/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) CR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) IFR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) BR [EQUIVALENT, 0 ms]
(8) HASKELL
(9) COR [EQUIVALENT, 15 ms]
(10) HASKELL
(11) NumRed [SOUND, 0 ms]
(12) HASKELL
(13) Narrow [SOUND, 0 ms]
(14) AND
    (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) TransformationProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : _) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (\vv1 ->case vv1 of { 
(x,i)->  if p x then i : [] else []; 
_-> []; 
 } ) (zip xs (enumFrom 0));

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\ab->(a,b)"
is transformed to
"zip0 a b = (a,b);
"
The following Lambda expression
"\vv1->case vv1 of {
(x,i)  -> if p x then i : [] else [];
_  -> []}
"
is transformed to
"findIndices0 p vv1 = case vv1 of {
(x,i)  -> if p x then i : [] else [];
_  -> []}
;
"

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : _) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));

findIndices0 p vv1 = case vv1 of { 
(x,i)->  if p x then i : [] else []; 
_-> []; 
 } ;

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(3) CR (EQUIVALENT)
Case Reductions:
The following Case expression
"case vv1 of {
(x,i)  -> if p x then i : [] else [];
_  -> []}
"
is transformed to
"findIndices00 p (x,i) = if p x then i : [] else [];
findIndices00 p _ = [];
"

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

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : _) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));

findIndices0 p vv1 = findIndices00 p vv1;

findIndices00 p (x,i) =  if p x then i : [] else [];
findIndices00 p _ = [];

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(5) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if p x then i : [] else []"
is transformed to
"findIndices000 i True = i : [];
findIndices000 i False = [];
"

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

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : _) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));

findIndices0 p vv1 = findIndices00 p vv1;

findIndices00 p (x,i) = findIndices000 i (p x);
findIndices00 p _ = [];

findIndices000 i True = i : [];
findIndices000 i False = [];

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

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

(8)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : wv) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));

findIndices0 p vv1 = findIndices00 p vv1;

findIndices00 p (x,i) = findIndices000 i (p x);
findIndices00 p ww = [];

findIndices000 i True = i : [];
findIndices000 i False = [];

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(9) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

(10)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : wv) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0));

findIndices0 p vv1 = findIndices00 p vv1;

findIndices00 p (x,i) = findIndices000 i (p x);
findIndices00 p ww = [];

findIndices000 i True = i : [];
findIndices000 i False = [];

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(11) NumRed (SOUND)
Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
----------------------------------------

(12)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
listToMaybe :: [a]  ->  Maybe a;
listToMaybe [] = Nothing;
listToMaybe (a : wv) = Just a;

}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int;
elemIndex x = findIndex (== x);

findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int;
findIndex p = Maybe.listToMaybe . findIndices p;

findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int];
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom (Pos Zero)));

findIndices0 p vv1 = findIndices00 p vv1;

findIndices00 p (x,i) = findIndices000 i (p x);
findIndices00 p ww = [];

findIndices000 i True = i : [];
findIndices000 i False = [];

}
module Main where {
import qualified List;
import qualified Maybe;
import qualified Prelude;
}

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

(13) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="List.elemIndex",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="List.elemIndex wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="List.elemIndex wx3 wx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="List.findIndex (wx3 ==) wx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="Maybe.listToMaybe . List.findIndices (wx3 ==)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="Maybe.listToMaybe (List.findIndices (wx3 ==) wx4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="Maybe.listToMaybe (concatMap (List.findIndices0 (wx3 ==)) (zip wx4 (enumFrom (Pos Zero))))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="Maybe.listToMaybe (concat . map (List.findIndices0 (wx3 ==)))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="Maybe.listToMaybe (concat (map (List.findIndices0 (wx3 ==)) (zip wx4 (enumFrom (Pos Zero)))))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zip wx4 (enumFrom (Pos Zero)))))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 wx4 (enumFrom (Pos Zero)))))",fontsize=16,color="burlywood",shape="box"];336[label="wx4/wx40 : wx41",fontsize=10,color="white",style="solid",shape="box"];12 -> 336[label="",style="solid", color="burlywood", weight=9];
336 -> 13[label="",style="solid", color="burlywood", weight=3];
337[label="wx4/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 337[label="",style="solid", color="burlywood", weight=9];
337 -> 14[label="",style="solid", color="burlywood", weight=3];
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14[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 [] (enumFrom (Pos Zero)))))",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 (wx40 : wx41) (numericEnumFrom (Pos Zero)))))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) []))",fontsize=16,color="black",shape="triangle"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 (wx40 : wx41) (Pos Zero : (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
18[label="Maybe.listToMaybe (foldr (++) [] [])",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
19[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zip0 wx40 (Pos Zero) : zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
20[label="Maybe.listToMaybe []",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
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22[label="Nothing",fontsize=16,color="green",shape="box"];23[label="Maybe.listToMaybe ((++) List.findIndices0 (wx3 ==) (zip0 wx40 (Pos Zero)) foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
24[label="Maybe.listToMaybe ((++) List.findIndices00 (wx3 ==) (zip0 wx40 (Pos Zero)) foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3];
25[label="Maybe.listToMaybe ((++) List.findIndices00 (wx3 ==) (wx40,Pos Zero) foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3];
26[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (wx3 == wx40) foldr (++) [] (map (List.findIndices0 (wx3 ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];338[label="wx3/LT",fontsize=10,color="white",style="solid",shape="box"];26 -> 338[label="",style="solid", color="burlywood", weight=9];
338 -> 27[label="",style="solid", color="burlywood", weight=3];
339[label="wx3/EQ",fontsize=10,color="white",style="solid",shape="box"];26 -> 339[label="",style="solid", color="burlywood", weight=9];
339 -> 28[label="",style="solid", color="burlywood", weight=3];
340[label="wx3/GT",fontsize=10,color="white",style="solid",shape="box"];26 -> 340[label="",style="solid", color="burlywood", weight=9];
340 -> 29[label="",style="solid", color="burlywood", weight=3];
27[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (LT == wx40) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];341[label="wx40/LT",fontsize=10,color="white",style="solid",shape="box"];27 -> 341[label="",style="solid", color="burlywood", weight=9];
341 -> 30[label="",style="solid", color="burlywood", weight=3];
342[label="wx40/EQ",fontsize=10,color="white",style="solid",shape="box"];27 -> 342[label="",style="solid", color="burlywood", weight=9];
342 -> 31[label="",style="solid", color="burlywood", weight=3];
343[label="wx40/GT",fontsize=10,color="white",style="solid",shape="box"];27 -> 343[label="",style="solid", color="burlywood", weight=9];
343 -> 32[label="",style="solid", color="burlywood", weight=3];
28[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (EQ == wx40) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];344[label="wx40/LT",fontsize=10,color="white",style="solid",shape="box"];28 -> 344[label="",style="solid", color="burlywood", weight=9];
344 -> 33[label="",style="solid", color="burlywood", weight=3];
345[label="wx40/EQ",fontsize=10,color="white",style="solid",shape="box"];28 -> 345[label="",style="solid", color="burlywood", weight=9];
345 -> 34[label="",style="solid", color="burlywood", weight=3];
346[label="wx40/GT",fontsize=10,color="white",style="solid",shape="box"];28 -> 346[label="",style="solid", color="burlywood", weight=9];
346 -> 35[label="",style="solid", color="burlywood", weight=3];
29[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (GT == wx40) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];347[label="wx40/LT",fontsize=10,color="white",style="solid",shape="box"];29 -> 347[label="",style="solid", color="burlywood", weight=9];
347 -> 36[label="",style="solid", color="burlywood", weight=3];
348[label="wx40/EQ",fontsize=10,color="white",style="solid",shape="box"];29 -> 348[label="",style="solid", color="burlywood", weight=9];
348 -> 37[label="",style="solid", color="burlywood", weight=3];
349[label="wx40/GT",fontsize=10,color="white",style="solid",shape="box"];29 -> 349[label="",style="solid", color="burlywood", weight=9];
349 -> 38[label="",style="solid", color="burlywood", weight=3];
30[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (LT == LT) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
31[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (LT == EQ) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
32[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (LT == GT) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
33[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (EQ == LT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
34[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (EQ == EQ) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
35[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (EQ == GT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
36[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (GT == LT) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
37[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (GT == EQ) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
38[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) (GT == GT) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
39[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) True foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
40[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="triangle"];40 -> 49[label="",style="solid", color="black", weight=3];
41 -> 40[label="",style="dashed", color="red", weight=0];
41[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="magenta"];42[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) False foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="triangle"];42 -> 50[label="",style="solid", color="black", weight=3];
43[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos Zero) True foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41 (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];43 -> 51[label="",style="solid", color="black", weight=3];
44 -> 42[label="",style="dashed", color="red", weight=0];
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298[label="primPlusNat (Succ wx500) Zero",fontsize=16,color="black",shape="box"];298 -> 301[label="",style="solid", color="black", weight=3];
299[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];299 -> 302[label="",style="solid", color="black", weight=3];
312[label="Maybe.listToMaybe ((++) List.findIndices0 (EQ ==) (zip0 wx41110 (Pos wx13)) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];312 -> 313[label="",style="solid", color="black", weight=3];
215[label="Maybe.listToMaybe ((++) List.findIndices00 (GT ==) (zip0 wx4110 (Pos (primPlusNat wx7 (Succ Zero)))) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];215 -> 218[label="",style="solid", color="black", weight=3];
216[label="Maybe.listToMaybe ((++) List.findIndices00 (LT ==) (wx4110,Pos (primPlusNat wx5 (Succ Zero))) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];216 -> 219[label="",style="solid", color="black", weight=3];
301[label="Succ wx500",fontsize=16,color="green",shape="box"];302[label="Zero",fontsize=16,color="green",shape="box"];313[label="Maybe.listToMaybe ((++) List.findIndices00 (EQ ==) (zip0 wx41110 (Pos wx13)) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];313 -> 314[label="",style="solid", color="black", weight=3];
218[label="Maybe.listToMaybe ((++) List.findIndices00 (GT ==) (wx4110,Pos (primPlusNat wx7 (Succ Zero))) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];218 -> 221[label="",style="solid", color="black", weight=3];
219[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) (LT == wx4110) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];360[label="wx4110/LT",fontsize=10,color="white",style="solid",shape="box"];219 -> 360[label="",style="solid", color="burlywood", weight=9];
360 -> 222[label="",style="solid", color="burlywood", weight=3];
361[label="wx4110/EQ",fontsize=10,color="white",style="solid",shape="box"];219 -> 361[label="",style="solid", color="burlywood", weight=9];
361 -> 223[label="",style="solid", color="burlywood", weight=3];
362[label="wx4110/GT",fontsize=10,color="white",style="solid",shape="box"];219 -> 362[label="",style="solid", color="burlywood", weight=9];
362 -> 224[label="",style="solid", color="burlywood", weight=3];
314[label="Maybe.listToMaybe ((++) List.findIndices00 (EQ ==) (wx41110,Pos wx13) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];314 -> 315[label="",style="solid", color="black", weight=3];
221[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) (GT == wx4110) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];363[label="wx4110/LT",fontsize=10,color="white",style="solid",shape="box"];221 -> 363[label="",style="solid", color="burlywood", weight=9];
363 -> 228[label="",style="solid", color="burlywood", weight=3];
364[label="wx4110/EQ",fontsize=10,color="white",style="solid",shape="box"];221 -> 364[label="",style="solid", color="burlywood", weight=9];
364 -> 229[label="",style="solid", color="burlywood", weight=3];
365[label="wx4110/GT",fontsize=10,color="white",style="solid",shape="box"];221 -> 365[label="",style="solid", color="burlywood", weight=9];
365 -> 230[label="",style="solid", color="burlywood", weight=3];
222[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) (LT == LT) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];222 -> 231[label="",style="solid", color="black", weight=3];
223[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) (LT == EQ) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];223 -> 232[label="",style="solid", color="black", weight=3];
224[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) (LT == GT) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];224 -> 233[label="",style="solid", color="black", weight=3];
315[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) (EQ == wx41110) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];366[label="wx41110/LT",fontsize=10,color="white",style="solid",shape="box"];315 -> 366[label="",style="solid", color="burlywood", weight=9];
366 -> 316[label="",style="solid", color="burlywood", weight=3];
367[label="wx41110/EQ",fontsize=10,color="white",style="solid",shape="box"];315 -> 367[label="",style="solid", color="burlywood", weight=9];
367 -> 317[label="",style="solid", color="burlywood", weight=3];
368[label="wx41110/GT",fontsize=10,color="white",style="solid",shape="box"];315 -> 368[label="",style="solid", color="burlywood", weight=9];
368 -> 318[label="",style="solid", color="burlywood", weight=3];
228[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) (GT == LT) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];228 -> 237[label="",style="solid", color="black", weight=3];
229[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) (GT == EQ) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];229 -> 238[label="",style="solid", color="black", weight=3];
230[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) (GT == GT) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];230 -> 239[label="",style="solid", color="black", weight=3];
231[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) True foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];231 -> 240[label="",style="solid", color="black", weight=3];
232[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="triangle"];232 -> 241[label="",style="solid", color="black", weight=3];
233 -> 232[label="",style="dashed", color="red", weight=0];
233[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx5 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="magenta"];316[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) (EQ == LT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];316 -> 319[label="",style="solid", color="black", weight=3];
317[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) (EQ == EQ) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];317 -> 320[label="",style="solid", color="black", weight=3];
318[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) (EQ == GT) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];318 -> 321[label="",style="solid", color="black", weight=3];
237[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="triangle"];237 -> 244[label="",style="solid", color="black", weight=3];
238 -> 237[label="",style="dashed", color="red", weight=0];
238[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) False foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="magenta"];239[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos (primPlusNat wx7 (Succ Zero))) True foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];239 -> 245[label="",style="solid", color="black", weight=3];
240[label="Maybe.listToMaybe ((++) (Pos (primPlusNat wx5 (Succ Zero)) : []) foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];240 -> 246[label="",style="solid", color="black", weight=3];
241[label="Maybe.listToMaybe ((++) [] foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];241 -> 247[label="",style="solid", color="black", weight=3];
319[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) False foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="triangle"];319 -> 322[label="",style="solid", color="black", weight=3];
320[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) True foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];320 -> 323[label="",style="solid", color="black", weight=3];
321 -> 319[label="",style="dashed", color="red", weight=0];
321[label="Maybe.listToMaybe ((++) List.findIndices000 (Pos wx13) False foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="magenta"];244[label="Maybe.listToMaybe ((++) [] foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];244 -> 250[label="",style="solid", color="black", weight=3];
245[label="Maybe.listToMaybe ((++) (Pos (primPlusNat wx7 (Succ Zero)) : []) foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];245 -> 251[label="",style="solid", color="black", weight=3];
246[label="Maybe.listToMaybe (Pos (primPlusNat wx5 (Succ Zero)) : [] ++ foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];246 -> 252[label="",style="solid", color="black", weight=3];
247[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];369[label="wx4111/wx41110 : wx41111",fontsize=10,color="white",style="solid",shape="box"];247 -> 369[label="",style="solid", color="burlywood", weight=9];
369 -> 253[label="",style="solid", color="burlywood", weight=3];
370[label="wx4111/[]",fontsize=10,color="white",style="solid",shape="box"];247 -> 370[label="",style="solid", color="burlywood", weight=9];
370 -> 254[label="",style="solid", color="burlywood", weight=3];
322[label="Maybe.listToMaybe ((++) [] foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];322 -> 324[label="",style="solid", color="black", weight=3];
323[label="Maybe.listToMaybe ((++) (Pos wx13 : []) foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];323 -> 325[label="",style="solid", color="black", weight=3];
250[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];371[label="wx4111/wx41110 : wx41111",fontsize=10,color="white",style="solid",shape="box"];250 -> 371[label="",style="solid", color="burlywood", weight=9];
371 -> 258[label="",style="solid", color="burlywood", weight=3];
372[label="wx4111/[]",fontsize=10,color="white",style="solid",shape="box"];250 -> 372[label="",style="solid", color="burlywood", weight=9];
372 -> 259[label="",style="solid", color="burlywood", weight=3];
251[label="Maybe.listToMaybe (Pos (primPlusNat wx7 (Succ Zero)) : [] ++ foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 wx4111 (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];251 -> 260[label="",style="solid", color="black", weight=3];
252[label="Just (Pos (primPlusNat wx5 (Succ Zero)))",fontsize=16,color="green",shape="box"];252 -> 261[label="",style="dashed", color="green", weight=3];
253[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 (wx41110 : wx41111) (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];253 -> 262[label="",style="solid", color="black", weight=3];
254[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 [] (numericEnumFrom $! Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];254 -> 263[label="",style="solid", color="black", weight=3];
324[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="burlywood",shape="box"];373[label="wx41111/wx411110 : wx411111",fontsize=10,color="white",style="solid",shape="box"];324 -> 373[label="",style="solid", color="burlywood", weight=9];
373 -> 326[label="",style="solid", color="burlywood", weight=3];
374[label="wx41111/[]",fontsize=10,color="white",style="solid",shape="box"];324 -> 374[label="",style="solid", color="burlywood", weight=9];
374 -> 327[label="",style="solid", color="burlywood", weight=3];
325[label="Maybe.listToMaybe (Pos wx13 : [] ++ foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 wx41111 (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];325 -> 328[label="",style="solid", color="black", weight=3];
258[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (wx41110 : wx41111) (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];258 -> 267[label="",style="solid", color="black", weight=3];
259[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 [] (numericEnumFrom $! Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];259 -> 268[label="",style="solid", color="black", weight=3];
260[label="Just (Pos (primPlusNat wx7 (Succ Zero)))",fontsize=16,color="green",shape="box"];260 -> 269[label="",style="dashed", color="green", weight=3];
262 -> 163[label="",style="dashed", color="red", weight=0];
262[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (LT ==)) (zipWith zip0 (wx41110 : wx41111) (Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (primPlusNat wx5 (Succ Zero)) + fromInt (Pos (Succ Zero)))))))",fontsize=16,color="magenta"];262 -> 272[label="",style="dashed", color="magenta", weight=3];
262 -> 273[label="",style="dashed", color="magenta", weight=3];
262 -> 274[label="",style="dashed", color="magenta", weight=3];
262 -> 275[label="",style="dashed", color="magenta", weight=3];
263 -> 16[label="",style="dashed", color="red", weight=0];
263[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (LT ==)) []))",fontsize=16,color="magenta"];263 -> 276[label="",style="dashed", color="magenta", weight=3];
326[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (wx411110 : wx411111) (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];326 -> 329[label="",style="solid", color="black", weight=3];
327[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 [] (numericEnumFrom $! Pos wx13 + fromInt (Pos (Succ Zero))))))",fontsize=16,color="black",shape="box"];327 -> 330[label="",style="solid", color="black", weight=3];
328[label="Just (Pos wx13)",fontsize=16,color="green",shape="box"];267 -> 174[label="",style="dashed", color="red", weight=0];
267[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (GT ==)) (zipWith zip0 (wx41110 : wx41111) (Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos (primPlusNat wx7 (Succ Zero)) + fromInt (Pos (Succ Zero)))))))",fontsize=16,color="magenta"];267 -> 285[label="",style="dashed", color="magenta", weight=3];
267 -> 286[label="",style="dashed", color="magenta", weight=3];
267 -> 287[label="",style="dashed", color="magenta", weight=3];
267 -> 288[label="",style="dashed", color="magenta", weight=3];
268 -> 16[label="",style="dashed", color="red", weight=0];
268[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (GT ==)) []))",fontsize=16,color="magenta"];268 -> 289[label="",style="dashed", color="magenta", weight=3];
269 -> 261[label="",style="dashed", color="red", weight=0];
269[label="primPlusNat wx7 (Succ Zero)",fontsize=16,color="magenta"];269 -> 290[label="",style="dashed", color="magenta", weight=3];
272 -> 261[label="",style="dashed", color="red", weight=0];
272[label="primPlusNat wx5 (Succ Zero)",fontsize=16,color="magenta"];273[label="wx41111",fontsize=16,color="green",shape="box"];274 -> 261[label="",style="dashed", color="red", weight=0];
274[label="primPlusNat wx5 (Succ Zero)",fontsize=16,color="magenta"];275[label="wx41110",fontsize=16,color="green",shape="box"];276[label="LT",fontsize=16,color="green",shape="box"];329 -> 277[label="",style="dashed", color="red", weight=0];
329[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (EQ ==)) (zipWith zip0 (wx411110 : wx411111) (Pos wx13 + fromInt (Pos (Succ Zero)) `seq` numericEnumFrom (Pos wx13 + fromInt (Pos (Succ Zero)))))))",fontsize=16,color="magenta"];329 -> 331[label="",style="dashed", color="magenta", weight=3];
329 -> 332[label="",style="dashed", color="magenta", weight=3];
329 -> 333[label="",style="dashed", color="magenta", weight=3];
329 -> 334[label="",style="dashed", color="magenta", weight=3];
330 -> 16[label="",style="dashed", color="red", weight=0];
330[label="Maybe.listToMaybe (foldr (++) [] (map (List.findIndices0 (EQ ==)) []))",fontsize=16,color="magenta"];330 -> 335[label="",style="dashed", color="magenta", weight=3];
285[label="wx41111",fontsize=16,color="green",shape="box"];286[label="wx41110",fontsize=16,color="green",shape="box"];287 -> 261[label="",style="dashed", color="red", weight=0];
287[label="primPlusNat wx7 (Succ Zero)",fontsize=16,color="magenta"];287 -> 294[label="",style="dashed", color="magenta", weight=3];
288 -> 261[label="",style="dashed", color="red", weight=0];
288[label="primPlusNat wx7 (Succ Zero)",fontsize=16,color="magenta"];288 -> 295[label="",style="dashed", color="magenta", weight=3];
289[label="GT",fontsize=16,color="green",shape="box"];290[label="wx7",fontsize=16,color="green",shape="box"];331[label="wx411110",fontsize=16,color="green",shape="box"];332[label="wx13",fontsize=16,color="green",shape="box"];333[label="wx13",fontsize=16,color="green",shape="box"];334[label="wx411111",fontsize=16,color="green",shape="box"];335[label="EQ",fontsize=16,color="green",shape="box"];294[label="wx7",fontsize=16,color="green",shape="box"];295[label="wx7",fontsize=16,color="green",shape="box"];}

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

(14)
Complex Obligation (AND)

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

(15)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_listToMaybe5(GT, wx4111, wx5, wx6) -> new_listToMaybe4(wx5, wx4111)
   new_listToMaybe4(wx5, :(wx41110, wx41111)) -> new_listToMaybe5(wx41110, wx41111, new_primPlusNat(wx5), new_primPlusNat(wx5))
   new_listToMaybe5(EQ, :(wx41110, wx41111), wx5, wx6) -> new_listToMaybe5(wx41110, wx41111, new_primPlusNat(wx5), new_primPlusNat(wx5))

The TRS R consists of the following rules:

   new_primPlusNat(Succ(wx50)) -> Succ(Succ(new_primPlusNat0(wx50)))
   new_primPlusNat(Zero) -> Succ(Zero)
   new_primPlusNat0(Succ(wx500)) -> Succ(wx500)
   new_primPlusNat0(Zero) -> Zero

The set Q consists of the following terms:

   new_primPlusNat0(Succ(x0))
   new_primPlusNat0(Zero)
   new_primPlusNat(Succ(x0))
   new_primPlusNat(Zero)

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

(16) 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_listToMaybe4(wx5, :(wx41110, wx41111)) -> new_listToMaybe5(wx41110, wx41111, new_primPlusNat(wx5), new_primPlusNat(wx5))
The graph contains the following edges 2 > 1, 2 > 2


*new_listToMaybe5(EQ, :(wx41110, wx41111), wx5, wx6) -> new_listToMaybe5(wx41110, wx41111, new_primPlusNat(wx5), new_primPlusNat(wx5))
The graph contains the following edges 2 > 1, 2 > 2


*new_listToMaybe5(GT, wx4111, wx5, wx6) -> new_listToMaybe4(wx5, wx4111)
The graph contains the following edges 3 >= 1, 2 >= 2


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(17)
YES

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(18)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_listToMaybe1(GT, wx41111, wx14, wx13) -> new_listToMaybe3(wx13, wx41111)
   new_listToMaybe2(wx41110, wx41111, wx11, wx12) -> new_listToMaybe1(wx41110, wx41111, new_primPlusNat(wx11), new_primPlusNat(wx11))
   new_listToMaybe1(LT, :(wx411110, wx411111), wx14, wx13) -> new_listToMaybe2(wx411110, wx411111, wx13, wx13)
   new_listToMaybe3(wx13, :(wx411110, wx411111)) -> new_listToMaybe2(wx411110, wx411111, wx13, wx13)

The TRS R consists of the following rules:

   new_primPlusNat(Succ(wx50)) -> Succ(Succ(new_primPlusNat0(wx50)))
   new_primPlusNat(Zero) -> Succ(Zero)
   new_primPlusNat0(Succ(wx500)) -> Succ(wx500)
   new_primPlusNat0(Zero) -> Zero

The set Q consists of the following terms:

   new_primPlusNat0(Succ(x0))
   new_primPlusNat0(Zero)
   new_primPlusNat(Succ(x0))
   new_primPlusNat(Zero)

We have to consider all minimal (P,Q,R)-chains.
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(19) TransformationProof (EQUIVALENT)
By instantiating [LPAR04] the rule new_listToMaybe2(wx41110, wx41111, wx11, wx12) -> new_listToMaybe1(wx41110, wx41111, new_primPlusNat(wx11), new_primPlusNat(wx11)) we obtained the following new rules [LPAR04]:

   (new_listToMaybe2(z0, z1, z3, z3) -> new_listToMaybe1(z0, z1, new_primPlusNat(z3), new_primPlusNat(z3)),new_listToMaybe2(z0, z1, z3, z3) -> new_listToMaybe1(z0, z1, new_primPlusNat(z3), new_primPlusNat(z3)))


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(20)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_listToMaybe1(GT, wx41111, wx14, wx13) -> new_listToMaybe3(wx13, wx41111)
   new_listToMaybe1(LT, :(wx411110, wx411111), wx14, wx13) -> new_listToMaybe2(wx411110, wx411111, wx13, wx13)
   new_listToMaybe3(wx13, :(wx411110, wx411111)) -> new_listToMaybe2(wx411110, wx411111, wx13, wx13)
   new_listToMaybe2(z0, z1, z3, z3) -> new_listToMaybe1(z0, z1, new_primPlusNat(z3), new_primPlusNat(z3))

The TRS R consists of the following rules:

   new_primPlusNat(Succ(wx50)) -> Succ(Succ(new_primPlusNat0(wx50)))
   new_primPlusNat(Zero) -> Succ(Zero)
   new_primPlusNat0(Succ(wx500)) -> Succ(wx500)
   new_primPlusNat0(Zero) -> Zero

The set Q consists of the following terms:

   new_primPlusNat0(Succ(x0))
   new_primPlusNat0(Zero)
   new_primPlusNat(Succ(x0))
   new_primPlusNat(Zero)

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

(21) 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_listToMaybe3(wx13, :(wx411110, wx411111)) -> new_listToMaybe2(wx411110, wx411111, wx13, wx13)
The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 1 >= 4


*new_listToMaybe2(z0, z1, z3, z3) -> new_listToMaybe1(z0, z1, new_primPlusNat(z3), new_primPlusNat(z3))
The graph contains the following edges 1 >= 1, 2 >= 2


*new_listToMaybe1(GT, wx41111, wx14, wx13) -> new_listToMaybe3(wx13, wx41111)
The graph contains the following edges 4 >= 1, 2 >= 2


*new_listToMaybe1(LT, :(wx411110, wx411111), wx14, wx13) -> new_listToMaybe2(wx411110, wx411111, wx13, wx13)
The graph contains the following edges 2 > 1, 2 > 2, 4 >= 3, 4 >= 4


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(22)
YES

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(23)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_listToMaybe(LT, :(wx41110, wx41111), wx7, wx8) -> new_listToMaybe(wx41110, wx41111, new_primPlusNat(wx7), new_primPlusNat(wx7))
   new_listToMaybe(EQ, wx4111, wx7, wx8) -> new_listToMaybe0(wx7, wx4111)
   new_listToMaybe0(wx7, :(wx41110, wx41111)) -> new_listToMaybe(wx41110, wx41111, new_primPlusNat(wx7), new_primPlusNat(wx7))

The TRS R consists of the following rules:

   new_primPlusNat(Succ(wx50)) -> Succ(Succ(new_primPlusNat0(wx50)))
   new_primPlusNat(Zero) -> Succ(Zero)
   new_primPlusNat0(Succ(wx500)) -> Succ(wx500)
   new_primPlusNat0(Zero) -> Zero

The set Q consists of the following terms:

   new_primPlusNat0(Succ(x0))
   new_primPlusNat0(Zero)
   new_primPlusNat(Succ(x0))
   new_primPlusNat(Zero)

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

(24) 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_listToMaybe(LT, :(wx41110, wx41111), wx7, wx8) -> new_listToMaybe(wx41110, wx41111, new_primPlusNat(wx7), new_primPlusNat(wx7))
The graph contains the following edges 2 > 1, 2 > 2


*new_listToMaybe(EQ, wx4111, wx7, wx8) -> new_listToMaybe0(wx7, wx4111)
The graph contains the following edges 3 >= 1, 2 >= 2


*new_listToMaybe0(wx7, :(wx41110, wx41111)) -> new_listToMaybe(wx41110, wx41111, new_primPlusNat(wx7), new_primPlusNat(wx7))
The graph contains the following edges 2 > 1, 2 > 2


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(25)
YES