/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [SOUND, 0 ms]
(6) AND
    (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) DependencyGraphProof [EQUIVALENT, 0 ms]
        (12) AND
            (13) QDP
                (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (15) YES
            (16) QDP
                (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (18) YES
    (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"lookup k [] = Nothing;
lookup k ((x,y) : xys)|k == xJust y|otherwiselookup k xys;
"
is transformed to
"lookup k [] = lookup3 k [];
lookup k ((x,y) : xys) = lookup2 k ((x,y) : xys);
"
"lookup1 k x y xys True = Just y;
lookup1 k x y xys False = lookup0 k x y xys otherwise;
"
"lookup0 k x y xys True = lookup k xys;
"
"lookup2 k ((x,y) : xys) = lookup1 k x y xys (k == x);
"
"lookup3 k [] = Nothing;
lookup3 xy xz = lookup2 xy xz;
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

----------------------------------------

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="lookup",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="lookup yu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="lookup yu3 yu4",fontsize=16,color="burlywood",shape="triangle"];758[label="yu4/yu40 : yu41",fontsize=10,color="white",style="solid",shape="box"];4 -> 758[label="",style="solid", color="burlywood", weight=9];
758 -> 5[label="",style="solid", color="burlywood", weight=3];
759[label="yu4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 759[label="",style="solid", color="burlywood", weight=9];
759 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="lookup yu3 (yu40 : yu41)",fontsize=16,color="burlywood",shape="box"];760[label="yu40/(yu400,yu401)",fontsize=10,color="white",style="solid",shape="box"];5 -> 760[label="",style="solid", color="burlywood", weight=9];
760 -> 7[label="",style="solid", color="burlywood", weight=3];
6[label="lookup yu3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
7[label="lookup yu3 ((yu400,yu401) : yu41)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="lookup3 yu3 []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="lookup2 yu3 ((yu400,yu401) : yu41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 yu3 yu400 yu401 yu41 (yu3 == yu400)",fontsize=16,color="burlywood",shape="box"];761[label="yu3/Left yu30",fontsize=10,color="white",style="solid",shape="box"];11 -> 761[label="",style="solid", color="burlywood", weight=9];
761 -> 12[label="",style="solid", color="burlywood", weight=3];
762[label="yu3/Right yu30",fontsize=10,color="white",style="solid",shape="box"];11 -> 762[label="",style="solid", color="burlywood", weight=9];
762 -> 13[label="",style="solid", color="burlywood", weight=3];
12[label="lookup1 (Left yu30) yu400 yu401 yu41 (Left yu30 == yu400)",fontsize=16,color="burlywood",shape="box"];763[label="yu400/Left yu4000",fontsize=10,color="white",style="solid",shape="box"];12 -> 763[label="",style="solid", color="burlywood", weight=9];
763 -> 14[label="",style="solid", color="burlywood", weight=3];
764[label="yu400/Right yu4000",fontsize=10,color="white",style="solid",shape="box"];12 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 15[label="",style="solid", color="burlywood", weight=3];
13[label="lookup1 (Right yu30) yu400 yu401 yu41 (Right yu30 == yu400)",fontsize=16,color="burlywood",shape="box"];765[label="yu400/Left yu4000",fontsize=10,color="white",style="solid",shape="box"];13 -> 765[label="",style="solid", color="burlywood", weight=9];
765 -> 16[label="",style="solid", color="burlywood", weight=3];
766[label="yu400/Right yu4000",fontsize=10,color="white",style="solid",shape="box"];13 -> 766[label="",style="solid", color="burlywood", weight=9];
766 -> 17[label="",style="solid", color="burlywood", weight=3];
14[label="lookup1 (Left yu30) (Left yu4000) yu401 yu41 (Left yu30 == Left yu4000)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="lookup1 (Left yu30) (Right yu4000) yu401 yu41 (Left yu30 == Right yu4000)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="lookup1 (Right yu30) (Left yu4000) yu401 yu41 (Right yu30 == Left yu4000)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="lookup1 (Right yu30) (Right yu4000) yu401 yu41 (Right yu30 == Right yu4000)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18 -> 22[label="",style="dashed", color="red", weight=0];
18[label="lookup1 (Left yu30) (Left yu4000) yu401 yu41 (yu30 == yu4000)",fontsize=16,color="magenta"];18 -> 23[label="",style="dashed", color="magenta", weight=3];
18 -> 24[label="",style="dashed", color="magenta", weight=3];
18 -> 25[label="",style="dashed", color="magenta", weight=3];
18 -> 26[label="",style="dashed", color="magenta", weight=3];
18 -> 27[label="",style="dashed", color="magenta", weight=3];
19[label="lookup1 (Left yu30) (Right yu4000) yu401 yu41 False",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
20[label="lookup1 (Right yu30) (Left yu4000) yu401 yu41 False",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
21 -> 30[label="",style="dashed", color="red", weight=0];
21[label="lookup1 (Right yu30) (Right yu4000) yu401 yu41 (yu30 == yu4000)",fontsize=16,color="magenta"];21 -> 31[label="",style="dashed", color="magenta", weight=3];
21 -> 32[label="",style="dashed", color="magenta", weight=3];
21 -> 33[label="",style="dashed", color="magenta", weight=3];
21 -> 34[label="",style="dashed", color="magenta", weight=3];
21 -> 35[label="",style="dashed", color="magenta", weight=3];
23[label="yu30 == yu4000",fontsize=16,color="blue",shape="box"];767[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 767[label="",style="solid", color="blue", weight=9];
767 -> 36[label="",style="solid", color="blue", weight=3];
768[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 768[label="",style="solid", color="blue", weight=9];
768 -> 37[label="",style="solid", color="blue", weight=3];
769[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 769[label="",style="solid", color="blue", weight=9];
769 -> 38[label="",style="solid", color="blue", weight=3];
770[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 770[label="",style="solid", color="blue", weight=9];
770 -> 39[label="",style="solid", color="blue", weight=3];
771[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 771[label="",style="solid", color="blue", weight=9];
771 -> 40[label="",style="solid", color="blue", weight=3];
772[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 772[label="",style="solid", color="blue", weight=9];
772 -> 41[label="",style="solid", color="blue", weight=3];
773[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 773[label="",style="solid", color="blue", weight=9];
773 -> 42[label="",style="solid", color="blue", weight=3];
774[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 774[label="",style="solid", color="blue", weight=9];
774 -> 43[label="",style="solid", color="blue", weight=3];
775[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 775[label="",style="solid", color="blue", weight=9];
775 -> 44[label="",style="solid", color="blue", weight=3];
776[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 776[label="",style="solid", color="blue", weight=9];
776 -> 45[label="",style="solid", color="blue", weight=3];
777[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 777[label="",style="solid", color="blue", weight=9];
777 -> 46[label="",style="solid", color="blue", weight=3];
778[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 778[label="",style="solid", color="blue", weight=9];
778 -> 47[label="",style="solid", color="blue", weight=3];
779[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 779[label="",style="solid", color="blue", weight=9];
779 -> 48[label="",style="solid", color="blue", weight=3];
780[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];23 -> 780[label="",style="solid", color="blue", weight=9];
780 -> 49[label="",style="solid", color="blue", weight=3];
24[label="yu4000",fontsize=16,color="green",shape="box"];25[label="yu30",fontsize=16,color="green",shape="box"];26[label="yu401",fontsize=16,color="green",shape="box"];27[label="yu41",fontsize=16,color="green",shape="box"];22[label="lookup1 (Left yu11) (Left yu12) yu13 yu14 yu15",fontsize=16,color="burlywood",shape="triangle"];781[label="yu15/False",fontsize=10,color="white",style="solid",shape="box"];22 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 50[label="",style="solid", color="burlywood", weight=3];
782[label="yu15/True",fontsize=10,color="white",style="solid",shape="box"];22 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 51[label="",style="solid", color="burlywood", weight=3];
28[label="lookup0 (Left yu30) (Right yu4000) yu401 yu41 otherwise",fontsize=16,color="black",shape="box"];28 -> 52[label="",style="solid", color="black", weight=3];
29[label="lookup0 (Right yu30) (Left yu4000) yu401 yu41 otherwise",fontsize=16,color="black",shape="box"];29 -> 53[label="",style="solid", color="black", weight=3];
31[label="yu4000",fontsize=16,color="green",shape="box"];32[label="yu30",fontsize=16,color="green",shape="box"];33[label="yu30 == yu4000",fontsize=16,color="blue",shape="box"];783[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 783[label="",style="solid", color="blue", weight=9];
783 -> 54[label="",style="solid", color="blue", weight=3];
784[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 784[label="",style="solid", color="blue", weight=9];
784 -> 55[label="",style="solid", color="blue", weight=3];
785[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 785[label="",style="solid", color="blue", weight=9];
785 -> 56[label="",style="solid", color="blue", weight=3];
786[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 786[label="",style="solid", color="blue", weight=9];
786 -> 57[label="",style="solid", color="blue", weight=3];
787[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 787[label="",style="solid", color="blue", weight=9];
787 -> 58[label="",style="solid", color="blue", weight=3];
788[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 788[label="",style="solid", color="blue", weight=9];
788 -> 59[label="",style="solid", color="blue", weight=3];
789[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 789[label="",style="solid", color="blue", weight=9];
789 -> 60[label="",style="solid", color="blue", weight=3];
790[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 790[label="",style="solid", color="blue", weight=9];
790 -> 61[label="",style="solid", color="blue", weight=3];
791[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 791[label="",style="solid", color="blue", weight=9];
791 -> 62[label="",style="solid", color="blue", weight=3];
792[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 792[label="",style="solid", color="blue", weight=9];
792 -> 63[label="",style="solid", color="blue", weight=3];
793[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 793[label="",style="solid", color="blue", weight=9];
793 -> 64[label="",style="solid", color="blue", weight=3];
794[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 794[label="",style="solid", color="blue", weight=9];
794 -> 65[label="",style="solid", color="blue", weight=3];
795[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 795[label="",style="solid", color="blue", weight=9];
795 -> 66[label="",style="solid", color="blue", weight=3];
796[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];33 -> 796[label="",style="solid", color="blue", weight=9];
796 -> 67[label="",style="solid", color="blue", weight=3];
34[label="yu41",fontsize=16,color="green",shape="box"];35[label="yu401",fontsize=16,color="green",shape="box"];30[label="lookup1 (Right yu22) (Right yu23) yu24 yu25 yu26",fontsize=16,color="burlywood",shape="triangle"];797[label="yu26/False",fontsize=10,color="white",style="solid",shape="box"];30 -> 797[label="",style="solid", color="burlywood", weight=9];
797 -> 68[label="",style="solid", color="burlywood", weight=3];
798[label="yu26/True",fontsize=10,color="white",style="solid",shape="box"];30 -> 798[label="",style="solid", color="burlywood", weight=9];
798 -> 69[label="",style="solid", color="burlywood", weight=3];
36[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];799[label="yu30/()",fontsize=10,color="white",style="solid",shape="box"];36 -> 799[label="",style="solid", color="burlywood", weight=9];
799 -> 70[label="",style="solid", color="burlywood", weight=3];
37[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];37 -> 71[label="",style="solid", color="black", weight=3];
38[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];800[label="yu30/False",fontsize=10,color="white",style="solid",shape="box"];38 -> 800[label="",style="solid", color="burlywood", weight=9];
800 -> 72[label="",style="solid", color="burlywood", weight=3];
801[label="yu30/True",fontsize=10,color="white",style="solid",shape="box"];38 -> 801[label="",style="solid", color="burlywood", weight=9];
801 -> 73[label="",style="solid", color="burlywood", weight=3];
39[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];39 -> 74[label="",style="solid", color="black", weight=3];
40[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];802[label="yu30/Integer yu300",fontsize=10,color="white",style="solid",shape="box"];40 -> 802[label="",style="solid", color="burlywood", weight=9];
802 -> 75[label="",style="solid", color="burlywood", weight=3];
41[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];41 -> 76[label="",style="solid", color="black", weight=3];
42[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];803[label="yu30/LT",fontsize=10,color="white",style="solid",shape="box"];42 -> 803[label="",style="solid", color="burlywood", weight=9];
803 -> 77[label="",style="solid", color="burlywood", weight=3];
804[label="yu30/EQ",fontsize=10,color="white",style="solid",shape="box"];42 -> 804[label="",style="solid", color="burlywood", weight=9];
804 -> 78[label="",style="solid", color="burlywood", weight=3];
805[label="yu30/GT",fontsize=10,color="white",style="solid",shape="box"];42 -> 805[label="",style="solid", color="burlywood", weight=9];
805 -> 79[label="",style="solid", color="burlywood", weight=3];
43[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];806[label="yu30/yu300 :% yu301",fontsize=10,color="white",style="solid",shape="box"];43 -> 806[label="",style="solid", color="burlywood", weight=9];
806 -> 80[label="",style="solid", color="burlywood", weight=3];
44[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];807[label="yu30/(yu300,yu301,yu302)",fontsize=10,color="white",style="solid",shape="box"];44 -> 807[label="",style="solid", color="burlywood", weight=9];
807 -> 81[label="",style="solid", color="burlywood", weight=3];
45[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];808[label="yu30/Nothing",fontsize=10,color="white",style="solid",shape="box"];45 -> 808[label="",style="solid", color="burlywood", weight=9];
808 -> 82[label="",style="solid", color="burlywood", weight=3];
809[label="yu30/Just yu300",fontsize=10,color="white",style="solid",shape="box"];45 -> 809[label="",style="solid", color="burlywood", weight=9];
809 -> 83[label="",style="solid", color="burlywood", weight=3];
46[label="yu30 == yu4000",fontsize=16,color="black",shape="triangle"];46 -> 84[label="",style="solid", color="black", weight=3];
47[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];810[label="yu30/Left yu300",fontsize=10,color="white",style="solid",shape="box"];47 -> 810[label="",style="solid", color="burlywood", weight=9];
810 -> 85[label="",style="solid", color="burlywood", weight=3];
811[label="yu30/Right yu300",fontsize=10,color="white",style="solid",shape="box"];47 -> 811[label="",style="solid", color="burlywood", weight=9];
811 -> 86[label="",style="solid", color="burlywood", weight=3];
48[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];812[label="yu30/(yu300,yu301)",fontsize=10,color="white",style="solid",shape="box"];48 -> 812[label="",style="solid", color="burlywood", weight=9];
812 -> 87[label="",style="solid", color="burlywood", weight=3];
49[label="yu30 == yu4000",fontsize=16,color="burlywood",shape="triangle"];813[label="yu30/yu300 : yu301",fontsize=10,color="white",style="solid",shape="box"];49 -> 813[label="",style="solid", color="burlywood", weight=9];
813 -> 88[label="",style="solid", color="burlywood", weight=3];
814[label="yu30/[]",fontsize=10,color="white",style="solid",shape="box"];49 -> 814[label="",style="solid", color="burlywood", weight=9];
814 -> 89[label="",style="solid", color="burlywood", weight=3];
50[label="lookup1 (Left yu11) (Left yu12) yu13 yu14 False",fontsize=16,color="black",shape="box"];50 -> 90[label="",style="solid", color="black", weight=3];
51[label="lookup1 (Left yu11) (Left yu12) yu13 yu14 True",fontsize=16,color="black",shape="box"];51 -> 91[label="",style="solid", color="black", weight=3];
52[label="lookup0 (Left yu30) (Right yu4000) yu401 yu41 True",fontsize=16,color="black",shape="box"];52 -> 92[label="",style="solid", color="black", weight=3];
53[label="lookup0 (Right yu30) (Left yu4000) yu401 yu41 True",fontsize=16,color="black",shape="box"];53 -> 93[label="",style="solid", color="black", weight=3];
54 -> 36[label="",style="dashed", color="red", weight=0];
54[label="yu30 == yu4000",fontsize=16,color="magenta"];54 -> 94[label="",style="dashed", color="magenta", weight=3];
54 -> 95[label="",style="dashed", color="magenta", weight=3];
55 -> 37[label="",style="dashed", color="red", weight=0];
55[label="yu30 == yu4000",fontsize=16,color="magenta"];55 -> 96[label="",style="dashed", color="magenta", weight=3];
55 -> 97[label="",style="dashed", color="magenta", weight=3];
56 -> 38[label="",style="dashed", color="red", weight=0];
56[label="yu30 == yu4000",fontsize=16,color="magenta"];56 -> 98[label="",style="dashed", color="magenta", weight=3];
56 -> 99[label="",style="dashed", color="magenta", weight=3];
57 -> 39[label="",style="dashed", color="red", weight=0];
57[label="yu30 == yu4000",fontsize=16,color="magenta"];57 -> 100[label="",style="dashed", color="magenta", weight=3];
57 -> 101[label="",style="dashed", color="magenta", weight=3];
58 -> 40[label="",style="dashed", color="red", weight=0];
58[label="yu30 == yu4000",fontsize=16,color="magenta"];58 -> 102[label="",style="dashed", color="magenta", weight=3];
58 -> 103[label="",style="dashed", color="magenta", weight=3];
59 -> 41[label="",style="dashed", color="red", weight=0];
59[label="yu30 == yu4000",fontsize=16,color="magenta"];59 -> 104[label="",style="dashed", color="magenta", weight=3];
59 -> 105[label="",style="dashed", color="magenta", weight=3];
60 -> 42[label="",style="dashed", color="red", weight=0];
60[label="yu30 == yu4000",fontsize=16,color="magenta"];60 -> 106[label="",style="dashed", color="magenta", weight=3];
60 -> 107[label="",style="dashed", color="magenta", weight=3];
61 -> 43[label="",style="dashed", color="red", weight=0];
61[label="yu30 == yu4000",fontsize=16,color="magenta"];61 -> 108[label="",style="dashed", color="magenta", weight=3];
61 -> 109[label="",style="dashed", color="magenta", weight=3];
62 -> 44[label="",style="dashed", color="red", weight=0];
62[label="yu30 == yu4000",fontsize=16,color="magenta"];62 -> 110[label="",style="dashed", color="magenta", weight=3];
62 -> 111[label="",style="dashed", color="magenta", weight=3];
63 -> 45[label="",style="dashed", color="red", weight=0];
63[label="yu30 == yu4000",fontsize=16,color="magenta"];63 -> 112[label="",style="dashed", color="magenta", weight=3];
63 -> 113[label="",style="dashed", color="magenta", weight=3];
64 -> 46[label="",style="dashed", color="red", weight=0];
64[label="yu30 == yu4000",fontsize=16,color="magenta"];64 -> 114[label="",style="dashed", color="magenta", weight=3];
64 -> 115[label="",style="dashed", color="magenta", weight=3];
65 -> 47[label="",style="dashed", color="red", weight=0];
65[label="yu30 == yu4000",fontsize=16,color="magenta"];65 -> 116[label="",style="dashed", color="magenta", weight=3];
65 -> 117[label="",style="dashed", color="magenta", weight=3];
66 -> 48[label="",style="dashed", color="red", weight=0];
66[label="yu30 == yu4000",fontsize=16,color="magenta"];66 -> 118[label="",style="dashed", color="magenta", weight=3];
66 -> 119[label="",style="dashed", color="magenta", weight=3];
67 -> 49[label="",style="dashed", color="red", weight=0];
67[label="yu30 == yu4000",fontsize=16,color="magenta"];67 -> 120[label="",style="dashed", color="magenta", weight=3];
67 -> 121[label="",style="dashed", color="magenta", weight=3];
68[label="lookup1 (Right yu22) (Right yu23) yu24 yu25 False",fontsize=16,color="black",shape="box"];68 -> 122[label="",style="solid", color="black", weight=3];
69[label="lookup1 (Right yu22) (Right yu23) yu24 yu25 True",fontsize=16,color="black",shape="box"];69 -> 123[label="",style="solid", color="black", weight=3];
70[label="() == yu4000",fontsize=16,color="burlywood",shape="box"];815[label="yu4000/()",fontsize=10,color="white",style="solid",shape="box"];70 -> 815[label="",style="solid", color="burlywood", weight=9];
815 -> 124[label="",style="solid", color="burlywood", weight=3];
71[label="primEqChar yu30 yu4000",fontsize=16,color="burlywood",shape="box"];816[label="yu30/Char yu300",fontsize=10,color="white",style="solid",shape="box"];71 -> 816[label="",style="solid", color="burlywood", weight=9];
816 -> 125[label="",style="solid", color="burlywood", weight=3];
72[label="False == yu4000",fontsize=16,color="burlywood",shape="box"];817[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];72 -> 817[label="",style="solid", color="burlywood", weight=9];
817 -> 126[label="",style="solid", color="burlywood", weight=3];
818[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];72 -> 818[label="",style="solid", color="burlywood", weight=9];
818 -> 127[label="",style="solid", color="burlywood", weight=3];
73[label="True == yu4000",fontsize=16,color="burlywood",shape="box"];819[label="yu4000/False",fontsize=10,color="white",style="solid",shape="box"];73 -> 819[label="",style="solid", color="burlywood", weight=9];
819 -> 128[label="",style="solid", color="burlywood", weight=3];
820[label="yu4000/True",fontsize=10,color="white",style="solid",shape="box"];73 -> 820[label="",style="solid", color="burlywood", weight=9];
820 -> 129[label="",style="solid", color="burlywood", weight=3];
74[label="primEqInt yu30 yu4000",fontsize=16,color="burlywood",shape="triangle"];821[label="yu30/Pos yu300",fontsize=10,color="white",style="solid",shape="box"];74 -> 821[label="",style="solid", color="burlywood", weight=9];
821 -> 130[label="",style="solid", color="burlywood", weight=3];
822[label="yu30/Neg yu300",fontsize=10,color="white",style="solid",shape="box"];74 -> 822[label="",style="solid", color="burlywood", weight=9];
822 -> 131[label="",style="solid", color="burlywood", weight=3];
75[label="Integer yu300 == yu4000",fontsize=16,color="burlywood",shape="box"];823[label="yu4000/Integer yu40000",fontsize=10,color="white",style="solid",shape="box"];75 -> 823[label="",style="solid", color="burlywood", weight=9];
823 -> 132[label="",style="solid", color="burlywood", weight=3];
76[label="primEqFloat yu30 yu4000",fontsize=16,color="burlywood",shape="box"];824[label="yu30/Float yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];76 -> 824[label="",style="solid", color="burlywood", weight=9];
824 -> 133[label="",style="solid", color="burlywood", weight=3];
77[label="LT == yu4000",fontsize=16,color="burlywood",shape="box"];825[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];77 -> 825[label="",style="solid", color="burlywood", weight=9];
825 -> 134[label="",style="solid", color="burlywood", weight=3];
826[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];77 -> 826[label="",style="solid", color="burlywood", weight=9];
826 -> 135[label="",style="solid", color="burlywood", weight=3];
827[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];77 -> 827[label="",style="solid", color="burlywood", weight=9];
827 -> 136[label="",style="solid", color="burlywood", weight=3];
78[label="EQ == yu4000",fontsize=16,color="burlywood",shape="box"];828[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];78 -> 828[label="",style="solid", color="burlywood", weight=9];
828 -> 137[label="",style="solid", color="burlywood", weight=3];
829[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];78 -> 829[label="",style="solid", color="burlywood", weight=9];
829 -> 138[label="",style="solid", color="burlywood", weight=3];
830[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];78 -> 830[label="",style="solid", color="burlywood", weight=9];
830 -> 139[label="",style="solid", color="burlywood", weight=3];
79[label="GT == yu4000",fontsize=16,color="burlywood",shape="box"];831[label="yu4000/LT",fontsize=10,color="white",style="solid",shape="box"];79 -> 831[label="",style="solid", color="burlywood", weight=9];
831 -> 140[label="",style="solid", color="burlywood", weight=3];
832[label="yu4000/EQ",fontsize=10,color="white",style="solid",shape="box"];79 -> 832[label="",style="solid", color="burlywood", weight=9];
832 -> 141[label="",style="solid", color="burlywood", weight=3];
833[label="yu4000/GT",fontsize=10,color="white",style="solid",shape="box"];79 -> 833[label="",style="solid", color="burlywood", weight=9];
833 -> 142[label="",style="solid", color="burlywood", weight=3];
80[label="yu300 :% yu301 == yu4000",fontsize=16,color="burlywood",shape="box"];834[label="yu4000/yu40000 :% yu40001",fontsize=10,color="white",style="solid",shape="box"];80 -> 834[label="",style="solid", color="burlywood", weight=9];
834 -> 143[label="",style="solid", color="burlywood", weight=3];
81[label="(yu300,yu301,yu302) == yu4000",fontsize=16,color="burlywood",shape="box"];835[label="yu4000/(yu40000,yu40001,yu40002)",fontsize=10,color="white",style="solid",shape="box"];81 -> 835[label="",style="solid", color="burlywood", weight=9];
835 -> 144[label="",style="solid", color="burlywood", weight=3];
82[label="Nothing == yu4000",fontsize=16,color="burlywood",shape="box"];836[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];82 -> 836[label="",style="solid", color="burlywood", weight=9];
836 -> 145[label="",style="solid", color="burlywood", weight=3];
837[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];82 -> 837[label="",style="solid", color="burlywood", weight=9];
837 -> 146[label="",style="solid", color="burlywood", weight=3];
83[label="Just yu300 == yu4000",fontsize=16,color="burlywood",shape="box"];838[label="yu4000/Nothing",fontsize=10,color="white",style="solid",shape="box"];83 -> 838[label="",style="solid", color="burlywood", weight=9];
838 -> 147[label="",style="solid", color="burlywood", weight=3];
839[label="yu4000/Just yu40000",fontsize=10,color="white",style="solid",shape="box"];83 -> 839[label="",style="solid", color="burlywood", weight=9];
839 -> 148[label="",style="solid", color="burlywood", weight=3];
84[label="primEqDouble yu30 yu4000",fontsize=16,color="burlywood",shape="box"];840[label="yu30/Double yu300 yu301",fontsize=10,color="white",style="solid",shape="box"];84 -> 840[label="",style="solid", color="burlywood", weight=9];
840 -> 149[label="",style="solid", color="burlywood", weight=3];
85[label="Left yu300 == yu4000",fontsize=16,color="burlywood",shape="box"];841[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];85 -> 841[label="",style="solid", color="burlywood", weight=9];
841 -> 150[label="",style="solid", color="burlywood", weight=3];
842[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];85 -> 842[label="",style="solid", color="burlywood", weight=9];
842 -> 151[label="",style="solid", color="burlywood", weight=3];
86[label="Right yu300 == yu4000",fontsize=16,color="burlywood",shape="box"];843[label="yu4000/Left yu40000",fontsize=10,color="white",style="solid",shape="box"];86 -> 843[label="",style="solid", color="burlywood", weight=9];
843 -> 152[label="",style="solid", color="burlywood", weight=3];
844[label="yu4000/Right yu40000",fontsize=10,color="white",style="solid",shape="box"];86 -> 844[label="",style="solid", color="burlywood", weight=9];
844 -> 153[label="",style="solid", color="burlywood", weight=3];
87[label="(yu300,yu301) == yu4000",fontsize=16,color="burlywood",shape="box"];845[label="yu4000/(yu40000,yu40001)",fontsize=10,color="white",style="solid",shape="box"];87 -> 845[label="",style="solid", color="burlywood", weight=9];
845 -> 154[label="",style="solid", color="burlywood", weight=3];
88[label="yu300 : yu301 == yu4000",fontsize=16,color="burlywood",shape="box"];846[label="yu4000/yu40000 : yu40001",fontsize=10,color="white",style="solid",shape="box"];88 -> 846[label="",style="solid", color="burlywood", weight=9];
846 -> 155[label="",style="solid", color="burlywood", weight=3];
847[label="yu4000/[]",fontsize=10,color="white",style="solid",shape="box"];88 -> 847[label="",style="solid", color="burlywood", weight=9];
847 -> 156[label="",style="solid", color="burlywood", weight=3];
89[label="[] == yu4000",fontsize=16,color="burlywood",shape="box"];848[label="yu4000/yu40000 : yu40001",fontsize=10,color="white",style="solid",shape="box"];89 -> 848[label="",style="solid", color="burlywood", weight=9];
848 -> 157[label="",style="solid", color="burlywood", weight=3];
849[label="yu4000/[]",fontsize=10,color="white",style="solid",shape="box"];89 -> 849[label="",style="solid", color="burlywood", weight=9];
849 -> 158[label="",style="solid", color="burlywood", weight=3];
90[label="lookup0 (Left yu11) (Left yu12) yu13 yu14 otherwise",fontsize=16,color="black",shape="box"];90 -> 159[label="",style="solid", color="black", weight=3];
91[label="Just yu13",fontsize=16,color="green",shape="box"];92 -> 4[label="",style="dashed", color="red", weight=0];
92[label="lookup (Left yu30) yu41",fontsize=16,color="magenta"];92 -> 160[label="",style="dashed", color="magenta", weight=3];
92 -> 161[label="",style="dashed", color="magenta", weight=3];
93 -> 4[label="",style="dashed", color="red", weight=0];
93[label="lookup (Right yu30) yu41",fontsize=16,color="magenta"];93 -> 162[label="",style="dashed", color="magenta", weight=3];
93 -> 163[label="",style="dashed", color="magenta", weight=3];
94[label="yu30",fontsize=16,color="green",shape="box"];95[label="yu4000",fontsize=16,color="green",shape="box"];96[label="yu30",fontsize=16,color="green",shape="box"];97[label="yu4000",fontsize=16,color="green",shape="box"];98[label="yu30",fontsize=16,color="green",shape="box"];99[label="yu4000",fontsize=16,color="green",shape="box"];100[label="yu30",fontsize=16,color="green",shape="box"];101[label="yu4000",fontsize=16,color="green",shape="box"];102[label="yu30",fontsize=16,color="green",shape="box"];103[label="yu4000",fontsize=16,color="green",shape="box"];104[label="yu30",fontsize=16,color="green",shape="box"];105[label="yu4000",fontsize=16,color="green",shape="box"];106[label="yu30",fontsize=16,color="green",shape="box"];107[label="yu4000",fontsize=16,color="green",shape="box"];108[label="yu30",fontsize=16,color="green",shape="box"];109[label="yu4000",fontsize=16,color="green",shape="box"];110[label="yu30",fontsize=16,color="green",shape="box"];111[label="yu4000",fontsize=16,color="green",shape="box"];112[label="yu30",fontsize=16,color="green",shape="box"];113[label="yu4000",fontsize=16,color="green",shape="box"];114[label="yu30",fontsize=16,color="green",shape="box"];115[label="yu4000",fontsize=16,color="green",shape="box"];116[label="yu30",fontsize=16,color="green",shape="box"];117[label="yu4000",fontsize=16,color="green",shape="box"];118[label="yu30",fontsize=16,color="green",shape="box"];119[label="yu4000",fontsize=16,color="green",shape="box"];120[label="yu30",fontsize=16,color="green",shape="box"];121[label="yu4000",fontsize=16,color="green",shape="box"];122[label="lookup0 (Right yu22) (Right yu23) yu24 yu25 otherwise",fontsize=16,color="black",shape="box"];122 -> 164[label="",style="solid", color="black", weight=3];
123[label="Just yu24",fontsize=16,color="green",shape="box"];124[label="() == ()",fontsize=16,color="black",shape="box"];124 -> 165[label="",style="solid", color="black", weight=3];
125[label="primEqChar (Char yu300) yu4000",fontsize=16,color="burlywood",shape="box"];850[label="yu4000/Char yu40000",fontsize=10,color="white",style="solid",shape="box"];125 -> 850[label="",style="solid", color="burlywood", weight=9];
850 -> 166[label="",style="solid", color="burlywood", weight=3];
126[label="False == False",fontsize=16,color="black",shape="box"];126 -> 167[label="",style="solid", color="black", weight=3];
127[label="False == True",fontsize=16,color="black",shape="box"];127 -> 168[label="",style="solid", color="black", weight=3];
128[label="True == False",fontsize=16,color="black",shape="box"];128 -> 169[label="",style="solid", color="black", weight=3];
129[label="True == True",fontsize=16,color="black",shape="box"];129 -> 170[label="",style="solid", color="black", weight=3];
130[label="primEqInt (Pos yu300) yu4000",fontsize=16,color="burlywood",shape="box"];851[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];130 -> 851[label="",style="solid", color="burlywood", weight=9];
851 -> 171[label="",style="solid", color="burlywood", weight=3];
852[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];130 -> 852[label="",style="solid", color="burlywood", weight=9];
852 -> 172[label="",style="solid", color="burlywood", weight=3];
131[label="primEqInt (Neg yu300) yu4000",fontsize=16,color="burlywood",shape="box"];853[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];131 -> 853[label="",style="solid", color="burlywood", weight=9];
853 -> 173[label="",style="solid", color="burlywood", weight=3];
854[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];131 -> 854[label="",style="solid", color="burlywood", weight=9];
854 -> 174[label="",style="solid", color="burlywood", weight=3];
132[label="Integer yu300 == Integer yu40000",fontsize=16,color="black",shape="box"];132 -> 175[label="",style="solid", color="black", weight=3];
133[label="primEqFloat (Float yu300 yu301) yu4000",fontsize=16,color="burlywood",shape="box"];855[label="yu4000/Float yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];133 -> 855[label="",style="solid", color="burlywood", weight=9];
855 -> 176[label="",style="solid", color="burlywood", weight=3];
134[label="LT == LT",fontsize=16,color="black",shape="box"];134 -> 177[label="",style="solid", color="black", weight=3];
135[label="LT == EQ",fontsize=16,color="black",shape="box"];135 -> 178[label="",style="solid", color="black", weight=3];
136[label="LT == GT",fontsize=16,color="black",shape="box"];136 -> 179[label="",style="solid", color="black", weight=3];
137[label="EQ == LT",fontsize=16,color="black",shape="box"];137 -> 180[label="",style="solid", color="black", weight=3];
138[label="EQ == EQ",fontsize=16,color="black",shape="box"];138 -> 181[label="",style="solid", color="black", weight=3];
139[label="EQ == GT",fontsize=16,color="black",shape="box"];139 -> 182[label="",style="solid", color="black", weight=3];
140[label="GT == LT",fontsize=16,color="black",shape="box"];140 -> 183[label="",style="solid", color="black", weight=3];
141[label="GT == EQ",fontsize=16,color="black",shape="box"];141 -> 184[label="",style="solid", color="black", weight=3];
142[label="GT == GT",fontsize=16,color="black",shape="box"];142 -> 185[label="",style="solid", color="black", weight=3];
143[label="yu300 :% yu301 == yu40000 :% yu40001",fontsize=16,color="black",shape="box"];143 -> 186[label="",style="solid", color="black", weight=3];
144[label="(yu300,yu301,yu302) == (yu40000,yu40001,yu40002)",fontsize=16,color="black",shape="box"];144 -> 187[label="",style="solid", color="black", weight=3];
145[label="Nothing == Nothing",fontsize=16,color="black",shape="box"];145 -> 188[label="",style="solid", color="black", weight=3];
146[label="Nothing == Just yu40000",fontsize=16,color="black",shape="box"];146 -> 189[label="",style="solid", color="black", weight=3];
147[label="Just yu300 == Nothing",fontsize=16,color="black",shape="box"];147 -> 190[label="",style="solid", color="black", weight=3];
148[label="Just yu300 == Just yu40000",fontsize=16,color="black",shape="box"];148 -> 191[label="",style="solid", color="black", weight=3];
149[label="primEqDouble (Double yu300 yu301) yu4000",fontsize=16,color="burlywood",shape="box"];856[label="yu4000/Double yu40000 yu40001",fontsize=10,color="white",style="solid",shape="box"];149 -> 856[label="",style="solid", color="burlywood", weight=9];
856 -> 192[label="",style="solid", color="burlywood", weight=3];
150[label="Left yu300 == Left yu40000",fontsize=16,color="black",shape="box"];150 -> 193[label="",style="solid", color="black", weight=3];
151[label="Left yu300 == Right yu40000",fontsize=16,color="black",shape="box"];151 -> 194[label="",style="solid", color="black", weight=3];
152[label="Right yu300 == Left yu40000",fontsize=16,color="black",shape="box"];152 -> 195[label="",style="solid", color="black", weight=3];
153[label="Right yu300 == Right yu40000",fontsize=16,color="black",shape="box"];153 -> 196[label="",style="solid", color="black", weight=3];
154[label="(yu300,yu301) == (yu40000,yu40001)",fontsize=16,color="black",shape="box"];154 -> 197[label="",style="solid", color="black", weight=3];
155[label="yu300 : yu301 == yu40000 : yu40001",fontsize=16,color="black",shape="box"];155 -> 198[label="",style="solid", color="black", weight=3];
156[label="yu300 : yu301 == []",fontsize=16,color="black",shape="box"];156 -> 199[label="",style="solid", color="black", weight=3];
157[label="[] == yu40000 : yu40001",fontsize=16,color="black",shape="box"];157 -> 200[label="",style="solid", color="black", weight=3];
158[label="[] == []",fontsize=16,color="black",shape="box"];158 -> 201[label="",style="solid", color="black", weight=3];
159[label="lookup0 (Left yu11) (Left yu12) yu13 yu14 True",fontsize=16,color="black",shape="box"];159 -> 202[label="",style="solid", color="black", weight=3];
160[label="yu41",fontsize=16,color="green",shape="box"];161[label="Left yu30",fontsize=16,color="green",shape="box"];162[label="yu41",fontsize=16,color="green",shape="box"];163[label="Right yu30",fontsize=16,color="green",shape="box"];164[label="lookup0 (Right yu22) (Right yu23) yu24 yu25 True",fontsize=16,color="black",shape="box"];164 -> 203[label="",style="solid", color="black", weight=3];
165[label="True",fontsize=16,color="green",shape="box"];166[label="primEqChar (Char yu300) (Char yu40000)",fontsize=16,color="black",shape="box"];166 -> 204[label="",style="solid", color="black", weight=3];
167[label="True",fontsize=16,color="green",shape="box"];168[label="False",fontsize=16,color="green",shape="box"];169[label="False",fontsize=16,color="green",shape="box"];170[label="True",fontsize=16,color="green",shape="box"];171[label="primEqInt (Pos (Succ yu3000)) yu4000",fontsize=16,color="burlywood",shape="box"];857[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];171 -> 857[label="",style="solid", color="burlywood", weight=9];
857 -> 205[label="",style="solid", color="burlywood", weight=3];
858[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];171 -> 858[label="",style="solid", color="burlywood", weight=9];
858 -> 206[label="",style="solid", color="burlywood", weight=3];
172[label="primEqInt (Pos Zero) yu4000",fontsize=16,color="burlywood",shape="box"];859[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];172 -> 859[label="",style="solid", color="burlywood", weight=9];
859 -> 207[label="",style="solid", color="burlywood", weight=3];
860[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];172 -> 860[label="",style="solid", color="burlywood", weight=9];
860 -> 208[label="",style="solid", color="burlywood", weight=3];
173[label="primEqInt (Neg (Succ yu3000)) yu4000",fontsize=16,color="burlywood",shape="box"];861[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];173 -> 861[label="",style="solid", color="burlywood", weight=9];
861 -> 209[label="",style="solid", color="burlywood", weight=3];
862[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];173 -> 862[label="",style="solid", color="burlywood", weight=9];
862 -> 210[label="",style="solid", color="burlywood", weight=3];
174[label="primEqInt (Neg Zero) yu4000",fontsize=16,color="burlywood",shape="box"];863[label="yu4000/Pos yu40000",fontsize=10,color="white",style="solid",shape="box"];174 -> 863[label="",style="solid", color="burlywood", weight=9];
863 -> 211[label="",style="solid", color="burlywood", weight=3];
864[label="yu4000/Neg yu40000",fontsize=10,color="white",style="solid",shape="box"];174 -> 864[label="",style="solid", color="burlywood", weight=9];
864 -> 212[label="",style="solid", color="burlywood", weight=3];
175 -> 74[label="",style="dashed", color="red", weight=0];
175[label="primEqInt yu300 yu40000",fontsize=16,color="magenta"];175 -> 213[label="",style="dashed", color="magenta", weight=3];
175 -> 214[label="",style="dashed", color="magenta", weight=3];
176[label="primEqFloat (Float yu300 yu301) (Float yu40000 yu40001)",fontsize=16,color="black",shape="box"];176 -> 215[label="",style="solid", color="black", weight=3];
177[label="True",fontsize=16,color="green",shape="box"];178[label="False",fontsize=16,color="green",shape="box"];179[label="False",fontsize=16,color="green",shape="box"];180[label="False",fontsize=16,color="green",shape="box"];181[label="True",fontsize=16,color="green",shape="box"];182[label="False",fontsize=16,color="green",shape="box"];183[label="False",fontsize=16,color="green",shape="box"];184[label="False",fontsize=16,color="green",shape="box"];185[label="True",fontsize=16,color="green",shape="box"];186 -> 304[label="",style="dashed", color="red", weight=0];
186[label="yu300 == yu40000 && yu301 == yu40001",fontsize=16,color="magenta"];186 -> 305[label="",style="dashed", color="magenta", weight=3];
186 -> 306[label="",style="dashed", color="magenta", weight=3];
187 -> 304[label="",style="dashed", color="red", weight=0];
187[label="yu300 == yu40000 && yu301 == yu40001 && yu302 == yu40002",fontsize=16,color="magenta"];187 -> 307[label="",style="dashed", color="magenta", weight=3];
187 -> 308[label="",style="dashed", color="magenta", weight=3];
188[label="True",fontsize=16,color="green",shape="box"];189[label="False",fontsize=16,color="green",shape="box"];190[label="False",fontsize=16,color="green",shape="box"];191[label="yu300 == yu40000",fontsize=16,color="blue",shape="box"];865[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 865[label="",style="solid", color="blue", weight=9];
865 -> 237[label="",style="solid", color="blue", weight=3];
866[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 866[label="",style="solid", color="blue", weight=9];
866 -> 238[label="",style="solid", color="blue", weight=3];
867[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 867[label="",style="solid", color="blue", weight=9];
867 -> 239[label="",style="solid", color="blue", weight=3];
868[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 868[label="",style="solid", color="blue", weight=9];
868 -> 240[label="",style="solid", color="blue", weight=3];
869[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 869[label="",style="solid", color="blue", weight=9];
869 -> 241[label="",style="solid", color="blue", weight=3];
870[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 870[label="",style="solid", color="blue", weight=9];
870 -> 242[label="",style="solid", color="blue", weight=3];
871[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 871[label="",style="solid", color="blue", weight=9];
871 -> 243[label="",style="solid", color="blue", weight=3];
872[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 872[label="",style="solid", color="blue", weight=9];
872 -> 244[label="",style="solid", color="blue", weight=3];
873[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 873[label="",style="solid", color="blue", weight=9];
873 -> 245[label="",style="solid", color="blue", weight=3];
874[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 874[label="",style="solid", color="blue", weight=9];
874 -> 246[label="",style="solid", color="blue", weight=3];
875[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 875[label="",style="solid", color="blue", weight=9];
875 -> 247[label="",style="solid", color="blue", weight=3];
876[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 876[label="",style="solid", color="blue", weight=9];
876 -> 248[label="",style="solid", color="blue", weight=3];
877[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 877[label="",style="solid", color="blue", weight=9];
877 -> 249[label="",style="solid", color="blue", weight=3];
878[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];191 -> 878[label="",style="solid", color="blue", weight=9];
878 -> 250[label="",style="solid", color="blue", weight=3];
192[label="primEqDouble (Double yu300 yu301) (Double yu40000 yu40001)",fontsize=16,color="black",shape="box"];192 -> 251[label="",style="solid", color="black", weight=3];
193[label="yu300 == yu40000",fontsize=16,color="blue",shape="box"];879[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 879[label="",style="solid", color="blue", weight=9];
879 -> 252[label="",style="solid", color="blue", weight=3];
880[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 880[label="",style="solid", color="blue", weight=9];
880 -> 253[label="",style="solid", color="blue", weight=3];
881[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 881[label="",style="solid", color="blue", weight=9];
881 -> 254[label="",style="solid", color="blue", weight=3];
882[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 882[label="",style="solid", color="blue", weight=9];
882 -> 255[label="",style="solid", color="blue", weight=3];
883[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 883[label="",style="solid", color="blue", weight=9];
883 -> 256[label="",style="solid", color="blue", weight=3];
884[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 884[label="",style="solid", color="blue", weight=9];
884 -> 257[label="",style="solid", color="blue", weight=3];
885[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 885[label="",style="solid", color="blue", weight=9];
885 -> 258[label="",style="solid", color="blue", weight=3];
886[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 886[label="",style="solid", color="blue", weight=9];
886 -> 259[label="",style="solid", color="blue", weight=3];
887[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 887[label="",style="solid", color="blue", weight=9];
887 -> 260[label="",style="solid", color="blue", weight=3];
888[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 888[label="",style="solid", color="blue", weight=9];
888 -> 261[label="",style="solid", color="blue", weight=3];
889[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 889[label="",style="solid", color="blue", weight=9];
889 -> 262[label="",style="solid", color="blue", weight=3];
890[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 890[label="",style="solid", color="blue", weight=9];
890 -> 263[label="",style="solid", color="blue", weight=3];
891[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 891[label="",style="solid", color="blue", weight=9];
891 -> 264[label="",style="solid", color="blue", weight=3];
892[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];193 -> 892[label="",style="solid", color="blue", weight=9];
892 -> 265[label="",style="solid", color="blue", weight=3];
194[label="False",fontsize=16,color="green",shape="box"];195[label="False",fontsize=16,color="green",shape="box"];196[label="yu300 == yu40000",fontsize=16,color="blue",shape="box"];893[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 893[label="",style="solid", color="blue", weight=9];
893 -> 266[label="",style="solid", color="blue", weight=3];
894[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 894[label="",style="solid", color="blue", weight=9];
894 -> 267[label="",style="solid", color="blue", weight=3];
895[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 895[label="",style="solid", color="blue", weight=9];
895 -> 268[label="",style="solid", color="blue", weight=3];
896[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 896[label="",style="solid", color="blue", weight=9];
896 -> 269[label="",style="solid", color="blue", weight=3];
897[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 897[label="",style="solid", color="blue", weight=9];
897 -> 270[label="",style="solid", color="blue", weight=3];
898[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 898[label="",style="solid", color="blue", weight=9];
898 -> 271[label="",style="solid", color="blue", weight=3];
899[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 899[label="",style="solid", color="blue", weight=9];
899 -> 272[label="",style="solid", color="blue", weight=3];
900[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 900[label="",style="solid", color="blue", weight=9];
900 -> 273[label="",style="solid", color="blue", weight=3];
901[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 901[label="",style="solid", color="blue", weight=9];
901 -> 274[label="",style="solid", color="blue", weight=3];
902[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 902[label="",style="solid", color="blue", weight=9];
902 -> 275[label="",style="solid", color="blue", weight=3];
903[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 903[label="",style="solid", color="blue", weight=9];
903 -> 276[label="",style="solid", color="blue", weight=3];
904[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 904[label="",style="solid", color="blue", weight=9];
904 -> 277[label="",style="solid", color="blue", weight=3];
905[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 905[label="",style="solid", color="blue", weight=9];
905 -> 278[label="",style="solid", color="blue", weight=3];
906[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];196 -> 906[label="",style="solid", color="blue", weight=9];
906 -> 279[label="",style="solid", color="blue", weight=3];
197 -> 304[label="",style="dashed", color="red", weight=0];
197[label="yu300 == yu40000 && yu301 == yu40001",fontsize=16,color="magenta"];197 -> 309[label="",style="dashed", color="magenta", weight=3];
197 -> 310[label="",style="dashed", color="magenta", weight=3];
198 -> 304[label="",style="dashed", color="red", weight=0];
198[label="yu300 == yu40000 && yu301 == yu40001",fontsize=16,color="magenta"];198 -> 311[label="",style="dashed", color="magenta", weight=3];
198 -> 312[label="",style="dashed", color="magenta", weight=3];
199[label="False",fontsize=16,color="green",shape="box"];200[label="False",fontsize=16,color="green",shape="box"];201[label="True",fontsize=16,color="green",shape="box"];202 -> 4[label="",style="dashed", color="red", weight=0];
202[label="lookup (Left yu11) yu14",fontsize=16,color="magenta"];202 -> 280[label="",style="dashed", color="magenta", weight=3];
202 -> 281[label="",style="dashed", color="magenta", weight=3];
203 -> 4[label="",style="dashed", color="red", weight=0];
203[label="lookup (Right yu22) yu25",fontsize=16,color="magenta"];203 -> 282[label="",style="dashed", color="magenta", weight=3];
203 -> 283[label="",style="dashed", color="magenta", weight=3];
204[label="primEqNat yu300 yu40000",fontsize=16,color="burlywood",shape="triangle"];907[label="yu300/Succ yu3000",fontsize=10,color="white",style="solid",shape="box"];204 -> 907[label="",style="solid", color="burlywood", weight=9];
907 -> 284[label="",style="solid", color="burlywood", weight=3];
908[label="yu300/Zero",fontsize=10,color="white",style="solid",shape="box"];204 -> 908[label="",style="solid", color="burlywood", weight=9];
908 -> 285[label="",style="solid", color="burlywood", weight=3];
205[label="primEqInt (Pos (Succ yu3000)) (Pos yu40000)",fontsize=16,color="burlywood",shape="box"];909[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];205 -> 909[label="",style="solid", color="burlywood", weight=9];
909 -> 286[label="",style="solid", color="burlywood", weight=3];
910[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];205 -> 910[label="",style="solid", color="burlywood", weight=9];
910 -> 287[label="",style="solid", color="burlywood", weight=3];
206[label="primEqInt (Pos (Succ yu3000)) (Neg yu40000)",fontsize=16,color="black",shape="box"];206 -> 288[label="",style="solid", color="black", weight=3];
207[label="primEqInt (Pos Zero) (Pos yu40000)",fontsize=16,color="burlywood",shape="box"];911[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];207 -> 911[label="",style="solid", color="burlywood", weight=9];
911 -> 289[label="",style="solid", color="burlywood", weight=3];
912[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];207 -> 912[label="",style="solid", color="burlywood", weight=9];
912 -> 290[label="",style="solid", color="burlywood", weight=3];
208[label="primEqInt (Pos Zero) (Neg yu40000)",fontsize=16,color="burlywood",shape="box"];913[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];208 -> 913[label="",style="solid", color="burlywood", weight=9];
913 -> 291[label="",style="solid", color="burlywood", weight=3];
914[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];208 -> 914[label="",style="solid", color="burlywood", weight=9];
914 -> 292[label="",style="solid", color="burlywood", weight=3];
209[label="primEqInt (Neg (Succ yu3000)) (Pos yu40000)",fontsize=16,color="black",shape="box"];209 -> 293[label="",style="solid", color="black", weight=3];
210[label="primEqInt (Neg (Succ yu3000)) (Neg yu40000)",fontsize=16,color="burlywood",shape="box"];915[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];210 -> 915[label="",style="solid", color="burlywood", weight=9];
915 -> 294[label="",style="solid", color="burlywood", weight=3];
916[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];210 -> 916[label="",style="solid", color="burlywood", weight=9];
916 -> 295[label="",style="solid", color="burlywood", weight=3];
211[label="primEqInt (Neg Zero) (Pos yu40000)",fontsize=16,color="burlywood",shape="box"];917[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];211 -> 917[label="",style="solid", color="burlywood", weight=9];
917 -> 296[label="",style="solid", color="burlywood", weight=3];
918[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];211 -> 918[label="",style="solid", color="burlywood", weight=9];
918 -> 297[label="",style="solid", color="burlywood", weight=3];
212[label="primEqInt (Neg Zero) (Neg yu40000)",fontsize=16,color="burlywood",shape="box"];919[label="yu40000/Succ yu400000",fontsize=10,color="white",style="solid",shape="box"];212 -> 919[label="",style="solid", color="burlywood", weight=9];
919 -> 298[label="",style="solid", color="burlywood", weight=3];
920[label="yu40000/Zero",fontsize=10,color="white",style="solid",shape="box"];212 -> 920[label="",style="solid", color="burlywood", weight=9];
920 -> 299[label="",style="solid", color="burlywood", weight=3];
213[label="yu300",fontsize=16,color="green",shape="box"];214[label="yu40000",fontsize=16,color="green",shape="box"];215 -> 39[label="",style="dashed", color="red", weight=0];
215[label="yu300 * yu40001 == yu301 * yu40000",fontsize=16,color="magenta"];215 -> 300[label="",style="dashed", color="magenta", weight=3];
215 -> 301[label="",style="dashed", color="magenta", weight=3];
305[label="yu301 == yu40001",fontsize=16,color="blue",shape="box"];921[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 921[label="",style="solid", color="blue", weight=9];
921 -> 317[label="",style="solid", color="blue", weight=3];
922[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];305 -> 922[label="",style="solid", color="blue", weight=9];
922 -> 318[label="",style="solid", color="blue", weight=3];
306[label="yu300 == yu40000",fontsize=16,color="blue",shape="box"];923[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];306 -> 923[label="",style="solid", color="blue", weight=9];
923 -> 319[label="",style="solid", color="blue", weight=3];
924[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];306 -> 924[label="",style="solid", color="blue", weight=9];
924 -> 320[label="",style="solid", color="blue", weight=3];
304[label="yu38 && yu39",fontsize=16,color="burlywood",shape="triangle"];925[label="yu38/False",fontsize=10,color="white",style="solid",shape="box"];304 -> 925[label="",style="solid", color="burlywood", weight=9];
925 -> 321[label="",style="solid", color="burlywood", weight=3];
926[label="yu38/True",fontsize=10,color="white",style="solid",shape="box"];304 -> 926[label="",style="solid", color="burlywood", weight=9];
926 -> 322[label="",style="solid", color="burlywood", weight=3];
307 -> 304[label="",style="dashed", color="red", weight=0];
307[label="yu301 == yu40001 && yu302 == yu40002",fontsize=16,color="magenta"];307 -> 323[label="",style="dashed", color="magenta", weight=3];
307 -> 324[label="",style="dashed", color="magenta", weight=3];
308[label="yu300 == yu40000",fontsize=16,color="blue",shape="box"];927[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 927[label="",style="solid", color="blue", weight=9];
927 -> 325[label="",style="solid", color="blue", weight=3];
928[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 928[label="",style="solid", color="blue", weight=9];
928 -> 326[label="",style="solid", color="blue", weight=3];
929[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 929[label="",style="solid", color="blue", weight=9];
929 -> 327[label="",style="solid", color="blue", weight=3];
930[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 930[label="",style="solid", color="blue", weight=9];
930 -> 328[label="",style="solid", color="blue", weight=3];
931[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 931[label="",style="solid", color="blue", weight=9];
931 -> 329[label="",style="solid", color="blue", weight=3];
932[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 932[label="",style="solid", color="blue", weight=9];
932 -> 330[label="",style="solid", color="blue", weight=3];
933[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 933[label="",style="solid", color="blue", weight=9];
933 -> 331[label="",style="solid", color="blue", weight=3];
934[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 934[label="",style="solid", color="blue", weight=9];
934 -> 332[label="",style="solid", color="blue", weight=3];
935[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 935[label="",style="solid", color="blue", weight=9];
935 -> 333[label="",style="solid", color="blue", weight=3];
936[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 936[label="",style="solid", color="blue", weight=9];
936 -> 334[label="",style="solid", color="blue", weight=3];
937[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 937[label="",style="solid", color="blue", weight=9];
937 -> 335[label="",style="solid", color="blue", weight=3];
938[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 938[label="",style="solid", color="blue", weight=9];
938 -> 336[label="",style="solid", color="blue", weight=3];
939[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 939[label="",style="solid", color="blue", weight=9];
939 -> 337[label="",style="solid", color="blue", weight=3];
940[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];308 -> 940[label="",style="solid", color="blue", weight=9];
940 -> 338[label="",style="solid", color="blue", weight=3];
237 -> 36[label="",style="dashed", color="red", weight=0];
237[label="yu300 == yu40000",fontsize=16,color="magenta"];237 -> 339[label="",style="dashed", color="magenta", weight=3];
237 -> 340[label="",style="dashed", color="magenta", weight=3];
238 -> 37[label="",style="dashed", color="red", weight=0];
238[label="yu300 == yu40000",fontsize=16,color="magenta"];238 -> 341[label="",style="dashed", color="magenta", weight=3];
238 -> 342[label="",style="dashed", color="magenta", weight=3];
239 -> 38[label="",style="dashed", color="red", weight=0];
239[label="yu300 == yu40000",fontsize=16,color="magenta"];239 -> 343[label="",style="dashed", color="magenta", weight=3];
239 -> 344[label="",style="dashed", color="magenta", weight=3];
240 -> 39[label="",style="dashed", color="red", weight=0];
240[label="yu300 == yu40000",fontsize=16,color="magenta"];240 -> 345[label="",style="dashed", color="magenta", weight=3];
240 -> 346[label="",style="dashed", color="magenta", weight=3];
241 -> 40[label="",style="dashed", color="red", weight=0];
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1018 -> 711[label="",style="solid", color="burlywood", weight=3];
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1019 -> 712[label="",style="solid", color="burlywood", weight=3];
1020[label="yu40001/Neg yu400010",fontsize=10,color="white",style="solid",shape="box"];651 -> 1020[label="",style="solid", color="burlywood", weight=9];
1020 -> 713[label="",style="solid", color="burlywood", weight=3];
652[label="yu302",fontsize=16,color="green",shape="box"];653[label="yu40002",fontsize=16,color="green",shape="box"];654[label="yu302",fontsize=16,color="green",shape="box"];655[label="yu40002",fontsize=16,color="green",shape="box"];656[label="yu302",fontsize=16,color="green",shape="box"];657[label="yu40002",fontsize=16,color="green",shape="box"];658[label="yu302",fontsize=16,color="green",shape="box"];659[label="yu40002",fontsize=16,color="green",shape="box"];660[label="yu302",fontsize=16,color="green",shape="box"];661[label="yu40002",fontsize=16,color="green",shape="box"];662[label="yu302",fontsize=16,color="green",shape="box"];663[label="yu40002",fontsize=16,color="green",shape="box"];664[label="yu302",fontsize=16,color="green",shape="box"];665[label="yu40002",fontsize=16,color="green",shape="box"];666[label="yu302",fontsize=16,color="green",shape="box"];667[label="yu40002",fontsize=16,color="green",shape="box"];668[label="yu302",fontsize=16,color="green",shape="box"];669[label="yu40002",fontsize=16,color="green",shape="box"];670[label="yu302",fontsize=16,color="green",shape="box"];671[label="yu40002",fontsize=16,color="green",shape="box"];672[label="yu302",fontsize=16,color="green",shape="box"];673[label="yu40002",fontsize=16,color="green",shape="box"];674[label="yu302",fontsize=16,color="green",shape="box"];675[label="yu40002",fontsize=16,color="green",shape="box"];676[label="yu302",fontsize=16,color="green",shape="box"];677[label="yu40002",fontsize=16,color="green",shape="box"];678[label="yu302",fontsize=16,color="green",shape="box"];679[label="yu40002",fontsize=16,color="green",shape="box"];680[label="yu301",fontsize=16,color="green",shape="box"];681[label="yu40001",fontsize=16,color="green",shape="box"];682[label="yu301",fontsize=16,color="green",shape="box"];683[label="yu40001",fontsize=16,color="green",shape="box"];684[label="yu301",fontsize=16,color="green",shape="box"];685[label="yu40001",fontsize=16,color="green",shape="box"];686[label="yu301",fontsize=16,color="green",shape="box"];687[label="yu40001",fontsize=16,color="green",shape="box"];688[label="yu301",fontsize=16,color="green",shape="box"];689[label="yu40001",fontsize=16,color="green",shape="box"];690[label="yu301",fontsize=16,color="green",shape="box"];691[label="yu40001",fontsize=16,color="green",shape="box"];692[label="yu301",fontsize=16,color="green",shape="box"];693[label="yu40001",fontsize=16,color="green",shape="box"];694[label="yu301",fontsize=16,color="green",shape="box"];695[label="yu40001",fontsize=16,color="green",shape="box"];696[label="yu301",fontsize=16,color="green",shape="box"];697[label="yu40001",fontsize=16,color="green",shape="box"];698[label="yu301",fontsize=16,color="green",shape="box"];699[label="yu40001",fontsize=16,color="green",shape="box"];700[label="yu301",fontsize=16,color="green",shape="box"];701[label="yu40001",fontsize=16,color="green",shape="box"];702[label="yu301",fontsize=16,color="green",shape="box"];703[label="yu40001",fontsize=16,color="green",shape="box"];704[label="yu301",fontsize=16,color="green",shape="box"];705[label="yu40001",fontsize=16,color="green",shape="box"];706[label="yu301",fontsize=16,color="green",shape="box"];707[label="yu40001",fontsize=16,color="green",shape="box"];708[label="yu400000",fontsize=16,color="green",shape="box"];709[label="yu3000",fontsize=16,color="green",shape="box"];710[label="primMulInt (Pos yu3000) (Pos yu400010)",fontsize=16,color="black",shape="box"];710 -> 714[label="",style="solid", color="black", weight=3];
711[label="primMulInt (Pos yu3000) (Neg yu400010)",fontsize=16,color="black",shape="box"];711 -> 715[label="",style="solid", color="black", weight=3];
712[label="primMulInt (Neg yu3000) (Pos yu400010)",fontsize=16,color="black",shape="box"];712 -> 716[label="",style="solid", color="black", weight=3];
713[label="primMulInt (Neg yu3000) (Neg yu400010)",fontsize=16,color="black",shape="box"];713 -> 717[label="",style="solid", color="black", weight=3];
714[label="Pos (primMulNat yu3000 yu400010)",fontsize=16,color="green",shape="box"];714 -> 718[label="",style="dashed", color="green", weight=3];
715[label="Neg (primMulNat yu3000 yu400010)",fontsize=16,color="green",shape="box"];715 -> 719[label="",style="dashed", color="green", weight=3];
716[label="Neg (primMulNat yu3000 yu400010)",fontsize=16,color="green",shape="box"];716 -> 720[label="",style="dashed", color="green", weight=3];
717[label="Pos (primMulNat yu3000 yu400010)",fontsize=16,color="green",shape="box"];717 -> 721[label="",style="dashed", color="green", weight=3];
718[label="primMulNat yu3000 yu400010",fontsize=16,color="burlywood",shape="triangle"];1021[label="yu3000/Succ yu30000",fontsize=10,color="white",style="solid",shape="box"];718 -> 1021[label="",style="solid", color="burlywood", weight=9];
1021 -> 722[label="",style="solid", color="burlywood", weight=3];
1022[label="yu3000/Zero",fontsize=10,color="white",style="solid",shape="box"];718 -> 1022[label="",style="solid", color="burlywood", weight=9];
1022 -> 723[label="",style="solid", color="burlywood", weight=3];
719 -> 718[label="",style="dashed", color="red", weight=0];
719[label="primMulNat yu3000 yu400010",fontsize=16,color="magenta"];719 -> 724[label="",style="dashed", color="magenta", weight=3];
720 -> 718[label="",style="dashed", color="red", weight=0];
720[label="primMulNat yu3000 yu400010",fontsize=16,color="magenta"];720 -> 725[label="",style="dashed", color="magenta", weight=3];
721 -> 718[label="",style="dashed", color="red", weight=0];
721[label="primMulNat yu3000 yu400010",fontsize=16,color="magenta"];721 -> 726[label="",style="dashed", color="magenta", weight=3];
721 -> 727[label="",style="dashed", color="magenta", weight=3];
722[label="primMulNat (Succ yu30000) yu400010",fontsize=16,color="burlywood",shape="box"];1023[label="yu400010/Succ yu4000100",fontsize=10,color="white",style="solid",shape="box"];722 -> 1023[label="",style="solid", color="burlywood", weight=9];
1023 -> 728[label="",style="solid", color="burlywood", weight=3];
1024[label="yu400010/Zero",fontsize=10,color="white",style="solid",shape="box"];722 -> 1024[label="",style="solid", color="burlywood", weight=9];
1024 -> 729[label="",style="solid", color="burlywood", weight=3];
723[label="primMulNat Zero yu400010",fontsize=16,color="burlywood",shape="box"];1025[label="yu400010/Succ yu4000100",fontsize=10,color="white",style="solid",shape="box"];723 -> 1025[label="",style="solid", color="burlywood", weight=9];
1025 -> 730[label="",style="solid", color="burlywood", weight=3];
1026[label="yu400010/Zero",fontsize=10,color="white",style="solid",shape="box"];723 -> 1026[label="",style="solid", color="burlywood", weight=9];
1026 -> 731[label="",style="solid", color="burlywood", weight=3];
724[label="yu400010",fontsize=16,color="green",shape="box"];725[label="yu3000",fontsize=16,color="green",shape="box"];726[label="yu3000",fontsize=16,color="green",shape="box"];727[label="yu400010",fontsize=16,color="green",shape="box"];728[label="primMulNat (Succ yu30000) (Succ yu4000100)",fontsize=16,color="black",shape="box"];728 -> 732[label="",style="solid", color="black", weight=3];
729[label="primMulNat (Succ yu30000) Zero",fontsize=16,color="black",shape="box"];729 -> 733[label="",style="solid", color="black", weight=3];
730[label="primMulNat Zero (Succ yu4000100)",fontsize=16,color="black",shape="box"];730 -> 734[label="",style="solid", color="black", weight=3];
731[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];731 -> 735[label="",style="solid", color="black", weight=3];
732 -> 736[label="",style="dashed", color="red", weight=0];
732[label="primPlusNat (primMulNat yu30000 (Succ yu4000100)) (Succ yu4000100)",fontsize=16,color="magenta"];732 -> 737[label="",style="dashed", color="magenta", weight=3];
733[label="Zero",fontsize=16,color="green",shape="box"];734[label="Zero",fontsize=16,color="green",shape="box"];735[label="Zero",fontsize=16,color="green",shape="box"];737 -> 718[label="",style="dashed", color="red", weight=0];
737[label="primMulNat yu30000 (Succ yu4000100)",fontsize=16,color="magenta"];737 -> 738[label="",style="dashed", color="magenta", weight=3];
737 -> 739[label="",style="dashed", color="magenta", weight=3];
736[label="primPlusNat yu40 (Succ yu4000100)",fontsize=16,color="burlywood",shape="triangle"];1027[label="yu40/Succ yu400",fontsize=10,color="white",style="solid",shape="box"];736 -> 1027[label="",style="solid", color="burlywood", weight=9];
1027 -> 740[label="",style="solid", color="burlywood", weight=3];
1028[label="yu40/Zero",fontsize=10,color="white",style="solid",shape="box"];736 -> 1028[label="",style="solid", color="burlywood", weight=9];
1028 -> 741[label="",style="solid", color="burlywood", weight=3];
738[label="yu30000",fontsize=16,color="green",shape="box"];739[label="Succ yu4000100",fontsize=16,color="green",shape="box"];740[label="primPlusNat (Succ yu400) (Succ yu4000100)",fontsize=16,color="black",shape="box"];740 -> 742[label="",style="solid", color="black", weight=3];
741[label="primPlusNat Zero (Succ yu4000100)",fontsize=16,color="black",shape="box"];741 -> 743[label="",style="solid", color="black", weight=3];
742[label="Succ (Succ (primPlusNat yu400 yu4000100))",fontsize=16,color="green",shape="box"];742 -> 744[label="",style="dashed", color="green", weight=3];
743[label="Succ yu4000100",fontsize=16,color="green",shape="box"];744[label="primPlusNat yu400 yu4000100",fontsize=16,color="burlywood",shape="triangle"];1029[label="yu400/Succ yu4000",fontsize=10,color="white",style="solid",shape="box"];744 -> 1029[label="",style="solid", color="burlywood", weight=9];
1029 -> 745[label="",style="solid", color="burlywood", weight=3];
1030[label="yu400/Zero",fontsize=10,color="white",style="solid",shape="box"];744 -> 1030[label="",style="solid", color="burlywood", weight=9];
1030 -> 746[label="",style="solid", color="burlywood", weight=3];
745[label="primPlusNat (Succ yu4000) yu4000100",fontsize=16,color="burlywood",shape="box"];1031[label="yu4000100/Succ yu40001000",fontsize=10,color="white",style="solid",shape="box"];745 -> 1031[label="",style="solid", color="burlywood", weight=9];
1031 -> 747[label="",style="solid", color="burlywood", weight=3];
1032[label="yu4000100/Zero",fontsize=10,color="white",style="solid",shape="box"];745 -> 1032[label="",style="solid", color="burlywood", weight=9];
1032 -> 748[label="",style="solid", color="burlywood", weight=3];
746[label="primPlusNat Zero yu4000100",fontsize=16,color="burlywood",shape="box"];1033[label="yu4000100/Succ yu40001000",fontsize=10,color="white",style="solid",shape="box"];746 -> 1033[label="",style="solid", color="burlywood", weight=9];
1033 -> 749[label="",style="solid", color="burlywood", weight=3];
1034[label="yu4000100/Zero",fontsize=10,color="white",style="solid",shape="box"];746 -> 1034[label="",style="solid", color="burlywood", weight=9];
1034 -> 750[label="",style="solid", color="burlywood", weight=3];
747[label="primPlusNat (Succ yu4000) (Succ yu40001000)",fontsize=16,color="black",shape="box"];747 -> 751[label="",style="solid", color="black", weight=3];
748[label="primPlusNat (Succ yu4000) Zero",fontsize=16,color="black",shape="box"];748 -> 752[label="",style="solid", color="black", weight=3];
749[label="primPlusNat Zero (Succ yu40001000)",fontsize=16,color="black",shape="box"];749 -> 753[label="",style="solid", color="black", weight=3];
750[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];750 -> 754[label="",style="solid", color="black", weight=3];
751[label="Succ (Succ (primPlusNat yu4000 yu40001000))",fontsize=16,color="green",shape="box"];751 -> 755[label="",style="dashed", color="green", weight=3];
752[label="Succ yu4000",fontsize=16,color="green",shape="box"];753[label="Succ yu40001000",fontsize=16,color="green",shape="box"];754[label="Zero",fontsize=16,color="green",shape="box"];755 -> 744[label="",style="dashed", color="red", weight=0];
755[label="primPlusNat yu4000 yu40001000",fontsize=16,color="magenta"];755 -> 756[label="",style="dashed", color="magenta", weight=3];
755 -> 757[label="",style="dashed", color="magenta", weight=3];
756[label="yu40001000",fontsize=16,color="green",shape="box"];757[label="yu4000",fontsize=16,color="green",shape="box"];}

----------------------------------------

(6)
Complex Obligation (AND)

----------------------------------------

(7)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(app(ty_@2, dc), dd), cf) -> new_esEs2(yu301, yu40001, dc, dd)
   new_esEs1(Left(yu300), Left(yu40000), app(app(ty_Either, gf), gg), gd) -> new_esEs1(yu300, yu40000, gf, gg)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(app(ty_@2, bh), ca)) -> new_esEs2(yu302, yu40002, bh, ca)
   new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_Either, bdf), bdg)) -> new_esEs1(yu300, yu40000, bdf, bdg)
   new_esEs1(Left(yu300), Left(yu40000), app(ty_[], hb), gd) -> new_esEs3(yu300, yu40000, hb)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(app(app(ty_@3, bb), bc), bd)) -> new_esEs(yu302, yu40002, bb, bc, bd)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(ty_[], cb)) -> new_esEs3(yu302, yu40002, cb)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(app(ty_@2, bbd), bbe)) -> new_esEs2(yu301, yu40001, bbd, bbe)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, bbg), bbh), bca), bcb) -> new_esEs(yu300, yu40000, bbg, bbh, bca)
   new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_[], beb)) -> new_esEs3(yu300, yu40000, beb)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(ty_[], de), cf) -> new_esEs3(yu301, yu40001, de)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, ea), ba, cf) -> new_esEs0(yu300, yu40000, ea)
   new_esEs0(Just(yu300), Just(yu40000), app(ty_[], fh)) -> new_esEs3(yu300, yu40000, fh)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], ef), ba, cf) -> new_esEs3(yu300, yu40000, ef)
   new_esEs0(Just(yu300), Just(yu40000), app(app(ty_@2, ff), fg)) -> new_esEs2(yu300, yu40000, ff, fg)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, bcc), bcb) -> new_esEs0(yu300, yu40000, bcc)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(ty_Maybe, cg), cf) -> new_esEs0(yu301, yu40001, cg)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, bcf), bcg), bcb) -> new_esEs2(yu300, yu40000, bcf, bcg)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(app(app(ty_@3, cc), cd), ce), cf) -> new_esEs(yu301, yu40001, cc, cd, ce)
   new_esEs1(Right(yu300), Right(yu40000), hc, app(app(ty_@2, bab), bac)) -> new_esEs2(yu300, yu40000, bab, bac)
   new_esEs1(Left(yu300), Left(yu40000), app(app(app(ty_@3, ga), gb), gc), gd) -> new_esEs(yu300, yu40000, ga, gb, gc)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(ty_Maybe, be)) -> new_esEs0(yu302, yu40002, be)
   new_esEs1(Right(yu300), Right(yu40000), hc, app(ty_Maybe, hg)) -> new_esEs0(yu300, yu40000, hg)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, ed), ee), ba, cf) -> new_esEs2(yu300, yu40000, ed, ee)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(app(ty_Either, da), db), cf) -> new_esEs1(yu301, yu40001, da, db)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(app(ty_Either, bf), bg)) -> new_esEs1(yu302, yu40002, bf, bg)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs(yu301, yu40001, baf, bag, bah)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, eb), ec), ba, cf) -> new_esEs1(yu300, yu40000, eb, ec)
   new_esEs3(:(yu300, yu301), :(yu40000, yu40001), bda) -> new_esEs3(yu301, yu40001, bda)
   new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(app(ty_@3, bdb), bdc), bdd)) -> new_esEs(yu300, yu40000, bdb, bdc, bdd)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(ty_Maybe, bba)) -> new_esEs0(yu301, yu40001, bba)
   new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, df), dg), dh), ba, cf) -> new_esEs(yu300, yu40000, df, dg, dh)
   new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_Maybe, bde)) -> new_esEs0(yu300, yu40000, bde)
   new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_@2, bdh), bea)) -> new_esEs2(yu300, yu40000, bdh, bea)
   new_esEs1(Left(yu300), Left(yu40000), app(app(ty_@2, gh), ha), gd) -> new_esEs2(yu300, yu40000, gh, ha)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(ty_[], bbf)) -> new_esEs3(yu301, yu40001, bbf)
   new_esEs0(Just(yu300), Just(yu40000), app(app(ty_Either, fc), fd)) -> new_esEs1(yu300, yu40000, fc, fd)
   new_esEs1(Right(yu300), Right(yu40000), hc, app(ty_[], bad)) -> new_esEs3(yu300, yu40000, bad)
   new_esEs1(Right(yu300), Right(yu40000), hc, app(app(app(ty_@3, hd), he), hf)) -> new_esEs(yu300, yu40000, hd, he, hf)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], bch), bcb) -> new_esEs3(yu300, yu40000, bch)
   new_esEs0(Just(yu300), Just(yu40000), app(ty_Maybe, fb)) -> new_esEs0(yu300, yu40000, fb)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, bcd), bce), bcb) -> new_esEs1(yu300, yu40000, bcd, bce)
   new_esEs1(Left(yu300), Left(yu40000), app(ty_Maybe, ge), gd) -> new_esEs0(yu300, yu40000, ge)
   new_esEs1(Right(yu300), Right(yu40000), hc, app(app(ty_Either, hh), baa)) -> new_esEs1(yu300, yu40000, hh, baa)
   new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(app(ty_Either, bbb), bbc)) -> new_esEs1(yu301, yu40001, bbb, bbc)
   new_esEs0(Just(yu300), Just(yu40000), app(app(app(ty_@3, eg), eh), fa)) -> new_esEs(yu300, yu40000, eg, eh, fa)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(8) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(app(ty_@3, bdb), bdc), bdd)) -> new_esEs(yu300, yu40000, bdb, bdc, bdd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5


*new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_Either, bdf), bdg)) -> new_esEs1(yu300, yu40000, bdf, bdg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs0(Just(yu300), Just(yu40000), app(app(app(ty_@3, eg), eh), fa)) -> new_esEs(yu300, yu40000, eg, eh, fa)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5


*new_esEs0(Just(yu300), Just(yu40000), app(app(ty_Either, fc), fd)) -> new_esEs1(yu300, yu40000, fc, fd)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs0(Just(yu300), Just(yu40000), app(ty_[], fh)) -> new_esEs3(yu300, yu40000, fh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(app(ty_@2, bdh), bea)) -> new_esEs2(yu300, yu40000, bdh, bea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_Maybe, bde)) -> new_esEs0(yu300, yu40000, bde)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs0(Just(yu300), Just(yu40000), app(app(ty_@2, ff), fg)) -> new_esEs2(yu300, yu40000, ff, fg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs0(Just(yu300), Just(yu40000), app(ty_Maybe, fb)) -> new_esEs0(yu300, yu40000, fb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(app(app(ty_@3, bbg), bbh), bca), bcb) -> new_esEs(yu300, yu40000, bbg, bbh, bca)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs(yu301, yu40001, baf, bag, bah)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_Either, bcd), bce), bcb) -> new_esEs1(yu300, yu40000, bcd, bce)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(app(ty_Either, bbb), bbc)) -> new_esEs1(yu301, yu40001, bbb, bbc)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(ty_[], bbf)) -> new_esEs3(yu301, yu40001, bbf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_[], bch), bcb) -> new_esEs3(yu300, yu40000, bch)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(app(ty_@2, bbd), bbe)) -> new_esEs2(yu301, yu40001, bbd, bbe)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(app(ty_@2, bcf), bcg), bcb) -> new_esEs2(yu300, yu40000, bcf, bcg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), app(ty_Maybe, bcc), bcb) -> new_esEs0(yu300, yu40000, bcc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs2(@2(yu300, yu301), @2(yu40000, yu40001), bae, app(ty_Maybe, bba)) -> new_esEs0(yu301, yu40001, bba)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3


*new_esEs1(Left(yu300), Left(yu40000), app(app(app(ty_@3, ga), gb), gc), gd) -> new_esEs(yu300, yu40000, ga, gb, gc)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5


*new_esEs1(Right(yu300), Right(yu40000), hc, app(app(app(ty_@3, hd), he), hf)) -> new_esEs(yu300, yu40000, hd, he, hf)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(app(app(ty_@3, bb), bc), bd)) -> new_esEs(yu302, yu40002, bb, bc, bd)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4, 5 > 5


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(app(app(ty_@3, cc), cd), ce), cf) -> new_esEs(yu301, yu40001, cc, cd, ce)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4, 4 > 5


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(app(ty_@3, df), dg), dh), ba, cf) -> new_esEs(yu300, yu40000, df, dg, dh)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4, 3 > 5


*new_esEs1(Left(yu300), Left(yu40000), app(app(ty_Either, gf), gg), gd) -> new_esEs1(yu300, yu40000, gf, gg)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs1(Right(yu300), Right(yu40000), hc, app(app(ty_Either, hh), baa)) -> new_esEs1(yu300, yu40000, hh, baa)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4


*new_esEs1(Left(yu300), Left(yu40000), app(ty_[], hb), gd) -> new_esEs3(yu300, yu40000, hb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs1(Right(yu300), Right(yu40000), hc, app(ty_[], bad)) -> new_esEs3(yu300, yu40000, bad)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3


*new_esEs1(Right(yu300), Right(yu40000), hc, app(app(ty_@2, bab), bac)) -> new_esEs2(yu300, yu40000, bab, bac)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4


*new_esEs1(Left(yu300), Left(yu40000), app(app(ty_@2, gh), ha), gd) -> new_esEs2(yu300, yu40000, gh, ha)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs1(Right(yu300), Right(yu40000), hc, app(ty_Maybe, hg)) -> new_esEs0(yu300, yu40000, hg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3


*new_esEs1(Left(yu300), Left(yu40000), app(ty_Maybe, ge), gd) -> new_esEs0(yu300, yu40000, ge)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(app(ty_Either, da), db), cf) -> new_esEs1(yu301, yu40001, da, db)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(app(ty_Either, bf), bg)) -> new_esEs1(yu302, yu40002, bf, bg)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_Either, eb), ec), ba, cf) -> new_esEs1(yu300, yu40000, eb, ec)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs3(:(yu300, yu301), :(yu40000, yu40001), app(ty_[], beb)) -> new_esEs3(yu300, yu40000, beb)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs3(:(yu300, yu301), :(yu40000, yu40001), bda) -> new_esEs3(yu301, yu40001, bda)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(ty_[], cb)) -> new_esEs3(yu302, yu40002, cb)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(ty_[], de), cf) -> new_esEs3(yu301, yu40001, de)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_[], ef), ba, cf) -> new_esEs3(yu300, yu40000, ef)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(app(ty_@2, dc), dd), cf) -> new_esEs2(yu301, yu40001, dc, dd)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3, 4 > 4


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(app(ty_@2, bh), ca)) -> new_esEs2(yu302, yu40002, bh, ca)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3, 5 > 4


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(app(ty_@2, ed), ee), ba, cf) -> new_esEs2(yu300, yu40000, ed, ee)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3, 3 > 4


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), app(ty_Maybe, ea), ba, cf) -> new_esEs0(yu300, yu40000, ea)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, app(ty_Maybe, cg), cf) -> new_esEs0(yu301, yu40001, cg)
The graph contains the following edges 1 > 1, 2 > 2, 4 > 3


*new_esEs(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), h, ba, app(ty_Maybe, be)) -> new_esEs0(yu302, yu40002, be)
The graph contains the following edges 1 > 1, 2 > 2, 5 > 3


----------------------------------------

(9)
YES

----------------------------------------

(10)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bc, bd, be) -> new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, bd), bc, bd, be)
   new_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bc, bd, be) -> new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, be), bc, bd, be)
   new_lookup10(yu22, yu23, yu24, yu25, False, bf, bg, bh) -> new_lookup(Right(yu22), yu25, bf, bg, bh)
   new_lookup1(yu11, yu12, yu13, yu14, False, h, ba, bb) -> new_lookup(Left(yu11), yu14, h, ba, bb)
   new_lookup(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bc, bd, be) -> new_lookup(Left(yu30), yu41, bc, bd, be)
   new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bc, bd, be) -> new_lookup(Right(yu30), yu41, bc, bd, be)

The TRS R consists of the following rules:

   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Float) -> new_esEs11(yu300, yu40000)
   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
   new_esEs26(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_esEs27(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Double, dd) -> new_esEs16(yu300, yu40000)
   new_esEs4(yu30, yu4000, ty_Float) -> new_esEs11(yu30, yu4000)
   new_esEs5(yu30, yu4000, app(ty_Maybe, ce)) -> new_esEs15(yu30, yu4000, ce)
   new_esEs24(yu301, yu40001, app(ty_Maybe, beg)) -> new_esEs15(yu301, yu40001, beg)
   new_esEs15(Just(yu300), Just(yu40000), app(app(ty_Either, bhd), bhe)) -> new_esEs17(yu300, yu40000, bhd, bhe)
   new_esEs18(@2(yu300, yu301), @2(yu40000, yu40001), gh, ha) -> new_asAs(new_esEs25(yu300, yu40000, gh), new_esEs24(yu301, yu40001, ha))
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(ty_@2, fh), ga)) -> new_esEs18(yu300, yu40000, fh, ga)
   new_esEs20(yu302, yu40002, ty_Ordering) -> new_esEs12(yu302, yu40002)
   new_esEs16(Double(yu300, yu301), Double(yu40000, yu40001)) -> new_esEs9(new_sr(yu300, yu40001), new_sr(yu301, yu40000))
   new_esEs6(False, True) -> False
   new_esEs6(True, False) -> False
   new_esEs24(yu301, yu40001, app(ty_[], bfd)) -> new_esEs19(yu301, yu40001, bfd)
   new_esEs19(:(yu300, yu301), [], hb) -> False
   new_esEs19([], :(yu40000, yu40001), hb) -> False
   new_esEs24(yu301, yu40001, ty_@0) -> new_esEs7(yu301, yu40001)
   new_esEs9(yu30, yu4000) -> new_primEqInt(yu30, yu4000)
   new_esEs21(yu301, yu40001, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs14(yu301, yu40001, baf, bag, bah)
   new_esEs5(yu30, yu4000, ty_Integer) -> new_esEs10(yu30, yu4000)
   new_esEs20(yu302, yu40002, ty_Bool) -> new_esEs6(yu302, yu40002)
   new_esEs21(yu301, yu40001, app(app(ty_Either, bbb), bbc)) -> new_esEs17(yu301, yu40001, bbb, bbc)
   new_esEs23(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Float, dd) -> new_esEs11(yu300, yu40000)
   new_esEs22(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs4(yu30, yu4000, app(app(app(ty_@3, gd), ge), gf)) -> new_esEs14(yu30, yu4000, gd, ge, gf)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs20(yu302, yu40002, app(ty_Ratio, hc)) -> new_esEs13(yu302, yu40002, hc)
   new_esEs15(Just(yu300), Just(yu40000), app(app(app(ty_@3, bgh), bha), bhb)) -> new_esEs14(yu300, yu40000, bgh, bha, bhb)
   new_esEs20(yu302, yu40002, ty_Int) -> new_esEs9(yu302, yu40002)
   new_esEs25(yu300, yu40000, app(ty_Ratio, bfe)) -> new_esEs13(yu300, yu40000, bfe)
   new_esEs12(GT, GT) -> True
   new_esEs19(:(yu300, yu301), :(yu40000, yu40001), hb) -> new_asAs(new_esEs23(yu300, yu40000, hb), new_esEs19(yu301, yu40001, hb))
   new_esEs25(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_asAs(True, yu39) -> yu39
   new_esEs15(Just(yu300), Just(yu40000), ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs10(Integer(yu300), Integer(yu40000)) -> new_primEqInt(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(ty_[], dc)) -> new_esEs19(yu30, yu4000, dc)
   new_esEs17(Left(yu300), Left(yu40000), app(ty_Maybe, ea), dd) -> new_esEs15(yu300, yu40000, ea)
   new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) -> False
   new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) -> False
   new_esEs5(yu30, yu4000, app(app(ty_@2, da), db)) -> new_esEs18(yu30, yu4000, da, db)
   new_esEs4(yu30, yu4000, app(ty_Ratio, gc)) -> new_esEs13(yu30, yu4000, gc)
   new_esEs21(yu301, yu40001, ty_Double) -> new_esEs16(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(app(ty_Either, bdf), bdg)) -> new_esEs17(yu300, yu40000, bdf, bdg)
   new_esEs20(yu302, yu40002, ty_Char) -> new_esEs8(yu302, yu40002)
   new_esEs4(yu30, yu4000, ty_Int) -> new_esEs9(yu30, yu4000)
   new_primEqNat0(Succ(yu3000), Succ(yu400000)) -> new_primEqNat0(yu3000, yu400000)
   new_esEs5(yu30, yu4000, ty_Bool) -> new_esEs6(yu30, yu4000)
   new_esEs22(yu300, yu40000, app(ty_Ratio, bbg)) -> new_esEs13(yu300, yu40000, bbg)
   new_esEs23(yu300, yu40000, app(app(app(ty_@3, bdb), bdc), bdd)) -> new_esEs14(yu300, yu40000, bdb, bdc, bdd)
   new_esEs5(yu30, yu4000, ty_@0) -> new_esEs7(yu30, yu4000)
   new_esEs17(Left(yu300), Left(yu40000), app(ty_[], ef), dd) -> new_esEs19(yu300, yu40000, ef)
   new_esEs12(EQ, EQ) -> True
   new_esEs17(Left(yu300), Left(yu40000), app(app(app(ty_@3, df), dg), dh), dd) -> new_esEs14(yu300, yu40000, df, dg, dh)
   new_esEs23(yu300, yu40000, app(app(ty_@2, bdh), bea)) -> new_esEs18(yu300, yu40000, bdh, bea)
   new_esEs17(Left(yu300), Left(yu40000), ty_Int, dd) -> new_esEs9(yu300, yu40000)
   new_esEs15(Nothing, Just(yu40000), gg) -> False
   new_esEs15(Just(yu300), Nothing, gg) -> False
   new_primMulNat0(Zero, Zero) -> Zero
   new_esEs20(yu302, yu40002, app(ty_Maybe, hg)) -> new_esEs15(yu302, yu40002, hg)
   new_esEs15(Nothing, Nothing, gg) -> True
   new_esEs22(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs21(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_[], gb)) -> new_esEs19(yu300, yu40000, gb)
   new_esEs21(yu301, yu40001, ty_@0) -> new_esEs7(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(ty_Ratio, bda)) -> new_esEs13(yu300, yu40000, bda)
   new_esEs20(yu302, yu40002, ty_Float) -> new_esEs11(yu302, yu40002)
   new_esEs24(yu301, yu40001, app(app(ty_@2, bfb), bfc)) -> new_esEs18(yu301, yu40001, bfb, bfc)
   new_esEs12(LT, LT) -> True
   new_esEs4(yu30, yu4000, ty_Ordering) -> new_esEs12(yu30, yu4000)
   new_primEqNat0(Succ(yu3000), Zero) -> False
   new_primEqNat0(Zero, Succ(yu400000)) -> False
   new_esEs24(yu301, yu40001, ty_Bool) -> new_esEs6(yu301, yu40001)
   new_esEs21(yu301, yu40001, ty_Float) -> new_esEs11(yu301, yu40001)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs23(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs24(yu301, yu40001, app(ty_Ratio, bec)) -> new_esEs13(yu301, yu40001, bec)
   new_esEs25(yu300, yu40000, app(app(app(ty_@3, bff), bfg), bfh)) -> new_esEs14(yu300, yu40000, bff, bfg, bfh)
   new_esEs25(yu300, yu40000, app(app(ty_@2, bgd), bge)) -> new_esEs18(yu300, yu40000, bgd, bge)
   new_esEs15(Just(yu300), Just(yu40000), app(app(ty_@2, bhf), bhg)) -> new_esEs18(yu300, yu40000, bhf, bhg)
   new_esEs5(yu30, yu4000, ty_Int) -> new_esEs9(yu30, yu4000)
   new_esEs5(yu30, yu4000, app(ty_Ratio, ca)) -> new_esEs13(yu30, yu4000, ca)
   new_esEs7(@0, @0) -> True
   new_esEs4(yu30, yu4000, app(app(ty_Either, eg), dd)) -> new_esEs17(yu30, yu4000, eg, dd)
   new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) -> False
   new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) -> False
   new_esEs24(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs24(yu301, yu40001, app(app(app(ty_@3, bed), bee), bef)) -> new_esEs14(yu301, yu40001, bed, bee, bef)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_Maybe, bhc)) -> new_esEs15(yu300, yu40000, bhc)
   new_esEs22(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) -> new_primEqNat0(yu3000, yu400000)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Left(yu300), Right(yu40000), eg, dd) -> False
   new_esEs17(Right(yu300), Left(yu40000), eg, dd) -> False
   new_esEs4(yu30, yu4000, ty_@0) -> new_esEs7(yu30, yu4000)
   new_sr(Pos(yu3000), Neg(yu400010)) -> Neg(new_primMulNat0(yu3000, yu400010))
   new_sr(Neg(yu3000), Pos(yu400010)) -> Neg(new_primMulNat0(yu3000, yu400010))
   new_esEs22(yu300, yu40000, app(ty_[], bch)) -> new_esEs19(yu300, yu40000, bch)
   new_esEs4(yu30, yu4000, app(ty_[], hb)) -> new_esEs19(yu30, yu4000, hb)
   new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) -> Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
   new_esEs4(yu30, yu4000, ty_Double) -> new_esEs16(yu30, yu4000)
   new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) -> False
   new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) -> False
   new_esEs22(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs27(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs12(EQ, GT) -> False
   new_esEs12(GT, EQ) -> False
   new_esEs14(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), gd, ge, gf) -> new_asAs(new_esEs22(yu300, yu40000, gd), new_asAs(new_esEs21(yu301, yu40001, ge), new_esEs20(yu302, yu40002, gf)))
   new_esEs17(Left(yu300), Left(yu40000), app(ty_Ratio, de), dd) -> new_esEs13(yu300, yu40000, de)
   new_esEs22(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs22(yu300, yu40000, app(app(ty_Either, bcd), bce)) -> new_esEs17(yu300, yu40000, bcd, bce)
   new_esEs21(yu301, yu40001, ty_Bool) -> new_esEs6(yu301, yu40001)
   new_esEs22(yu300, yu40000, app(app(app(ty_@3, bbh), bca), bcb)) -> new_esEs14(yu300, yu40000, bbh, bca, bcb)
   new_esEs25(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs21(yu301, yu40001, ty_Char) -> new_esEs8(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(ty_[], beb)) -> new_esEs19(yu300, yu40000, beb)
   new_esEs24(yu301, yu40001, ty_Float) -> new_esEs11(yu301, yu40001)
   new_esEs19([], [], hb) -> True
   new_esEs25(yu300, yu40000, app(ty_Maybe, bga)) -> new_esEs15(yu300, yu40000, bga)
   new_esEs15(Just(yu300), Just(yu40000), ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_Ratio, eh)) -> new_esEs13(yu300, yu40000, eh)
   new_sr(Neg(yu3000), Neg(yu400010)) -> Pos(new_primMulNat0(yu3000, yu400010))
   new_esEs15(Just(yu300), Just(yu40000), ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs15(Just(yu300), Just(yu40000), ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs23(yu300, yu40000, app(ty_Maybe, bde)) -> new_esEs15(yu300, yu40000, bde)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Bool, dd) -> new_esEs6(yu300, yu40000)
   new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) -> False
   new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) -> False
   new_esEs12(LT, EQ) -> False
   new_esEs12(EQ, LT) -> False
   new_esEs21(yu301, yu40001, ty_Ordering) -> new_esEs12(yu301, yu40001)
   new_esEs6(True, True) -> True
   new_esEs4(yu30, yu4000, ty_Char) -> new_esEs8(yu30, yu4000)
   new_esEs4(yu30, yu4000, ty_Integer) -> new_esEs10(yu30, yu4000)
   new_esEs20(yu302, yu40002, app(app(app(ty_@3, hd), he), hf)) -> new_esEs14(yu302, yu40002, hd, he, hf)
   new_esEs17(Left(yu300), Left(yu40000), app(app(ty_@2, ed), ee), dd) -> new_esEs18(yu300, yu40000, ed, ee)
   new_esEs17(Left(yu300), Left(yu40000), ty_Ordering, dd) -> new_esEs12(yu300, yu40000)
   new_esEs20(yu302, yu40002, app(app(ty_Either, hh), baa)) -> new_esEs17(yu302, yu40002, hh, baa)
   new_esEs22(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs24(yu301, yu40001, ty_Double) -> new_esEs16(yu301, yu40001)
   new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) -> new_primEqNat0(yu3000, yu400000)
   new_esEs23(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Double) -> new_esEs16(yu30, yu4000)
   new_esEs23(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs12(LT, GT) -> False
   new_esEs12(GT, LT) -> False
   new_esEs20(yu302, yu40002, app(app(ty_@2, bab), bac)) -> new_esEs18(yu302, yu40002, bab, bac)
   new_esEs21(yu301, yu40001, app(ty_[], bbf)) -> new_esEs19(yu301, yu40001, bbf)
   new_primPlusNat0(Succ(yu400), yu4000100) -> Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
   new_esEs17(Left(yu300), Left(yu40000), ty_@0, dd) -> new_esEs7(yu300, yu40000)
   new_esEs6(False, False) -> True
   new_esEs23(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(app(app(ty_@3, cb), cc), cd)) -> new_esEs14(yu30, yu4000, cb, cc, cd)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_Ratio, bgg)) -> new_esEs13(yu300, yu40000, bgg)
   new_esEs17(Left(yu300), Left(yu40000), app(app(ty_Either, eb), ec), dd) -> new_esEs17(yu300, yu40000, eb, ec)
   new_esEs21(yu301, yu40001, app(ty_Maybe, bba)) -> new_esEs15(yu301, yu40001, bba)
   new_esEs15(Just(yu300), Just(yu40000), ty_Int) -> new_esEs9(yu300, yu40000)
   new_primPlusNat1(Zero, Zero) -> Zero
   new_esEs23(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_primMulNat0(Succ(yu30000), Zero) -> Zero
   new_primMulNat0(Zero, Succ(yu4000100)) -> Zero
   new_sr(Pos(yu3000), Pos(yu400010)) -> Pos(new_primMulNat0(yu3000, yu400010))
   new_esEs20(yu302, yu40002, ty_Integer) -> new_esEs10(yu302, yu40002)
   new_primPlusNat0(Zero, yu4000100) -> Succ(yu4000100)
   new_esEs23(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(app(ty_Either, cf), cg)) -> new_esEs17(yu30, yu4000, cf, cg)
   new_esEs15(Just(yu300), Just(yu40000), ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Ordering) -> new_esEs12(yu30, yu4000)
   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
   new_esEs22(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_primMulNat0(Succ(yu30000), Succ(yu4000100)) -> new_primPlusNat0(new_primMulNat0(yu30000, Succ(yu4000100)), yu4000100)
   new_esEs24(yu301, yu40001, ty_Ordering) -> new_esEs12(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Char) -> new_esEs8(yu30, yu4000)
   new_esEs22(yu300, yu40000, app(app(ty_@2, bcf), bcg)) -> new_esEs18(yu300, yu40000, bcf, bcg)
   new_primPlusNat1(Succ(yu4000), Zero) -> Succ(yu4000)
   new_primPlusNat1(Zero, Succ(yu40001000)) -> Succ(yu40001000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Integer, dd) -> new_esEs10(yu300, yu40000)
   new_esEs11(Float(yu300, yu301), Float(yu40000, yu40001)) -> new_esEs9(new_sr(yu300, yu40001), new_sr(yu301, yu40000))
   new_esEs4(yu30, yu4000, app(app(ty_@2, gh), ha)) -> new_esEs18(yu30, yu4000, gh, ha)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(ty_Either, ff), fg)) -> new_esEs17(yu300, yu40000, ff, fg)
   new_esEs20(yu302, yu40002, app(ty_[], bad)) -> new_esEs19(yu302, yu40002, bad)
   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
   new_esEs21(yu301, yu40001, app(app(ty_@2, bbd), bbe)) -> new_esEs18(yu301, yu40001, bbd, bbe)
   new_esEs20(yu302, yu40002, ty_@0) -> new_esEs7(yu302, yu40002)
   new_esEs22(yu300, yu40000, app(ty_Maybe, bcc)) -> new_esEs15(yu300, yu40000, bcc)
   new_esEs24(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_primEqNat0(Zero, Zero) -> True
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(app(ty_@3, fa), fb), fc)) -> new_esEs14(yu300, yu40000, fa, fb, fc)
   new_esEs20(yu302, yu40002, ty_Double) -> new_esEs16(yu302, yu40002)
   new_esEs24(yu301, yu40001, app(app(ty_Either, beh), bfa)) -> new_esEs17(yu301, yu40001, beh, bfa)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_Maybe, fd)) -> new_esEs15(yu300, yu40000, fd)
   new_esEs4(yu30, yu4000, ty_Bool) -> new_esEs6(yu30, yu4000)
   new_esEs25(yu300, yu40000, app(ty_[], bgf)) -> new_esEs19(yu300, yu40000, bgf)
   new_esEs13(:%(yu300, yu301), :%(yu40000, yu40001), gc) -> new_asAs(new_esEs27(yu300, yu40000, gc), new_esEs26(yu301, yu40001, gc))
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs25(yu300, yu40000, app(app(ty_Either, bgb), bgc)) -> new_esEs17(yu300, yu40000, bgb, bgc)
   new_esEs21(yu301, yu40001, app(ty_Ratio, bae)) -> new_esEs13(yu301, yu40001, bae)
   new_asAs(False, yu39) -> False
   new_esEs8(Char(yu300), Char(yu40000)) -> new_primEqNat0(yu300, yu40000)
   new_esEs22(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Char, dd) -> new_esEs8(yu300, yu40000)
   new_esEs26(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs23(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_[], bhh)) -> new_esEs19(yu300, yu40000, bhh)
   new_esEs15(Just(yu300), Just(yu40000), ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs4(yu30, yu4000, app(ty_Maybe, gg)) -> new_esEs15(yu30, yu4000, gg)
   new_esEs15(Just(yu300), Just(yu40000), ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Float) -> new_esEs11(yu30, yu4000)
   new_esEs21(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs24(yu301, yu40001, ty_Char) -> new_esEs8(yu301, yu40001)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Integer) -> new_esEs10(yu300, yu40000)

The set Q consists of the following terms:

   new_esEs20(x0, x1, app(ty_Ratio, x2))
   new_esEs20(x0, x1, ty_Int)
   new_esEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
   new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs17(Right(x0), Right(x1), x2, ty_Double)
   new_esEs12(EQ, EQ)
   new_esEs25(x0, x1, ty_Integer)
   new_esEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
   new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs17(Right(x0), Right(x1), x2, ty_Ordering)
   new_esEs21(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Integer)
   new_esEs20(x0, x1, ty_Char)
   new_primMulNat0(Zero, Zero)
   new_primPlusNat1(Zero, Zero)
   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
   new_esEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
   new_esEs15(Nothing, Just(x0), x1)
   new_esEs21(x0, x1, ty_Double)
   new_esEs24(x0, x1, ty_Double)
   new_esEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
   new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs4(x0, x1, ty_Ordering)
   new_esEs23(x0, x1, app(ty_[], x2))
   new_esEs17(Right(x0), Right(x1), x2, ty_Float)
   new_esEs15(Just(x0), Just(x1), ty_Double)
   new_esEs5(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Float)
   new_esEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
   new_esEs24(x0, x1, ty_Float)
   new_esEs19(:(x0, x1), :(x2, x3), x4)
   new_primEqInt(Pos(Zero), Pos(Zero))
   new_primPlusNat1(Succ(x0), Succ(x1))
   new_esEs17(Left(x0), Left(x1), ty_Float, x2)
   new_esEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
   new_esEs8(Char(x0), Char(x1))
   new_esEs19([], :(x0, x1), x2)
   new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_asAs(False, x0)
   new_esEs21(x0, x1, ty_Float)
   new_esEs4(x0, x1, ty_Float)
   new_esEs25(x0, x1, ty_Bool)
   new_esEs14(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
   new_esEs21(x0, x1, app(ty_Ratio, x2))
   new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs21(x0, x1, ty_Ordering)
   new_primEqInt(Neg(Zero), Neg(Zero))
   new_esEs24(x0, x1, ty_Ordering)
   new_esEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
   new_esEs15(Just(x0), Just(x1), ty_Ordering)
   new_esEs27(x0, x1, ty_Integer)
   new_esEs23(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Int)
   new_esEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
   new_esEs24(x0, x1, app(ty_Maybe, x2))
   new_esEs6(False, True)
   new_esEs6(True, False)
   new_esEs25(x0, x1, ty_@0)
   new_esEs21(x0, x1, app(ty_[], x2))
   new_esEs12(EQ, GT)
   new_esEs12(GT, EQ)
   new_primPlusNat0(Succ(x0), x1)
   new_esEs25(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs23(x0, x1, ty_Bool)
   new_esEs17(Right(x0), Right(x1), x2, ty_Char)
   new_esEs5(x0, x1, ty_Int)
   new_esEs22(x0, x1, ty_@0)
   new_esEs22(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Integer)
   new_primPlusNat1(Succ(x0), Zero)
   new_esEs17(Left(x0), Left(x1), ty_Integer, x2)
   new_esEs17(Left(x0), Left(x1), ty_Ordering, x2)
   new_esEs25(x0, x1, ty_Double)
   new_esEs5(x0, x1, app(ty_[], x2))
   new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs5(x0, x1, ty_Char)
   new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs6(False, False)
   new_esEs15(Just(x0), Just(x1), ty_Char)
   new_esEs22(x0, x1, ty_Int)
   new_primEqInt(Pos(Succ(x0)), Neg(x1))
   new_primEqInt(Neg(Succ(x0)), Pos(x1))
   new_esEs17(Right(x0), Right(x1), x2, ty_Int)
   new_primEqInt(Pos(Zero), Neg(Zero))
   new_primEqInt(Neg(Zero), Pos(Zero))
   new_esEs15(Just(x0), Just(x1), ty_Bool)
   new_esEs12(LT, GT)
   new_esEs12(GT, LT)
   new_sr(Pos(x0), Neg(x1))
   new_sr(Neg(x0), Pos(x1))
   new_esEs5(x0, x1, ty_Float)
   new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs12(LT, LT)
   new_esEs25(x0, x1, ty_Float)
   new_esEs26(x0, x1, ty_Integer)
   new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs23(x0, x1, app(ty_Ratio, x2))
   new_esEs5(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, ty_@0)
   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
   new_esEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
   new_esEs19(:(x0, x1), [], x2)
   new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs20(x0, x1, ty_Ordering)
   new_esEs25(x0, x1, app(ty_Ratio, x2))
   new_primMulNat0(Succ(x0), Zero)
   new_esEs15(Just(x0), Nothing, x1)
   new_esEs22(x0, x1, ty_Float)
   new_esEs17(Right(x0), Right(x1), x2, ty_Bool)
   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
   new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs25(x0, x1, app(ty_[], x2))
   new_esEs4(x0, x1, ty_@0)
   new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs24(x0, x1, app(ty_Ratio, x2))
   new_esEs21(x0, x1, ty_@0)
   new_esEs22(x0, x1, ty_Char)
   new_esEs4(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Char)
   new_esEs20(x0, x1, ty_Integer)
   new_esEs25(x0, x1, ty_Int)
   new_esEs17(Right(x0), Right(x1), x2, ty_@0)
   new_esEs4(x0, x1, ty_Bool)
   new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs5(x0, x1, app(ty_Ratio, x2))
   new_esEs4(x0, x1, app(ty_[], x2))
   new_primMulNat0(Succ(x0), Succ(x1))
   new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs7(@0, @0)
   new_primEqNat0(Succ(x0), Succ(x1))
   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
   new_esEs16(Double(x0, x1), Double(x2, x3))
   new_esEs25(x0, x1, ty_Char)
   new_esEs17(Left(x0), Left(x1), ty_@0, x2)
   new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
   new_esEs12(GT, GT)
   new_esEs12(LT, EQ)
   new_esEs12(EQ, LT)
   new_esEs27(x0, x1, ty_Int)
   new_primEqNat0(Succ(x0), Zero)
   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
   new_esEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
   new_esEs20(x0, x1, app(ty_[], x2))
   new_esEs20(x0, x1, ty_Bool)
   new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs23(x0, x1, app(ty_Maybe, x2))
   new_primEqNat0(Zero, Succ(x0))
   new_esEs4(x0, x1, app(ty_Ratio, x2))
   new_esEs5(x0, x1, ty_Bool)
   new_esEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
   new_esEs4(x0, x1, ty_Integer)
   new_esEs23(x0, x1, ty_Ordering)
   new_esEs22(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Int)
   new_esEs15(Just(x0), Just(x1), ty_@0)
   new_esEs9(x0, x1)
   new_esEs24(x0, x1, ty_@0)
   new_esEs15(Just(x0), Just(x1), app(ty_[], x2))
   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
   new_esEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
   new_primMulNat0(Zero, Succ(x0))
   new_sr(Pos(x0), Pos(x1))
   new_esEs13(:%(x0, x1), :%(x2, x3), x4)
   new_esEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
   new_esEs24(x0, x1, ty_Int)
   new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_primEqNat0(Zero, Zero)
   new_esEs6(True, True)
   new_esEs22(x0, x1, ty_Bool)
   new_esEs21(x0, x1, ty_Char)
   new_esEs23(x0, x1, ty_Float)
   new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs4(x0, x1, ty_Char)
   new_esEs23(x0, x1, ty_@0)
   new_esEs24(x0, x1, ty_Integer)
   new_esEs22(x0, x1, ty_Ordering)
   new_esEs21(x0, x1, ty_Integer)
   new_esEs17(Left(x0), Left(x1), ty_Int, x2)
   new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs11(Float(x0, x1), Float(x2, x3))
   new_esEs5(x0, x1, ty_Integer)
   new_esEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
   new_esEs21(x0, x1, ty_Int)
   new_esEs22(x0, x1, app(ty_[], x2))
   new_sr(Neg(x0), Neg(x1))
   new_esEs26(x0, x1, ty_Int)
   new_asAs(True, x0)
   new_esEs4(x0, x1, ty_Int)
   new_esEs24(x0, x1, ty_Char)
   new_esEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
   new_esEs17(Left(x0), Left(x1), ty_Bool, x2)
   new_esEs17(Right(x0), Right(x1), x2, ty_Integer)
   new_esEs20(x0, x1, ty_Double)
   new_esEs18(@2(x0, x1), @2(x2, x3), x4, x5)
   new_esEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
   new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs17(Left(x0), Right(x1), x2, x3)
   new_esEs17(Right(x0), Left(x1), x2, x3)
   new_esEs17(Left(x0), Left(x1), ty_Double, x2)
   new_esEs20(x0, x1, ty_Float)
   new_esEs15(Nothing, Nothing, x0)
   new_esEs22(x0, x1, app(ty_Ratio, x2))
   new_esEs24(x0, x1, ty_Bool)
   new_esEs20(x0, x1, ty_@0)
   new_primPlusNat0(Zero, x0)
   new_esEs21(x0, x1, ty_Bool)
   new_primPlusNat1(Zero, Succ(x0))
   new_esEs10(Integer(x0), Integer(x1))
   new_esEs19([], [], x0)
   new_esEs22(x0, x1, ty_Integer)
   new_esEs24(x0, x1, app(ty_[], x2))
   new_esEs25(x0, x1, ty_Ordering)
   new_esEs4(x0, x1, ty_Double)
   new_esEs20(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, ty_Ordering)
   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
   new_esEs17(Left(x0), Left(x1), ty_Char, x2)
   new_esEs22(x0, x1, app(app(ty_Either, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(11) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs.
----------------------------------------

(12)
Complex Obligation (AND)

----------------------------------------

(13)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_lookup10(yu22, yu23, yu24, yu25, False, bf, bg, bh) -> new_lookup(Right(yu22), yu25, bf, bg, bh)
   new_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bc, bd, be) -> new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, be), bc, bd, be)
   new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bc, bd, be) -> new_lookup(Right(yu30), yu41, bc, bd, be)

The TRS R consists of the following rules:

   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Float) -> new_esEs11(yu300, yu40000)
   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
   new_esEs26(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_esEs27(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Double, dd) -> new_esEs16(yu300, yu40000)
   new_esEs4(yu30, yu4000, ty_Float) -> new_esEs11(yu30, yu4000)
   new_esEs5(yu30, yu4000, app(ty_Maybe, ce)) -> new_esEs15(yu30, yu4000, ce)
   new_esEs24(yu301, yu40001, app(ty_Maybe, beg)) -> new_esEs15(yu301, yu40001, beg)
   new_esEs15(Just(yu300), Just(yu40000), app(app(ty_Either, bhd), bhe)) -> new_esEs17(yu300, yu40000, bhd, bhe)
   new_esEs18(@2(yu300, yu301), @2(yu40000, yu40001), gh, ha) -> new_asAs(new_esEs25(yu300, yu40000, gh), new_esEs24(yu301, yu40001, ha))
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(ty_@2, fh), ga)) -> new_esEs18(yu300, yu40000, fh, ga)
   new_esEs20(yu302, yu40002, ty_Ordering) -> new_esEs12(yu302, yu40002)
   new_esEs16(Double(yu300, yu301), Double(yu40000, yu40001)) -> new_esEs9(new_sr(yu300, yu40001), new_sr(yu301, yu40000))
   new_esEs6(False, True) -> False
   new_esEs6(True, False) -> False
   new_esEs24(yu301, yu40001, app(ty_[], bfd)) -> new_esEs19(yu301, yu40001, bfd)
   new_esEs19(:(yu300, yu301), [], hb) -> False
   new_esEs19([], :(yu40000, yu40001), hb) -> False
   new_esEs24(yu301, yu40001, ty_@0) -> new_esEs7(yu301, yu40001)
   new_esEs9(yu30, yu4000) -> new_primEqInt(yu30, yu4000)
   new_esEs21(yu301, yu40001, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs14(yu301, yu40001, baf, bag, bah)
   new_esEs5(yu30, yu4000, ty_Integer) -> new_esEs10(yu30, yu4000)
   new_esEs20(yu302, yu40002, ty_Bool) -> new_esEs6(yu302, yu40002)
   new_esEs21(yu301, yu40001, app(app(ty_Either, bbb), bbc)) -> new_esEs17(yu301, yu40001, bbb, bbc)
   new_esEs23(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Float, dd) -> new_esEs11(yu300, yu40000)
   new_esEs22(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs4(yu30, yu4000, app(app(app(ty_@3, gd), ge), gf)) -> new_esEs14(yu30, yu4000, gd, ge, gf)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs20(yu302, yu40002, app(ty_Ratio, hc)) -> new_esEs13(yu302, yu40002, hc)
   new_esEs15(Just(yu300), Just(yu40000), app(app(app(ty_@3, bgh), bha), bhb)) -> new_esEs14(yu300, yu40000, bgh, bha, bhb)
   new_esEs20(yu302, yu40002, ty_Int) -> new_esEs9(yu302, yu40002)
   new_esEs25(yu300, yu40000, app(ty_Ratio, bfe)) -> new_esEs13(yu300, yu40000, bfe)
   new_esEs12(GT, GT) -> True
   new_esEs19(:(yu300, yu301), :(yu40000, yu40001), hb) -> new_asAs(new_esEs23(yu300, yu40000, hb), new_esEs19(yu301, yu40001, hb))
   new_esEs25(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_asAs(True, yu39) -> yu39
   new_esEs15(Just(yu300), Just(yu40000), ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs10(Integer(yu300), Integer(yu40000)) -> new_primEqInt(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(ty_[], dc)) -> new_esEs19(yu30, yu4000, dc)
   new_esEs17(Left(yu300), Left(yu40000), app(ty_Maybe, ea), dd) -> new_esEs15(yu300, yu40000, ea)
   new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) -> False
   new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) -> False
   new_esEs5(yu30, yu4000, app(app(ty_@2, da), db)) -> new_esEs18(yu30, yu4000, da, db)
   new_esEs4(yu30, yu4000, app(ty_Ratio, gc)) -> new_esEs13(yu30, yu4000, gc)
   new_esEs21(yu301, yu40001, ty_Double) -> new_esEs16(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(app(ty_Either, bdf), bdg)) -> new_esEs17(yu300, yu40000, bdf, bdg)
   new_esEs20(yu302, yu40002, ty_Char) -> new_esEs8(yu302, yu40002)
   new_esEs4(yu30, yu4000, ty_Int) -> new_esEs9(yu30, yu4000)
   new_primEqNat0(Succ(yu3000), Succ(yu400000)) -> new_primEqNat0(yu3000, yu400000)
   new_esEs5(yu30, yu4000, ty_Bool) -> new_esEs6(yu30, yu4000)
   new_esEs22(yu300, yu40000, app(ty_Ratio, bbg)) -> new_esEs13(yu300, yu40000, bbg)
   new_esEs23(yu300, yu40000, app(app(app(ty_@3, bdb), bdc), bdd)) -> new_esEs14(yu300, yu40000, bdb, bdc, bdd)
   new_esEs5(yu30, yu4000, ty_@0) -> new_esEs7(yu30, yu4000)
   new_esEs17(Left(yu300), Left(yu40000), app(ty_[], ef), dd) -> new_esEs19(yu300, yu40000, ef)
   new_esEs12(EQ, EQ) -> True
   new_esEs17(Left(yu300), Left(yu40000), app(app(app(ty_@3, df), dg), dh), dd) -> new_esEs14(yu300, yu40000, df, dg, dh)
   new_esEs23(yu300, yu40000, app(app(ty_@2, bdh), bea)) -> new_esEs18(yu300, yu40000, bdh, bea)
   new_esEs17(Left(yu300), Left(yu40000), ty_Int, dd) -> new_esEs9(yu300, yu40000)
   new_esEs15(Nothing, Just(yu40000), gg) -> False
   new_esEs15(Just(yu300), Nothing, gg) -> False
   new_primMulNat0(Zero, Zero) -> Zero
   new_esEs20(yu302, yu40002, app(ty_Maybe, hg)) -> new_esEs15(yu302, yu40002, hg)
   new_esEs15(Nothing, Nothing, gg) -> True
   new_esEs22(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs21(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_[], gb)) -> new_esEs19(yu300, yu40000, gb)
   new_esEs21(yu301, yu40001, ty_@0) -> new_esEs7(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(ty_Ratio, bda)) -> new_esEs13(yu300, yu40000, bda)
   new_esEs20(yu302, yu40002, ty_Float) -> new_esEs11(yu302, yu40002)
   new_esEs24(yu301, yu40001, app(app(ty_@2, bfb), bfc)) -> new_esEs18(yu301, yu40001, bfb, bfc)
   new_esEs12(LT, LT) -> True
   new_esEs4(yu30, yu4000, ty_Ordering) -> new_esEs12(yu30, yu4000)
   new_primEqNat0(Succ(yu3000), Zero) -> False
   new_primEqNat0(Zero, Succ(yu400000)) -> False
   new_esEs24(yu301, yu40001, ty_Bool) -> new_esEs6(yu301, yu40001)
   new_esEs21(yu301, yu40001, ty_Float) -> new_esEs11(yu301, yu40001)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs23(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs24(yu301, yu40001, app(ty_Ratio, bec)) -> new_esEs13(yu301, yu40001, bec)
   new_esEs25(yu300, yu40000, app(app(app(ty_@3, bff), bfg), bfh)) -> new_esEs14(yu300, yu40000, bff, bfg, bfh)
   new_esEs25(yu300, yu40000, app(app(ty_@2, bgd), bge)) -> new_esEs18(yu300, yu40000, bgd, bge)
   new_esEs15(Just(yu300), Just(yu40000), app(app(ty_@2, bhf), bhg)) -> new_esEs18(yu300, yu40000, bhf, bhg)
   new_esEs5(yu30, yu4000, ty_Int) -> new_esEs9(yu30, yu4000)
   new_esEs5(yu30, yu4000, app(ty_Ratio, ca)) -> new_esEs13(yu30, yu4000, ca)
   new_esEs7(@0, @0) -> True
   new_esEs4(yu30, yu4000, app(app(ty_Either, eg), dd)) -> new_esEs17(yu30, yu4000, eg, dd)
   new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) -> False
   new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) -> False
   new_esEs24(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs24(yu301, yu40001, app(app(app(ty_@3, bed), bee), bef)) -> new_esEs14(yu301, yu40001, bed, bee, bef)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_Maybe, bhc)) -> new_esEs15(yu300, yu40000, bhc)
   new_esEs22(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) -> new_primEqNat0(yu3000, yu400000)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Left(yu300), Right(yu40000), eg, dd) -> False
   new_esEs17(Right(yu300), Left(yu40000), eg, dd) -> False
   new_esEs4(yu30, yu4000, ty_@0) -> new_esEs7(yu30, yu4000)
   new_sr(Pos(yu3000), Neg(yu400010)) -> Neg(new_primMulNat0(yu3000, yu400010))
   new_sr(Neg(yu3000), Pos(yu400010)) -> Neg(new_primMulNat0(yu3000, yu400010))
   new_esEs22(yu300, yu40000, app(ty_[], bch)) -> new_esEs19(yu300, yu40000, bch)
   new_esEs4(yu30, yu4000, app(ty_[], hb)) -> new_esEs19(yu30, yu4000, hb)
   new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) -> Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
   new_esEs4(yu30, yu4000, ty_Double) -> new_esEs16(yu30, yu4000)
   new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) -> False
   new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) -> False
   new_esEs22(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs27(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs12(EQ, GT) -> False
   new_esEs12(GT, EQ) -> False
   new_esEs14(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), gd, ge, gf) -> new_asAs(new_esEs22(yu300, yu40000, gd), new_asAs(new_esEs21(yu301, yu40001, ge), new_esEs20(yu302, yu40002, gf)))
   new_esEs17(Left(yu300), Left(yu40000), app(ty_Ratio, de), dd) -> new_esEs13(yu300, yu40000, de)
   new_esEs22(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs22(yu300, yu40000, app(app(ty_Either, bcd), bce)) -> new_esEs17(yu300, yu40000, bcd, bce)
   new_esEs21(yu301, yu40001, ty_Bool) -> new_esEs6(yu301, yu40001)
   new_esEs22(yu300, yu40000, app(app(app(ty_@3, bbh), bca), bcb)) -> new_esEs14(yu300, yu40000, bbh, bca, bcb)
   new_esEs25(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs21(yu301, yu40001, ty_Char) -> new_esEs8(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(ty_[], beb)) -> new_esEs19(yu300, yu40000, beb)
   new_esEs24(yu301, yu40001, ty_Float) -> new_esEs11(yu301, yu40001)
   new_esEs19([], [], hb) -> True
   new_esEs25(yu300, yu40000, app(ty_Maybe, bga)) -> new_esEs15(yu300, yu40000, bga)
   new_esEs15(Just(yu300), Just(yu40000), ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_Ratio, eh)) -> new_esEs13(yu300, yu40000, eh)
   new_sr(Neg(yu3000), Neg(yu400010)) -> Pos(new_primMulNat0(yu3000, yu400010))
   new_esEs15(Just(yu300), Just(yu40000), ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs15(Just(yu300), Just(yu40000), ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs23(yu300, yu40000, app(ty_Maybe, bde)) -> new_esEs15(yu300, yu40000, bde)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Bool, dd) -> new_esEs6(yu300, yu40000)
   new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) -> False
   new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) -> False
   new_esEs12(LT, EQ) -> False
   new_esEs12(EQ, LT) -> False
   new_esEs21(yu301, yu40001, ty_Ordering) -> new_esEs12(yu301, yu40001)
   new_esEs6(True, True) -> True
   new_esEs4(yu30, yu4000, ty_Char) -> new_esEs8(yu30, yu4000)
   new_esEs4(yu30, yu4000, ty_Integer) -> new_esEs10(yu30, yu4000)
   new_esEs20(yu302, yu40002, app(app(app(ty_@3, hd), he), hf)) -> new_esEs14(yu302, yu40002, hd, he, hf)
   new_esEs17(Left(yu300), Left(yu40000), app(app(ty_@2, ed), ee), dd) -> new_esEs18(yu300, yu40000, ed, ee)
   new_esEs17(Left(yu300), Left(yu40000), ty_Ordering, dd) -> new_esEs12(yu300, yu40000)
   new_esEs20(yu302, yu40002, app(app(ty_Either, hh), baa)) -> new_esEs17(yu302, yu40002, hh, baa)
   new_esEs22(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs24(yu301, yu40001, ty_Double) -> new_esEs16(yu301, yu40001)
   new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) -> new_primEqNat0(yu3000, yu400000)
   new_esEs23(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Double) -> new_esEs16(yu30, yu4000)
   new_esEs23(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs12(LT, GT) -> False
   new_esEs12(GT, LT) -> False
   new_esEs20(yu302, yu40002, app(app(ty_@2, bab), bac)) -> new_esEs18(yu302, yu40002, bab, bac)
   new_esEs21(yu301, yu40001, app(ty_[], bbf)) -> new_esEs19(yu301, yu40001, bbf)
   new_primPlusNat0(Succ(yu400), yu4000100) -> Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
   new_esEs17(Left(yu300), Left(yu40000), ty_@0, dd) -> new_esEs7(yu300, yu40000)
   new_esEs6(False, False) -> True
   new_esEs23(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(app(app(ty_@3, cb), cc), cd)) -> new_esEs14(yu30, yu4000, cb, cc, cd)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_Ratio, bgg)) -> new_esEs13(yu300, yu40000, bgg)
   new_esEs17(Left(yu300), Left(yu40000), app(app(ty_Either, eb), ec), dd) -> new_esEs17(yu300, yu40000, eb, ec)
   new_esEs21(yu301, yu40001, app(ty_Maybe, bba)) -> new_esEs15(yu301, yu40001, bba)
   new_esEs15(Just(yu300), Just(yu40000), ty_Int) -> new_esEs9(yu300, yu40000)
   new_primPlusNat1(Zero, Zero) -> Zero
   new_esEs23(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_primMulNat0(Succ(yu30000), Zero) -> Zero
   new_primMulNat0(Zero, Succ(yu4000100)) -> Zero
   new_sr(Pos(yu3000), Pos(yu400010)) -> Pos(new_primMulNat0(yu3000, yu400010))
   new_esEs20(yu302, yu40002, ty_Integer) -> new_esEs10(yu302, yu40002)
   new_primPlusNat0(Zero, yu4000100) -> Succ(yu4000100)
   new_esEs23(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(app(ty_Either, cf), cg)) -> new_esEs17(yu30, yu4000, cf, cg)
   new_esEs15(Just(yu300), Just(yu40000), ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Ordering) -> new_esEs12(yu30, yu4000)
   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
   new_esEs22(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_primMulNat0(Succ(yu30000), Succ(yu4000100)) -> new_primPlusNat0(new_primMulNat0(yu30000, Succ(yu4000100)), yu4000100)
   new_esEs24(yu301, yu40001, ty_Ordering) -> new_esEs12(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Char) -> new_esEs8(yu30, yu4000)
   new_esEs22(yu300, yu40000, app(app(ty_@2, bcf), bcg)) -> new_esEs18(yu300, yu40000, bcf, bcg)
   new_primPlusNat1(Succ(yu4000), Zero) -> Succ(yu4000)
   new_primPlusNat1(Zero, Succ(yu40001000)) -> Succ(yu40001000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Integer, dd) -> new_esEs10(yu300, yu40000)
   new_esEs11(Float(yu300, yu301), Float(yu40000, yu40001)) -> new_esEs9(new_sr(yu300, yu40001), new_sr(yu301, yu40000))
   new_esEs4(yu30, yu4000, app(app(ty_@2, gh), ha)) -> new_esEs18(yu30, yu4000, gh, ha)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(ty_Either, ff), fg)) -> new_esEs17(yu300, yu40000, ff, fg)
   new_esEs20(yu302, yu40002, app(ty_[], bad)) -> new_esEs19(yu302, yu40002, bad)
   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
   new_esEs21(yu301, yu40001, app(app(ty_@2, bbd), bbe)) -> new_esEs18(yu301, yu40001, bbd, bbe)
   new_esEs20(yu302, yu40002, ty_@0) -> new_esEs7(yu302, yu40002)
   new_esEs22(yu300, yu40000, app(ty_Maybe, bcc)) -> new_esEs15(yu300, yu40000, bcc)
   new_esEs24(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_primEqNat0(Zero, Zero) -> True
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(app(ty_@3, fa), fb), fc)) -> new_esEs14(yu300, yu40000, fa, fb, fc)
   new_esEs20(yu302, yu40002, ty_Double) -> new_esEs16(yu302, yu40002)
   new_esEs24(yu301, yu40001, app(app(ty_Either, beh), bfa)) -> new_esEs17(yu301, yu40001, beh, bfa)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_Maybe, fd)) -> new_esEs15(yu300, yu40000, fd)
   new_esEs4(yu30, yu4000, ty_Bool) -> new_esEs6(yu30, yu4000)
   new_esEs25(yu300, yu40000, app(ty_[], bgf)) -> new_esEs19(yu300, yu40000, bgf)
   new_esEs13(:%(yu300, yu301), :%(yu40000, yu40001), gc) -> new_asAs(new_esEs27(yu300, yu40000, gc), new_esEs26(yu301, yu40001, gc))
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs25(yu300, yu40000, app(app(ty_Either, bgb), bgc)) -> new_esEs17(yu300, yu40000, bgb, bgc)
   new_esEs21(yu301, yu40001, app(ty_Ratio, bae)) -> new_esEs13(yu301, yu40001, bae)
   new_asAs(False, yu39) -> False
   new_esEs8(Char(yu300), Char(yu40000)) -> new_primEqNat0(yu300, yu40000)
   new_esEs22(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Char, dd) -> new_esEs8(yu300, yu40000)
   new_esEs26(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs23(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_[], bhh)) -> new_esEs19(yu300, yu40000, bhh)
   new_esEs15(Just(yu300), Just(yu40000), ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs4(yu30, yu4000, app(ty_Maybe, gg)) -> new_esEs15(yu30, yu4000, gg)
   new_esEs15(Just(yu300), Just(yu40000), ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Float) -> new_esEs11(yu30, yu4000)
   new_esEs21(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs24(yu301, yu40001, ty_Char) -> new_esEs8(yu301, yu40001)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Integer) -> new_esEs10(yu300, yu40000)

The set Q consists of the following terms:

   new_esEs20(x0, x1, app(ty_Ratio, x2))
   new_esEs20(x0, x1, ty_Int)
   new_esEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
   new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs17(Right(x0), Right(x1), x2, ty_Double)
   new_esEs12(EQ, EQ)
   new_esEs25(x0, x1, ty_Integer)
   new_esEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
   new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs17(Right(x0), Right(x1), x2, ty_Ordering)
   new_esEs21(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Integer)
   new_esEs20(x0, x1, ty_Char)
   new_primMulNat0(Zero, Zero)
   new_primPlusNat1(Zero, Zero)
   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
   new_esEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
   new_esEs15(Nothing, Just(x0), x1)
   new_esEs21(x0, x1, ty_Double)
   new_esEs24(x0, x1, ty_Double)
   new_esEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
   new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs4(x0, x1, ty_Ordering)
   new_esEs23(x0, x1, app(ty_[], x2))
   new_esEs17(Right(x0), Right(x1), x2, ty_Float)
   new_esEs15(Just(x0), Just(x1), ty_Double)
   new_esEs5(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Float)
   new_esEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
   new_esEs24(x0, x1, ty_Float)
   new_esEs19(:(x0, x1), :(x2, x3), x4)
   new_primEqInt(Pos(Zero), Pos(Zero))
   new_primPlusNat1(Succ(x0), Succ(x1))
   new_esEs17(Left(x0), Left(x1), ty_Float, x2)
   new_esEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
   new_esEs8(Char(x0), Char(x1))
   new_esEs19([], :(x0, x1), x2)
   new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_asAs(False, x0)
   new_esEs21(x0, x1, ty_Float)
   new_esEs4(x0, x1, ty_Float)
   new_esEs25(x0, x1, ty_Bool)
   new_esEs14(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
   new_esEs21(x0, x1, app(ty_Ratio, x2))
   new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs21(x0, x1, ty_Ordering)
   new_primEqInt(Neg(Zero), Neg(Zero))
   new_esEs24(x0, x1, ty_Ordering)
   new_esEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
   new_esEs15(Just(x0), Just(x1), ty_Ordering)
   new_esEs27(x0, x1, ty_Integer)
   new_esEs23(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Int)
   new_esEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
   new_esEs24(x0, x1, app(ty_Maybe, x2))
   new_esEs6(False, True)
   new_esEs6(True, False)
   new_esEs25(x0, x1, ty_@0)
   new_esEs21(x0, x1, app(ty_[], x2))
   new_esEs12(EQ, GT)
   new_esEs12(GT, EQ)
   new_primPlusNat0(Succ(x0), x1)
   new_esEs25(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs23(x0, x1, ty_Bool)
   new_esEs17(Right(x0), Right(x1), x2, ty_Char)
   new_esEs5(x0, x1, ty_Int)
   new_esEs22(x0, x1, ty_@0)
   new_esEs22(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Integer)
   new_primPlusNat1(Succ(x0), Zero)
   new_esEs17(Left(x0), Left(x1), ty_Integer, x2)
   new_esEs17(Left(x0), Left(x1), ty_Ordering, x2)
   new_esEs25(x0, x1, ty_Double)
   new_esEs5(x0, x1, app(ty_[], x2))
   new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs5(x0, x1, ty_Char)
   new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs6(False, False)
   new_esEs15(Just(x0), Just(x1), ty_Char)
   new_esEs22(x0, x1, ty_Int)
   new_primEqInt(Pos(Succ(x0)), Neg(x1))
   new_primEqInt(Neg(Succ(x0)), Pos(x1))
   new_esEs17(Right(x0), Right(x1), x2, ty_Int)
   new_primEqInt(Pos(Zero), Neg(Zero))
   new_primEqInt(Neg(Zero), Pos(Zero))
   new_esEs15(Just(x0), Just(x1), ty_Bool)
   new_esEs12(LT, GT)
   new_esEs12(GT, LT)
   new_sr(Pos(x0), Neg(x1))
   new_sr(Neg(x0), Pos(x1))
   new_esEs5(x0, x1, ty_Float)
   new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs12(LT, LT)
   new_esEs25(x0, x1, ty_Float)
   new_esEs26(x0, x1, ty_Integer)
   new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs23(x0, x1, app(ty_Ratio, x2))
   new_esEs5(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, ty_@0)
   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
   new_esEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
   new_esEs19(:(x0, x1), [], x2)
   new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs20(x0, x1, ty_Ordering)
   new_esEs25(x0, x1, app(ty_Ratio, x2))
   new_primMulNat0(Succ(x0), Zero)
   new_esEs15(Just(x0), Nothing, x1)
   new_esEs22(x0, x1, ty_Float)
   new_esEs17(Right(x0), Right(x1), x2, ty_Bool)
   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
   new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs25(x0, x1, app(ty_[], x2))
   new_esEs4(x0, x1, ty_@0)
   new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs24(x0, x1, app(ty_Ratio, x2))
   new_esEs21(x0, x1, ty_@0)
   new_esEs22(x0, x1, ty_Char)
   new_esEs4(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Char)
   new_esEs20(x0, x1, ty_Integer)
   new_esEs25(x0, x1, ty_Int)
   new_esEs17(Right(x0), Right(x1), x2, ty_@0)
   new_esEs4(x0, x1, ty_Bool)
   new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs5(x0, x1, app(ty_Ratio, x2))
   new_esEs4(x0, x1, app(ty_[], x2))
   new_primMulNat0(Succ(x0), Succ(x1))
   new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs7(@0, @0)
   new_primEqNat0(Succ(x0), Succ(x1))
   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
   new_esEs16(Double(x0, x1), Double(x2, x3))
   new_esEs25(x0, x1, ty_Char)
   new_esEs17(Left(x0), Left(x1), ty_@0, x2)
   new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
   new_esEs12(GT, GT)
   new_esEs12(LT, EQ)
   new_esEs12(EQ, LT)
   new_esEs27(x0, x1, ty_Int)
   new_primEqNat0(Succ(x0), Zero)
   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
   new_esEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
   new_esEs20(x0, x1, app(ty_[], x2))
   new_esEs20(x0, x1, ty_Bool)
   new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs23(x0, x1, app(ty_Maybe, x2))
   new_primEqNat0(Zero, Succ(x0))
   new_esEs4(x0, x1, app(ty_Ratio, x2))
   new_esEs5(x0, x1, ty_Bool)
   new_esEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
   new_esEs4(x0, x1, ty_Integer)
   new_esEs23(x0, x1, ty_Ordering)
   new_esEs22(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Int)
   new_esEs15(Just(x0), Just(x1), ty_@0)
   new_esEs9(x0, x1)
   new_esEs24(x0, x1, ty_@0)
   new_esEs15(Just(x0), Just(x1), app(ty_[], x2))
   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
   new_esEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
   new_primMulNat0(Zero, Succ(x0))
   new_sr(Pos(x0), Pos(x1))
   new_esEs13(:%(x0, x1), :%(x2, x3), x4)
   new_esEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
   new_esEs24(x0, x1, ty_Int)
   new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_primEqNat0(Zero, Zero)
   new_esEs6(True, True)
   new_esEs22(x0, x1, ty_Bool)
   new_esEs21(x0, x1, ty_Char)
   new_esEs23(x0, x1, ty_Float)
   new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs4(x0, x1, ty_Char)
   new_esEs23(x0, x1, ty_@0)
   new_esEs24(x0, x1, ty_Integer)
   new_esEs22(x0, x1, ty_Ordering)
   new_esEs21(x0, x1, ty_Integer)
   new_esEs17(Left(x0), Left(x1), ty_Int, x2)
   new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs11(Float(x0, x1), Float(x2, x3))
   new_esEs5(x0, x1, ty_Integer)
   new_esEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
   new_esEs21(x0, x1, ty_Int)
   new_esEs22(x0, x1, app(ty_[], x2))
   new_sr(Neg(x0), Neg(x1))
   new_esEs26(x0, x1, ty_Int)
   new_asAs(True, x0)
   new_esEs4(x0, x1, ty_Int)
   new_esEs24(x0, x1, ty_Char)
   new_esEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
   new_esEs17(Left(x0), Left(x1), ty_Bool, x2)
   new_esEs17(Right(x0), Right(x1), x2, ty_Integer)
   new_esEs20(x0, x1, ty_Double)
   new_esEs18(@2(x0, x1), @2(x2, x3), x4, x5)
   new_esEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
   new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs17(Left(x0), Right(x1), x2, x3)
   new_esEs17(Right(x0), Left(x1), x2, x3)
   new_esEs17(Left(x0), Left(x1), ty_Double, x2)
   new_esEs20(x0, x1, ty_Float)
   new_esEs15(Nothing, Nothing, x0)
   new_esEs22(x0, x1, app(ty_Ratio, x2))
   new_esEs24(x0, x1, ty_Bool)
   new_esEs20(x0, x1, ty_@0)
   new_primPlusNat0(Zero, x0)
   new_esEs21(x0, x1, ty_Bool)
   new_primPlusNat1(Zero, Succ(x0))
   new_esEs10(Integer(x0), Integer(x1))
   new_esEs19([], [], x0)
   new_esEs22(x0, x1, ty_Integer)
   new_esEs24(x0, x1, app(ty_[], x2))
   new_esEs25(x0, x1, ty_Ordering)
   new_esEs4(x0, x1, ty_Double)
   new_esEs20(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, ty_Ordering)
   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
   new_esEs17(Left(x0), Left(x1), ty_Char, x2)
   new_esEs22(x0, x1, app(app(ty_Either, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(14) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_lookup(Right(yu30), :(@2(Right(yu4000), yu401), yu41), bc, bd, be) -> new_lookup10(yu30, yu4000, yu401, yu41, new_esEs5(yu30, yu4000, be), bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 3 >= 6, 4 >= 7, 5 >= 8


*new_lookup(Right(yu30), :(@2(Left(yu4000), yu401), yu41), bc, bd, be) -> new_lookup(Right(yu30), yu41, bc, bd, be)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5


*new_lookup10(yu22, yu23, yu24, yu25, False, bf, bg, bh) -> new_lookup(Right(yu22), yu25, bf, bg, bh)
The graph contains the following edges 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5


----------------------------------------

(15)
YES

----------------------------------------

(16)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_lookup1(yu11, yu12, yu13, yu14, False, h, ba, bb) -> new_lookup(Left(yu11), yu14, h, ba, bb)
   new_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bc, bd, be) -> new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, bd), bc, bd, be)
   new_lookup(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bc, bd, be) -> new_lookup(Left(yu30), yu41, bc, bd, be)

The TRS R consists of the following rules:

   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Float) -> new_esEs11(yu300, yu40000)
   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
   new_esEs26(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_esEs27(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Double, dd) -> new_esEs16(yu300, yu40000)
   new_esEs4(yu30, yu4000, ty_Float) -> new_esEs11(yu30, yu4000)
   new_esEs5(yu30, yu4000, app(ty_Maybe, ce)) -> new_esEs15(yu30, yu4000, ce)
   new_esEs24(yu301, yu40001, app(ty_Maybe, beg)) -> new_esEs15(yu301, yu40001, beg)
   new_esEs15(Just(yu300), Just(yu40000), app(app(ty_Either, bhd), bhe)) -> new_esEs17(yu300, yu40000, bhd, bhe)
   new_esEs18(@2(yu300, yu301), @2(yu40000, yu40001), gh, ha) -> new_asAs(new_esEs25(yu300, yu40000, gh), new_esEs24(yu301, yu40001, ha))
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(ty_@2, fh), ga)) -> new_esEs18(yu300, yu40000, fh, ga)
   new_esEs20(yu302, yu40002, ty_Ordering) -> new_esEs12(yu302, yu40002)
   new_esEs16(Double(yu300, yu301), Double(yu40000, yu40001)) -> new_esEs9(new_sr(yu300, yu40001), new_sr(yu301, yu40000))
   new_esEs6(False, True) -> False
   new_esEs6(True, False) -> False
   new_esEs24(yu301, yu40001, app(ty_[], bfd)) -> new_esEs19(yu301, yu40001, bfd)
   new_esEs19(:(yu300, yu301), [], hb) -> False
   new_esEs19([], :(yu40000, yu40001), hb) -> False
   new_esEs24(yu301, yu40001, ty_@0) -> new_esEs7(yu301, yu40001)
   new_esEs9(yu30, yu4000) -> new_primEqInt(yu30, yu4000)
   new_esEs21(yu301, yu40001, app(app(app(ty_@3, baf), bag), bah)) -> new_esEs14(yu301, yu40001, baf, bag, bah)
   new_esEs5(yu30, yu4000, ty_Integer) -> new_esEs10(yu30, yu4000)
   new_esEs20(yu302, yu40002, ty_Bool) -> new_esEs6(yu302, yu40002)
   new_esEs21(yu301, yu40001, app(app(ty_Either, bbb), bbc)) -> new_esEs17(yu301, yu40001, bbb, bbc)
   new_esEs23(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Float, dd) -> new_esEs11(yu300, yu40000)
   new_esEs22(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs4(yu30, yu4000, app(app(app(ty_@3, gd), ge), gf)) -> new_esEs14(yu30, yu4000, gd, ge, gf)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs20(yu302, yu40002, app(ty_Ratio, hc)) -> new_esEs13(yu302, yu40002, hc)
   new_esEs15(Just(yu300), Just(yu40000), app(app(app(ty_@3, bgh), bha), bhb)) -> new_esEs14(yu300, yu40000, bgh, bha, bhb)
   new_esEs20(yu302, yu40002, ty_Int) -> new_esEs9(yu302, yu40002)
   new_esEs25(yu300, yu40000, app(ty_Ratio, bfe)) -> new_esEs13(yu300, yu40000, bfe)
   new_esEs12(GT, GT) -> True
   new_esEs19(:(yu300, yu301), :(yu40000, yu40001), hb) -> new_asAs(new_esEs23(yu300, yu40000, hb), new_esEs19(yu301, yu40001, hb))
   new_esEs25(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_asAs(True, yu39) -> yu39
   new_esEs15(Just(yu300), Just(yu40000), ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs10(Integer(yu300), Integer(yu40000)) -> new_primEqInt(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(ty_[], dc)) -> new_esEs19(yu30, yu4000, dc)
   new_esEs17(Left(yu300), Left(yu40000), app(ty_Maybe, ea), dd) -> new_esEs15(yu300, yu40000, ea)
   new_primEqInt(Pos(Succ(yu3000)), Pos(Zero)) -> False
   new_primEqInt(Pos(Zero), Pos(Succ(yu400000))) -> False
   new_esEs5(yu30, yu4000, app(app(ty_@2, da), db)) -> new_esEs18(yu30, yu4000, da, db)
   new_esEs4(yu30, yu4000, app(ty_Ratio, gc)) -> new_esEs13(yu30, yu4000, gc)
   new_esEs21(yu301, yu40001, ty_Double) -> new_esEs16(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(app(ty_Either, bdf), bdg)) -> new_esEs17(yu300, yu40000, bdf, bdg)
   new_esEs20(yu302, yu40002, ty_Char) -> new_esEs8(yu302, yu40002)
   new_esEs4(yu30, yu4000, ty_Int) -> new_esEs9(yu30, yu4000)
   new_primEqNat0(Succ(yu3000), Succ(yu400000)) -> new_primEqNat0(yu3000, yu400000)
   new_esEs5(yu30, yu4000, ty_Bool) -> new_esEs6(yu30, yu4000)
   new_esEs22(yu300, yu40000, app(ty_Ratio, bbg)) -> new_esEs13(yu300, yu40000, bbg)
   new_esEs23(yu300, yu40000, app(app(app(ty_@3, bdb), bdc), bdd)) -> new_esEs14(yu300, yu40000, bdb, bdc, bdd)
   new_esEs5(yu30, yu4000, ty_@0) -> new_esEs7(yu30, yu4000)
   new_esEs17(Left(yu300), Left(yu40000), app(ty_[], ef), dd) -> new_esEs19(yu300, yu40000, ef)
   new_esEs12(EQ, EQ) -> True
   new_esEs17(Left(yu300), Left(yu40000), app(app(app(ty_@3, df), dg), dh), dd) -> new_esEs14(yu300, yu40000, df, dg, dh)
   new_esEs23(yu300, yu40000, app(app(ty_@2, bdh), bea)) -> new_esEs18(yu300, yu40000, bdh, bea)
   new_esEs17(Left(yu300), Left(yu40000), ty_Int, dd) -> new_esEs9(yu300, yu40000)
   new_esEs15(Nothing, Just(yu40000), gg) -> False
   new_esEs15(Just(yu300), Nothing, gg) -> False
   new_primMulNat0(Zero, Zero) -> Zero
   new_esEs20(yu302, yu40002, app(ty_Maybe, hg)) -> new_esEs15(yu302, yu40002, hg)
   new_esEs15(Nothing, Nothing, gg) -> True
   new_esEs22(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs21(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_[], gb)) -> new_esEs19(yu300, yu40000, gb)
   new_esEs21(yu301, yu40001, ty_@0) -> new_esEs7(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(ty_Ratio, bda)) -> new_esEs13(yu300, yu40000, bda)
   new_esEs20(yu302, yu40002, ty_Float) -> new_esEs11(yu302, yu40002)
   new_esEs24(yu301, yu40001, app(app(ty_@2, bfb), bfc)) -> new_esEs18(yu301, yu40001, bfb, bfc)
   new_esEs12(LT, LT) -> True
   new_esEs4(yu30, yu4000, ty_Ordering) -> new_esEs12(yu30, yu4000)
   new_primEqNat0(Succ(yu3000), Zero) -> False
   new_primEqNat0(Zero, Succ(yu400000)) -> False
   new_esEs24(yu301, yu40001, ty_Bool) -> new_esEs6(yu301, yu40001)
   new_esEs21(yu301, yu40001, ty_Float) -> new_esEs11(yu301, yu40001)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs23(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_esEs24(yu301, yu40001, app(ty_Ratio, bec)) -> new_esEs13(yu301, yu40001, bec)
   new_esEs25(yu300, yu40000, app(app(app(ty_@3, bff), bfg), bfh)) -> new_esEs14(yu300, yu40000, bff, bfg, bfh)
   new_esEs25(yu300, yu40000, app(app(ty_@2, bgd), bge)) -> new_esEs18(yu300, yu40000, bgd, bge)
   new_esEs15(Just(yu300), Just(yu40000), app(app(ty_@2, bhf), bhg)) -> new_esEs18(yu300, yu40000, bhf, bhg)
   new_esEs5(yu30, yu4000, ty_Int) -> new_esEs9(yu30, yu4000)
   new_esEs5(yu30, yu4000, app(ty_Ratio, ca)) -> new_esEs13(yu30, yu4000, ca)
   new_esEs7(@0, @0) -> True
   new_esEs4(yu30, yu4000, app(app(ty_Either, eg), dd)) -> new_esEs17(yu30, yu4000, eg, dd)
   new_primEqInt(Neg(Succ(yu3000)), Neg(Zero)) -> False
   new_primEqInt(Neg(Zero), Neg(Succ(yu400000))) -> False
   new_esEs24(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs24(yu301, yu40001, app(app(app(ty_@3, bed), bee), bef)) -> new_esEs14(yu301, yu40001, bed, bee, bef)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_Maybe, bhc)) -> new_esEs15(yu300, yu40000, bhc)
   new_esEs22(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_primEqInt(Pos(Succ(yu3000)), Pos(Succ(yu400000))) -> new_primEqNat0(yu3000, yu400000)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Left(yu300), Right(yu40000), eg, dd) -> False
   new_esEs17(Right(yu300), Left(yu40000), eg, dd) -> False
   new_esEs4(yu30, yu4000, ty_@0) -> new_esEs7(yu30, yu4000)
   new_sr(Pos(yu3000), Neg(yu400010)) -> Neg(new_primMulNat0(yu3000, yu400010))
   new_sr(Neg(yu3000), Pos(yu400010)) -> Neg(new_primMulNat0(yu3000, yu400010))
   new_esEs22(yu300, yu40000, app(ty_[], bch)) -> new_esEs19(yu300, yu40000, bch)
   new_esEs4(yu30, yu4000, app(ty_[], hb)) -> new_esEs19(yu30, yu4000, hb)
   new_primPlusNat1(Succ(yu4000), Succ(yu40001000)) -> Succ(Succ(new_primPlusNat1(yu4000, yu40001000)))
   new_esEs4(yu30, yu4000, ty_Double) -> new_esEs16(yu30, yu4000)
   new_primEqInt(Pos(Succ(yu3000)), Neg(yu40000)) -> False
   new_primEqInt(Neg(Succ(yu3000)), Pos(yu40000)) -> False
   new_esEs22(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs27(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs12(EQ, GT) -> False
   new_esEs12(GT, EQ) -> False
   new_esEs14(@3(yu300, yu301, yu302), @3(yu40000, yu40001, yu40002), gd, ge, gf) -> new_asAs(new_esEs22(yu300, yu40000, gd), new_asAs(new_esEs21(yu301, yu40001, ge), new_esEs20(yu302, yu40002, gf)))
   new_esEs17(Left(yu300), Left(yu40000), app(ty_Ratio, de), dd) -> new_esEs13(yu300, yu40000, de)
   new_esEs22(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs22(yu300, yu40000, app(app(ty_Either, bcd), bce)) -> new_esEs17(yu300, yu40000, bcd, bce)
   new_esEs21(yu301, yu40001, ty_Bool) -> new_esEs6(yu301, yu40001)
   new_esEs22(yu300, yu40000, app(app(app(ty_@3, bbh), bca), bcb)) -> new_esEs14(yu300, yu40000, bbh, bca, bcb)
   new_esEs25(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs21(yu301, yu40001, ty_Char) -> new_esEs8(yu301, yu40001)
   new_esEs23(yu300, yu40000, app(ty_[], beb)) -> new_esEs19(yu300, yu40000, beb)
   new_esEs24(yu301, yu40001, ty_Float) -> new_esEs11(yu301, yu40001)
   new_esEs19([], [], hb) -> True
   new_esEs25(yu300, yu40000, app(ty_Maybe, bga)) -> new_esEs15(yu300, yu40000, bga)
   new_esEs15(Just(yu300), Just(yu40000), ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_Ratio, eh)) -> new_esEs13(yu300, yu40000, eh)
   new_sr(Neg(yu3000), Neg(yu400010)) -> Pos(new_primMulNat0(yu3000, yu400010))
   new_esEs15(Just(yu300), Just(yu40000), ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs15(Just(yu300), Just(yu40000), ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs23(yu300, yu40000, app(ty_Maybe, bde)) -> new_esEs15(yu300, yu40000, bde)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Bool, dd) -> new_esEs6(yu300, yu40000)
   new_primEqInt(Pos(Zero), Neg(Succ(yu400000))) -> False
   new_primEqInt(Neg(Zero), Pos(Succ(yu400000))) -> False
   new_esEs12(LT, EQ) -> False
   new_esEs12(EQ, LT) -> False
   new_esEs21(yu301, yu40001, ty_Ordering) -> new_esEs12(yu301, yu40001)
   new_esEs6(True, True) -> True
   new_esEs4(yu30, yu4000, ty_Char) -> new_esEs8(yu30, yu4000)
   new_esEs4(yu30, yu4000, ty_Integer) -> new_esEs10(yu30, yu4000)
   new_esEs20(yu302, yu40002, app(app(app(ty_@3, hd), he), hf)) -> new_esEs14(yu302, yu40002, hd, he, hf)
   new_esEs17(Left(yu300), Left(yu40000), app(app(ty_@2, ed), ee), dd) -> new_esEs18(yu300, yu40000, ed, ee)
   new_esEs17(Left(yu300), Left(yu40000), ty_Ordering, dd) -> new_esEs12(yu300, yu40000)
   new_esEs20(yu302, yu40002, app(app(ty_Either, hh), baa)) -> new_esEs17(yu302, yu40002, hh, baa)
   new_esEs22(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs24(yu301, yu40001, ty_Double) -> new_esEs16(yu301, yu40001)
   new_primEqInt(Neg(Succ(yu3000)), Neg(Succ(yu400000))) -> new_primEqNat0(yu3000, yu400000)
   new_esEs23(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Double) -> new_esEs16(yu30, yu4000)
   new_esEs23(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs12(LT, GT) -> False
   new_esEs12(GT, LT) -> False
   new_esEs20(yu302, yu40002, app(app(ty_@2, bab), bac)) -> new_esEs18(yu302, yu40002, bab, bac)
   new_esEs21(yu301, yu40001, app(ty_[], bbf)) -> new_esEs19(yu301, yu40001, bbf)
   new_primPlusNat0(Succ(yu400), yu4000100) -> Succ(Succ(new_primPlusNat1(yu400, yu4000100)))
   new_esEs17(Left(yu300), Left(yu40000), ty_@0, dd) -> new_esEs7(yu300, yu40000)
   new_esEs6(False, False) -> True
   new_esEs23(yu300, yu40000, ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(app(app(ty_@3, cb), cc), cd)) -> new_esEs14(yu30, yu4000, cb, cc, cd)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_Ratio, bgg)) -> new_esEs13(yu300, yu40000, bgg)
   new_esEs17(Left(yu300), Left(yu40000), app(app(ty_Either, eb), ec), dd) -> new_esEs17(yu300, yu40000, eb, ec)
   new_esEs21(yu301, yu40001, app(ty_Maybe, bba)) -> new_esEs15(yu301, yu40001, bba)
   new_esEs15(Just(yu300), Just(yu40000), ty_Int) -> new_esEs9(yu300, yu40000)
   new_primPlusNat1(Zero, Zero) -> Zero
   new_esEs23(yu300, yu40000, ty_Integer) -> new_esEs10(yu300, yu40000)
   new_primMulNat0(Succ(yu30000), Zero) -> Zero
   new_primMulNat0(Zero, Succ(yu4000100)) -> Zero
   new_sr(Pos(yu3000), Pos(yu400010)) -> Pos(new_primMulNat0(yu3000, yu400010))
   new_esEs20(yu302, yu40002, ty_Integer) -> new_esEs10(yu302, yu40002)
   new_primPlusNat0(Zero, yu4000100) -> Succ(yu4000100)
   new_esEs23(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, app(app(ty_Either, cf), cg)) -> new_esEs17(yu30, yu4000, cf, cg)
   new_esEs15(Just(yu300), Just(yu40000), ty_Integer) -> new_esEs10(yu300, yu40000)
   new_esEs25(yu300, yu40000, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Ordering) -> new_esEs12(yu30, yu4000)
   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
   new_esEs22(yu300, yu40000, ty_Int) -> new_esEs9(yu300, yu40000)
   new_primMulNat0(Succ(yu30000), Succ(yu4000100)) -> new_primPlusNat0(new_primMulNat0(yu30000, Succ(yu4000100)), yu4000100)
   new_esEs24(yu301, yu40001, ty_Ordering) -> new_esEs12(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Char) -> new_esEs8(yu30, yu4000)
   new_esEs22(yu300, yu40000, app(app(ty_@2, bcf), bcg)) -> new_esEs18(yu300, yu40000, bcf, bcg)
   new_primPlusNat1(Succ(yu4000), Zero) -> Succ(yu4000)
   new_primPlusNat1(Zero, Succ(yu40001000)) -> Succ(yu40001000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Integer, dd) -> new_esEs10(yu300, yu40000)
   new_esEs11(Float(yu300, yu301), Float(yu40000, yu40001)) -> new_esEs9(new_sr(yu300, yu40001), new_sr(yu301, yu40000))
   new_esEs4(yu30, yu4000, app(app(ty_@2, gh), ha)) -> new_esEs18(yu30, yu4000, gh, ha)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(ty_Either, ff), fg)) -> new_esEs17(yu300, yu40000, ff, fg)
   new_esEs20(yu302, yu40002, app(ty_[], bad)) -> new_esEs19(yu302, yu40002, bad)
   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
   new_esEs21(yu301, yu40001, app(app(ty_@2, bbd), bbe)) -> new_esEs18(yu301, yu40001, bbd, bbe)
   new_esEs20(yu302, yu40002, ty_@0) -> new_esEs7(yu302, yu40002)
   new_esEs22(yu300, yu40000, app(ty_Maybe, bcc)) -> new_esEs15(yu300, yu40000, bcc)
   new_esEs24(yu301, yu40001, ty_Integer) -> new_esEs10(yu301, yu40001)
   new_primEqNat0(Zero, Zero) -> True
   new_esEs17(Right(yu300), Right(yu40000), eg, app(app(app(ty_@3, fa), fb), fc)) -> new_esEs14(yu300, yu40000, fa, fb, fc)
   new_esEs20(yu302, yu40002, ty_Double) -> new_esEs16(yu302, yu40002)
   new_esEs24(yu301, yu40001, app(app(ty_Either, beh), bfa)) -> new_esEs17(yu301, yu40001, beh, bfa)
   new_esEs17(Right(yu300), Right(yu40000), eg, app(ty_Maybe, fd)) -> new_esEs15(yu300, yu40000, fd)
   new_esEs4(yu30, yu4000, ty_Bool) -> new_esEs6(yu30, yu4000)
   new_esEs25(yu300, yu40000, app(ty_[], bgf)) -> new_esEs19(yu300, yu40000, bgf)
   new_esEs13(:%(yu300, yu301), :%(yu40000, yu40001), gc) -> new_asAs(new_esEs27(yu300, yu40000, gc), new_esEs26(yu301, yu40001, gc))
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Char) -> new_esEs8(yu300, yu40000)
   new_esEs25(yu300, yu40000, app(app(ty_Either, bgb), bgc)) -> new_esEs17(yu300, yu40000, bgb, bgc)
   new_esEs21(yu301, yu40001, app(ty_Ratio, bae)) -> new_esEs13(yu301, yu40001, bae)
   new_asAs(False, yu39) -> False
   new_esEs8(Char(yu300), Char(yu40000)) -> new_primEqNat0(yu300, yu40000)
   new_esEs22(yu300, yu40000, ty_Bool) -> new_esEs6(yu300, yu40000)
   new_esEs17(Left(yu300), Left(yu40000), ty_Char, dd) -> new_esEs8(yu300, yu40000)
   new_esEs26(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs23(yu300, yu40000, ty_Float) -> new_esEs11(yu300, yu40000)
   new_esEs15(Just(yu300), Just(yu40000), app(ty_[], bhh)) -> new_esEs19(yu300, yu40000, bhh)
   new_esEs15(Just(yu300), Just(yu40000), ty_@0) -> new_esEs7(yu300, yu40000)
   new_esEs4(yu30, yu4000, app(ty_Maybe, gg)) -> new_esEs15(yu30, yu4000, gg)
   new_esEs15(Just(yu300), Just(yu40000), ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Ordering) -> new_esEs12(yu300, yu40000)
   new_esEs5(yu30, yu4000, ty_Float) -> new_esEs11(yu30, yu4000)
   new_esEs21(yu301, yu40001, ty_Int) -> new_esEs9(yu301, yu40001)
   new_esEs25(yu300, yu40000, ty_Double) -> new_esEs16(yu300, yu40000)
   new_esEs24(yu301, yu40001, ty_Char) -> new_esEs8(yu301, yu40001)
   new_esEs17(Right(yu300), Right(yu40000), eg, ty_Integer) -> new_esEs10(yu300, yu40000)

The set Q consists of the following terms:

   new_esEs20(x0, x1, app(ty_Ratio, x2))
   new_esEs20(x0, x1, ty_Int)
   new_esEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
   new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs17(Right(x0), Right(x1), x2, ty_Double)
   new_esEs12(EQ, EQ)
   new_esEs25(x0, x1, ty_Integer)
   new_esEs17(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
   new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs17(Right(x0), Right(x1), x2, ty_Ordering)
   new_esEs21(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Integer)
   new_esEs20(x0, x1, ty_Char)
   new_primMulNat0(Zero, Zero)
   new_primPlusNat1(Zero, Zero)
   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
   new_esEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
   new_esEs15(Nothing, Just(x0), x1)
   new_esEs21(x0, x1, ty_Double)
   new_esEs24(x0, x1, ty_Double)
   new_esEs17(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
   new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs4(x0, x1, ty_Ordering)
   new_esEs23(x0, x1, app(ty_[], x2))
   new_esEs17(Right(x0), Right(x1), x2, ty_Float)
   new_esEs15(Just(x0), Just(x1), ty_Double)
   new_esEs5(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Float)
   new_esEs17(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
   new_esEs24(x0, x1, ty_Float)
   new_esEs19(:(x0, x1), :(x2, x3), x4)
   new_primEqInt(Pos(Zero), Pos(Zero))
   new_primPlusNat1(Succ(x0), Succ(x1))
   new_esEs17(Left(x0), Left(x1), ty_Float, x2)
   new_esEs17(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
   new_esEs8(Char(x0), Char(x1))
   new_esEs19([], :(x0, x1), x2)
   new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_asAs(False, x0)
   new_esEs21(x0, x1, ty_Float)
   new_esEs4(x0, x1, ty_Float)
   new_esEs25(x0, x1, ty_Bool)
   new_esEs14(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
   new_esEs21(x0, x1, app(ty_Ratio, x2))
   new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs21(x0, x1, ty_Ordering)
   new_primEqInt(Neg(Zero), Neg(Zero))
   new_esEs24(x0, x1, ty_Ordering)
   new_esEs17(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
   new_esEs15(Just(x0), Just(x1), ty_Ordering)
   new_esEs27(x0, x1, ty_Integer)
   new_esEs23(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Int)
   new_esEs17(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
   new_esEs24(x0, x1, app(ty_Maybe, x2))
   new_esEs6(False, True)
   new_esEs6(True, False)
   new_esEs25(x0, x1, ty_@0)
   new_esEs21(x0, x1, app(ty_[], x2))
   new_esEs12(EQ, GT)
   new_esEs12(GT, EQ)
   new_primPlusNat0(Succ(x0), x1)
   new_esEs25(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs23(x0, x1, ty_Bool)
   new_esEs17(Right(x0), Right(x1), x2, ty_Char)
   new_esEs5(x0, x1, ty_Int)
   new_esEs22(x0, x1, ty_@0)
   new_esEs22(x0, x1, ty_Double)
   new_esEs15(Just(x0), Just(x1), ty_Integer)
   new_primPlusNat1(Succ(x0), Zero)
   new_esEs17(Left(x0), Left(x1), ty_Integer, x2)
   new_esEs17(Left(x0), Left(x1), ty_Ordering, x2)
   new_esEs25(x0, x1, ty_Double)
   new_esEs5(x0, x1, app(ty_[], x2))
   new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs5(x0, x1, ty_Char)
   new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs6(False, False)
   new_esEs15(Just(x0), Just(x1), ty_Char)
   new_esEs22(x0, x1, ty_Int)
   new_primEqInt(Pos(Succ(x0)), Neg(x1))
   new_primEqInt(Neg(Succ(x0)), Pos(x1))
   new_esEs17(Right(x0), Right(x1), x2, ty_Int)
   new_primEqInt(Pos(Zero), Neg(Zero))
   new_primEqInt(Neg(Zero), Pos(Zero))
   new_esEs15(Just(x0), Just(x1), ty_Bool)
   new_esEs12(LT, GT)
   new_esEs12(GT, LT)
   new_sr(Pos(x0), Neg(x1))
   new_sr(Neg(x0), Pos(x1))
   new_esEs5(x0, x1, ty_Float)
   new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs12(LT, LT)
   new_esEs25(x0, x1, ty_Float)
   new_esEs26(x0, x1, ty_Integer)
   new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs23(x0, x1, app(ty_Ratio, x2))
   new_esEs5(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, ty_@0)
   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
   new_esEs17(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
   new_esEs19(:(x0, x1), [], x2)
   new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs20(x0, x1, ty_Ordering)
   new_esEs25(x0, x1, app(ty_Ratio, x2))
   new_primMulNat0(Succ(x0), Zero)
   new_esEs15(Just(x0), Nothing, x1)
   new_esEs22(x0, x1, ty_Float)
   new_esEs17(Right(x0), Right(x1), x2, ty_Bool)
   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
   new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs25(x0, x1, app(ty_[], x2))
   new_esEs4(x0, x1, ty_@0)
   new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs24(x0, x1, app(ty_Ratio, x2))
   new_esEs21(x0, x1, ty_@0)
   new_esEs22(x0, x1, ty_Char)
   new_esEs4(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Char)
   new_esEs20(x0, x1, ty_Integer)
   new_esEs25(x0, x1, ty_Int)
   new_esEs17(Right(x0), Right(x1), x2, ty_@0)
   new_esEs4(x0, x1, ty_Bool)
   new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs5(x0, x1, app(ty_Ratio, x2))
   new_esEs4(x0, x1, app(ty_[], x2))
   new_primMulNat0(Succ(x0), Succ(x1))
   new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs7(@0, @0)
   new_primEqNat0(Succ(x0), Succ(x1))
   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
   new_esEs16(Double(x0, x1), Double(x2, x3))
   new_esEs25(x0, x1, ty_Char)
   new_esEs17(Left(x0), Left(x1), ty_@0, x2)
   new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
   new_esEs17(Right(x0), Right(x1), x2, app(ty_[], x3))
   new_esEs12(GT, GT)
   new_esEs12(LT, EQ)
   new_esEs12(EQ, LT)
   new_esEs27(x0, x1, ty_Int)
   new_primEqNat0(Succ(x0), Zero)
   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
   new_esEs17(Left(x0), Left(x1), app(ty_[], x2), x3)
   new_esEs20(x0, x1, app(ty_[], x2))
   new_esEs20(x0, x1, ty_Bool)
   new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs23(x0, x1, app(ty_Maybe, x2))
   new_primEqNat0(Zero, Succ(x0))
   new_esEs4(x0, x1, app(ty_Ratio, x2))
   new_esEs5(x0, x1, ty_Bool)
   new_esEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
   new_esEs4(x0, x1, ty_Integer)
   new_esEs23(x0, x1, ty_Ordering)
   new_esEs22(x0, x1, app(ty_Maybe, x2))
   new_esEs23(x0, x1, ty_Int)
   new_esEs15(Just(x0), Just(x1), ty_@0)
   new_esEs9(x0, x1)
   new_esEs24(x0, x1, ty_@0)
   new_esEs15(Just(x0), Just(x1), app(ty_[], x2))
   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
   new_esEs17(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
   new_primMulNat0(Zero, Succ(x0))
   new_sr(Pos(x0), Pos(x1))
   new_esEs13(:%(x0, x1), :%(x2, x3), x4)
   new_esEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
   new_esEs24(x0, x1, ty_Int)
   new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_primEqNat0(Zero, Zero)
   new_esEs6(True, True)
   new_esEs22(x0, x1, ty_Bool)
   new_esEs21(x0, x1, ty_Char)
   new_esEs23(x0, x1, ty_Float)
   new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs4(x0, x1, ty_Char)
   new_esEs23(x0, x1, ty_@0)
   new_esEs24(x0, x1, ty_Integer)
   new_esEs22(x0, x1, ty_Ordering)
   new_esEs21(x0, x1, ty_Integer)
   new_esEs17(Left(x0), Left(x1), ty_Int, x2)
   new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
   new_esEs11(Float(x0, x1), Float(x2, x3))
   new_esEs5(x0, x1, ty_Integer)
   new_esEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
   new_esEs21(x0, x1, ty_Int)
   new_esEs22(x0, x1, app(ty_[], x2))
   new_sr(Neg(x0), Neg(x1))
   new_esEs26(x0, x1, ty_Int)
   new_asAs(True, x0)
   new_esEs4(x0, x1, ty_Int)
   new_esEs24(x0, x1, ty_Char)
   new_esEs17(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
   new_esEs17(Left(x0), Left(x1), ty_Bool, x2)
   new_esEs17(Right(x0), Right(x1), x2, ty_Integer)
   new_esEs20(x0, x1, ty_Double)
   new_esEs18(@2(x0, x1), @2(x2, x3), x4, x5)
   new_esEs17(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
   new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
   new_esEs17(Left(x0), Right(x1), x2, x3)
   new_esEs17(Right(x0), Left(x1), x2, x3)
   new_esEs17(Left(x0), Left(x1), ty_Double, x2)
   new_esEs20(x0, x1, ty_Float)
   new_esEs15(Nothing, Nothing, x0)
   new_esEs22(x0, x1, app(ty_Ratio, x2))
   new_esEs24(x0, x1, ty_Bool)
   new_esEs20(x0, x1, ty_@0)
   new_primPlusNat0(Zero, x0)
   new_esEs21(x0, x1, ty_Bool)
   new_primPlusNat1(Zero, Succ(x0))
   new_esEs10(Integer(x0), Integer(x1))
   new_esEs19([], [], x0)
   new_esEs22(x0, x1, ty_Integer)
   new_esEs24(x0, x1, app(ty_[], x2))
   new_esEs25(x0, x1, ty_Ordering)
   new_esEs4(x0, x1, ty_Double)
   new_esEs20(x0, x1, app(ty_Maybe, x2))
   new_esEs5(x0, x1, ty_Ordering)
   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
   new_esEs17(Left(x0), Left(x1), ty_Char, x2)
   new_esEs22(x0, x1, app(app(ty_Either, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(17) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_lookup(Left(yu30), :(@2(Left(yu4000), yu401), yu41), bc, bd, be) -> new_lookup1(yu30, yu4000, yu401, yu41, new_esEs4(yu30, yu4000, bd), bc, bd, be)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4, 3 >= 6, 4 >= 7, 5 >= 8


*new_lookup(Left(yu30), :(@2(Right(yu4000), yu401), yu41), bc, bd, be) -> new_lookup(Left(yu30), yu41, bc, bd, be)
The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5


*new_lookup1(yu11, yu12, yu13, yu14, False, h, ba, bb) -> new_lookup(Left(yu11), yu14, h, ba, bb)
The graph contains the following edges 4 >= 2, 6 >= 3, 7 >= 4, 8 >= 5


----------------------------------------

(18)
YES

----------------------------------------

(19)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMulNat(Succ(yu30000), Succ(yu4000100)) -> new_primMulNat(yu30000, Succ(yu4000100))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(20) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_primMulNat(Succ(yu30000), Succ(yu4000100)) -> new_primMulNat(yu30000, Succ(yu4000100))
The graph contains the following edges 1 > 1, 2 >= 2


----------------------------------------

(21)
YES

----------------------------------------

(22)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat(Succ(yu4000), Succ(yu40001000)) -> new_primPlusNat(yu4000, yu40001000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(23) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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(yu4000), Succ(yu40001000)) -> new_primPlusNat(yu4000, yu40001000)
The graph contains the following edges 1 > 1, 2 > 2


----------------------------------------

(24)
YES

----------------------------------------

(25)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primEqNat(Succ(yu3000), Succ(yu400000)) -> new_primEqNat(yu3000, yu400000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(26) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] 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_primEqNat(Succ(yu3000), Succ(yu400000)) -> new_primEqNat(yu3000, yu400000)
The graph contains the following edges 1 > 1, 2 > 2


----------------------------------------

(27)
YES