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

YES 1.2510000000000001 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:

↳ HASKELL

  ↳ BR

mainModule Main

(((==) :: Eq a => a -> a -> Bool) :: Eq a => a -> a -> Bool)

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

mainModule Main

(((==) :: Eq a => a -> a -> Bool) :: Eq a => a -> a -> Bool)

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

mainModule Main

((==) :: Eq a => a -> a -> Bool)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="(==)\n  Eq a",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="(==) xv3\n  Eq a",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="(==) xv3 xv4\n  Eq a",fontsize=16,color="blue",shape="box"];667[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 667[label="",style="solid", color="blue", weight=9];
667 -> 5[label="",style="solid", color="blue", weight=3];
668[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 668[label="",style="solid", color="blue", weight=9];
668 -> 6[label="",style="solid", color="blue", weight=3];
669[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 669[label="",style="solid", color="blue", weight=9];
669 -> 7[label="",style="solid", color="blue", weight=3];
670[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 670[label="",style="solid", color="blue", weight=9];
670 -> 8[label="",style="solid", color="blue", weight=3];
671[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 671[label="",style="solid", color="blue", weight=9];
671 -> 9[label="",style="solid", color="blue", weight=3];
672[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 672[label="",style="solid", color="blue", weight=9];
672 -> 10[label="",style="solid", color="blue", weight=3];
673[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 673[label="",style="solid", color="blue", weight=9];
673 -> 11[label="",style="solid", color="blue", weight=3];
674[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 674[label="",style="solid", color="blue", weight=9];
674 -> 12[label="",style="solid", color="blue", weight=3];
675[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 675[label="",style="solid", color="blue", weight=9];
675 -> 13[label="",style="solid", color="blue", weight=3];
676[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 676[label="",style="solid", color="blue", weight=9];
676 -> 14[label="",style="solid", color="blue", weight=3];
677[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 677[label="",style="solid", color="blue", weight=9];
677 -> 15[label="",style="solid", color="blue", weight=3];
678[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 678[label="",style="solid", color="blue", weight=9];
678 -> 16[label="",style="solid", color="blue", weight=3];
679[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 679[label="",style="solid", color="blue", weight=9];
679 -> 17[label="",style="solid", color="blue", weight=3];
680[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];4 -> 680[label="",style="solid", color="blue", weight=9];
680 -> 18[label="",style="solid", color="blue", weight=3];
5[label="(==) xv3 xv4",fontsize=16,color="black",shape="triangle"];5 -> 19[label="",style="solid", color="black", weight=3];
6[label="(==) xv3 xv4",fontsize=16,color="burlywood",shape="triangle"];681[label="xv3/False",fontsize=10,color="white",style="solid",shape="box"];6 -> 681[label="",style="solid", color="burlywood", weight=9];
681 -> 20[label="",style="solid", color="burlywood", weight=3];
682[label="xv3/True",fontsize=10,color="white",style="solid",shape="box"];6 -> 682[label="",style="solid", color="burlywood", weight=9];
682 -> 21[label="",style="solid", color="burlywood", weight=3];
7[label="(==) xv3 xv4",fontsize=16,color="black",shape="triangle"];7 -> 22[label="",style="solid", color="black", weight=3];
8[label="(==) xv3 xv4",fontsize=16,color="black",shape="triangle"];8 -> 23[label="",style="solid", color="black", weight=3];
9[label="(==) xv3 xv4",fontsize=16,color="burlywood",shape="triangle"];683[label="xv3/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 683[label="",style="solid", color="burlywood", weight=9];
683 -> 24[label="",style="solid", color="burlywood", weight=3];
684[label="xv3/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 684[label="",style="solid", color="burlywood", weight=9];
684 -> 25[label="",style="solid", color="burlywood", weight=3];
685[label="xv3/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 685[label="",style="solid", color="burlywood", weight=9];
685 -> 26[label="",style="solid", color="burlywood", weight=3];
10[label="(==) xv3 xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];686[label="xv3/Left xv30",fontsize=10,color="white",style="solid",shape="box"];10 -> 686[label="",style="solid", color="burlywood", weight=9];
686 -> 27[label="",style="solid", color="burlywood", weight=3];
687[label="xv3/Right xv30",fontsize=10,color="white",style="solid",shape="box"];10 -> 687[label="",style="solid", color="burlywood", weight=9];
687 -> 28[label="",style="solid", color="burlywood", weight=3];
11[label="(==) xv3 xv4\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="triangle"];688[label="xv3/(xv30,xv31,xv32)",fontsize=10,color="white",style="solid",shape="box"];11 -> 688[label="",style="solid", color="burlywood", weight=9];
688 -> 29[label="",style="solid", color="burlywood", weight=3];
12[label="(==) xv3 xv4",fontsize=16,color="burlywood",shape="triangle"];689[label="xv3/Integer xv30",fontsize=10,color="white",style="solid",shape="box"];12 -> 689[label="",style="solid", color="burlywood", weight=9];
689 -> 30[label="",style="solid", color="burlywood", weight=3];
13[label="(==) xv3 xv4\n  Integral a",fontsize=16,color="burlywood",shape="triangle"];690[label="xv3/xv30 :% xv31",fontsize=10,color="white",style="solid",shape="box"];13 -> 690[label="",style="solid", color="burlywood", weight=9];
690 -> 31[label="",style="solid", color="burlywood", weight=3];
14[label="(==) xv3 xv4",fontsize=16,color="black",shape="triangle"];14 -> 32[label="",style="solid", color="black", weight=3];
15[label="(==) xv3 xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="triangle"];691[label="xv3/(xv30,xv31)",fontsize=10,color="white",style="solid",shape="box"];15 -> 691[label="",style="solid", color="burlywood", weight=9];
691 -> 33[label="",style="solid", color="burlywood", weight=3];
16[label="(==) xv3 xv4\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];692[label="xv3/xv30 : xv31",fontsize=10,color="white",style="solid",shape="box"];16 -> 692[label="",style="solid", color="burlywood", weight=9];
692 -> 34[label="",style="solid", color="burlywood", weight=3];
693[label="xv3/[]",fontsize=10,color="white",style="solid",shape="box"];16 -> 693[label="",style="solid", color="burlywood", weight=9];
693 -> 35[label="",style="solid", color="burlywood", weight=3];
17[label="(==) xv3 xv4",fontsize=16,color="burlywood",shape="triangle"];694[label="xv3/()",fontsize=10,color="white",style="solid",shape="box"];17 -> 694[label="",style="solid", color="burlywood", weight=9];
694 -> 36[label="",style="solid", color="burlywood", weight=3];
18[label="(==) xv3 xv4\n  Eq a",fontsize=16,color="burlywood",shape="triangle"];695[label="xv3/Nothing",fontsize=10,color="white",style="solid",shape="box"];18 -> 695[label="",style="solid", color="burlywood", weight=9];
695 -> 37[label="",style="solid", color="burlywood", weight=3];
696[label="xv3/Just xv30",fontsize=10,color="white",style="solid",shape="box"];18 -> 696[label="",style="solid", color="burlywood", weight=9];
696 -> 38[label="",style="solid", color="burlywood", weight=3];
19[label="primEqDouble xv3 xv4",fontsize=16,color="burlywood",shape="box"];697[label="xv3/Double xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];19 -> 697[label="",style="solid", color="burlywood", weight=9];
697 -> 39[label="",style="solid", color="burlywood", weight=3];
20[label="(==) False xv4",fontsize=16,color="burlywood",shape="box"];698[label="xv4/False",fontsize=10,color="white",style="solid",shape="box"];20 -> 698[label="",style="solid", color="burlywood", weight=9];
698 -> 40[label="",style="solid", color="burlywood", weight=3];
699[label="xv4/True",fontsize=10,color="white",style="solid",shape="box"];20 -> 699[label="",style="solid", color="burlywood", weight=9];
699 -> 41[label="",style="solid", color="burlywood", weight=3];
21[label="(==) True xv4",fontsize=16,color="burlywood",shape="box"];700[label="xv4/False",fontsize=10,color="white",style="solid",shape="box"];21 -> 700[label="",style="solid", color="burlywood", weight=9];
700 -> 42[label="",style="solid", color="burlywood", weight=3];
701[label="xv4/True",fontsize=10,color="white",style="solid",shape="box"];21 -> 701[label="",style="solid", color="burlywood", weight=9];
701 -> 43[label="",style="solid", color="burlywood", weight=3];
22[label="primEqFloat xv3 xv4",fontsize=16,color="burlywood",shape="box"];702[label="xv3/Float xv30 xv31",fontsize=10,color="white",style="solid",shape="box"];22 -> 702[label="",style="solid", color="burlywood", weight=9];
702 -> 44[label="",style="solid", color="burlywood", weight=3];
23[label="primEqInt xv3 xv4",fontsize=16,color="burlywood",shape="triangle"];703[label="xv3/Pos xv30",fontsize=10,color="white",style="solid",shape="box"];23 -> 703[label="",style="solid", color="burlywood", weight=9];
703 -> 45[label="",style="solid", color="burlywood", weight=3];
704[label="xv3/Neg xv30",fontsize=10,color="white",style="solid",shape="box"];23 -> 704[label="",style="solid", color="burlywood", weight=9];
704 -> 46[label="",style="solid", color="burlywood", weight=3];
24[label="(==) LT xv4",fontsize=16,color="burlywood",shape="box"];705[label="xv4/LT",fontsize=10,color="white",style="solid",shape="box"];24 -> 705[label="",style="solid", color="burlywood", weight=9];
705 -> 47[label="",style="solid", color="burlywood", weight=3];
706[label="xv4/EQ",fontsize=10,color="white",style="solid",shape="box"];24 -> 706[label="",style="solid", color="burlywood", weight=9];
706 -> 48[label="",style="solid", color="burlywood", weight=3];
707[label="xv4/GT",fontsize=10,color="white",style="solid",shape="box"];24 -> 707[label="",style="solid", color="burlywood", weight=9];
707 -> 49[label="",style="solid", color="burlywood", weight=3];
25[label="(==) EQ xv4",fontsize=16,color="burlywood",shape="box"];708[label="xv4/LT",fontsize=10,color="white",style="solid",shape="box"];25 -> 708[label="",style="solid", color="burlywood", weight=9];
708 -> 50[label="",style="solid", color="burlywood", weight=3];
709[label="xv4/EQ",fontsize=10,color="white",style="solid",shape="box"];25 -> 709[label="",style="solid", color="burlywood", weight=9];
709 -> 51[label="",style="solid", color="burlywood", weight=3];
710[label="xv4/GT",fontsize=10,color="white",style="solid",shape="box"];25 -> 710[label="",style="solid", color="burlywood", weight=9];
710 -> 52[label="",style="solid", color="burlywood", weight=3];
26[label="(==) GT xv4",fontsize=16,color="burlywood",shape="box"];711[label="xv4/LT",fontsize=10,color="white",style="solid",shape="box"];26 -> 711[label="",style="solid", color="burlywood", weight=9];
711 -> 53[label="",style="solid", color="burlywood", weight=3];
712[label="xv4/EQ",fontsize=10,color="white",style="solid",shape="box"];26 -> 712[label="",style="solid", color="burlywood", weight=9];
712 -> 54[label="",style="solid", color="burlywood", weight=3];
713[label="xv4/GT",fontsize=10,color="white",style="solid",shape="box"];26 -> 713[label="",style="solid", color="burlywood", weight=9];
713 -> 55[label="",style="solid", color="burlywood", weight=3];
27[label="(==) Left xv30 xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];714[label="xv4/Left xv40",fontsize=10,color="white",style="solid",shape="box"];27 -> 714[label="",style="solid", color="burlywood", weight=9];
714 -> 56[label="",style="solid", color="burlywood", weight=3];
715[label="xv4/Right xv40",fontsize=10,color="white",style="solid",shape="box"];27 -> 715[label="",style="solid", color="burlywood", weight=9];
715 -> 57[label="",style="solid", color="burlywood", weight=3];
28[label="(==) Right xv30 xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];716[label="xv4/Left xv40",fontsize=10,color="white",style="solid",shape="box"];28 -> 716[label="",style="solid", color="burlywood", weight=9];
716 -> 58[label="",style="solid", color="burlywood", weight=3];
717[label="xv4/Right xv40",fontsize=10,color="white",style="solid",shape="box"];28 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 59[label="",style="solid", color="burlywood", weight=3];
29[label="(==) (xv30,xv31,xv32) xv4\n  Eq a  Eq b  Eq c",fontsize=16,color="burlywood",shape="box"];718[label="xv4/(xv40,xv41,xv42)",fontsize=10,color="white",style="solid",shape="box"];29 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 60[label="",style="solid", color="burlywood", weight=3];
30[label="(==) Integer xv30 xv4",fontsize=16,color="burlywood",shape="box"];719[label="xv4/Integer xv40",fontsize=10,color="white",style="solid",shape="box"];30 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 61[label="",style="solid", color="burlywood", weight=3];
31[label="(==) xv30 :% xv31 xv4\n  Integral a",fontsize=16,color="burlywood",shape="box"];720[label="xv4/xv40 :% xv41",fontsize=10,color="white",style="solid",shape="box"];31 -> 720[label="",style="solid", color="burlywood", weight=9];
720 -> 62[label="",style="solid", color="burlywood", weight=3];
32[label="primEqChar xv3 xv4",fontsize=16,color="burlywood",shape="box"];721[label="xv3/Char xv30",fontsize=10,color="white",style="solid",shape="box"];32 -> 721[label="",style="solid", color="burlywood", weight=9];
721 -> 63[label="",style="solid", color="burlywood", weight=3];
33[label="(==) (xv30,xv31) xv4\n  Eq a  Eq b",fontsize=16,color="burlywood",shape="box"];722[label="xv4/(xv40,xv41)",fontsize=10,color="white",style="solid",shape="box"];33 -> 722[label="",style="solid", color="burlywood", weight=9];
722 -> 64[label="",style="solid", color="burlywood", weight=3];
34[label="(==) xv30 : xv31 xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];723[label="xv4/xv40 : xv41",fontsize=10,color="white",style="solid",shape="box"];34 -> 723[label="",style="solid", color="burlywood", weight=9];
723 -> 65[label="",style="solid", color="burlywood", weight=3];
724[label="xv4/[]",fontsize=10,color="white",style="solid",shape="box"];34 -> 724[label="",style="solid", color="burlywood", weight=9];
724 -> 66[label="",style="solid", color="burlywood", weight=3];
35[label="(==) [] xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];725[label="xv4/xv40 : xv41",fontsize=10,color="white",style="solid",shape="box"];35 -> 725[label="",style="solid", color="burlywood", weight=9];
725 -> 67[label="",style="solid", color="burlywood", weight=3];
726[label="xv4/[]",fontsize=10,color="white",style="solid",shape="box"];35 -> 726[label="",style="solid", color="burlywood", weight=9];
726 -> 68[label="",style="solid", color="burlywood", weight=3];
36[label="(==) () xv4",fontsize=16,color="burlywood",shape="box"];727[label="xv4/()",fontsize=10,color="white",style="solid",shape="box"];36 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 69[label="",style="solid", color="burlywood", weight=3];
37[label="(==) Nothing xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];728[label="xv4/Nothing",fontsize=10,color="white",style="solid",shape="box"];37 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 70[label="",style="solid", color="burlywood", weight=3];
729[label="xv4/Just xv40",fontsize=10,color="white",style="solid",shape="box"];37 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 71[label="",style="solid", color="burlywood", weight=3];
38[label="(==) Just xv30 xv4\n  Eq a",fontsize=16,color="burlywood",shape="box"];730[label="xv4/Nothing",fontsize=10,color="white",style="solid",shape="box"];38 -> 730[label="",style="solid", color="burlywood", weight=9];
730 -> 72[label="",style="solid", color="burlywood", weight=3];
731[label="xv4/Just xv40",fontsize=10,color="white",style="solid",shape="box"];38 -> 731[label="",style="solid", color="burlywood", weight=9];
731 -> 73[label="",style="solid", color="burlywood", weight=3];
39[label="primEqDouble (Double xv30 xv31) xv4",fontsize=16,color="burlywood",shape="box"];732[label="xv4/Double xv40 xv41",fontsize=10,color="white",style="solid",shape="box"];39 -> 732[label="",style="solid", color="burlywood", weight=9];
732 -> 74[label="",style="solid", color="burlywood", weight=3];
40[label="(==) False False",fontsize=16,color="black",shape="box"];40 -> 75[label="",style="solid", color="black", weight=3];
41[label="(==) False True",fontsize=16,color="black",shape="box"];41 -> 76[label="",style="solid", color="black", weight=3];
42[label="(==) True False",fontsize=16,color="black",shape="box"];42 -> 77[label="",style="solid", color="black", weight=3];
43[label="(==) True True",fontsize=16,color="black",shape="box"];43 -> 78[label="",style="solid", color="black", weight=3];
44[label="primEqFloat (Float xv30 xv31) xv4",fontsize=16,color="burlywood",shape="box"];733[label="xv4/Float xv40 xv41",fontsize=10,color="white",style="solid",shape="box"];44 -> 733[label="",style="solid", color="burlywood", weight=9];
733 -> 79[label="",style="solid", color="burlywood", weight=3];
45[label="primEqInt (Pos xv30) xv4",fontsize=16,color="burlywood",shape="box"];734[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];45 -> 734[label="",style="solid", color="burlywood", weight=9];
734 -> 80[label="",style="solid", color="burlywood", weight=3];
735[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 735[label="",style="solid", color="burlywood", weight=9];
735 -> 81[label="",style="solid", color="burlywood", weight=3];
46[label="primEqInt (Neg xv30) xv4",fontsize=16,color="burlywood",shape="box"];736[label="xv30/Succ xv300",fontsize=10,color="white",style="solid",shape="box"];46 -> 736[label="",style="solid", color="burlywood", weight=9];
736 -> 82[label="",style="solid", color="burlywood", weight=3];
737[label="xv30/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 737[label="",style="solid", color="burlywood", weight=9];
737 -> 83[label="",style="solid", color="burlywood", weight=3];
47[label="(==) LT LT",fontsize=16,color="black",shape="box"];47 -> 84[label="",style="solid", color="black", weight=3];
48[label="(==) LT EQ",fontsize=16,color="black",shape="box"];48 -> 85[label="",style="solid", color="black", weight=3];
49[label="(==) LT GT",fontsize=16,color="black",shape="box"];49 -> 86[label="",style="solid", color="black", weight=3];
50[label="(==) EQ LT",fontsize=16,color="black",shape="box"];50 -> 87[label="",style="solid", color="black", weight=3];
51[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];51 -> 88[label="",style="solid", color="black", weight=3];
52[label="(==) EQ GT",fontsize=16,color="black",shape="box"];52 -> 89[label="",style="solid", color="black", weight=3];
53[label="(==) GT LT",fontsize=16,color="black",shape="box"];53 -> 90[label="",style="solid", color="black", weight=3];
54[label="(==) GT EQ",fontsize=16,color="black",shape="box"];54 -> 91[label="",style="solid", color="black", weight=3];
55[label="(==) GT GT",fontsize=16,color="black",shape="box"];55 -> 92[label="",style="solid", color="black", weight=3];
56[label="(==) Left xv30 Left xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];56 -> 93[label="",style="solid", color="black", weight=3];
57[label="(==) Left xv30 Right xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];57 -> 94[label="",style="solid", color="black", weight=3];
58[label="(==) Right xv30 Left xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];58 -> 95[label="",style="solid", color="black", weight=3];
59[label="(==) Right xv30 Right xv40\n  Eq a  Eq b",fontsize=16,color="black",shape="box"];59 -> 96[label="",style="solid", color="black", weight=3];
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467[label="xv30",fontsize=16,color="green",shape="box"];468[label="xv40",fontsize=16,color="green",shape="box"];469[label="xv30",fontsize=16,color="green",shape="box"];470[label="xv40",fontsize=16,color="green",shape="box"];471[label="xv30",fontsize=16,color="green",shape="box"];472[label="xv40",fontsize=16,color="green",shape="box"];473[label="xv30",fontsize=16,color="green",shape="box"];474[label="xv40",fontsize=16,color="green",shape="box"];475[label="xv30",fontsize=16,color="green",shape="box"];476[label="xv40",fontsize=16,color="green",shape="box"];477[label="xv30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];478[label="xv40\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];479[label="xv30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];480[label="xv40\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];481[label="xv30",fontsize=16,color="green",shape="box"];482[label="xv40",fontsize=16,color="green",shape="box"];483[label="xv30\n  Integral a",fontsize=16,color="green",shape="box"];484[label="xv40\n  Integral a",fontsize=16,color="green",shape="box"];485[label="xv30",fontsize=16,color="green",shape="box"];486[label="xv40",fontsize=16,color="green",shape="box"];487[label="xv30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];488[label="xv40\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];489[label="xv30\n  Eq a",fontsize=16,color="green",shape="box"];490[label="xv40\n  Eq a",fontsize=16,color="green",shape="box"];491[label="xv30",fontsize=16,color="green",shape="box"];492[label="xv40",fontsize=16,color="green",shape="box"];493[label="xv30\n  Eq a",fontsize=16,color="green",shape="box"];494[label="xv40\n  Eq a",fontsize=16,color="green",shape="box"];495[label="xv31",fontsize=16,color="green",shape="box"];496[label="xv41",fontsize=16,color="green",shape="box"];497[label="xv31",fontsize=16,color="green",shape="box"];498[label="xv41",fontsize=16,color="green",shape="box"];499[label="xv31",fontsize=16,color="green",shape="box"];500[label="xv41",fontsize=16,color="green",shape="box"];501[label="xv31",fontsize=16,color="green",shape="box"];502[label="xv41",fontsize=16,color="green",shape="box"];503[label="xv31",fontsize=16,color="green",shape="box"];504[label="xv41",fontsize=16,color="green",shape="box"];505[label="xv31\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];506[label="xv41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];507[label="xv31\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];508[label="xv41\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];509[label="xv31",fontsize=16,color="green",shape="box"];510[label="xv41",fontsize=16,color="green",shape="box"];511[label="xv31\n  Integral a",fontsize=16,color="green",shape="box"];512[label="xv41\n  Integral a",fontsize=16,color="green",shape="box"];513[label="xv31",fontsize=16,color="green",shape="box"];514[label="xv41",fontsize=16,color="green",shape="box"];515[label="xv31\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];516[label="xv41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];517[label="xv31\n  Eq a",fontsize=16,color="green",shape="box"];518[label="xv41\n  Eq a",fontsize=16,color="green",shape="box"];519[label="xv31",fontsize=16,color="green",shape="box"];520[label="xv41",fontsize=16,color="green",shape="box"];521[label="xv31\n  Eq a",fontsize=16,color="green",shape="box"];522[label="xv41\n  Eq a",fontsize=16,color="green",shape="box"];523[label="xv30",fontsize=16,color="green",shape="box"];524[label="xv40",fontsize=16,color="green",shape="box"];525[label="xv30",fontsize=16,color="green",shape="box"];526[label="xv40",fontsize=16,color="green",shape="box"];527[label="xv30",fontsize=16,color="green",shape="box"];528[label="xv40",fontsize=16,color="green",shape="box"];529[label="xv30",fontsize=16,color="green",shape="box"];530[label="xv40",fontsize=16,color="green",shape="box"];531[label="xv30",fontsize=16,color="green",shape="box"];532[label="xv40",fontsize=16,color="green",shape="box"];533[label="xv30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];534[label="xv40\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];535[label="xv30\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];536[label="xv40\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];537[label="xv30",fontsize=16,color="green",shape="box"];538[label="xv40",fontsize=16,color="green",shape="box"];539[label="xv30\n  Integral a",fontsize=16,color="green",shape="box"];540[label="xv40\n  Integral a",fontsize=16,color="green",shape="box"];541[label="xv30",fontsize=16,color="green",shape="box"];542[label="xv40",fontsize=16,color="green",shape="box"];543[label="xv30\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];544[label="xv40\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];545[label="xv30\n  Eq a",fontsize=16,color="green",shape="box"];546[label="xv40\n  Eq a",fontsize=16,color="green",shape="box"];547[label="xv30",fontsize=16,color="green",shape="box"];548[label="xv40",fontsize=16,color="green",shape="box"];549[label="xv30\n  Eq a",fontsize=16,color="green",shape="box"];550[label="xv40\n  Eq a",fontsize=16,color="green",shape="box"];551[label="primMulInt (Pos xv300) xv40",fontsize=16,color="burlywood",shape="box"];1043[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];551 -> 1043[label="",style="solid", color="burlywood", weight=9];
1043 -> 617[label="",style="solid", color="burlywood", weight=3];
1044[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];551 -> 1044[label="",style="solid", color="burlywood", weight=9];
1044 -> 618[label="",style="solid", color="burlywood", weight=3];
552[label="primMulInt (Neg xv300) xv40",fontsize=16,color="burlywood",shape="box"];1045[label="xv40/Pos xv400",fontsize=10,color="white",style="solid",shape="box"];552 -> 1045[label="",style="solid", color="burlywood", weight=9];
1045 -> 619[label="",style="solid", color="burlywood", weight=3];
1046[label="xv40/Neg xv400",fontsize=10,color="white",style="solid",shape="box"];552 -> 1046[label="",style="solid", color="burlywood", weight=9];
1046 -> 620[label="",style="solid", color="burlywood", weight=3];
553[label="xv400",fontsize=16,color="green",shape="box"];554[label="xv300",fontsize=16,color="green",shape="box"];555[label="xv400",fontsize=16,color="green",shape="box"];556[label="xv300",fontsize=16,color="green",shape="box"];557[label="xv31",fontsize=16,color="green",shape="box"];558[label="xv41",fontsize=16,color="green",shape="box"];559[label="xv31",fontsize=16,color="green",shape="box"];560[label="xv41",fontsize=16,color="green",shape="box"];561[label="xv31",fontsize=16,color="green",shape="box"];562[label="xv41",fontsize=16,color="green",shape="box"];563[label="xv31",fontsize=16,color="green",shape="box"];564[label="xv41",fontsize=16,color="green",shape="box"];565[label="xv31",fontsize=16,color="green",shape="box"];566[label="xv41",fontsize=16,color="green",shape="box"];567[label="xv31\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];568[label="xv41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];569[label="xv31\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];570[label="xv41\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];571[label="xv31",fontsize=16,color="green",shape="box"];572[label="xv41",fontsize=16,color="green",shape="box"];573[label="xv31\n  Integral a",fontsize=16,color="green",shape="box"];574[label="xv41\n  Integral a",fontsize=16,color="green",shape="box"];575[label="xv31",fontsize=16,color="green",shape="box"];576[label="xv41",fontsize=16,color="green",shape="box"];577[label="xv31\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];578[label="xv41\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];579[label="xv31\n  Eq a",fontsize=16,color="green",shape="box"];580[label="xv41\n  Eq a",fontsize=16,color="green",shape="box"];581[label="xv31",fontsize=16,color="green",shape="box"];582[label="xv41",fontsize=16,color="green",shape="box"];583[label="xv31\n  Eq a",fontsize=16,color="green",shape="box"];584[label="xv41\n  Eq a",fontsize=16,color="green",shape="box"];585[label="xv32",fontsize=16,color="green",shape="box"];586[label="xv42",fontsize=16,color="green",shape="box"];587[label="xv32",fontsize=16,color="green",shape="box"];588[label="xv42",fontsize=16,color="green",shape="box"];589[label="xv32",fontsize=16,color="green",shape="box"];590[label="xv42",fontsize=16,color="green",shape="box"];591[label="xv32",fontsize=16,color="green",shape="box"];592[label="xv42",fontsize=16,color="green",shape="box"];593[label="xv32",fontsize=16,color="green",shape="box"];594[label="xv42",fontsize=16,color="green",shape="box"];595[label="xv32\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];596[label="xv42\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];597[label="xv32\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];598[label="xv42\n  Eq a  Eq b  Eq c",fontsize=16,color="green",shape="box"];599[label="xv32",fontsize=16,color="green",shape="box"];600[label="xv42",fontsize=16,color="green",shape="box"];601[label="xv32\n  Integral a",fontsize=16,color="green",shape="box"];602[label="xv42\n  Integral a",fontsize=16,color="green",shape="box"];603[label="xv32",fontsize=16,color="green",shape="box"];604[label="xv42",fontsize=16,color="green",shape="box"];605[label="xv32\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];606[label="xv42\n  Eq a  Eq b",fontsize=16,color="green",shape="box"];607[label="xv32\n  Eq a",fontsize=16,color="green",shape="box"];608[label="xv42\n  Eq a",fontsize=16,color="green",shape="box"];609[label="xv32",fontsize=16,color="green",shape="box"];610[label="xv42",fontsize=16,color="green",shape="box"];611[label="xv32\n  Eq a",fontsize=16,color="green",shape="box"];612[label="xv42\n  Eq a",fontsize=16,color="green",shape="box"];613 -> 167[label="",style="dashed", color="red", weight=0];
613[label="primEqNat xv300 xv400",fontsize=16,color="magenta"];613 -> 621[label="",style="dashed", color="magenta", weight=3];
613 -> 622[label="",style="dashed", color="magenta", weight=3];
614[label="False",fontsize=16,color="green",shape="box"];615[label="False",fontsize=16,color="green",shape="box"];616[label="True",fontsize=16,color="green",shape="box"];617[label="primMulInt (Pos xv300) (Pos xv400)",fontsize=16,color="black",shape="box"];617 -> 623[label="",style="solid", color="black", weight=3];
618[label="primMulInt (Pos xv300) (Neg xv400)",fontsize=16,color="black",shape="box"];618 -> 624[label="",style="solid", color="black", weight=3];
619[label="primMulInt (Neg xv300) (Pos xv400)",fontsize=16,color="black",shape="box"];619 -> 625[label="",style="solid", color="black", weight=3];
620[label="primMulInt (Neg xv300) (Neg xv400)",fontsize=16,color="black",shape="box"];620 -> 626[label="",style="solid", color="black", weight=3];
621[label="xv400",fontsize=16,color="green",shape="box"];622[label="xv300",fontsize=16,color="green",shape="box"];623[label="Pos (primMulNat xv300 xv400)",fontsize=16,color="green",shape="box"];623 -> 627[label="",style="dashed", color="green", weight=3];
624[label="Neg (primMulNat xv300 xv400)",fontsize=16,color="green",shape="box"];624 -> 628[label="",style="dashed", color="green", weight=3];
625[label="Neg (primMulNat xv300 xv400)",fontsize=16,color="green",shape="box"];625 -> 629[label="",style="dashed", color="green", weight=3];
626[label="Pos (primMulNat xv300 xv400)",fontsize=16,color="green",shape="box"];626 -> 630[label="",style="dashed", color="green", weight=3];
627[label="primMulNat xv300 xv400",fontsize=16,color="burlywood",shape="triangle"];1048[label="xv300/Succ xv3000",fontsize=10,color="white",style="solid",shape="box"];627 -> 1048[label="",style="solid", color="burlywood", weight=9];
1048 -> 631[label="",style="solid", color="burlywood", weight=3];
1049[label="xv300/Zero",fontsize=10,color="white",style="solid",shape="box"];627 -> 1049[label="",style="solid", color="burlywood", weight=9];
1049 -> 632[label="",style="solid", color="burlywood", weight=3];
628 -> 627[label="",style="dashed", color="red", weight=0];
628[label="primMulNat xv300 xv400",fontsize=16,color="magenta"];628 -> 633[label="",style="dashed", color="magenta", weight=3];
629 -> 627[label="",style="dashed", color="red", weight=0];
629[label="primMulNat xv300 xv400",fontsize=16,color="magenta"];629 -> 634[label="",style="dashed", color="magenta", weight=3];
630 -> 627[label="",style="dashed", color="red", weight=0];
630[label="primMulNat xv300 xv400",fontsize=16,color="magenta"];630 -> 635[label="",style="dashed", color="magenta", weight=3];
630 -> 636[label="",style="dashed", color="magenta", weight=3];
631[label="primMulNat (Succ xv3000) xv400",fontsize=16,color="burlywood",shape="box"];1053[label="xv400/Succ xv4000",fontsize=10,color="white",style="solid",shape="box"];631 -> 1053[label="",style="solid", color="burlywood", weight=9];
1053 -> 637[label="",style="solid", color="burlywood", weight=3];
1054[label="xv400/Zero",fontsize=10,color="white",style="solid",shape="box"];631 -> 1054[label="",style="solid", color="burlywood", weight=9];
1054 -> 638[label="",style="solid", color="burlywood", weight=3];
632[label="primMulNat Zero xv400",fontsize=16,color="burlywood",shape="box"];1055[label="xv400/Succ xv4000",fontsize=10,color="white",style="solid",shape="box"];632 -> 1055[label="",style="solid", color="burlywood", weight=9];
1055 -> 639[label="",style="solid", color="burlywood", weight=3];
1056[label="xv400/Zero",fontsize=10,color="white",style="solid",shape="box"];632 -> 1056[label="",style="solid", color="burlywood", weight=9];
1056 -> 640[label="",style="solid", color="burlywood", weight=3];
633[label="xv400",fontsize=16,color="green",shape="box"];634[label="xv300",fontsize=16,color="green",shape="box"];635[label="xv400",fontsize=16,color="green",shape="box"];636[label="xv300",fontsize=16,color="green",shape="box"];637[label="primMulNat (Succ xv3000) (Succ xv4000)",fontsize=16,color="black",shape="box"];637 -> 641[label="",style="solid", color="black", weight=3];
638[label="primMulNat (Succ xv3000) Zero",fontsize=16,color="black",shape="box"];638 -> 642[label="",style="solid", color="black", weight=3];
639[label="primMulNat Zero (Succ xv4000)",fontsize=16,color="black",shape="box"];639 -> 643[label="",style="solid", color="black", weight=3];
640[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];640 -> 644[label="",style="solid", color="black", weight=3];
641 -> 645[label="",style="dashed", color="red", weight=0];
641[label="primPlusNat (primMulNat xv3000 (Succ xv4000)) (Succ xv4000)",fontsize=16,color="magenta"];641 -> 646[label="",style="dashed", color="magenta", weight=3];
642[label="Zero",fontsize=16,color="green",shape="box"];643[label="Zero",fontsize=16,color="green",shape="box"];644[label="Zero",fontsize=16,color="green",shape="box"];646 -> 627[label="",style="dashed", color="red", weight=0];
646[label="primMulNat xv3000 (Succ xv4000)",fontsize=16,color="magenta"];646 -> 647[label="",style="dashed", color="magenta", weight=3];
646 -> 648[label="",style="dashed", color="magenta", weight=3];
645[label="primPlusNat xv24 (Succ xv4000)",fontsize=16,color="burlywood",shape="triangle"];1059[label="xv24/Succ xv240",fontsize=10,color="white",style="solid",shape="box"];645 -> 1059[label="",style="solid", color="burlywood", weight=9];
1059 -> 649[label="",style="solid", color="burlywood", weight=3];
1060[label="xv24/Zero",fontsize=10,color="white",style="solid",shape="box"];645 -> 1060[label="",style="solid", color="burlywood", weight=9];
1060 -> 650[label="",style="solid", color="burlywood", weight=3];
647[label="Succ xv4000",fontsize=16,color="green",shape="box"];648[label="xv3000",fontsize=16,color="green",shape="box"];649[label="primPlusNat (Succ xv240) (Succ xv4000)",fontsize=16,color="black",shape="box"];649 -> 651[label="",style="solid", color="black", weight=3];
650[label="primPlusNat Zero (Succ xv4000)",fontsize=16,color="black",shape="box"];650 -> 652[label="",style="solid", color="black", weight=3];
651[label="Succ (Succ (primPlusNat xv240 xv4000))",fontsize=16,color="green",shape="box"];651 -> 653[label="",style="dashed", color="green", weight=3];
652[label="Succ xv4000",fontsize=16,color="green",shape="box"];653[label="primPlusNat xv240 xv4000",fontsize=16,color="burlywood",shape="triangle"];1061[label="xv240/Succ xv2400",fontsize=10,color="white",style="solid",shape="box"];653 -> 1061[label="",style="solid", color="burlywood", weight=9];
1061 -> 654[label="",style="solid", color="burlywood", weight=3];
1062[label="xv240/Zero",fontsize=10,color="white",style="solid",shape="box"];653 -> 1062[label="",style="solid", color="burlywood", weight=9];
1062 -> 655[label="",style="solid", color="burlywood", weight=3];
654[label="primPlusNat (Succ xv2400) xv4000",fontsize=16,color="burlywood",shape="box"];1063[label="xv4000/Succ xv40000",fontsize=10,color="white",style="solid",shape="box"];654 -> 1063[label="",style="solid", color="burlywood", weight=9];
1063 -> 656[label="",style="solid", color="burlywood", weight=3];
1064[label="xv4000/Zero",fontsize=10,color="white",style="solid",shape="box"];654 -> 1064[label="",style="solid", color="burlywood", weight=9];
1064 -> 657[label="",style="solid", color="burlywood", weight=3];
655[label="primPlusNat Zero xv4000",fontsize=16,color="burlywood",shape="box"];1065[label="xv4000/Succ xv40000",fontsize=10,color="white",style="solid",shape="box"];655 -> 1065[label="",style="solid", color="burlywood", weight=9];
1065 -> 658[label="",style="solid", color="burlywood", weight=3];
1066[label="xv4000/Zero",fontsize=10,color="white",style="solid",shape="box"];655 -> 1066[label="",style="solid", color="burlywood", weight=9];
1066 -> 659[label="",style="solid", color="burlywood", weight=3];
656[label="primPlusNat (Succ xv2400) (Succ xv40000)",fontsize=16,color="black",shape="box"];656 -> 660[label="",style="solid", color="black", weight=3];
657[label="primPlusNat (Succ xv2400) Zero",fontsize=16,color="black",shape="box"];657 -> 661[label="",style="solid", color="black", weight=3];
658[label="primPlusNat Zero (Succ xv40000)",fontsize=16,color="black",shape="box"];658 -> 662[label="",style="solid", color="black", weight=3];
659[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];659 -> 663[label="",style="solid", color="black", weight=3];
660[label="Succ (Succ (primPlusNat xv2400 xv40000))",fontsize=16,color="green",shape="box"];660 -> 664[label="",style="dashed", color="green", weight=3];
661[label="Succ xv2400",fontsize=16,color="green",shape="box"];662[label="Succ xv40000",fontsize=16,color="green",shape="box"];663[label="Zero",fontsize=16,color="green",shape="box"];664 -> 653[label="",style="dashed", color="red", weight=0];
664[label="primPlusNat xv2400 xv40000",fontsize=16,color="magenta"];664 -> 665[label="",style="dashed", color="magenta", weight=3];
664 -> 666[label="",style="dashed", color="magenta", weight=3];
665[label="xv40000",fontsize=16,color="green",shape="box"];666[label="xv2400",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

              ↳ QDP

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

new_primPlusNat(Succ(xv2400), Succ(xv40000)) → new_primPlusNat(xv2400, xv40000)

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(xv2400), Succ(xv40000)) → new_primPlusNat(xv2400, xv40000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

              ↳ QDP

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

new_primMulNat(Succ(xv3000), Succ(xv4000)) → new_primMulNat(xv3000, Succ(xv4000))

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

new_primMulNat(Succ(xv3000), Succ(xv4000)) → new_primMulNat(xv3000, Succ(xv4000))
The graph contains the following edges 1 > 1, 2 >= 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

              ↳ QDP

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

new_primEqNat(Succ(xv300), Succ(xv400)) → new_primEqNat(xv300, xv400)

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

new_primEqNat(Succ(xv300), Succ(xv400)) → new_primEqNat(xv300, xv400)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ BR

    ↳ HASKELL

      ↳ COR

        ↳ HASKELL

          ↳ Narrow

            ↳ AND

              ↳ QDP

              ↳ QDP

              ↳ QDP

              ↳ QDP

                ↳ QDPSizeChangeProof

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

new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(app(ty_@2, fh), ga), ea) → new_esEs1(xv31, xv41, fh, ga)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(xv30, xv40, hh, baa, bab)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(ty_Maybe, bbh)) → new_esEs3(xv31, xv41, bbh)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_Either, he), hf), hg) → new_esEs(xv30, xv40, he, hf)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_Maybe, eh), dh, ea) → new_esEs3(xv30, xv40, eh)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_Maybe, bda)) → new_esEs3(xv30, xv40, bda)
new_esEs3(Just(xv30), Just(xv40), app(app(ty_@2, bdh), bea)) → new_esEs1(xv30, xv40, bdh, bea)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_Either, df), dg), dh, ea) → new_esEs(xv30, xv40, df, dg)
new_esEs(Left(xv30), Left(xv40), app(app(ty_@2, bg), bh), bc) → new_esEs1(xv30, xv40, bg, bh)
new_esEs3(Just(xv30), Just(xv40), app(ty_[], beb)) → new_esEs2(xv30, xv40, beb)
new_esEs(Right(xv30), Right(xv40), cc, app(ty_Maybe, de)) → new_esEs3(xv30, xv40, de)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(xv30, xv40, bcc, bcd, bce)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_[], eg), dh, ea) → new_esEs2(xv30, xv40, eg)
new_esEs(Right(xv30), Right(xv40), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(xv30, xv40, cf, cg, da)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(app(ty_Either, gd), ge)) → new_esEs(xv32, xv42, gd, ge)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(ty_Maybe, baf), hg) → new_esEs3(xv30, xv40, baf)
new_esEs(Left(xv30), Left(xv40), app(ty_[], ca), bc) → new_esEs2(xv30, xv40, ca)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(ty_[], bae), hg) → new_esEs2(xv30, xv40, bae)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(xv31, xv41, fd, ff, fg)
new_esEs(Left(xv30), Left(xv40), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(xv30, xv40, bd, be, bf)
new_esEs3(Just(xv30), Just(xv40), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(xv30, xv40, bde, bdf, bdg)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(ty_Maybe, gc), ea) → new_esEs3(xv31, xv41, gc)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(ty_[], bbg)) → new_esEs2(xv31, xv41, bbg)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(ty_Maybe, hd)) → new_esEs3(xv32, xv42, hd)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_Either, bca), bcb)) → new_esEs(xv30, xv40, bca, bcb)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(app(ty_@2, bbe), bbf)) → new_esEs1(xv31, xv41, bbe, bbf)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(app(ty_@2, ha), hb)) → new_esEs1(xv32, xv42, ha, hb)
new_esEs(Right(xv30), Right(xv40), cc, app(ty_[], dd)) → new_esEs2(xv30, xv40, dd)
new_esEs(Right(xv30), Right(xv40), cc, app(app(ty_Either, cd), ce)) → new_esEs(xv30, xv40, cd, ce)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(ty_[], gb), ea) → new_esEs2(xv31, xv41, gb)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_@2, bcf), bcg)) → new_esEs1(xv30, xv40, bcf, bcg)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(xv32, xv42, gf, gg, gh)
new_esEs2(:(xv30, xv31), :(xv40, xv41), bdb) → new_esEs2(xv31, xv41, bdb)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_@2, bac), bad), hg) → new_esEs1(xv30, xv40, bac, bad)
new_esEs3(Just(xv30), Just(xv40), app(ty_Maybe, bec)) → new_esEs3(xv30, xv40, bec)
new_esEs(Left(xv30), Left(xv40), app(ty_Maybe, cb), bc) → new_esEs3(xv30, xv40, cb)
new_esEs3(Just(xv30), Just(xv40), app(app(ty_Either, bdc), bdd)) → new_esEs(xv30, xv40, bdc, bdd)
new_esEs(Right(xv30), Right(xv40), cc, app(app(ty_@2, db), dc)) → new_esEs1(xv30, xv40, db, dc)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(ty_[], hc)) → new_esEs2(xv32, xv42, hc)
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_[], bch)) → new_esEs2(xv30, xv40, bch)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_@2, ee), ef), dh, ea) → new_esEs1(xv30, xv40, ee, ef)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(app(ty_Either, fb), fc), ea) → new_esEs(xv31, xv41, fb, fc)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(app(ty_Either, bah), bba)) → new_esEs(xv31, xv41, bah, bba)
new_esEs(Left(xv30), Left(xv40), app(app(ty_Either, ba), bb), bc) → new_esEs(xv30, xv40, ba, bb)
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(xv30, xv40, eb, ec, ed)
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(xv31, xv41, bbb, bbc, bbd)

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

new_esEs3(Just(xv30), Just(xv40), app(app(ty_@2, bdh), bea)) → new_esEs1(xv30, xv40, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs3(Just(xv30), Just(xv40), app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs0(xv30, xv40, bde, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_@2, bcf), bcg)) → new_esEs1(xv30, xv40, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs0(xv30, xv40, bcc, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs3(Just(xv30), Just(xv40), app(ty_Maybe, bec)) → new_esEs3(xv30, xv40, bec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_Maybe, bda)) → new_esEs3(xv30, xv40, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xv30), Just(xv40), app(ty_[], beb)) → new_esEs2(xv30, xv40, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs3(Just(xv30), Just(xv40), app(app(ty_Either, bdc), bdd)) → new_esEs(xv30, xv40, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(app(ty_Either, bca), bcb)) → new_esEs(xv30, xv40, bca, bcb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(app(ty_@2, fh), ga), ea) → new_esEs1(xv31, xv41, fh, ga)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(app(ty_@2, ha), hb)) → new_esEs1(xv32, xv42, ha, hb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_@2, ee), ef), dh, ea) → new_esEs1(xv30, xv40, ee, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(app(ty_@2, bbe), bbf)) → new_esEs1(xv31, xv41, bbe, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_@2, bac), bad), hg) → new_esEs1(xv30, xv40, bac, bad)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Left(xv30), Left(xv40), app(app(ty_@2, bg), bh), bc) → new_esEs1(xv30, xv40, bg, bh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs(Right(xv30), Right(xv40), cc, app(app(ty_@2, db), dc)) → new_esEs1(xv30, xv40, db, dc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(app(app(ty_@3, fd), ff), fg), ea) → new_esEs0(xv31, xv41, fd, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(app(app(ty_@3, gf), gg), gh)) → new_esEs0(xv32, xv42, gf, gg, gh)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(app(ty_@3, eb), ec), ed), dh, ea) → new_esEs0(xv30, xv40, eb, ec, ed)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_Maybe, eh), dh, ea) → new_esEs3(xv30, xv40, eh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(ty_Maybe, gc), ea) → new_esEs3(xv31, xv41, gc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(ty_Maybe, hd)) → new_esEs3(xv32, xv42, hd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(ty_[], eg), dh, ea) → new_esEs2(xv30, xv40, eg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(ty_[], gb), ea) → new_esEs2(xv31, xv41, gb)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(ty_[], hc)) → new_esEs2(xv32, xv42, hc)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), app(app(ty_Either, df), dg), dh, ea) → new_esEs(xv30, xv40, df, dg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, dh, app(app(ty_Either, gd), ge)) → new_esEs(xv32, xv42, gd, ge)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4
new_esEs0(@3(xv30, xv31, xv32), @3(xv40, xv41, xv42), fa, app(app(ty_Either, fb), fc), ea) → new_esEs(xv31, xv41, fb, fc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(app(app(ty_@3, hh), baa), bab), hg) → new_esEs0(xv30, xv40, hh, baa, bab)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs0(xv31, xv41, bbb, bbc, bbd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(ty_Maybe, bbh)) → new_esEs3(xv31, xv41, bbh)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(ty_Maybe, baf), hg) → new_esEs3(xv30, xv40, baf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(ty_[], bae), hg) → new_esEs2(xv30, xv40, bae)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(ty_[], bbg)) → new_esEs2(xv31, xv41, bbg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), app(app(ty_Either, he), hf), hg) → new_esEs(xv30, xv40, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs1(@2(xv30, xv31), @2(xv40, xv41), bag, app(app(ty_Either, bah), bba)) → new_esEs(xv31, xv41, bah, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Right(xv30), Right(xv40), cc, app(app(app(ty_@3, cf), cg), da)) → new_esEs0(xv30, xv40, cf, cg, da)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5
new_esEs(Left(xv30), Left(xv40), app(app(app(ty_@3, bd), be), bf), bc) → new_esEs0(xv30, xv40, bd, be, bf)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5
new_esEs(Right(xv30), Right(xv40), cc, app(ty_Maybe, de)) → new_esEs3(xv30, xv40, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Left(xv30), Left(xv40), app(ty_Maybe, cb), bc) → new_esEs3(xv30, xv40, cb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Left(xv30), Left(xv40), app(ty_[], ca), bc) → new_esEs2(xv30, xv40, ca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
new_esEs(Right(xv30), Right(xv40), cc, app(ty_[], dd)) → new_esEs2(xv30, xv40, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3
new_esEs(Right(xv30), Right(xv40), cc, app(app(ty_Either, cd), ce)) → new_esEs(xv30, xv40, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4
new_esEs(Left(xv30), Left(xv40), app(app(ty_Either, ba), bb), bc) → new_esEs(xv30, xv40, ba, bb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4
new_esEs2(:(xv30, xv31), :(xv40, xv41), bdb) → new_esEs2(xv31, xv41, bdb)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
new_esEs2(:(xv30, xv31), :(xv40, xv41), app(ty_[], bch)) → new_esEs2(xv30, xv40, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3