="burlywood", weight=9];
1300 -> 614[label="",style="solid", color="burlywood", weight=3];
1301[label="xy260/Just xy2600",fontsize=10,color="white",style="solid",shape="box"];582 -> 1301[label="",style="solid", color="burlywood", weight=9];
1301 -> 615[label="",style="solid", color="burlywood", weight=3];
583[label="Just xy230 == xy260\n  Eq a",fontsize=16,color="burlywood",shape="box"];1302[label="xy260/Nothing",fontsize=10,color="white",style="solid",shape="box"];583 -> 1302[label="",style="solid", color="burlywood", weight=9];
1302 -> 616[label="",style="solid", color="burlywood", weight=3];
1303[label="xy260/Just xy2600",fontsize=10,color="white",style="solid",shape="box"];583 -> 1303[label="",style="solid", color="burlywood", weight=9];
1303 -> 617[label="",style="solid", color="burlywood", weight=3];
584[label="xy230 :% xy231 == xy260\n  Integral a",fontsize=16,color="burlywood",shape="box"];1304[label="xy260/xy2600 :% xy2601",fontsize=10,color="white",style="solid",shape="box"];584 -> 1304[label="",style="solid", color="burlywood", weight=9];
1304 -> 618[label="",style="solid", color="burlywood", weight=3];
585[label="(xy230,xy231) == xy260\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1305[label="xy260/(xy2600,xy2601)",fontsize=10,color="white",style="solid",shape="box"];585 -> 1305[label="",style="solid", color="burlywood", weight=9];
1305 -> 619[label="",style="solid", color="burlywood", weight=3];
586[label="() == xy260",fontsize=16,color="burlywood",shape="box"];1306[label="xy260/()",fontsize=10,color="white",style="solid",shape="box"];586 -> 1306[label="",style="solid", color="burlywood", weight=9];
1306 -> 620[label="",style="solid", color="burlywood", weight=3];
587[label="primEqInt xy23 xy260",fontsize=16,color="burlywood",shape="triangle"];1307[label="xy23/Pos xy230",fontsize=10,color="white",style="solid",shape="box"];587 -> 1307[label="",style="solid", color="burlywood", weight=9];
1307 -> 621[label="",style="solid", color="burlywood", weight=3];
1308[label="xy23/Neg xy230",fontsize=10,color="white",style="solid",shape="box"];587 -> 1308[label="",style="solid", color="burlywood", weight=9];
1308 -> 622[label="",style="solid", color="burlywood", weight=3];
588[label="Integer xy230 == xy260",fontsize=16,color="burlywood",shape="box"];1309[label="xy260/Integer xy2600",fontsize=10,color="white",style="solid",shape="box"];588 -> 1309[label="",style="solid", color="burlywood", weight=9];
1309 -> 623[label="",style="solid", color="burlywood", weight=3];
589[label="False == xy260",fontsize=16,color="burlywood",shape="box"];1310[label="xy260/False",fontsize=10,color="white",style="solid",shape="box"];589 -> 1310[label="",style="solid", color="burlywood", weight=9];
1310 -> 624[label="",style="solid", color="burlywood", weight=3];
1311[label="xy260/True",fontsize=10,color="white",style="solid",shape="box"];589 -> 1311[label="",style="solid", color="burlywood", weight=9];
1311 -> 625[label="",style="solid", color="burlywood", weight=3];
590[label="True == xy260",fontsize=16,color="burlywood",shape="box"];1312[label="xy260/False",fontsize=10,color="white",style="solid",shape="box"];590 -> 1312[label="",style="solid", color="burlywood", weight=9];
1312 -> 626[label="",style="solid", color="burlywood", weight=3];
1313[label="xy260/True",fontsize=10,color="white",style="solid",shape="box"];590 -> 1313[label="",style="solid", color="burlywood", weight=9];
1313 -> 627[label="",style="solid", color="burlywood", weight=3];
591[label="Left xy230 == xy260\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1314[label="xy260/Left xy2600",fontsize=10,color="white",style="solid",shape="box"];591 -> 1314[label="",style="solid", color="burlywood", weight=9];
1314 -> 628[label="",style="solid", color="burlywood", weight=3];
1315[label="xy260/Right xy2600",fontsize=10,color="white",style="solid",shape="box"];591 -> 1315[label="",style="solid", color="burlywood", weight=9];
1315 -> 629[label="",style="solid", color="burlywood", weight=3];
592[label="Right xy230 == xy260\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];1316[label="xy260/Left xy2600",fontsize=10,color="white",style="solid",shape="box"];592 -> 1316[label="",style="solid", color="burlywood", weight=9];
1316 -> 630[label="",style="solid", color="burlywood", weight=3];
1317[label="xy260/Right xy2600",fontsize=10,color="white",style="solid",shape="box"];592 -> 1317[label="",style="solid", color="burlywood", weight=9];
1317 -> 631[label="",style="solid", color="burlywood", weight=3];
593[label="primEqDouble xy23 xy260",fontsize=16,color="burlywood",shape="box"];1318[label="xy23/Double xy230 xy231",fontsize=10,color="white",style="solid",shape="box"];593 -> 1318[label="",style="solid", color="burlywood", weight=9];
1318 -> 632[label="",style="solid", color="burlywood", weight=3];
594[label="False",fontsize=16,color="green",shape="box"];595[label="xy50",fontsize=16,color="green",shape="box"];596 -> 548[label="",style="dashed", color="red", weight=0];
596[label="xy220 == xy2610 && isPrefixOf xy221 xy2611\n  Eq a",fontsize=16,color="magenta"];596 -> 633[label="",style="dashed", color="magenta", weight=3];
596 -> 634[label="",style="dashed", color="magenta", weight=3];
597[label="False",fontsize=16,color="green",shape="box"];598[label="(xy230,xy231,xy232) == (xy2600,xy2601,xy2602)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];598 -> 635[label="",style="solid", color="black", weight=3];
599[label="xy230 : xy231 == xy2600 : xy2601\n  Eq a",fontsize=16,color="black",shape="box"];599 -> 636[label="",style="solid", color="black", weight=3];
600[label="xy230 : xy231 == []\n  Eq a",fontsize=16,color="black",shape="box"];600 -> 637[label="",style="solid", color="black", weight=3];
601[label="[] == xy2600 : xy2601\n  Eq a",fontsize=16,color="black",shape="box"];601 -> 638[label="",style="solid", color="black", weight=3];
602[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];602 -> 639[label="",style="solid", color="black", weight=3];
603[label="primEqChar (Char xy230) xy260",fontsize=16,color="burlywood",shape="box"];1320[label="xy260/Char xy2600",fontsize=10,color="white",style="solid",shape="box"];603 -> 1320[label="",style="solid", color="burlywood", weight=9];
1320 -> 640[label="",style="solid", color="burlywood", weight=3];
604[label="primEqFloat (Float xy230 xy231) xy260",fontsize=16,color="burlywood",shape="box"];1321[label="xy260/Float xy2600 xy2601",fontsize=10,color="white",style="solid",shape="box"];604 -> 1321[label="",style="solid", color="burlywood", weight=9];
1321 -> 641[label="",style="solid", color="burlywood", weight=3];
605[label="LT == LT",fontsize=16,color="black",shape="box"];605 -> 642[label="",style="solid", color="black", weight=3];
606[label="LT == EQ",fontsize=16,color="black",shape="box"];606 -> 643[label="",style="solid", color="black", weight=3];
607[label="LT == GT",fontsize=16,color="black",shape="box"];607 -> 644[label="",style="solid", color="black", weight=3];
608[label="EQ == LT",fontsize=16,color="black",shape="box"];608 -> 645[label="",style="solid", color="black", weight=3];
609[label="EQ == EQ",fontsize=16,color="black",shape="box"];609 -> 646[label="",style="solid", color="black", weight=3];
610[label="EQ == GT",fontsize=16,color="black",shape="box"];610 -> 647[label="",style="solid", color="black", weight=3];
611[label="GT == LT",fontsize=16,color="black",shape="box"];611 -> 648[label="",style="solid", color="black", weight=3];
612[label="GT == EQ",fontsize=16,color="black",shape="box"];612 -> 649[label="",style="solid", color="black", weight=3];
613[label="GT == GT",fontsize=16,color="black",shape="box"];613 -> 650[label="",style="solid", color="black", weight=3];
614[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];614 -> 651[label="",style="solid", color="black", weight=3];
615[label="Nothing == Just xy2600\n  Eq a",fontsize=16,color="black",shape="box"];615 -> 652[label="",style="solid", color="black", weight=3];
616[label="Just xy230 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];616 -> 653[label="",style="solid", color="black", weight=3];
617[label="Just xy230 == Just xy2600\n  Eq a",fontsize=16,color="black",shape="box"];617 -> 654[label="",style="solid", color="black", weight=3];
618[label="xy230 :% xy231 == xy2600 :% xy2601\n  Integral a",fontsize=16,color="black",shape="box"];618 -> 655[label="",style="solid", color="black", weight=3];
619[label="(xy230,xy231) == (xy2600,xy2601)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];619 -> 656[label="",style="solid", color="black", weight=3];
620[label="() == ()",fontsize=16,color="black",shape="box"];620 -> 657[label="",style="solid", color="black", weight=3];
621[label="primEqInt (Pos xy230) xy260",fontsize=16,color="burlywood",shape="box"];1322[label="xy230/Succ xy2300",fontsize=10,color="white",style="solid",shape="box"];621 -> 1322[label="",style="solid", color="burlywood", weight=9];
1322 -> 658[label="",style="solid", color="burlywood", weight=3];
1323[label="xy230/Zero",fontsize=10,color="white",style="solid",shape="box"];621 -> 1323[label="",style="solid", color="burlywood", weight=9];
1323 -> 659[label="",style="solid", color="burlywood", weight=3];
622[label="primEqInt (Neg xy230) xy260",fontsize=16,color="burlywood",shape="box"];1324[label="xy230/Succ xy2300",fontsize=10,color="white",style="solid",shape="box"];622 -> 1324[label="",style="solid", color="burlywood", weight=9];
1324 -> 660[label="",style="solid", color="burlywood", weight=3];
1325[label="xy230/Zero",fontsize=10,color="white",style="solid",shape="box"];622 -> 1325[label="",style="solid", color="burlywood", weight=9];
1325 -> 661[label="",style="solid", color="burlywood", weight=3];
623[label="Integer xy230 == Integer xy2600",fontsize=16,color="black",shape="box"];623 -> 662[label="",style="solid", color="black", weight=3];
624[label="False == False",fontsize=16,color="black",shape="box"];624 -> 663[label="",style="solid", color="black", weight=3];
625[label="False == True",fontsize=16,color="black",shape="box"];625 -> 664[label="",style="solid", color="black", weight=3];
626[label="True == False",fontsize=16,color="black",shape="box"];626 -> 665[label="",style="solid", color="black", weight=3];
627[label="True == True",fontsize=16,color="black",shape="box"];627 -> 666[label="",style="solid", color="black", weight=3];
628[label="Left xy230 == Left xy2600\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];628 -> 667[label="",style="solid", color="black", weight=3];
629[label="Left xy230 == Right xy2600\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];629 -> 668[label="",style="solid", color="black", weight=3];
630[label="Right xy230 == Left xy2600\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];630 -> 669[label="",style="solid", color="black", weight=3];
631[label="Right xy230 == Right xy2600\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];631 -> 670[label="",style="solid", color="black", weight=3];
632[label="primEqDouble (Double xy230 xy231) xy260",fontsize=16,color="burlywood",shape="box"];1326[label="xy260/Double xy2600 xy2601",fontsize=10,color="white",style="solid",shape="box"];632 -> 1326[label="",style="solid", color="burlywood", weight=9];
1326 -> 671[label="",style="solid", color="burlywood", weight=3];
633 -> 549[label="",style="dashed", color="red", weight=0];
633[label="isPrefixOf xy221 xy2611\n  Eq a",fontsize=16,color="magenta"];633 -> 672[label="",style="dashed", color="magenta", weight=3];
633 -> 673[label="",style="dashed", color="magenta", weight=3];
634[label="xy220 == xy2610\n  Eq a",fontsize=16,color="blue",shape="box"];1328[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1328[label="",style="solid", color="blue", weight=9];
1328 -> 674[label="",style="solid", color="blue", weight=3];
1329[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1329[label="",style="solid", color="blue", weight=9];
1329 -> 675[label="",style="solid", color="blue", weight=3];
1330[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1330[label="",style="solid", color="blue", weight=9];
1330 -> 676[label="",style="solid", color="blue", weight=3];
1331[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1331[label="",style="solid", color="blue", weight=9];
1331 -> 677[label="",style="solid", color="blue", weight=3];
1332[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1332[label="",style="solid", color="blue", weight=9];
1332 -> 678[label="",style="solid", color="blue", weight=3];
1333[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1333[label="",style="solid", color="blue", weight=9];
1333 -> 679[label="",style="solid", color="blue", weight=3];
1334[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1334[label="",style="solid", color="blue", weight=9];
1334 -> 680[label="",style="solid", color="blue", weight=3];
1335[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1335[label="",style="solid", color="blue", weight=9];
1335 -> 681[label="",style="solid", color="blue", weight=3];
1336[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1336[label="",style="solid", color="blue", weight=9];
1336 -> 682[label="",style="solid", color="blue", weight=3];
1337[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1337[label="",style="solid", color="blue", weight=9];
1337 -> 683[label="",style="solid", color="blue", weight=3];
1338[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1338[label="",style="solid", color="blue", weight=9];
1338 -> 684[label="",style="solid", color="blue", weight=3];
1339[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1339[label="",style="solid", color="blue", weight=9];
1339 -> 685[label="",style="solid", color="blue", weight=3];
1340[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1340[label="",style="solid", color="blue", weight=9];
1340 -> 686[label="",style="solid", color="blue", weight=3];
1341[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];634 -> 1341[label="",style="solid", color="blue", weight=9];
1341 -> 687[label="",style="solid", color="blue", weight=3];
635 -> 548[label="",style="dashed", color="red", weight=0];
635[label="xy230 == xy2600 && xy231 == xy2601 && xy232 == xy2602\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];635 -> 688[label="",style="dashed", color="magenta", weight=3];
635 -> 689[label="",style="dashed", color="magenta", weight=3];
636 -> 548[label="",style="dashed", color="red", weight=0];
636[label="xy230 == xy2600 && xy231 == xy2601\n  Eq a",fontsize=16,color="magenta"];636 -> 690[label="",style="dashed", color="magenta", weight=3];
636 -> 691[label="",style="dashed", color="magenta", weight=3];
637[label="False",fontsize=16,color="green",shape="box"];638[label="False",fontsize=16,color="green",shape="box"];639[label="True",fontsize=16,color="green",shape="box"];640[label="primEqChar (Char xy230) (Char xy2600)",fontsize=16,color="black",shape="box"];640 -> 692[label="",style="solid", color="black", weight=3];
641[label="primEqFloat (Float xy230 xy231) (Float xy2600 xy2601)",fontsize=16,color="black",shape="box"];641 -> 693[label="",style="solid", color="black", weight=3];
642[label="True",fontsize=16,color="green",shape="box"];643[label="False",fontsize=16,color="green",shape="box"];644[label="False",fontsize=16,color="green",shape="box"];645[label="False",fontsize=16,color="green",shape="box"];646[label="True",fontsize=16,color="green",shape="box"];647[label="False",fontsize=16,color="green",shape="box"];648[label="False",fontsize=16,color="green",shape="box"];649[label="False",fontsize=16,color="green",shape="box"];650[label="True",fontsize=16,color="green",shape="box"];651[label="True",fontsize=16,color="green",shape="box"];652[label="False",fontsize=16,color="green",shape="box"];653[label="False",fontsize=16,color="green",shape="box"];654[label="xy230 == xy2600\n  Eq a",fontsize=16,color="blue",shape="box"];1344[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1344[label="",style="solid", color="blue", weight=9];
1344 -> 694[label="",style="solid", color="blue", weight=3];
1345[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1345[label="",style="solid", color="blue", weight=9];
1345 -> 695[label="",style="solid", color="blue", weight=3];
1346[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1346[label="",style="solid", color="blue", weight=9];
1346 -> 696[label="",style="solid", color="blue", weight=3];
1347[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1347[label="",style="solid", color="blue", weight=9];
1347 -> 697[label="",style="solid", color="blue", weight=3];
1348[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1348[label="",style="solid", color="blue", weight=9];
1348 -> 698[label="",style="solid", color="blue", weight=3];
1349[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1349[label="",style="solid", color="blue", weight=9];
1349 -> 699[label="",style="solid", color="blue", weight=3];
1350[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1350[label="",style="solid", color="blue", weight=9];
1350 -> 700[label="",style="solid", color="blue", weight=3];
1351[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1351[label="",style="solid", color="blue", weight=9];
1351 -> 701[label="",style="solid", color="blue", weight=3];
1352[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1352[label="",style="solid", color="blue", weight=9];
1352 -> 702[label="",style="solid", color="blue", weight=3];
1353[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1353[label="",style="solid", color="blue", weight=9];
1353 -> 703[label="",style="solid", color="blue", weight=3];
1354[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1354[label="",style="solid", color="blue", weight=9];
1354 -> 704[label="",style="solid", color="blue", weight=3];
1355[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1355[label="",style="solid", color="blue", weight=9];
1355 -> 705[label="",style="solid", color="blue", weight=3];
1356[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1356[label="",style="solid", color="blue", weight=9];
1356 -> 706[label="",style="solid", color="blue", weight=3];
1357[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];654 -> 1357[label="",style="solid", color="blue", weight=9];
1357 -> 707[label="",style="solid", color="blue", weight=3];
655 -> 548[label="",style="dashed", color="red", weight=0];
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1214[label="Succ xy260000",fontsize=16,color="green",shape="box"];1215[label="xy23000",fontsize=16,color="green",shape="box"];1216[label="primPlusNat (Succ xy510) (Succ xy260000)",fontsize=16,color="black",shape="box"];1216 -> 1218[label="",style="solid", color="black", weight=3];
1217[label="primPlusNat Zero (Succ xy260000)",fontsize=16,color="black",shape="box"];1217 -> 1219[label="",style="solid", color="black", weight=3];
1218[label="Succ (Succ (primPlusNat xy510 xy260000))",fontsize=16,color="green",shape="box"];1218 -> 1220[label="",style="dashed", color="green", weight=3];
1219[label="Succ xy260000",fontsize=16,color="green",shape="box"];1220[label="primPlusNat xy510 xy260000",fontsize=16,color="burlywood",shape="triangle"];1676[label="xy510/Succ xy5100",fontsize=10,color="white",style="solid",shape="box"];1220 -> 1676[label="",style="solid", color="burlywood", weight=9];
1676 -> 1221[label="",style="solid", color="burlywood", weight=3];
1677[label="xy510/Zero",fontsize=10,color="white",style="solid",shape="box"];1220 -> 1677[label="",style="solid", color="burlywood", weight=9];
1677 -> 1222[label="",style="solid", color="burlywood", weight=3];
1221[label="primPlusNat (Succ xy5100) xy260000",fontsize=16,color="burlywood",shape="box"];1678[label="xy260000/Succ xy2600000",fontsize=10,color="white",style="solid",shape="box"];1221 -> 1678[label="",style="solid", color="burlywood", weight=9];
1678 -> 1223[label="",style="solid", color="burlywood", weight=3];
1679[label="xy260000/Zero",fontsize=10,color="white",style="solid",shape="box"];1221 -> 1679[label="",style="solid", color="burlywood", weight=9];
1679 -> 1224[label="",style="solid", color="burlywood", weight=3];
1222[label="primPlusNat Zero xy260000",fontsize=16,color="burlywood",shape="box"];1680[label="xy260000/Succ xy2600000",fontsize=10,color="white",style="solid",shape="box"];1222 -> 1680[label="",style="solid", color="burlywood", weight=9];
1680 -> 1225[label="",style="solid", color="burlywood", weight=3];
1681[label="xy260000/Zero",fontsize=10,color="white",style="solid",shape="box"];1222 -> 1681[label="",style="solid", color="burlywood", weight=9];
1681 -> 1226[label="",style="solid", color="burlywood", weight=3];
1223[label="primPlusNat (Succ xy5100) (Succ xy2600000)",fontsize=16,color="black",shape="box"];1223 -> 1227[label="",style="solid", color="black", weight=3];
1224[label="primPlusNat (Succ xy5100) Zero",fontsize=16,color="black",shape="box"];1224 -> 1228[label="",style="solid", color="black", weight=3];
1225[label="primPlusNat Zero (Succ xy2600000)",fontsize=16,color="black",shape="box"];1225 -> 1229[label="",style="solid", color="black", weight=3];
1226[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];1226 -> 1230[label="",style="solid", color="black", weight=3];
1227[label="Succ (Succ (primPlusNat xy5100 xy2600000))",fontsize=16,color="green",shape="box"];1227 -> 1231[label="",style="dashed", color="green", weight=3];
1228[label="Succ xy5100",fontsize=16,color="green",shape="box"];1229[label="Succ xy2600000",fontsize=16,color="green",shape="box"];1230[label="Zero",fontsize=16,color="green",shape="box"];1231 -> 1220[label="",style="dashed", color="red", weight=0];
1231[label="primPlusNat xy5100 xy2600000",fontsize=16,color="magenta"];1231 -> 1232[label="",style="dashed", color="magenta", weight=3];
1231 -> 1233[label="",style="dashed", color="magenta", weight=3];
1232[label="xy2600000",fontsize=16,color="green",shape="box"];1233[label="xy5100",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(xy5100), Succ(xy2600000)) → new_primPlusNat(xy5100, xy2600000)

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(xy5100), Succ(xy2600000)) → new_primPlusNat(xy5100, xy2600000)
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(xy23000), Succ(xy260000)) → new_primMulNat(xy23000, Succ(xy260000))

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

new_primMulNat(Succ(xy23000), Succ(xy260000)) → new_primMulNat(xy23000, Succ(xy260000))
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(xy2300), Succ(xy26000)) → new_primEqNat(xy2300, xy26000)

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

new_primEqNat(Succ(xy2300), Succ(xy26000)) → new_primEqNat(xy2300, xy26000)
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_esEs1(Just(xy230), Just(xy2600), app(app(app(ty_@3, gc), gd), ge)) → new_esEs(xy230, xy2600, gc, gd, ge)
new_esEs3(Right(xy230), Right(xy2600), bdb, app(app(ty_@2, bdh), bea)) → new_esEs2(xy230, xy2600, bdh, bea)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(ty_[], da), cg) → new_esEs0(xy231, xy2601, da)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(ty_Maybe, bg)) → new_esEs1(xy232, xy2602, bg)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(app(ty_Either, ef), eg), bb, cg) → new_esEs3(xy230, xy2600, ef, eg)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(ty_[], bbb), bba) → new_esEs0(xy230, xy2600, bbb)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(ty_Maybe, baa)) → new_esEs1(xy231, xy2601, baa)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(app(ty_@2, bab), bac)) → new_esEs2(xy231, xy2601, bab, bac)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(ty_[], bf)) → new_esEs0(xy232, xy2602, bf)
new_esEs3(Left(xy230), Left(xy2600), app(ty_Maybe, bce), bcc) → new_esEs1(xy230, xy2600, bce)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(ty_Maybe, bbc), bba) → new_esEs1(xy230, xy2600, bbc)
new_esEs3(Right(xy230), Right(xy2600), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(xy230, xy2600, beb, bec)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(app(ty_@2, bbd), bbe), bba) → new_esEs2(xy230, xy2600, bbd, bbe)
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(app(app(ty_@3, fa), fb), fc)) → new_esEs(xy230, xy2600, fa, fb, fc)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(app(app(ty_@3, dg), dh), ea), bb, cg) → new_esEs(xy230, xy2600, dg, dh, ea)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(xy231, xy2601, he, hf, hg)
new_esEs1(Just(xy230), Just(xy2600), app(ty_[], gf)) → new_esEs0(xy230, xy2600, gf)
new_esEs3(Left(xy230), Left(xy2600), app(app(ty_Either, bch), bda), bcc) → new_esEs3(xy230, xy2600, bch, bda)
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(app(ty_Either, ga), gb)) → new_esEs3(xy230, xy2600, ga, gb)
new_esEs1(Just(xy230), Just(xy2600), app(app(ty_Either, hb), hc)) → new_esEs3(xy230, xy2600, hb, hc)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(ty_Maybe, ec), bb, cg) → new_esEs1(xy230, xy2600, ec)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(ty_Maybe, db), cg) → new_esEs1(xy231, xy2601, db)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(app(ty_@2, ed), ee), bb, cg) → new_esEs2(xy230, xy2600, ed, ee)
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(ty_Maybe, ff)) → new_esEs1(xy230, xy2600, ff)
new_esEs3(Right(xy230), Right(xy2600), bdb, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs(xy230, xy2600, bdc, bdd, bde)
new_esEs3(Left(xy230), Left(xy2600), app(app(ty_@2, bcf), bcg), bcc) → new_esEs2(xy230, xy2600, bcf, bcg)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(app(app(ty_@3, baf), bag), bah), bba) → new_esEs(xy230, xy2600, baf, bag, bah)
new_esEs3(Left(xy230), Left(xy2600), app(ty_[], bcd), bcc) → new_esEs0(xy230, xy2600, bcd)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(app(ty_Either, bad), bae)) → new_esEs3(xy231, xy2601, bad, bae)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(app(ty_@2, dc), dd), cg) → new_esEs2(xy231, xy2601, dc, dd)
new_esEs3(Right(xy230), Right(xy2600), bdb, app(ty_[], bdf)) → new_esEs0(xy230, xy2600, bdf)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(app(app(ty_@3, cd), ce), cf), cg) → new_esEs(xy231, xy2601, cd, ce, cf)
new_esEs3(Right(xy230), Right(xy2600), bdb, app(ty_Maybe, bdg)) → new_esEs1(xy230, xy2600, bdg)
new_esEs1(Just(xy230), Just(xy2600), app(ty_Maybe, gg)) → new_esEs1(xy230, xy2600, gg)
new_esEs1(Just(xy230), Just(xy2600), app(app(ty_@2, gh), ha)) → new_esEs2(xy230, xy2600, gh, ha)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(ty_[], eb), bb, cg) → new_esEs0(xy230, xy2600, eb)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(app(ty_@2, bh), ca)) → new_esEs2(xy232, xy2602, bh, ca)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(ty_[], hh)) → new_esEs0(xy231, xy2601, hh)
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(ty_[], fd)) → new_esEs0(xy230, xy2600, fd)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(app(ty_Either, de), df), cg) → new_esEs3(xy231, xy2601, de, df)
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(app(ty_Either, bbf), bbg), bba) → new_esEs3(xy230, xy2600, bbf, bbg)
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(app(ty_@2, fg), fh)) → new_esEs2(xy230, xy2600, fg, fh)
new_esEs3(Left(xy230), Left(xy2600), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_esEs(xy230, xy2600, bbh, bca, bcb)
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), eh) → new_esEs0(xy231, xy2601, eh)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(app(ty_Either, cb), cc)) → new_esEs3(xy232, xy2602, cb, cc)
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(app(app(ty_@3, bc), bd), be)) → new_esEs(xy232, xy2602, bc, bd, be)

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

new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(ty_Maybe, ff)) → new_esEs1(xy230, xy2600, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(app(ty_Either, ga), gb)) → new_esEs3(xy230, xy2600, ga, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(app(app(ty_@3, fa), fb), fc)) → new_esEs(xy230, xy2600, fa, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(Just(xy230), Just(xy2600), app(ty_Maybe, gg)) → new_esEs1(xy230, xy2600, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(Just(xy230), Just(xy2600), app(app(ty_Either, hb), hc)) → new_esEs3(xy230, xy2600, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xy230), Just(xy2600), app(app(app(ty_@3, gc), gd), ge)) → new_esEs(xy230, xy2600, gc, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(app(ty_@2, fg), fh)) → new_esEs2(xy230, xy2600, fg, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xy230), Just(xy2600), app(app(ty_@2, gh), ha)) → new_esEs2(xy230, xy2600, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(Just(xy230), Just(xy2600), app(ty_[], gf)) → new_esEs0(xy230, xy2600, gf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(ty_Maybe, bg)) → new_esEs1(xy232, xy2602, bg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(ty_Maybe, ec), bb, cg) → new_esEs1(xy230, xy2600, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(ty_Maybe, db), cg) → new_esEs1(xy231, xy2601, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(app(ty_Either, ef), eg), bb, cg) → new_esEs3(xy230, xy2600, ef, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(app(ty_Either, de), df), cg) → new_esEs3(xy231, xy2601, de, df)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(app(ty_Either, cb), cc)) → new_esEs3(xy232, xy2602, cb, cc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(app(app(ty_@3, dg), dh), ea), bb, cg) → new_esEs(xy230, xy2600, dg, dh, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(app(app(ty_@3, cd), ce), cf), cg) → new_esEs(xy231, xy2601, cd, ce, cf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(app(app(ty_@3, bc), bd), be)) → new_esEs(xy232, xy2602, bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(app(ty_@2, ed), ee), bb, cg) → new_esEs2(xy230, xy2600, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(app(ty_@2, dc), dd), cg) → new_esEs2(xy231, xy2601, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(app(ty_@2, bh), ca)) → new_esEs2(xy232, xy2602, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, app(ty_[], da), cg) → new_esEs0(xy231, xy2601, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), ba, bb, app(ty_[], bf)) → new_esEs0(xy232, xy2602, bf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs(@3(xy230, xy231, xy232), @3(xy2600, xy2601, xy2602), app(ty_[], eb), bb, cg) → new_esEs0(xy230, xy2600, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(ty_Maybe, baa)) → new_esEs1(xy231, xy2601, baa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(ty_Maybe, bbc), bba) → new_esEs1(xy230, xy2600, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Left(xy230), Left(xy2600), app(ty_Maybe, bce), bcc) → new_esEs1(xy230, xy2600, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy230), Right(xy2600), bdb, app(ty_Maybe, bdg)) → new_esEs1(xy230, xy2600, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(app(ty_Either, bad), bae)) → new_esEs3(xy231, xy2601, bad, bae)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(app(ty_Either, bbf), bbg), bba) → new_esEs3(xy230, xy2600, bbf, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(app(app(ty_@3, he), hf), hg)) → new_esEs(xy231, xy2601, he, hf, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(app(app(ty_@3, baf), bag), bah), bba) → new_esEs(xy230, xy2600, baf, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(app(ty_@2, bab), bac)) → new_esEs2(xy231, xy2601, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(app(ty_@2, bbd), bbe), bba) → new_esEs2(xy230, xy2600, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), app(ty_[], bbb), bba) → new_esEs0(xy230, xy2600, bbb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@2(xy230, xy231), @2(xy2600, xy2601), hd, app(ty_[], hh)) → new_esEs0(xy231, xy2601, hh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(Right(xy230), Right(xy2600), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(xy230, xy2600, beb, bec)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(Left(xy230), Left(xy2600), app(app(ty_Either, bch), bda), bcc) → new_esEs3(xy230, xy2600, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), app(ty_[], fd)) → new_esEs0(xy230, xy2600, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(:(xy230, xy231), :(xy2600, xy2601), eh) → new_esEs0(xy231, xy2601, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs3(Right(xy230), Right(xy2600), bdb, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs(xy230, xy2600, bdc, bdd, bde)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs3(Left(xy230), Left(xy2600), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_esEs(xy230, xy2600, bbh, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Right(xy230), Right(xy2600), bdb, app(app(ty_@2, bdh), bea)) → new_esEs2(xy230, xy2600, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(Left(xy230), Left(xy2600), app(app(ty_@2, bcf), bcg), bcc) → new_esEs2(xy230, xy2600, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Left(xy230), Left(xy2600), app(ty_[], bcd), bcc) → new_esEs0(xy230, xy2600, bcd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Right(xy230), Right(xy2600), bdb, app(ty_[], bdf)) → new_esEs0(xy230, xy2600, bdf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 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(:(xy220, xy221), :(xy2610, xy2611), ba) → new_isPrefixOf(xy221, xy2611, ba)

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

new_isPrefixOf(:(xy220, xy221), :(xy2610, xy2611), ba) → new_isPrefixOf(xy221, xy2611, 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(xy23, xy22, xy26, :(xy2510, xy2511), ba) → new_isPrefixOf0(xy23, xy22, new_flip(xy26, xy2510, ba), xy2511, ba)

The TRS R consists of the following rules:

new_flip(xy22, xy23, ba) → :(xy23, xy22)

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(xy23, xy22, xy26, :(xy2510, xy2511), ba) → new_isPrefixOf0(xy23, xy22, new_flip(xy26, xy2510, ba), xy2511, 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(xy22, xy23, :(xy240, xy241), xy25, ba) → new_isPrefixOf1(new_flip(xy22, xy23, ba), xy240, xy241, xy25, ba)

The TRS R consists of the following rules:

new_flip(xy22, xy23, ba) → :(xy23, xy22)

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(xy22, xy23, :(xy240, xy241), xy25, ba) → new_isPrefixOf1(new_flip(xy22, xy23, ba), xy240, xy241, xy25, ba)
The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4, 5 >= 5