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

YES 1.55 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

((isPrefixOf :: Eq a => [Maybe a] -> [Maybe a] -> Bool) :: Eq a => [Maybe a] -> [Maybe 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

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

((isPrefixOf :: Eq a => [Maybe a] -> [Maybe a] -> Bool) :: Eq a => [Maybe a] -> [Maybe 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

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

(isPrefixOf :: Eq a => [Maybe a] -> [Maybe 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

module Maybe where

import qualified List
import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="isPrefixOf\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
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631 -> 5[label="",style="solid", color="burlywood", weight=3];
632[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 632[label="",style="solid", color="burlywood", weight=9];
632 -> 6[label="",style="solid", color="burlywood", weight=3];
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633 -> 7[label="",style="solid", color="burlywood", weight=3];
634[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 634[label="",style="solid", color="burlywood", weight=9];
634 -> 8[label="",style="solid", color="burlywood", weight=3];
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8[label="isPrefixOf (xy30 : xy31) []\n  Eq a",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9[label="True",fontsize=16,color="green",shape="box"];10 -> 28[label="",style="dashed", color="red", weight=0];
10[label="xy30 == xy40 && isPrefixOf xy31 xy41\n  Eq a",fontsize=16,color="magenta"];10 -> 29[label="",style="dashed", color="magenta", weight=3];
10 -> 30[label="",style="dashed", color="magenta", weight=3];
11[label="False",fontsize=16,color="green",shape="box"];29 -> 4[label="",style="dashed", color="red", weight=0];
29[label="isPrefixOf xy31 xy41\n  Eq a",fontsize=16,color="magenta"];29 -> 41[label="",style="dashed", color="magenta", weight=3];
29 -> 42[label="",style="dashed", color="magenta", weight=3];
30[label="xy30 == xy40\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];637[label="xy30/Nothing",fontsize=10,color="white",style="solid",shape="box"];30 -> 637[label="",style="solid", color="burlywood", weight=9];
637 -> 43[label="",style="solid", color="burlywood", weight=3];
638[label="xy30/Just xy300",fontsize=10,color="white",style="solid",shape="box"];30 -> 638[label="",style="solid", color="burlywood", weight=9];
638 -> 44[label="",style="solid", color="burlywood", weight=3];
28[label="xy9 && xy10",fontsize=16,color="burlywood",shape="triangle"];639[label="xy9/False",fontsize=10,color="white",style="solid",shape="box"];28 -> 639[label="",style="solid", color="burlywood", weight=9];
639 -> 45[label="",style="solid", color="burlywood", weight=3];
640[label="xy9/True",fontsize=10,color="white",style="solid",shape="box"];28 -> 640[label="",style="solid", color="burlywood", weight=9];
640 -> 46[label="",style="solid", color="burlywood", weight=3];
41[label="xy31\n  Eq a",fontsize=16,color="green",shape="box"];42[label="xy41\n  Eq a",fontsize=16,color="green",shape="box"];43[label="Nothing == xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];641[label="xy40/Nothing",fontsize=10,color="white",style="solid",shape="box"];43 -> 641[label="",style="solid", color="burlywood", weight=9];
641 -> 47[label="",style="solid", color="burlywood", weight=3];
642[label="xy40/Just xy400",fontsize=10,color="white",style="solid",shape="box"];43 -> 642[label="",style="solid", color="burlywood", weight=9];
642 -> 48[label="",style="solid", color="burlywood", weight=3];
44[label="Just xy300 == xy40\n  Eq a",fontsize=16,color="burlywood",shape="box"];643[label="xy40/Nothing",fontsize=10,color="white",style="solid",shape="box"];44 -> 643[label="",style="solid", color="burlywood", weight=9];
643 -> 49[label="",style="solid", color="burlywood", weight=3];
644[label="xy40/Just xy400",fontsize=10,color="white",style="solid",shape="box"];44 -> 644[label="",style="solid", color="burlywood", weight=9];
644 -> 50[label="",style="solid", color="burlywood", weight=3];
45[label="False && xy10",fontsize=16,color="black",shape="box"];45 -> 51[label="",style="solid", color="black", weight=3];
46[label="True && xy10",fontsize=16,color="black",shape="box"];46 -> 52[label="",style="solid", color="black", weight=3];
47[label="Nothing == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];47 -> 53[label="",style="solid", color="black", weight=3];
48[label="Nothing == Just xy400\n  Eq a",fontsize=16,color="black",shape="box"];48 -> 54[label="",style="solid", color="black", weight=3];
49[label="Just xy300 == Nothing\n  Eq a",fontsize=16,color="black",shape="box"];49 -> 55[label="",style="solid", color="black", weight=3];
50[label="Just xy300 == Just xy400\n  Eq a",fontsize=16,color="black",shape="box"];50 -> 56[label="",style="solid", color="black", weight=3];
51[label="False",fontsize=16,color="green",shape="box"];52[label="xy10",fontsize=16,color="green",shape="box"];53[label="True",fontsize=16,color="green",shape="box"];54[label="False",fontsize=16,color="green",shape="box"];55[label="False",fontsize=16,color="green",shape="box"];56[label="xy300 == xy400\n  Eq a",fontsize=16,color="blue",shape="box"];645[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 645[label="",style="solid", color="blue", weight=9];
645 -> 57[label="",style="solid", color="blue", weight=3];
646[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 646[label="",style="solid", color="blue", weight=9];
646 -> 58[label="",style="solid", color="blue", weight=3];
647[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 647[label="",style="solid", color="blue", weight=9];
647 -> 59[label="",style="solid", color="blue", weight=3];
648[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 648[label="",style="solid", color="blue", weight=9];
648 -> 60[label="",style="solid", color="blue", weight=3];
649[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 649[label="",style="solid", color="blue", weight=9];
649 -> 61[label="",style="solid", color="blue", weight=3];
650[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 650[label="",style="solid", color="blue", weight=9];
650 -> 62[label="",style="solid", color="blue", weight=3];
651[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 651[label="",style="solid", color="blue", weight=9];
651 -> 63[label="",style="solid", color="blue", weight=3];
652[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 652[label="",style="solid", color="blue", weight=9];
652 -> 64[label="",style="solid", color="blue", weight=3];
653[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 653[label="",style="solid", color="blue", weight=9];
653 -> 65[label="",style="solid", color="blue", weight=3];
654[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 654[label="",style="solid", color="blue", weight=9];
654 -> 66[label="",style="solid", color="blue", weight=3];
655[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 655[label="",style="solid", color="blue", weight=9];
655 -> 67[label="",style="solid", color="blue", weight=3];
656[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 656[label="",style="solid", color="blue", weight=9];
656 -> 68[label="",style="solid", color="blue", weight=3];
657[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 657[label="",style="solid", color="blue", weight=9];
657 -> 69[label="",style="solid", color="blue", weight=3];
658[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];56 -> 658[label="",style="solid", color="blue", weight=9];
658 -> 70[label="",style="solid", color="blue", weight=3];
57[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];57 -> 71[label="",style="solid", color="black", weight=3];
58[label="xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];659[label="xy300/(xy3000,xy3001)",fontsize=10,color="white",style="solid",shape="box"];58 -> 659[label="",style="solid", color="burlywood", weight=9];
659 -> 72[label="",style="solid", color="burlywood", weight=3];
59[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];59 -> 73[label="",style="solid", color="black", weight=3];
60[label="xy300 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];660[label="xy300/Left xy3000",fontsize=10,color="white",style="solid",shape="box"];60 -> 660[label="",style="solid", color="burlywood", weight=9];
660 -> 74[label="",style="solid", color="burlywood", weight=3];
661[label="xy300/Right xy3000",fontsize=10,color="white",style="solid",shape="box"];60 -> 661[label="",style="solid", color="burlywood", weight=9];
661 -> 75[label="",style="solid", color="burlywood", weight=3];
61[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];662[label="xy300/LT",fontsize=10,color="white",style="solid",shape="box"];61 -> 662[label="",style="solid", color="burlywood", weight=9];
662 -> 76[label="",style="solid", color="burlywood", weight=3];
663[label="xy300/EQ",fontsize=10,color="white",style="solid",shape="box"];61 -> 663[label="",style="solid", color="burlywood", weight=9];
663 -> 77[label="",style="solid", color="burlywood", weight=3];
664[label="xy300/GT",fontsize=10,color="white",style="solid",shape="box"];61 -> 664[label="",style="solid", color="burlywood", weight=9];
664 -> 78[label="",style="solid", color="burlywood", weight=3];
62[label="xy300 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];665[label="xy300/xy3000 : xy3001",fontsize=10,color="white",style="solid",shape="box"];62 -> 665[label="",style="solid", color="burlywood", weight=9];
665 -> 79[label="",style="solid", color="burlywood", weight=3];
666[label="xy300/[]",fontsize=10,color="white",style="solid",shape="box"];62 -> 666[label="",style="solid", color="burlywood", weight=9];
666 -> 80[label="",style="solid", color="burlywood", weight=3];
63[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];667[label="xy300/False",fontsize=10,color="white",style="solid",shape="box"];63 -> 667[label="",style="solid", color="burlywood", weight=9];
667 -> 81[label="",style="solid", color="burlywood", weight=3];
668[label="xy300/True",fontsize=10,color="white",style="solid",shape="box"];63 -> 668[label="",style="solid", color="burlywood", weight=9];
668 -> 82[label="",style="solid", color="burlywood", weight=3];
64[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];64 -> 83[label="",style="solid", color="black", weight=3];
65[label="xy300 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];669[label="xy300/xy3000 :% xy3001",fontsize=10,color="white",style="solid",shape="box"];65 -> 669[label="",style="solid", color="burlywood", weight=9];
669 -> 84[label="",style="solid", color="burlywood", weight=3];
66[label="xy300 == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];670[label="xy300/(xy3000,xy3001,xy3002)",fontsize=10,color="white",style="solid",shape="box"];66 -> 670[label="",style="solid", color="burlywood", weight=9];
670 -> 85[label="",style="solid", color="burlywood", weight=3];
67 -> 30[label="",style="dashed", color="red", weight=0];
67[label="xy300 == xy400\n  Eq a",fontsize=16,color="magenta"];67 -> 86[label="",style="dashed", color="magenta", weight=3];
67 -> 87[label="",style="dashed", color="magenta", weight=3];
68[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];672[label="xy300/Integer xy3000",fontsize=10,color="white",style="solid",shape="box"];68 -> 672[label="",style="solid", color="burlywood", weight=9];
672 -> 88[label="",style="solid", color="burlywood", weight=3];
69[label="xy300 == xy400",fontsize=16,color="black",shape="triangle"];69 -> 89[label="",style="solid", color="black", weight=3];
70[label="xy300 == xy400",fontsize=16,color="burlywood",shape="triangle"];673[label="xy300/()",fontsize=10,color="white",style="solid",shape="box"];70 -> 673[label="",style="solid", color="burlywood", weight=9];
673 -> 90[label="",style="solid", color="burlywood", weight=3];
71[label="primEqFloat xy300 xy400",fontsize=16,color="burlywood",shape="box"];674[label="xy300/Float xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];71 -> 674[label="",style="solid", color="burlywood", weight=9];
674 -> 91[label="",style="solid", color="burlywood", weight=3];
72[label="(xy3000,xy3001) == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];675[label="xy400/(xy4000,xy4001)",fontsize=10,color="white",style="solid",shape="box"];72 -> 675[label="",style="solid", color="burlywood", weight=9];
675 -> 92[label="",style="solid", color="burlywood", weight=3];
73[label="primEqInt xy300 xy400",fontsize=16,color="burlywood",shape="triangle"];676[label="xy300/Pos xy3000",fontsize=10,color="white",style="solid",shape="box"];73 -> 676[label="",style="solid", color="burlywood", weight=9];
676 -> 93[label="",style="solid", color="burlywood", weight=3];
677[label="xy300/Neg xy3000",fontsize=10,color="white",style="solid",shape="box"];73 -> 677[label="",style="solid", color="burlywood", weight=9];
677 -> 94[label="",style="solid", color="burlywood", weight=3];
74[label="Left xy3000 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];678[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];74 -> 678[label="",style="solid", color="burlywood", weight=9];
678 -> 95[label="",style="solid", color="burlywood", weight=3];
679[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];74 -> 679[label="",style="solid", color="burlywood", weight=9];
679 -> 96[label="",style="solid", color="burlywood", weight=3];
75[label="Right xy3000 == xy400\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];680[label="xy400/Left xy4000",fontsize=10,color="white",style="solid",shape="box"];75 -> 680[label="",style="solid", color="burlywood", weight=9];
680 -> 97[label="",style="solid", color="burlywood", weight=3];
681[label="xy400/Right xy4000",fontsize=10,color="white",style="solid",shape="box"];75 -> 681[label="",style="solid", color="burlywood", weight=9];
681 -> 98[label="",style="solid", color="burlywood", weight=3];
76[label="LT == xy400",fontsize=16,color="burlywood",shape="box"];682[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];76 -> 682[label="",style="solid", color="burlywood", weight=9];
682 -> 99[label="",style="solid", color="burlywood", weight=3];
683[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];76 -> 683[label="",style="solid", color="burlywood", weight=9];
683 -> 100[label="",style="solid", color="burlywood", weight=3];
684[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];76 -> 684[label="",style="solid", color="burlywood", weight=9];
684 -> 101[label="",style="solid", color="burlywood", weight=3];
77[label="EQ == xy400",fontsize=16,color="burlywood",shape="box"];685[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];77 -> 685[label="",style="solid", color="burlywood", weight=9];
685 -> 102[label="",style="solid", color="burlywood", weight=3];
686[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];77 -> 686[label="",style="solid", color="burlywood", weight=9];
686 -> 103[label="",style="solid", color="burlywood", weight=3];
687[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];77 -> 687[label="",style="solid", color="burlywood", weight=9];
687 -> 104[label="",style="solid", color="burlywood", weight=3];
78[label="GT == xy400",fontsize=16,color="burlywood",shape="box"];688[label="xy400/LT",fontsize=10,color="white",style="solid",shape="box"];78 -> 688[label="",style="solid", color="burlywood", weight=9];
688 -> 105[label="",style="solid", color="burlywood", weight=3];
689[label="xy400/EQ",fontsize=10,color="white",style="solid",shape="box"];78 -> 689[label="",style="solid", color="burlywood", weight=9];
689 -> 106[label="",style="solid", color="burlywood", weight=3];
690[label="xy400/GT",fontsize=10,color="white",style="solid",shape="box"];78 -> 690[label="",style="solid", color="burlywood", weight=9];
690 -> 107[label="",style="solid", color="burlywood", weight=3];
79[label="xy3000 : xy3001 == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];691[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];79 -> 691[label="",style="solid", color="burlywood", weight=9];
691 -> 108[label="",style="solid", color="burlywood", weight=3];
692[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];79 -> 692[label="",style="solid", color="burlywood", weight=9];
692 -> 109[label="",style="solid", color="burlywood", weight=3];
80[label="[] == xy400\n  Eq a",fontsize=16,color="burlywood",shape="box"];693[label="xy400/xy4000 : xy4001",fontsize=10,color="white",style="solid",shape="box"];80 -> 693[label="",style="solid", color="burlywood", weight=9];
693 -> 110[label="",style="solid", color="burlywood", weight=3];
694[label="xy400/[]",fontsize=10,color="white",style="solid",shape="box"];80 -> 694[label="",style="solid", color="burlywood", weight=9];
694 -> 111[label="",style="solid", color="burlywood", weight=3];
81[label="False == xy400",fontsize=16,color="burlywood",shape="box"];695[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];81 -> 695[label="",style="solid", color="burlywood", weight=9];
695 -> 112[label="",style="solid", color="burlywood", weight=3];
696[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];81 -> 696[label="",style="solid", color="burlywood", weight=9];
696 -> 113[label="",style="solid", color="burlywood", weight=3];
82[label="True == xy400",fontsize=16,color="burlywood",shape="box"];697[label="xy400/False",fontsize=10,color="white",style="solid",shape="box"];82 -> 697[label="",style="solid", color="burlywood", weight=9];
697 -> 114[label="",style="solid", color="burlywood", weight=3];
698[label="xy400/True",fontsize=10,color="white",style="solid",shape="box"];82 -> 698[label="",style="solid", color="burlywood", weight=9];
698 -> 115[label="",style="solid", color="burlywood", weight=3];
83[label="primEqChar xy300 xy400",fontsize=16,color="burlywood",shape="box"];699[label="xy300/Char xy3000",fontsize=10,color="white",style="solid",shape="box"];83 -> 699[label="",style="solid", color="burlywood", weight=9];
699 -> 116[label="",style="solid", color="burlywood", weight=3];
84[label="xy3000 :% xy3001 == xy400\n  Integral a",fontsize=16,color="burlywood",shape="box"];700[label="xy400/xy4000 :% xy4001",fontsize=10,color="white",style="solid",shape="box"];84 -> 700[label="",style="solid", color="burlywood", weight=9];
700 -> 117[label="",style="solid", color="burlywood", weight=3];
85[label="(xy3000,xy3001,xy3002) == xy400\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];701[label="xy400/(xy4000,xy4001,xy4002)",fontsize=10,color="white",style="solid",shape="box"];85 -> 701[label="",style="solid", color="burlywood", weight=9];
701 -> 118[label="",style="solid", color="burlywood", weight=3];
86[label="xy400\n  Eq a",fontsize=16,color="green",shape="box"];87[label="xy300\n  Eq a",fontsize=16,color="green",shape="box"];88[label="Integer xy3000 == xy400",fontsize=16,color="burlywood",shape="box"];702[label="xy400/Integer xy4000",fontsize=10,color="white",style="solid",shape="box"];88 -> 702[label="",style="solid", color="burlywood", weight=9];
702 -> 119[label="",style="solid", color="burlywood", weight=3];
89[label="primEqDouble xy300 xy400",fontsize=16,color="burlywood",shape="box"];703[label="xy300/Double xy3000 xy3001",fontsize=10,color="white",style="solid",shape="box"];89 -> 703[label="",style="solid", color="burlywood", weight=9];
703 -> 120[label="",style="solid", color="burlywood", weight=3];
90[label="() == xy400",fontsize=16,color="burlywood",shape="box"];704[label="xy400/()",fontsize=10,color="white",style="solid",shape="box"];90 -> 704[label="",style="solid", color="burlywood", weight=9];
704 -> 121[label="",style="solid", color="burlywood", weight=3];
91[label="primEqFloat (Float xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];705[label="xy400/Float xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];91 -> 705[label="",style="solid", color="burlywood", weight=9];
705 -> 122[label="",style="solid", color="burlywood", weight=3];
92[label="(xy3000,xy3001) == (xy4000,xy4001)\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];92 -> 123[label="",style="solid", color="black", weight=3];
93[label="primEqInt (Pos xy3000) xy400",fontsize=16,color="burlywood",shape="box"];706[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];93 -> 706[label="",style="solid", color="burlywood", weight=9];
706 -> 124[label="",style="solid", color="burlywood", weight=3];
707[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];93 -> 707[label="",style="solid", color="burlywood", weight=9];
707 -> 125[label="",style="solid", color="burlywood", weight=3];
94[label="primEqInt (Neg xy3000) xy400",fontsize=16,color="burlywood",shape="box"];708[label="xy3000/Succ xy30000",fontsize=10,color="white",style="solid",shape="box"];94 -> 708[label="",style="solid", color="burlywood", weight=9];
708 -> 126[label="",style="solid", color="burlywood", weight=3];
709[label="xy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 709[label="",style="solid", color="burlywood", weight=9];
709 -> 127[label="",style="solid", color="burlywood", weight=3];
95[label="Left xy3000 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];95 -> 128[label="",style="solid", color="black", weight=3];
96[label="Left xy3000 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];96 -> 129[label="",style="solid", color="black", weight=3];
97[label="Right xy3000 == Left xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];97 -> 130[label="",style="solid", color="black", weight=3];
98[label="Right xy3000 == Right xy4000\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];98 -> 131[label="",style="solid", color="black", weight=3];
99[label="LT == LT",fontsize=16,color="black",shape="box"];99 -> 132[label="",style="solid", color="black", weight=3];
100[label="LT == EQ",fontsize=16,color="black",shape="box"];100 -> 133[label="",style="solid", color="black", weight=3];
101[label="LT == GT",fontsize=16,color="black",shape="box"];101 -> 134[label="",style="solid", color="black", weight=3];
102[label="EQ == LT",fontsize=16,color="black",shape="box"];102 -> 135[label="",style="solid", color="black", weight=3];
103[label="EQ == EQ",fontsize=16,color="black",shape="box"];103 -> 136[label="",style="solid", color="black", weight=3];
104[label="EQ == GT",fontsize=16,color="black",shape="box"];104 -> 137[label="",style="solid", color="black", weight=3];
105[label="GT == LT",fontsize=16,color="black",shape="box"];105 -> 138[label="",style="solid", color="black", weight=3];
106[label="GT == EQ",fontsize=16,color="black",shape="box"];106 -> 139[label="",style="solid", color="black", weight=3];
107[label="GT == GT",fontsize=16,color="black",shape="box"];107 -> 140[label="",style="solid", color="black", weight=3];
108[label="xy3000 : xy3001 == xy4000 : xy4001\n  Eq a",fontsize=16,color="black",shape="box"];108 -> 141[label="",style="solid", color="black", weight=3];
109[label="xy3000 : xy3001 == []\n  Eq a",fontsize=16,color="black",shape="box"];109 -> 142[label="",style="solid", color="black", weight=3];
110[label="[] == xy4000 : xy4001\n  Eq a",fontsize=16,color="black",shape="box"];110 -> 143[label="",style="solid", color="black", weight=3];
111[label="[] == []\n  Eq a",fontsize=16,color="black",shape="box"];111 -> 144[label="",style="solid", color="black", weight=3];
112[label="False == False",fontsize=16,color="black",shape="box"];112 -> 145[label="",style="solid", color="black", weight=3];
113[label="False == True",fontsize=16,color="black",shape="box"];113 -> 146[label="",style="solid", color="black", weight=3];
114[label="True == False",fontsize=16,color="black",shape="box"];114 -> 147[label="",style="solid", color="black", weight=3];
115[label="True == True",fontsize=16,color="black",shape="box"];115 -> 148[label="",style="solid", color="black", weight=3];
116[label="primEqChar (Char xy3000) xy400",fontsize=16,color="burlywood",shape="box"];710[label="xy400/Char xy4000",fontsize=10,color="white",style="solid",shape="box"];116 -> 710[label="",style="solid", color="burlywood", weight=9];
710 -> 149[label="",style="solid", color="burlywood", weight=3];
117[label="xy3000 :% xy3001 == xy4000 :% xy4001\n  Integral a",fontsize=16,color="black",shape="box"];117 -> 150[label="",style="solid", color="black", weight=3];
118[label="(xy3000,xy3001,xy3002) == (xy4000,xy4001,xy4002)\n  Eq a  Eq b  Eq c",fontsize=16,color="black",shape="box"];118 -> 151[label="",style="solid", color="black", weight=3];
119[label="Integer xy3000 == Integer xy4000",fontsize=16,color="black",shape="box"];119 -> 152[label="",style="solid", color="black", weight=3];
120[label="primEqDouble (Double xy3000 xy3001) xy400",fontsize=16,color="burlywood",shape="box"];711[label="xy400/Double xy4000 xy4001",fontsize=10,color="white",style="solid",shape="box"];120 -> 711[label="",style="solid", color="burlywood", weight=9];
711 -> 153[label="",style="solid", color="burlywood", weight=3];
121[label="() == ()",fontsize=16,color="black",shape="box"];121 -> 154[label="",style="solid", color="black", weight=3];
122[label="primEqFloat (Float xy3000 xy3001) (Float xy4000 xy4001)",fontsize=16,color="black",shape="box"];122 -> 155[label="",style="solid", color="black", weight=3];
123 -> 28[label="",style="dashed", color="red", weight=0];
123[label="xy3000 == xy4000 && xy3001 == xy4001\n  Eq a  Eq b",fontsize=16,color="magenta"];123 -> 156[label="",style="dashed", color="magenta", weight=3];
123 -> 157[label="",style="dashed", color="magenta", weight=3];
124[label="primEqInt (Pos (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];713[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];124 -> 713[label="",style="solid", color="burlywood", weight=9];
713 -> 158[label="",style="solid", color="burlywood", weight=3];
714[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];124 -> 714[label="",style="solid", color="burlywood", weight=9];
714 -> 159[label="",style="solid", color="burlywood", weight=3];
125[label="primEqInt (Pos Zero) xy400",fontsize=16,color="burlywood",shape="box"];715[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];125 -> 715[label="",style="solid", color="burlywood", weight=9];
715 -> 160[label="",style="solid", color="burlywood", weight=3];
716[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];125 -> 716[label="",style="solid", color="burlywood", weight=9];
716 -> 161[label="",style="solid", color="burlywood", weight=3];
126[label="primEqInt (Neg (Succ xy30000)) xy400",fontsize=16,color="burlywood",shape="box"];717[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];126 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 162[label="",style="solid", color="burlywood", weight=3];
718[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];126 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 163[label="",style="solid", color="burlywood", weight=3];
127[label="primEqInt (Neg Zero) xy400",fontsize=16,color="burlywood",shape="box"];719[label="xy400/Pos xy4000",fontsize=10,color="white",style="solid",shape="box"];127 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 164[label="",style="solid", color="burlywood", weight=3];
720[label="xy400/Neg xy4000",fontsize=10,color="white",style="solid",shape="box"];127 -> 720[label="",style="solid", color="burlywood", weight=9];
720 -> 165[label="",style="solid", color="burlywood", weight=3];
128[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];721[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 721[label="",style="solid", color="blue", weight=9];
721 -> 166[label="",style="solid", color="blue", weight=3];
722[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 722[label="",style="solid", color="blue", weight=9];
722 -> 167[label="",style="solid", color="blue", weight=3];
723[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 723[label="",style="solid", color="blue", weight=9];
723 -> 168[label="",style="solid", color="blue", weight=3];
724[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 724[label="",style="solid", color="blue", weight=9];
724 -> 169[label="",style="solid", color="blue", weight=3];
725[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 725[label="",style="solid", color="blue", weight=9];
725 -> 170[label="",style="solid", color="blue", weight=3];
726[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 726[label="",style="solid", color="blue", weight=9];
726 -> 171[label="",style="solid", color="blue", weight=3];
727[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 727[label="",style="solid", color="blue", weight=9];
727 -> 172[label="",style="solid", color="blue", weight=3];
728[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 728[label="",style="solid", color="blue", weight=9];
728 -> 173[label="",style="solid", color="blue", weight=3];
729[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 729[label="",style="solid", color="blue", weight=9];
729 -> 174[label="",style="solid", color="blue", weight=3];
730[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 730[label="",style="solid", color="blue", weight=9];
730 -> 175[label="",style="solid", color="blue", weight=3];
731[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 731[label="",style="solid", color="blue", weight=9];
731 -> 176[label="",style="solid", color="blue", weight=3];
732[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 732[label="",style="solid", color="blue", weight=9];
732 -> 177[label="",style="solid", color="blue", weight=3];
733[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 733[label="",style="solid", color="blue", weight=9];
733 -> 178[label="",style="solid", color="blue", weight=3];
734[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];128 -> 734[label="",style="solid", color="blue", weight=9];
734 -> 179[label="",style="solid", color="blue", weight=3];
129[label="False",fontsize=16,color="green",shape="box"];130[label="False",fontsize=16,color="green",shape="box"];131[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];735[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 735[label="",style="solid", color="blue", weight=9];
735 -> 180[label="",style="solid", color="blue", weight=3];
736[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 736[label="",style="solid", color="blue", weight=9];
736 -> 181[label="",style="solid", color="blue", weight=3];
737[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 737[label="",style="solid", color="blue", weight=9];
737 -> 182[label="",style="solid", color="blue", weight=3];
738[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 738[label="",style="solid", color="blue", weight=9];
738 -> 183[label="",style="solid", color="blue", weight=3];
739[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 739[label="",style="solid", color="blue", weight=9];
739 -> 184[label="",style="solid", color="blue", weight=3];
740[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 740[label="",style="solid", color="blue", weight=9];
740 -> 185[label="",style="solid", color="blue", weight=3];
741[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 741[label="",style="solid", color="blue", weight=9];
741 -> 186[label="",style="solid", color="blue", weight=3];
742[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 742[label="",style="solid", color="blue", weight=9];
742 -> 187[label="",style="solid", color="blue", weight=3];
743[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 743[label="",style="solid", color="blue", weight=9];
743 -> 188[label="",style="solid", color="blue", weight=3];
744[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 744[label="",style="solid", color="blue", weight=9];
744 -> 189[label="",style="solid", color="blue", weight=3];
745[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 745[label="",style="solid", color="blue", weight=9];
745 -> 190[label="",style="solid", color="blue", weight=3];
746[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 746[label="",style="solid", color="blue", weight=9];
746 -> 191[label="",style="solid", color="blue", weight=3];
747[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 747[label="",style="solid", color="blue", weight=9];
747 -> 192[label="",style="solid", color="blue", weight=3];
748[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];131 -> 748[label="",style="solid", color="blue", weight=9];
748 -> 193[label="",style="solid", color="blue", weight=3];
132[label="True",fontsize=16,color="green",shape="box"];133[label="False",fontsize=16,color="green",shape="box"];134[label="False",fontsize=16,color="green",shape="box"];135[label="False",fontsize=16,color="green",shape="box"];136[label="True",fontsize=16,color="green",shape="box"];137[label="False",fontsize=16,color="green",shape="box"];138[label="False",fontsize=16,color="green",shape="box"];139[label="False",fontsize=16,color="green",shape="box"];140[label="True",fontsize=16,color="green",shape="box"];141 -> 28[label="",style="dashed", color="red", weight=0];
141[label="xy3000 == xy4000 && xy3001 == xy4001\n  Eq a",fontsize=16,color="magenta"];141 -> 194[label="",style="dashed", color="magenta", weight=3];
141 -> 195[label="",style="dashed", color="magenta", weight=3];
142[label="False",fontsize=16,color="green",shape="box"];143[label="False",fontsize=16,color="green",shape="box"];144[label="True",fontsize=16,color="green",shape="box"];145[label="True",fontsize=16,color="green",shape="box"];146[label="False",fontsize=16,color="green",shape="box"];147[label="False",fontsize=16,color="green",shape="box"];148[label="True",fontsize=16,color="green",shape="box"];149[label="primEqChar (Char xy3000) (Char xy4000)",fontsize=16,color="black",shape="box"];149 -> 196[label="",style="solid", color="black", weight=3];
150 -> 28[label="",style="dashed", color="red", weight=0];
150[label="xy3000 == xy4000 && xy3001 == xy4001\n  Integral a",fontsize=16,color="magenta"];150 -> 197[label="",style="dashed", color="magenta", weight=3];
150 -> 198[label="",style="dashed", color="magenta", weight=3];
151 -> 28[label="",style="dashed", color="red", weight=0];
151[label="xy3000 == xy4000 && xy3001 == xy4001 && xy3002 == xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="magenta"];151 -> 199[label="",style="dashed", color="magenta", weight=3];
151 -> 200[label="",style="dashed", color="magenta", weight=3];
152 -> 73[label="",style="dashed", color="red", weight=0];
152[label="primEqInt xy3000 xy4000",fontsize=16,color="magenta"];152 -> 201[label="",style="dashed", color="magenta", weight=3];
152 -> 202[label="",style="dashed", color="magenta", weight=3];
153[label="primEqDouble (Double xy3000 xy3001) (Double xy4000 xy4001)",fontsize=16,color="black",shape="box"];153 -> 203[label="",style="solid", color="black", weight=3];
154[label="True",fontsize=16,color="green",shape="box"];155 -> 59[label="",style="dashed", color="red", weight=0];
155[label="xy3000 * xy4000 == xy3001 * xy4001",fontsize=16,color="magenta"];155 -> 204[label="",style="dashed", color="magenta", weight=3];
155 -> 205[label="",style="dashed", color="magenta", weight=3];
156[label="xy3001 == xy4001\n  Eq a",fontsize=16,color="blue",shape="box"];754[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 754[label="",style="solid", color="blue", weight=9];
754 -> 206[label="",style="solid", color="blue", weight=3];
755[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 755[label="",style="solid", color="blue", weight=9];
755 -> 207[label="",style="solid", color="blue", weight=3];
756[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 756[label="",style="solid", color="blue", weight=9];
756 -> 208[label="",style="solid", color="blue", weight=3];
757[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 757[label="",style="solid", color="blue", weight=9];
757 -> 209[label="",style="solid", color="blue", weight=3];
758[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 758[label="",style="solid", color="blue", weight=9];
758 -> 210[label="",style="solid", color="blue", weight=3];
759[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 759[label="",style="solid", color="blue", weight=9];
759 -> 211[label="",style="solid", color="blue", weight=3];
760[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 760[label="",style="solid", color="blue", weight=9];
760 -> 212[label="",style="solid", color="blue", weight=3];
761[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 761[label="",style="solid", color="blue", weight=9];
761 -> 213[label="",style="solid", color="blue", weight=3];
762[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 762[label="",style="solid", color="blue", weight=9];
762 -> 214[label="",style="solid", color="blue", weight=3];
763[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 763[label="",style="solid", color="blue", weight=9];
763 -> 215[label="",style="solid", color="blue", weight=3];
764[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 764[label="",style="solid", color="blue", weight=9];
764 -> 216[label="",style="solid", color="blue", weight=3];
765[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 765[label="",style="solid", color="blue", weight=9];
765 -> 217[label="",style="solid", color="blue", weight=3];
766[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 766[label="",style="solid", color="blue", weight=9];
766 -> 218[label="",style="solid", color="blue", weight=3];
767[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];156 -> 767[label="",style="solid", color="blue", weight=9];
767 -> 219[label="",style="solid", color="blue", weight=3];
157[label="xy3000 == xy4000\n  Eq a",fontsize=16,color="blue",shape="box"];768[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 768[label="",style="solid", color="blue", weight=9];
768 -> 220[label="",style="solid", color="blue", weight=3];
769[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 769[label="",style="solid", color="blue", weight=9];
769 -> 221[label="",style="solid", color="blue", weight=3];
770[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 770[label="",style="solid", color="blue", weight=9];
770 -> 222[label="",style="solid", color="blue", weight=3];
771[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 771[label="",style="solid", color="blue", weight=9];
771 -> 223[label="",style="solid", color="blue", weight=3];
772[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 772[label="",style="solid", color="blue", weight=9];
772 -> 224[label="",style="solid", color="blue", weight=3];
773[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 773[label="",style="solid", color="blue", weight=9];
773 -> 225[label="",style="solid", color="blue", weight=3];
774[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];157 -> 774[label="",style="solid", color="blue", weight=9];
774 -> 226[label="",style="solid", color="blue", weight=3];
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987 -> 582[label="",style="solid", color="burlywood", weight=3];
516[label="primMulInt (Neg xy30010) xy4001",fontsize=16,color="burlywood",shape="box"];988[label="xy4001/Pos xy40010",fontsize=10,color="white",style="solid",shape="box"];516 -> 988[label="",style="solid", color="burlywood", weight=9];
988 -> 583[label="",style="solid", color="burlywood", weight=3];
989[label="xy4001/Neg xy40010",fontsize=10,color="white",style="solid",shape="box"];516 -> 989[label="",style="solid", color="burlywood", weight=9];
989 -> 584[label="",style="solid", color="burlywood", weight=3];
517[label="xy40000",fontsize=16,color="green",shape="box"];518[label="xy30000",fontsize=16,color="green",shape="box"];519[label="xy40000",fontsize=16,color="green",shape="box"];520[label="xy30000",fontsize=16,color="green",shape="box"];521 -> 196[label="",style="dashed", color="red", weight=0];
521[label="primEqNat xy30000 xy40000",fontsize=16,color="magenta"];521 -> 585[label="",style="dashed", color="magenta", weight=3];
521 -> 586[label="",style="dashed", color="magenta", weight=3];
522[label="False",fontsize=16,color="green",shape="box"];523[label="False",fontsize=16,color="green",shape="box"];524[label="True",fontsize=16,color="green",shape="box"];525[label="xy4002",fontsize=16,color="green",shape="box"];526[label="xy3002",fontsize=16,color="green",shape="box"];527[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];528[label="xy3002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];529[label="xy4002",fontsize=16,color="green",shape="box"];530[label="xy3002",fontsize=16,color="green",shape="box"];531[label="xy4002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];532[label="xy3002\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];533[label="xy4002",fontsize=16,color="green",shape="box"];534[label="xy3002",fontsize=16,color="green",shape="box"];535[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];536[label="xy3002\n  Eq a",fontsize=16,color="green",shape="box"];537[label="xy4002",fontsize=16,color="green",shape="box"];538[label="xy3002",fontsize=16,color="green",shape="box"];539[label="xy4002",fontsize=16,color="green",shape="box"];540[label="xy3002",fontsize=16,color="green",shape="box"];541[label="xy4002\n  Integral a",fontsize=16,color="green",shape="box"];542[label="xy3002\n  Integral a",fontsize=16,color="green",shape="box"];543[label="xy4002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];544[label="xy3002\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];545[label="xy4002\n  Eq a",fontsize=16,color="green",shape="box"];546[label="xy3002\n  Eq a",fontsize=16,color="green",shape="box"];547[label="xy4002",fontsize=16,color="green",shape="box"];548[label="xy3002",fontsize=16,color="green",shape="box"];549[label="xy4002",fontsize=16,color="green",shape="box"];550[label="xy3002",fontsize=16,color="green",shape="box"];551[label="xy4002",fontsize=16,color="green",shape="box"];552[label="xy3002",fontsize=16,color="green",shape="box"];553[label="xy4001",fontsize=16,color="green",shape="box"];554[label="xy3001",fontsize=16,color="green",shape="box"];555[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];556[label="xy3001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];557[label="xy4001",fontsize=16,color="green",shape="box"];558[label="xy3001",fontsize=16,color="green",shape="box"];559[label="xy4001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];560[label="xy3001\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];561[label="xy4001",fontsize=16,color="green",shape="box"];562[label="xy3001",fontsize=16,color="green",shape="box"];563[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];564[label="xy3001\n  Eq a",fontsize=16,color="green",shape="box"];565[label="xy4001",fontsize=16,color="green",shape="box"];566[label="xy3001",fontsize=16,color="green",shape="box"];567[label="xy4001",fontsize=16,color="green",shape="box"];568[label="xy3001",fontsize=16,color="green",shape="box"];569[label="xy4001\n  Integral a",fontsize=16,color="green",shape="box"];570[label="xy3001\n  Integral a",fontsize=16,color="green",shape="box"];571[label="xy4001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];572[label="xy3001\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];573[label="xy4001\n  Eq a",fontsize=16,color="green",shape="box"];574[label="xy3001\n  Eq a",fontsize=16,color="green",shape="box"];575[label="xy4001",fontsize=16,color="green",shape="box"];576[label="xy3001",fontsize=16,color="green",shape="box"];577[label="xy4001",fontsize=16,color="green",shape="box"];578[label="xy3001",fontsize=16,color="green",shape="box"];579[label="xy4001",fontsize=16,color="green",shape="box"];580[label="xy3001",fontsize=16,color="green",shape="box"];581[label="primMulInt (Pos xy30010) (Pos xy40010)",fontsize=16,color="black",shape="box"];581 -> 587[label="",style="solid", color="black", weight=3];
582[label="primMulInt (Pos xy30010) (Neg xy40010)",fontsize=16,color="black",shape="box"];582 -> 588[label="",style="solid", color="black", weight=3];
583[label="primMulInt (Neg xy30010) (Pos xy40010)",fontsize=16,color="black",shape="box"];583 -> 589[label="",style="solid", color="black", weight=3];
584[label="primMulInt (Neg xy30010) (Neg xy40010)",fontsize=16,color="black",shape="box"];584 -> 590[label="",style="solid", color="black", weight=3];
585[label="xy40000",fontsize=16,color="green",shape="box"];586[label="xy30000",fontsize=16,color="green",shape="box"];587[label="Pos (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];587 -> 591[label="",style="dashed", color="green", weight=3];
588[label="Neg (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];588 -> 592[label="",style="dashed", color="green", weight=3];
589[label="Neg (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];589 -> 593[label="",style="dashed", color="green", weight=3];
590[label="Pos (primMulNat xy30010 xy40010)",fontsize=16,color="green",shape="box"];590 -> 594[label="",style="dashed", color="green", weight=3];
591[label="primMulNat xy30010 xy40010",fontsize=16,color="burlywood",shape="triangle"];991[label="xy30010/Succ xy300100",fontsize=10,color="white",style="solid",shape="box"];591 -> 991[label="",style="solid", color="burlywood", weight=9];
991 -> 595[label="",style="solid", color="burlywood", weight=3];
992[label="xy30010/Zero",fontsize=10,color="white",style="solid",shape="box"];591 -> 992[label="",style="solid", color="burlywood", weight=9];
992 -> 596[label="",style="solid", color="burlywood", weight=3];
592 -> 591[label="",style="dashed", color="red", weight=0];
592[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];592 -> 597[label="",style="dashed", color="magenta", weight=3];
593 -> 591[label="",style="dashed", color="red", weight=0];
593[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];593 -> 598[label="",style="dashed", color="magenta", weight=3];
594 -> 591[label="",style="dashed", color="red", weight=0];
594[label="primMulNat xy30010 xy40010",fontsize=16,color="magenta"];594 -> 599[label="",style="dashed", color="magenta", weight=3];
594 -> 600[label="",style="dashed", color="magenta", weight=3];
595[label="primMulNat (Succ xy300100) xy40010",fontsize=16,color="burlywood",shape="box"];996[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];595 -> 996[label="",style="solid", color="burlywood", weight=9];
996 -> 601[label="",style="solid", color="burlywood", weight=3];
997[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];595 -> 997[label="",style="solid", color="burlywood", weight=9];
997 -> 602[label="",style="solid", color="burlywood", weight=3];
596[label="primMulNat Zero xy40010",fontsize=16,color="burlywood",shape="box"];998[label="xy40010/Succ xy400100",fontsize=10,color="white",style="solid",shape="box"];596 -> 998[label="",style="solid", color="burlywood", weight=9];
998 -> 603[label="",style="solid", color="burlywood", weight=3];
999[label="xy40010/Zero",fontsize=10,color="white",style="solid",shape="box"];596 -> 999[label="",style="solid", color="burlywood", weight=9];
999 -> 604[label="",style="solid", color="burlywood", weight=3];
597[label="xy40010",fontsize=16,color="green",shape="box"];598[label="xy30010",fontsize=16,color="green",shape="box"];599[label="xy30010",fontsize=16,color="green",shape="box"];600[label="xy40010",fontsize=16,color="green",shape="box"];601[label="primMulNat (Succ xy300100) (Succ xy400100)",fontsize=16,color="black",shape="box"];601 -> 605[label="",style="solid", color="black", weight=3];
602[label="primMulNat (Succ xy300100) Zero",fontsize=16,color="black",shape="box"];602 -> 606[label="",style="solid", color="black", weight=3];
603[label="primMulNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];603 -> 607[label="",style="solid", color="black", weight=3];
604[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];604 -> 608[label="",style="solid", color="black", weight=3];
605 -> 609[label="",style="dashed", color="red", weight=0];
605[label="primPlusNat (primMulNat xy300100 (Succ xy400100)) (Succ xy400100)",fontsize=16,color="magenta"];605 -> 610[label="",style="dashed", color="magenta", weight=3];
606[label="Zero",fontsize=16,color="green",shape="box"];607[label="Zero",fontsize=16,color="green",shape="box"];608[label="Zero",fontsize=16,color="green",shape="box"];610 -> 591[label="",style="dashed", color="red", weight=0];
610[label="primMulNat xy300100 (Succ xy400100)",fontsize=16,color="magenta"];610 -> 611[label="",style="dashed", color="magenta", weight=3];
610 -> 612[label="",style="dashed", color="magenta", weight=3];
609[label="primPlusNat xy11 (Succ xy400100)",fontsize=16,color="burlywood",shape="triangle"];1002[label="xy11/Succ xy110",fontsize=10,color="white",style="solid",shape="box"];609 -> 1002[label="",style="solid", color="burlywood", weight=9];
1002 -> 613[label="",style="solid", color="burlywood", weight=3];
1003[label="xy11/Zero",fontsize=10,color="white",style="solid",shape="box"];609 -> 1003[label="",style="solid", color="burlywood", weight=9];
1003 -> 614[label="",style="solid", color="burlywood", weight=3];
611[label="xy300100",fontsize=16,color="green",shape="box"];612[label="Succ xy400100",fontsize=16,color="green",shape="box"];613[label="primPlusNat (Succ xy110) (Succ xy400100)",fontsize=16,color="black",shape="box"];613 -> 615[label="",style="solid", color="black", weight=3];
614[label="primPlusNat Zero (Succ xy400100)",fontsize=16,color="black",shape="box"];614 -> 616[label="",style="solid", color="black", weight=3];
615[label="Succ (Succ (primPlusNat xy110 xy400100))",fontsize=16,color="green",shape="box"];615 -> 617[label="",style="dashed", color="green", weight=3];
616[label="Succ xy400100",fontsize=16,color="green",shape="box"];617[label="primPlusNat xy110 xy400100",fontsize=16,color="burlywood",shape="triangle"];1004[label="xy110/Succ xy1100",fontsize=10,color="white",style="solid",shape="box"];617 -> 1004[label="",style="solid", color="burlywood", weight=9];
1004 -> 618[label="",style="solid", color="burlywood", weight=3];
1005[label="xy110/Zero",fontsize=10,color="white",style="solid",shape="box"];617 -> 1005[label="",style="solid", color="burlywood", weight=9];
1005 -> 619[label="",style="solid", color="burlywood", weight=3];
618[label="primPlusNat (Succ xy1100) xy400100",fontsize=16,color="burlywood",shape="box"];1006[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];618 -> 1006[label="",style="solid", color="burlywood", weight=9];
1006 -> 620[label="",style="solid", color="burlywood", weight=3];
1007[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];618 -> 1007[label="",style="solid", color="burlywood", weight=9];
1007 -> 621[label="",style="solid", color="burlywood", weight=3];
619[label="primPlusNat Zero xy400100",fontsize=16,color="burlywood",shape="box"];1008[label="xy400100/Succ xy4001000",fontsize=10,color="white",style="solid",shape="box"];619 -> 1008[label="",style="solid", color="burlywood", weight=9];
1008 -> 622[label="",style="solid", color="burlywood", weight=3];
1009[label="xy400100/Zero",fontsize=10,color="white",style="solid",shape="box"];619 -> 1009[label="",style="solid", color="burlywood", weight=9];
1009 -> 623[label="",style="solid", color="burlywood", weight=3];
620[label="primPlusNat (Succ xy1100) (Succ xy4001000)",fontsize=16,color="black",shape="box"];620 -> 624[label="",style="solid", color="black", weight=3];
621[label="primPlusNat (Succ xy1100) Zero",fontsize=16,color="black",shape="box"];621 -> 625[label="",style="solid", color="black", weight=3];
622[label="primPlusNat Zero (Succ xy4001000)",fontsize=16,color="black",shape="box"];622 -> 626[label="",style="solid", color="black", weight=3];
623[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];623 -> 627[label="",style="solid", color="black", weight=3];
624[label="Succ (Succ (primPlusNat xy1100 xy4001000))",fontsize=16,color="green",shape="box"];624 -> 628[label="",style="dashed", color="green", weight=3];
625[label="Succ xy1100",fontsize=16,color="green",shape="box"];626[label="Succ xy4001000",fontsize=16,color="green",shape="box"];627[label="Zero",fontsize=16,color="green",shape="box"];628 -> 617[label="",style="dashed", color="red", weight=0];
628[label="primPlusNat xy1100 xy4001000",fontsize=16,color="magenta"];628 -> 629[label="",style="dashed", color="magenta", weight=3];
628 -> 630[label="",style="dashed", color="magenta", weight=3];
629[label="xy4001000",fontsize=16,color="green",shape="box"];630[label="xy1100",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(xy1100), Succ(xy4001000)) → new_primPlusNat(xy1100, xy4001000)

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(xy1100), Succ(xy4001000)) → new_primPlusNat(xy1100, xy4001000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(xy300100), Succ(xy400100)) → new_primMulNat(xy300100, Succ(xy400100))

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

new_primMulNat(Succ(xy300100), Succ(xy400100)) → new_primMulNat(xy300100, Succ(xy400100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_primEqNat(Succ(xy30000), Succ(xy40000)) → new_primEqNat(xy30000, xy40000)

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

new_primEqNat(Succ(xy30000), Succ(xy40000)) → new_primEqNat(xy30000, xy40000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, cc), cd), ce) → new_esEs(xy3000, xy4000, cc, cd)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(app(ty_@3, bcg), bch), bda)), hf), bbb)) → new_esEs2(xy3000, xy4000, bcg, bch, bda)
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_@2, gd), ge)) → new_esEs(xy3000, xy4000, gd, ge)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, de), ce) → new_esEs3(xy3000, xy4000, de)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(ty_Maybe, bag)) → new_esEs3(xy3002, xy4002, bag)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_[], bcf)), hf), bbb)) → new_esEs1(xy3000, xy4000, bcf)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_Either, bd), be)) → new_esEs0(xy3001, xy4001, bd, be)
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(ty_[], ec)), dh)) → new_esEs1(xy3000, xy4000, ec)
new_esEs0(Left(xy3000), Left(xy4000), app(app(ty_@2, df), dg), dh) → new_esEs(xy3000, xy4000, df, dg)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(app(app(ty_@3, db), dc), dd)), ce)) → new_esEs2(xy3000, xy4000, db, dc, dd)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, cf), cg), ce) → new_esEs0(xy3000, xy4000, cf, cg)
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(app(ty_Either, fc), fd))) → new_esEs0(xy3000, xy4000, fc, fd)
new_esEs0(Right(xy3000), Right(xy4000), eh, app(app(ty_Either, fc), fd)) → new_esEs0(xy3000, xy4000, fc, fd)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_Either, bd), be))) → new_esEs0(xy3001, xy4001, bd, be)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_[], bf)) → new_esEs1(xy3001, xy4001, bf)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_@2, bcb), bcc)), hf), bbb)) → new_esEs(xy3000, xy4000, bcb, bcc)
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(app(ty_@2, df), dg)), dh)) → new_esEs(xy3000, xy4000, df, dg)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_Maybe, de)), ce)) → new_esEs3(xy3000, xy4000, de)
new_esEs0(Right(xy3000), Right(xy4000), eh, app(app(app(ty_@3, fg), fh), ga)) → new_esEs2(xy3000, xy4000, fg, fh, ga)
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(app(ty_Either, gf), gg))) → new_esEs0(xy3000, xy4000, gf, gg)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_@2, bb), bc)) → new_esEs(xy3001, xy4001, bb, bc)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_Either, cf), cg)), ce)) → new_esEs0(xy3000, xy4000, cf, cg)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, db), dc), dd), ce) → new_esEs2(xy3000, xy4000, db, dc, dd)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(ty_[], bac)) → new_esEs1(xy3002, xy4002, bac)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bcb), bcc), hf, bbb) → new_esEs(xy3000, xy4000, bcb, bcc)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], bcf), hf, bbb) → new_esEs1(xy3000, xy4000, bcf)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(app(app(ty_@3, bad), bae), baf))) → new_esEs2(xy3002, xy4002, bad, bae, baf)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(app(ty_@2, hg), hh))) → new_esEs(xy3002, xy4002, hg, hh)
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(app(app(ty_@3, ha), hb), hc)) → new_esEs2(xy3000, xy4000, ha, hb, hc)
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_Maybe, hd)) → new_esEs3(xy3000, xy4000, hd)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(app(ty_Either, baa), bab)) → new_esEs0(xy3002, xy4002, baa, bab)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_Either, bcd), bce)), hf), bbb)) → new_esEs0(xy3000, xy4000, bcd, bce)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(app(app(ty_@3, bad), bae), baf)) → new_esEs2(xy3002, xy4002, bad, bae, baf)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(ty_[], bbe)), bbb)) → new_esEs1(xy3001, xy4001, bbe)
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(app(app(ty_@3, ed), ee), ef)), dh)) → new_esEs2(xy3000, xy4000, ed, ee, ef)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, bcg), bch), bda), hf, bbb) → new_esEs2(xy3000, xy4000, bcg, bch, bda)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(app(ty_@3, bg), bh), ca))) → new_esEs2(xy3001, xy4001, bg, bh, ca)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_Maybe, bdb)), hf), bbb)) → new_esEs3(xy3000, xy4000, bdb)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(ty_Maybe, bca), bbb) → new_esEs3(xy3001, xy4001, bca)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(app(ty_@2, bah), bba)), bbb)) → new_esEs(xy3001, xy4001, bah, bba)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], da), ce) → new_esEs1(xy3000, xy4000, da)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_Maybe, cb))) → new_esEs3(xy3001, xy4001, cb)
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(app(ty_@2, gd), ge))) → new_esEs(xy3000, xy4000, gd, ge)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bcd), bce), hf, bbb) → new_esEs0(xy3000, xy4000, bcd, bce)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_[], bf))) → new_esEs1(xy3001, xy4001, bf)
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), gc) → new_esEs1(xy3001, xy4001, gc)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(ty_[], bbe), bbb) → new_esEs1(xy3001, xy4001, bbe)
new_esEs0(Left(xy3000), Left(xy4000), app(ty_Maybe, eg), dh) → new_esEs3(xy3000, xy4000, eg)
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_[], gh)) → new_esEs1(xy3000, xy4000, gh)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(app(ty_Either, baa), bab))) → new_esEs0(xy3002, xy4002, baa, bab)
new_esEs0(Left(xy3000), Left(xy4000), app(app(app(ty_@3, ed), ee), ef), dh) → new_esEs2(xy3000, xy4000, ed, ee, ef)
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(ty_Maybe, hd))) → new_esEs3(xy3000, xy4000, hd)
new_esEs0(Left(xy3000), Left(xy4000), app(app(ty_Either, ea), eb), dh) → new_esEs0(xy3000, xy4000, ea, eb)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_Maybe, cb)) → new_esEs3(xy3001, xy4001, cb)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(ty_[], bac))) → new_esEs1(xy3002, xy4002, bac)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(ty_Maybe, bca)), bbb)) → new_esEs3(xy3001, xy4001, bca)
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(app(ty_@3, bg), bh), ca)) → new_esEs2(xy3001, xy4001, bg, bh, ca)
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(ty_Maybe, eg)), dh)) → new_esEs3(xy3000, xy4000, eg)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(app(ty_Either, bbc), bbd)), bbb)) → new_esEs0(xy3001, xy4001, bbc, bbd)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_@2, bb), bc))) → new_esEs(xy3001, xy4001, bb, bc)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(ty_Maybe, bag))) → new_esEs3(xy3002, xy4002, bag)
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_Either, gf), gg)) → new_esEs0(xy3000, xy4000, gf, gg)
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], gc)) → new_esEs1(xy3001, xy4001, gc)
new_esEs0(Right(xy3000), Right(xy4000), eh, app(ty_[], ff)) → new_esEs1(xy3000, xy4000, ff)
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(app(app(ty_@3, fg), fh), ga))) → new_esEs2(xy3000, xy4000, fg, fh, ga)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_[], da)), ce)) → new_esEs1(xy3000, xy4000, da)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_esEs2(xy3001, xy4001, bbf, bbg, bbh)
new_esEs0(Left(xy3000), Left(xy4000), app(ty_[], ec), dh) → new_esEs1(xy3000, xy4000, ec)
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(app(ty_Either, ea), eb)), dh)) → new_esEs0(xy3000, xy4000, ea, eb)
new_esEs3(Just(xy300), Just(xy400), app(ty_Maybe, bdc)) → new_esEs3(xy300, xy400, bdc)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bdb), hf, bbb) → new_esEs3(xy3000, xy4000, bdb)
new_esEs0(Right(xy3000), Right(xy4000), eh, app(ty_Maybe, gb)) → new_esEs3(xy3000, xy4000, gb)
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(ty_Maybe, gb))) → new_esEs3(xy3000, xy4000, gb)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(app(ty_@2, bah), bba), bbb) → new_esEs(xy3001, xy4001, bah, bba)
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(app(ty_@2, fa), fb))) → new_esEs(xy3000, xy4000, fa, fb)
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(app(app(ty_@3, bbf), bbg), bbh)), bbb)) → new_esEs2(xy3001, xy4001, bbf, bbg, bbh)
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_@2, cc), cd)), ce)) → new_esEs(xy3000, xy4000, cc, cd)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(app(ty_Either, bbc), bbd), bbb) → new_esEs0(xy3001, xy4001, bbc, bbd)
new_esEs0(Right(xy3000), Right(xy4000), eh, app(app(ty_@2, fa), fb)) → new_esEs(xy3000, xy4000, fa, fb)
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(app(ty_@2, hg), hh)) → new_esEs(xy3002, xy4002, hg, hh)
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(app(app(ty_@3, ha), hb), hc))) → new_esEs2(xy3000, xy4000, ha, hb, hc)
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(ty_[], ff))) → new_esEs1(xy3000, xy4000, ff)
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(ty_[], gh))) → new_esEs1(xy3000, xy4000, gh)

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

new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_@2, gd), ge)) → new_esEs(xy3000, xy4000, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_Maybe, hd)) → new_esEs3(xy3000, xy4000, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(app(app(ty_@3, ha), hb), hc)) → new_esEs2(xy3000, xy4000, ha, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(app(ty_Either, gf), gg)) → new_esEs0(xy3000, xy4000, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_@2, cc), cd), ce) → new_esEs(xy3000, xy4000, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_@2, bb), bc)) → new_esEs(xy3001, xy4001, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_Maybe, de), ce) → new_esEs3(xy3000, xy4000, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_Maybe, cb)) → new_esEs3(xy3001, xy4001, cb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(ty_[], bf)) → new_esEs1(xy3001, xy4001, bf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(ty_[], da), ce) → new_esEs1(xy3000, xy4000, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(app(ty_@3, db), dc), dd), ce) → new_esEs2(xy3000, xy4000, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(app(ty_@3, bg), bh), ca)) → new_esEs2(xy3001, xy4001, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), ba, app(app(ty_Either, bd), be)) → new_esEs0(xy3001, xy4001, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(@2(xy3000, xy3001), @2(xy4000, xy4001), app(app(ty_Either, cf), cg), ce) → new_esEs0(xy3000, xy4000, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_@2, bcb), bcc), hf, bbb) → new_esEs(xy3000, xy4000, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(app(ty_@2, bah), bba), bbb) → new_esEs(xy3001, xy4001, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(app(ty_@2, hg), hh)) → new_esEs(xy3002, xy4002, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_@2, bcb), bcc)), hf), bbb)) → new_esEs(xy3000, xy4000, bcb, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(app(ty_@2, df), dg)), dh)) → new_esEs(xy3000, xy4000, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(app(ty_@2, hg), hh))) → new_esEs(xy3002, xy4002, hg, hh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(app(ty_@2, bah), bba)), bbb)) → new_esEs(xy3001, xy4001, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(app(ty_@2, gd), ge))) → new_esEs(xy3000, xy4000, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_@2, bb), bc))) → new_esEs(xy3001, xy4001, bb, bc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(app(ty_@2, fa), fb))) → new_esEs(xy3000, xy4000, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_@2, cc), cd)), ce)) → new_esEs(xy3000, xy4000, cc, cd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Left(xy3000), Left(xy4000), app(app(ty_@2, df), dg), dh) → new_esEs(xy3000, xy4000, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(xy3000), Right(xy4000), eh, app(app(ty_@2, fa), fb)) → new_esEs(xy3000, xy4000, fa, fb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(ty_Maybe, bag)) → new_esEs3(xy3002, xy4002, bag)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(ty_Maybe, bca), bbb) → new_esEs3(xy3001, xy4001, bca)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_Maybe, bdb), hf, bbb) → new_esEs3(xy3000, xy4000, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(ty_[], bac)) → new_esEs1(xy3002, xy4002, bac)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(ty_[], bcf), hf, bbb) → new_esEs1(xy3000, xy4000, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(ty_[], bbe), bbb) → new_esEs1(xy3001, xy4001, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(app(app(ty_@3, bad), bae), baf)) → new_esEs2(xy3002, xy4002, bad, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(app(ty_@3, bcg), bch), bda), hf, bbb) → new_esEs2(xy3000, xy4000, bcg, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_esEs2(xy3001, xy4001, bbf, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, hf, app(app(ty_Either, baa), bab)) → new_esEs0(xy3002, xy4002, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), app(app(ty_Either, bcd), bce), hf, bbb) → new_esEs0(xy3000, xy4000, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(@3(xy3000, xy3001, xy3002), @3(xy4000, xy4001, xy4002), he, app(app(ty_Either, bbc), bbd), bbb) → new_esEs0(xy3001, xy4001, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_Maybe, de)), ce)) → new_esEs3(xy3000, xy4000, de)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_Maybe, bdb)), hf), bbb)) → new_esEs3(xy3000, xy4000, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_Maybe, cb))) → new_esEs3(xy3001, xy4001, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(ty_Maybe, hd))) → new_esEs3(xy3000, xy4000, hd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(ty_Maybe, bca)), bbb)) → new_esEs3(xy3001, xy4001, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(ty_Maybe, eg)), dh)) → new_esEs3(xy3000, xy4000, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(ty_Maybe, bag))) → new_esEs3(xy3002, xy4002, bag)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xy300), Just(xy400), app(ty_Maybe, bdc)) → new_esEs3(xy300, xy400, bdc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(ty_Maybe, gb))) → new_esEs3(xy3000, xy4000, gb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Left(xy3000), Left(xy4000), app(ty_Maybe, eg), dh) → new_esEs3(xy3000, xy4000, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xy3000), Right(xy4000), eh, app(ty_Maybe, gb)) → new_esEs3(xy3000, xy4000, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(ty_[], bcf)), hf), bbb)) → new_esEs1(xy3000, xy4000, bcf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(ty_[], ec)), dh)) → new_esEs1(xy3000, xy4000, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(ty_[], bbe)), bbb)) → new_esEs1(xy3001, xy4001, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(ty_[], bf))) → new_esEs1(xy3001, xy4001, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(ty_[], bac))) → new_esEs1(xy3002, xy4002, bac)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], gc)) → new_esEs1(xy3001, xy4001, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(ty_[], da)), ce)) → new_esEs1(xy3000, xy4000, da)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(ty_[], ff))) → new_esEs1(xy3000, xy4000, ff)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(ty_[], gh))) → new_esEs1(xy3000, xy4000, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), gc) → new_esEs1(xy3001, xy4001, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs1(:(xy3000, xy3001), :(xy4000, xy4001), app(ty_[], gh)) → new_esEs1(xy3000, xy4000, gh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(Right(xy3000), Right(xy4000), eh, app(ty_[], ff)) → new_esEs1(xy3000, xy4000, ff)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(Left(xy3000), Left(xy4000), app(ty_[], ec), dh) → new_esEs1(xy3000, xy4000, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(app(ty_@3, bcg), bch), bda)), hf), bbb)) → new_esEs2(xy3000, xy4000, bcg, bch, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(app(app(ty_@3, db), dc), dd)), ce)) → new_esEs2(xy3000, xy4000, db, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(app(app(ty_@3, bad), bae), baf))) → new_esEs2(xy3002, xy4002, bad, bae, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(app(app(ty_@3, ed), ee), ef)), dh)) → new_esEs2(xy3000, xy4000, ed, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(app(ty_@3, bg), bh), ca))) → new_esEs2(xy3001, xy4001, bg, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(app(app(ty_@3, fg), fh), ga))) → new_esEs2(xy3000, xy4000, fg, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(app(app(ty_@3, bbf), bbg), bbh)), bbb)) → new_esEs2(xy3001, xy4001, bbf, bbg, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(app(app(ty_@3, ha), hb), hc))) → new_esEs2(xy3000, xy4000, ha, hb, hc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(Right(xy3000)), Just(Right(xy4000)), app(app(ty_Either, eh), app(app(ty_Either, fc), fd))) → new_esEs0(xy3000, xy4000, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, ba), app(app(ty_Either, bd), be))) → new_esEs0(xy3001, xy4001, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(:(xy3000, xy3001)), Just(:(xy4000, xy4001)), app(ty_[], app(app(ty_Either, gf), gg))) → new_esEs0(xy3000, xy4000, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@2(xy3000, xy3001)), Just(@2(xy4000, xy4001)), app(app(ty_@2, app(app(ty_Either, cf), cg)), ce)) → new_esEs0(xy3000, xy4000, cf, cg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, app(app(ty_Either, bcd), bce)), hf), bbb)) → new_esEs0(xy3000, xy4000, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), hf), app(app(ty_Either, baa), bab))) → new_esEs0(xy3002, xy4002, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(@3(xy3000, xy3001, xy3002)), Just(@3(xy4000, xy4001, xy4002)), app(app(app(ty_@3, he), app(app(ty_Either, bbc), bbd)), bbb)) → new_esEs0(xy3001, xy4001, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(Left(xy3000)), Just(Left(xy4000)), app(app(ty_Either, app(app(ty_Either, ea), eb)), dh)) → new_esEs0(xy3000, xy4000, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(Right(xy3000), Right(xy4000), eh, app(app(app(ty_@3, fg), fh), ga)) → new_esEs2(xy3000, xy4000, fg, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(Left(xy3000), Left(xy4000), app(app(app(ty_@3, ed), ee), ef), dh) → new_esEs2(xy3000, xy4000, ed, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(Right(xy3000), Right(xy4000), eh, app(app(ty_Either, fc), fd)) → new_esEs0(xy3000, xy4000, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(Left(xy3000), Left(xy4000), app(app(ty_Either, ea), eb), dh) → new_esEs0(xy3000, xy4000, ea, eb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba) → new_isPrefixOf(xy31, xy41, ba)

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

new_isPrefixOf(:(xy30, xy31), :(xy40, xy41), ba) → new_isPrefixOf(xy31, xy41, ba)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3