/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) HASKELL
(1) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) BR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) COR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) LetRed [EQUIVALENT, 0 ms]
(8) HASKELL
(9) NumRed [SOUND, 0 ms]
(10) HASKELL
(11) Narrow [SOUND, 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 Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
replicateM_ :: Monad a => Int  ->  a b  ->  a ();
replicateM_ n x = sequence_ (replicate n x);

}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\_->q"
is transformed to
"gtGt0 q _ = q;
"

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
replicateM_ :: Monad b => Int  ->  b a  ->  b ();
replicateM_ n x = sequence_ (replicate n x);

}

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

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

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
replicateM_ :: Monad b => Int  ->  b a  ->  b ();
replicateM_ n x = sequence_ (replicate n x);

}

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

(5) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"
The following Function with conditions
"take n vx|n <= 0[];
take vy [] = [];
take n (x : xs) = x : take (n - 1) xs;
"
is transformed to
"take n vx = take3 n vx;
take vy [] = take1 vy [];
take n (x : xs) = take0 n (x : xs);
"
"take0 n (x : xs) = x : take (n - 1) xs;
"
"take1 vy [] = [];
take1 wx wy = take0 wx wy;
"
"take2 n vx True = [];
take2 n vx False = take1 n vx;
"
"take3 n vx = take2 n vx (n <= 0);
take3 wz xu = take1 wz xu;
"

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

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
replicateM_ :: Monad b => Int  ->  b a  ->  b ();
replicateM_ n x = sequence_ (replicate n x);

}

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

(7) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"xs where {
xs  = x : xs;
} 
"
are unpacked to the following functions on top level
"repeatXs xv = xv : repeatXs xv;
"

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

(8)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
replicateM_ :: Monad b => Int  ->  b a  ->  b ();
replicateM_ n x = sequence_ (replicate n x);

}

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

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

(10)
Obligation:
mainModule Main 
module Maybe where {
import qualified Main;
import qualified Monad;
import qualified Prelude;
}
module Main where {
import qualified Maybe;
import qualified Monad;
import qualified Prelude;
}
module Monad where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
replicateM_ :: Monad b => Int  ->  b a  ->  b ();
replicateM_ n x = sequence_ (replicate n x);

}

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

(11) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="Monad.replicateM_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="Monad.replicateM_ xw3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="Monad.replicateM_ xw3 xw4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="sequence_ (replicate xw3 xw4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="foldr (>>) (return ()) (replicate xw3 xw4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="foldr (>>) (return ()) (take xw3 (repeat xw4))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="foldr (>>) (return ()) (take3 xw3 (repeat xw4))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (xw3 <= Pos Zero))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (compare xw3 (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (not (compare xw3 (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="foldr (>>) (return ()) (take2 xw3 (repeat xw4) (not (primCmpInt xw3 (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];398[label="xw3/Pos xw30",fontsize=10,color="white",style="solid",shape="box"];12 -> 398[label="",style="solid", color="burlywood", weight=9];
398 -> 13[label="",style="solid", color="burlywood", weight=3];
399[label="xw3/Neg xw30",fontsize=10,color="white",style="solid",shape="box"];12 -> 399[label="",style="solid", color="burlywood", weight=9];
399 -> 14[label="",style="solid", color="burlywood", weight=3];
13[label="foldr (>>) (return ()) (take2 (Pos xw30) (repeat xw4) (not (primCmpInt (Pos xw30) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];400[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];13 -> 400[label="",style="solid", color="burlywood", weight=9];
400 -> 15[label="",style="solid", color="burlywood", weight=3];
401[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 401[label="",style="solid", color="burlywood", weight=9];
401 -> 16[label="",style="solid", color="burlywood", weight=3];
14[label="foldr (>>) (return ()) (take2 (Neg xw30) (repeat xw4) (not (primCmpInt (Neg xw30) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];402[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];14 -> 402[label="",style="solid", color="burlywood", weight=9];
402 -> 17[label="",style="solid", color="burlywood", weight=3];
403[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 403[label="",style="solid", color="burlywood", weight=9];
403 -> 18[label="",style="solid", color="burlywood", weight=3];
15[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not (primCmpInt (Pos (Succ xw300)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) (not (primCmpInt (Neg (Succ xw300)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not (primCmpNat (Succ xw300) Zero == GT)))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) (not (LT == GT)))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not (GT == GT)))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) (not False))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) (not False))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) (not False))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
27[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) (not True))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28[label="foldr (>>) (return ()) (take2 (Pos Zero) (repeat xw4) True)",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
29[label="foldr (>>) (return ()) (take2 (Neg (Succ xw300)) (repeat xw4) True)",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
30[label="foldr (>>) (return ()) (take2 (Neg Zero) (repeat xw4) True)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
31[label="foldr (>>) (return ()) (take2 (Pos (Succ xw300)) (repeat xw4) False)",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
32[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="triangle"];32 -> 36[label="",style="solid", color="black", weight=3];
33 -> 32[label="",style="dashed", color="red", weight=0];
33[label="foldr (>>) (return ()) []",fontsize=16,color="magenta"];34 -> 32[label="",style="dashed", color="red", weight=0];
34[label="foldr (>>) (return ()) []",fontsize=16,color="magenta"];35[label="foldr (>>) (return ()) (take1 (Pos (Succ xw300)) (repeat xw4))",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
36[label="return ()",fontsize=16,color="blue",shape="box"];404[label="return :: () -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];36 -> 404[label="",style="solid", color="blue", weight=9];
404 -> 38[label="",style="solid", color="blue", weight=3];
405[label="return :: () -> [] ()",fontsize=10,color="white",style="solid",shape="box"];36 -> 405[label="",style="solid", color="blue", weight=9];
405 -> 39[label="",style="solid", color="blue", weight=3];
406[label="return :: () -> IO ()",fontsize=10,color="white",style="solid",shape="box"];36 -> 406[label="",style="solid", color="blue", weight=9];
406 -> 40[label="",style="solid", color="blue", weight=3];
37[label="foldr (>>) (return ()) (take1 (Pos (Succ xw300)) (repeatXs xw4))",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3];
38[label="return ()",fontsize=16,color="black",shape="triangle"];38 -> 42[label="",style="solid", color="black", weight=3];
39[label="return ()",fontsize=16,color="black",shape="triangle"];39 -> 43[label="",style="solid", color="black", weight=3];
40[label="return ()",fontsize=16,color="black",shape="triangle"];40 -> 44[label="",style="solid", color="black", weight=3];
41[label="foldr (>>) (return ()) (take1 (Pos (Succ xw300)) (xw4 : repeatXs xw4))",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3];
42[label="Just ()",fontsize=16,color="green",shape="box"];43[label="() : []",fontsize=16,color="green",shape="box"];44[label="primretIO ()",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
45[label="foldr (>>) (return ()) (take0 (Pos (Succ xw300)) (xw4 : repeatXs xw4))",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
46[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];47[label="foldr (>>) (return ()) (xw4 : take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="box"];47 -> 48[label="",style="solid", color="black", weight=3];
48[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="blue",shape="box"];407[label=">> :: (Maybe a) -> (Maybe ()) -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];48 -> 407[label="",style="solid", color="blue", weight=9];
407 -> 49[label="",style="solid", color="blue", weight=3];
408[label=">> :: ([] a) -> ([] ()) -> [] ()",fontsize=10,color="white",style="solid",shape="box"];48 -> 408[label="",style="solid", color="blue", weight=9];
408 -> 50[label="",style="solid", color="blue", weight=3];
409[label=">> :: (IO a) -> (IO ()) -> IO ()",fontsize=10,color="white",style="solid",shape="box"];48 -> 409[label="",style="solid", color="blue", weight=9];
409 -> 51[label="",style="solid", color="blue", weight=3];
49 -> 52[label="",style="dashed", color="red", weight=0];
49[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="magenta"];49 -> 53[label="",style="dashed", color="magenta", weight=3];
50 -> 54[label="",style="dashed", color="red", weight=0];
50[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="magenta"];50 -> 55[label="",style="dashed", color="magenta", weight=3];
51 -> 56[label="",style="dashed", color="red", weight=0];
51[label="(>>) xw4 foldr (>>) (return ()) (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="magenta"];51 -> 57[label="",style="dashed", color="magenta", weight=3];
53 -> 38[label="",style="dashed", color="red", weight=0];
53[label="return ()",fontsize=16,color="magenta"];52[label="(>>) xw4 foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="triangle"];52 -> 58[label="",style="solid", color="black", weight=3];
55 -> 39[label="",style="dashed", color="red", weight=0];
55[label="return ()",fontsize=16,color="magenta"];54[label="(>>) xw4 foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="triangle"];54 -> 59[label="",style="solid", color="black", weight=3];
57 -> 40[label="",style="dashed", color="red", weight=0];
57[label="return ()",fontsize=16,color="magenta"];56[label="(>>) xw4 foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))",fontsize=16,color="black",shape="triangle"];56 -> 60[label="",style="solid", color="black", weight=3];
58[label="xw4 >>= gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4)))",fontsize=16,color="burlywood",shape="box"];410[label="xw4/Nothing",fontsize=10,color="white",style="solid",shape="box"];58 -> 410[label="",style="solid", color="burlywood", weight=9];
410 -> 61[label="",style="solid", color="burlywood", weight=3];
411[label="xw4/Just xw40",fontsize=10,color="white",style="solid",shape="box"];58 -> 411[label="",style="solid", color="burlywood", weight=9];
411 -> 62[label="",style="solid", color="burlywood", weight=3];
59[label="xw4 >>= gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4)))",fontsize=16,color="burlywood",shape="box"];412[label="xw4/xw40 : xw41",fontsize=10,color="white",style="solid",shape="box"];59 -> 412[label="",style="solid", color="burlywood", weight=9];
412 -> 63[label="",style="solid", color="burlywood", weight=3];
413[label="xw4/[]",fontsize=10,color="white",style="solid",shape="box"];59 -> 413[label="",style="solid", color="burlywood", weight=9];
413 -> 64[label="",style="solid", color="burlywood", weight=3];
60[label="xw4 >>= gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4)))",fontsize=16,color="black",shape="box"];60 -> 65[label="",style="solid", color="black", weight=3];
61[label="Nothing >>= gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs Nothing)))",fontsize=16,color="black",shape="box"];61 -> 66[label="",style="solid", color="black", weight=3];
62[label="Just xw40 >>= gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40))))",fontsize=16,color="black",shape="box"];62 -> 67[label="",style="solid", color="black", weight=3];
63[label="xw40 : xw41 >>= gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41))))",fontsize=16,color="black",shape="box"];63 -> 68[label="",style="solid", color="black", weight=3];
64[label="[] >>= gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs [])))",fontsize=16,color="black",shape="box"];64 -> 69[label="",style="solid", color="black", weight=3];
65[label="primbindIO xw4 (gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs xw4))))",fontsize=16,color="burlywood",shape="box"];414[label="xw4/IO xw40",fontsize=10,color="white",style="solid",shape="box"];65 -> 414[label="",style="solid", color="burlywood", weight=9];
414 -> 70[label="",style="solid", color="burlywood", weight=3];
415[label="xw4/AProVE_IO xw40",fontsize=10,color="white",style="solid",shape="box"];65 -> 415[label="",style="solid", color="burlywood", weight=9];
415 -> 71[label="",style="solid", color="burlywood", weight=3];
416[label="xw4/AProVE_Exception xw40",fontsize=10,color="white",style="solid",shape="box"];65 -> 416[label="",style="solid", color="burlywood", weight=9];
416 -> 72[label="",style="solid", color="burlywood", weight=3];
417[label="xw4/AProVE_Error xw40",fontsize=10,color="white",style="solid",shape="box"];65 -> 417[label="",style="solid", color="burlywood", weight=9];
417 -> 73[label="",style="solid", color="burlywood", weight=3];
66[label="Nothing",fontsize=16,color="green",shape="box"];67[label="gtGt0 (foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)))) xw40",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
68[label="gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))) xw40 ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];68 -> 75[label="",style="solid", color="black", weight=3];
69[label="[]",fontsize=16,color="green",shape="box"];70[label="primbindIO (IO xw40) (gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (IO xw40)))))",fontsize=16,color="black",shape="box"];70 -> 76[label="",style="solid", color="black", weight=3];
71[label="primbindIO (AProVE_IO xw40) (gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))))",fontsize=16,color="black",shape="box"];71 -> 77[label="",style="solid", color="black", weight=3];
72[label="primbindIO (AProVE_Exception xw40) (gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_Exception xw40)))))",fontsize=16,color="black",shape="box"];72 -> 78[label="",style="solid", color="black", weight=3];
73[label="primbindIO (AProVE_Error xw40) (gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_Error xw40)))))",fontsize=16,color="black",shape="box"];73 -> 79[label="",style="solid", color="black", weight=3];
74[label="foldr (>>) xw5 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];74 -> 80[label="",style="solid", color="black", weight=3];
75[label="foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];75 -> 81[label="",style="solid", color="black", weight=3];
76[label="error []",fontsize=16,color="red",shape="box"];77[label="gtGt0 (foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))) xw40",fontsize=16,color="black",shape="box"];77 -> 82[label="",style="solid", color="black", weight=3];
78[label="AProVE_Exception xw40",fontsize=16,color="green",shape="box"];79[label="AProVE_Error xw40",fontsize=16,color="green",shape="box"];80[label="foldr (>>) xw5 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];80 -> 83[label="",style="solid", color="black", weight=3];
81[label="foldr (>>) xw6 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];81 -> 84[label="",style="solid", color="black", weight=3];
82[label="foldr (>>) xw7 (take (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];82 -> 85[label="",style="solid", color="black", weight=3];
83[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero))",fontsize=16,color="black",shape="box"];83 -> 86[label="",style="solid", color="black", weight=3];
84[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero)) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero))))",fontsize=16,color="black",shape="box"];84 -> 87[label="",style="solid", color="black", weight=3];
85[label="foldr (>>) xw7 (take3 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];85 -> 88[label="",style="solid", color="black", weight=3];
86[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];86 -> 89[label="",style="solid", color="black", weight=3];
87[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT)) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT))))",fontsize=16,color="black",shape="box"];87 -> 90[label="",style="solid", color="black", weight=3];
88[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (Pos (Succ xw300) - Pos (Succ Zero) <= Pos Zero))",fontsize=16,color="black",shape="box"];88 -> 91[label="",style="solid", color="black", weight=3];
89[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];89 -> 92[label="",style="solid", color="black", weight=3];
90[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];90 -> 93[label="",style="solid", color="black", weight=3];
91[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) /= GT))",fontsize=16,color="black",shape="box"];91 -> 94[label="",style="solid", color="black", weight=3];
92[label="foldr (>>) xw5 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (Just xw40)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];92 -> 95[label="",style="solid", color="black", weight=3];
93[label="foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];93 -> 96[label="",style="solid", color="black", weight=3];
94[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (not (compare (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];94 -> 97[label="",style="solid", color="black", weight=3];
95[label="foldr (>>) xw5 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (Just xw40)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];95 -> 98[label="",style="solid", color="black", weight=3];
96[label="foldr (>>) xw6 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];96 -> 99[label="",style="solid", color="black", weight=3];
97[label="foldr (>>) xw7 (take2 (Pos (Succ xw300) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (Pos (Succ xw300) - Pos (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];97 -> 100[label="",style="solid", color="black", weight=3];
98[label="foldr (>>) xw5 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];98 -> 101[label="",style="solid", color="black", weight=3];
99[label="foldr (>>) xw6 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];99 -> 102[label="",style="solid", color="black", weight=3];
100[label="foldr (>>) xw7 (take2 (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];100 -> 103[label="",style="solid", color="black", weight=3];
101[label="foldr (>>) xw5 (take2 (primMinusNat xw300 Zero) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];418[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];101 -> 418[label="",style="solid", color="burlywood", weight=9];
418 -> 104[label="",style="solid", color="burlywood", weight=3];
419[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];101 -> 419[label="",style="solid", color="burlywood", weight=9];
419 -> 105[label="",style="solid", color="burlywood", weight=3];
102[label="foldr (>>) xw6 (take2 (primMinusNat xw300 Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (primMinusNat xw300 Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT)))))",fontsize=16,color="burlywood",shape="box"];420[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];102 -> 420[label="",style="solid", color="burlywood", weight=9];
420 -> 106[label="",style="solid", color="burlywood", weight=3];
421[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];102 -> 421[label="",style="solid", color="burlywood", weight=9];
421 -> 107[label="",style="solid", color="burlywood", weight=3];
103[label="foldr (>>) xw7 (take2 (primMinusNat (Succ xw300) (Succ Zero)) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat (Succ xw300) (Succ Zero)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];103 -> 108[label="",style="solid", color="black", weight=3];
104[label="foldr (>>) xw5 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];104 -> 109[label="",style="solid", color="black", weight=3];
105[label="foldr (>>) xw5 (take2 (primMinusNat Zero Zero) (repeatXs (Just xw40)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];105 -> 110[label="",style="solid", color="black", weight=3];
106[label="foldr (>>) xw6 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];106 -> 111[label="",style="solid", color="black", weight=3];
107[label="foldr (>>) xw6 (take2 (primMinusNat Zero Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (primMinusNat Zero Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];107 -> 112[label="",style="solid", color="black", weight=3];
108[label="foldr (>>) xw7 (take2 (primMinusNat xw300 Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat xw300 Zero) (Pos Zero) == GT)))",fontsize=16,color="burlywood",shape="box"];422[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];108 -> 422[label="",style="solid", color="burlywood", weight=9];
422 -> 113[label="",style="solid", color="burlywood", weight=3];
423[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 423[label="",style="solid", color="burlywood", weight=9];
423 -> 114[label="",style="solid", color="burlywood", weight=3];
109[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];109 -> 115[label="",style="solid", color="black", weight=3];
110[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];110 -> 116[label="",style="solid", color="black", weight=3];
111[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];111 -> 117[label="",style="solid", color="black", weight=3];
112[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))))",fontsize=16,color="black",shape="box"];112 -> 118[label="",style="solid", color="black", weight=3];
113[label="foldr (>>) xw7 (take2 (primMinusNat (Succ xw3000) Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat (Succ xw3000) Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];113 -> 119[label="",style="solid", color="black", weight=3];
114[label="foldr (>>) xw7 (take2 (primMinusNat Zero Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (primMinusNat Zero Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];114 -> 120[label="",style="solid", color="black", weight=3];
115[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not (primCmpNat (Succ xw3000) Zero == GT)))",fontsize=16,color="black",shape="box"];115 -> 121[label="",style="solid", color="black", weight=3];
116[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];116 -> 122[label="",style="solid", color="black", weight=3];
117[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpNat (Succ xw3000) Zero == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (primCmpNat (Succ xw3000) Zero == GT)))))",fontsize=16,color="black",shape="box"];117 -> 123[label="",style="solid", color="black", weight=3];
118[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (EQ == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not (EQ == GT)))))",fontsize=16,color="black",shape="box"];118 -> 124[label="",style="solid", color="black", weight=3];
119[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (Pos (Succ xw3000)) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];119 -> 125[label="",style="solid", color="black", weight=3];
120[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];120 -> 126[label="",style="solid", color="black", weight=3];
121[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not (GT == GT)))",fontsize=16,color="black",shape="box"];121 -> 127[label="",style="solid", color="black", weight=3];
122[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) (not False))",fontsize=16,color="black",shape="box"];122 -> 128[label="",style="solid", color="black", weight=3];
123[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (GT == GT))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not (GT == GT)))))",fontsize=16,color="black",shape="box"];123 -> 129[label="",style="solid", color="black", weight=3];
124[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not False)) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) (not False))))",fontsize=16,color="black",shape="box"];124 -> 130[label="",style="solid", color="black", weight=3];
125[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not (primCmpNat (Succ xw3000) Zero == GT)))",fontsize=16,color="black",shape="box"];125 -> 131[label="",style="solid", color="black", weight=3];
126[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) (not (EQ == GT)))",fontsize=16,color="black",shape="box"];126 -> 132[label="",style="solid", color="black", weight=3];
127[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) (not True))",fontsize=16,color="black",shape="box"];127 -> 133[label="",style="solid", color="black", weight=3];
128[label="foldr (>>) xw5 (take2 (Pos Zero) (repeatXs (Just xw40)) True)",fontsize=16,color="black",shape="box"];128 -> 134[label="",style="solid", color="black", weight=3];
129[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not True)) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) (not True))))",fontsize=16,color="black",shape="box"];129 -> 135[label="",style="solid", color="black", weight=3];
130[label="foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) True) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos Zero) (repeatXs (xw40 : xw41)) True)))",fontsize=16,color="black",shape="box"];130 -> 136[label="",style="solid", color="black", weight=3];
131[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not (GT == GT)))",fontsize=16,color="black",shape="box"];131 -> 137[label="",style="solid", color="black", weight=3];
132[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) (not False))",fontsize=16,color="black",shape="box"];132 -> 138[label="",style="solid", color="black", weight=3];
133[label="foldr (>>) xw5 (take2 (Pos (Succ xw3000)) (repeatXs (Just xw40)) False)",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3];
134[label="foldr (>>) xw5 []",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3];
135[label="foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) False) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take2 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)) False)))",fontsize=16,color="black",shape="box"];135 -> 141[label="",style="solid", color="black", weight=3];
136[label="foldr (>>) xw6 [] ++ (xw41 >>= gtGt0 (foldr (>>) xw6 []))",fontsize=16,color="black",shape="box"];136 -> 142[label="",style="solid", color="black", weight=3];
137[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) (not True))",fontsize=16,color="black",shape="box"];137 -> 143[label="",style="solid", color="black", weight=3];
138[label="foldr (>>) xw7 (take2 (Pos Zero) (repeatXs (AProVE_IO xw40)) True)",fontsize=16,color="black",shape="box"];138 -> 144[label="",style="solid", color="black", weight=3];
139[label="foldr (>>) xw5 (take1 (Pos (Succ xw3000)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];139 -> 145[label="",style="solid", color="black", weight=3];
140[label="xw5",fontsize=16,color="green",shape="box"];141[label="foldr (>>) xw6 (take1 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take1 (Pos (Succ xw3000)) (repeatXs (xw40 : xw41)))))",fontsize=16,color="black",shape="box"];141 -> 146[label="",style="solid", color="black", weight=3];
142[label="xw6 ++ (xw41 >>= gtGt0 xw6)",fontsize=16,color="burlywood",shape="triangle"];424[label="xw6/xw60 : xw61",fontsize=10,color="white",style="solid",shape="box"];142 -> 424[label="",style="solid", color="burlywood", weight=9];
424 -> 147[label="",style="solid", color="burlywood", weight=3];
425[label="xw6/[]",fontsize=10,color="white",style="solid",shape="box"];142 -> 425[label="",style="solid", color="burlywood", weight=9];
425 -> 148[label="",style="solid", color="burlywood", weight=3];
143[label="foldr (>>) xw7 (take2 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)) False)",fontsize=16,color="black",shape="box"];143 -> 149[label="",style="solid", color="black", weight=3];
144[label="foldr (>>) xw7 []",fontsize=16,color="black",shape="box"];144 -> 150[label="",style="solid", color="black", weight=3];
145[label="foldr (>>) xw5 (take1 (Pos (Succ xw3000)) (Just xw40 : repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];145 -> 151[label="",style="solid", color="black", weight=3];
146 -> 142[label="",style="dashed", color="red", weight=0];
146[label="foldr (>>) xw6 (take1 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41))) ++ (xw41 >>= gtGt0 (foldr (>>) xw6 (take1 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41)))))",fontsize=16,color="magenta"];146 -> 152[label="",style="dashed", color="magenta", weight=3];
147[label="(xw60 : xw61) ++ (xw41 >>= gtGt0 (xw60 : xw61))",fontsize=16,color="black",shape="box"];147 -> 153[label="",style="solid", color="black", weight=3];
148[label="[] ++ (xw41 >>= gtGt0 [])",fontsize=16,color="black",shape="box"];148 -> 154[label="",style="solid", color="black", weight=3];
149[label="foldr (>>) xw7 (take1 (Pos (Succ xw3000)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];149 -> 155[label="",style="solid", color="black", weight=3];
150[label="xw7",fontsize=16,color="green",shape="box"];151[label="foldr (>>) xw5 (take0 (Pos (Succ xw3000)) (Just xw40 : repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];151 -> 156[label="",style="solid", color="black", weight=3];
152[label="foldr (>>) xw6 (take1 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41)))",fontsize=16,color="black",shape="box"];152 -> 157[label="",style="solid", color="black", weight=3];
153[label="xw60 : xw61 ++ (xw41 >>= gtGt0 (xw60 : xw61))",fontsize=16,color="green",shape="box"];153 -> 158[label="",style="dashed", color="green", weight=3];
154[label="xw41 >>= gtGt0 []",fontsize=16,color="burlywood",shape="triangle"];426[label="xw41/xw410 : xw411",fontsize=10,color="white",style="solid",shape="box"];154 -> 426[label="",style="solid", color="burlywood", weight=9];
426 -> 159[label="",style="solid", color="burlywood", weight=3];
427[label="xw41/[]",fontsize=10,color="white",style="solid",shape="box"];154 -> 427[label="",style="solid", color="burlywood", weight=9];
427 -> 160[label="",style="solid", color="burlywood", weight=3];
155[label="foldr (>>) xw7 (take1 (Pos (Succ xw3000)) (AProVE_IO xw40 : repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];155 -> 161[label="",style="solid", color="black", weight=3];
156[label="foldr (>>) xw5 (Just xw40 : take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="black",shape="box"];156 -> 162[label="",style="solid", color="black", weight=3];
157[label="foldr (>>) xw6 (take0 (Pos (Succ xw3000)) ((xw40 : xw41) : repeatXs (xw40 : xw41)))",fontsize=16,color="black",shape="box"];157 -> 163[label="",style="solid", color="black", weight=3];
158 -> 348[label="",style="dashed", color="red", weight=0];
158[label="xw61 ++ (xw41 >>= gtGt0 (xw60 : xw61))",fontsize=16,color="magenta"];158 -> 349[label="",style="dashed", color="magenta", weight=3];
158 -> 350[label="",style="dashed", color="magenta", weight=3];
158 -> 351[label="",style="dashed", color="magenta", weight=3];
158 -> 352[label="",style="dashed", color="magenta", weight=3];
159[label="xw410 : xw411 >>= gtGt0 []",fontsize=16,color="black",shape="box"];159 -> 166[label="",style="solid", color="black", weight=3];
160[label="[] >>= gtGt0 []",fontsize=16,color="black",shape="box"];160 -> 167[label="",style="solid", color="black", weight=3];
161[label="foldr (>>) xw7 (take0 (Pos (Succ xw3000)) (AProVE_IO xw40 : repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];161 -> 168[label="",style="solid", color="black", weight=3];
162 -> 52[label="",style="dashed", color="red", weight=0];
162[label="(>>) Just xw40 foldr (>>) xw5 (take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (Just xw40)))",fontsize=16,color="magenta"];162 -> 169[label="",style="dashed", color="magenta", weight=3];
162 -> 170[label="",style="dashed", color="magenta", weight=3];
163[label="foldr (>>) xw6 ((xw40 : xw41) : take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))",fontsize=16,color="black",shape="box"];163 -> 171[label="",style="solid", color="black", weight=3];
349[label="xw61",fontsize=16,color="green",shape="box"];350[label="xw61",fontsize=16,color="green",shape="box"];351[label="xw60",fontsize=16,color="green",shape="box"];352[label="xw41",fontsize=16,color="green",shape="box"];348[label="xw24 ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="burlywood",shape="triangle"];428[label="xw24/xw240 : xw241",fontsize=10,color="white",style="solid",shape="box"];348 -> 428[label="",style="solid", color="burlywood", weight=9];
428 -> 385[label="",style="solid", color="burlywood", weight=3];
429[label="xw24/[]",fontsize=10,color="white",style="solid",shape="box"];348 -> 429[label="",style="solid", color="burlywood", weight=9];
429 -> 386[label="",style="solid", color="burlywood", weight=3];
166 -> 174[label="",style="dashed", color="red", weight=0];
166[label="gtGt0 [] xw410 ++ (xw411 >>= gtGt0 [])",fontsize=16,color="magenta"];166 -> 175[label="",style="dashed", color="magenta", weight=3];
167[label="[]",fontsize=16,color="green",shape="box"];168[label="foldr (>>) xw7 (AProVE_IO xw40 : take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="black",shape="box"];168 -> 176[label="",style="solid", color="black", weight=3];
169[label="xw3000",fontsize=16,color="green",shape="box"];170[label="Just xw40",fontsize=16,color="green",shape="box"];171 -> 54[label="",style="dashed", color="red", weight=0];
171[label="(>>) xw40 : xw41 foldr (>>) xw6 (take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (xw40 : xw41)))",fontsize=16,color="magenta"];171 -> 177[label="",style="dashed", color="magenta", weight=3];
171 -> 178[label="",style="dashed", color="magenta", weight=3];
385[label="(xw240 : xw241) ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="black",shape="box"];385 -> 387[label="",style="solid", color="black", weight=3];
386[label="[] ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="black",shape="box"];386 -> 388[label="",style="solid", color="black", weight=3];
175 -> 154[label="",style="dashed", color="red", weight=0];
175[label="xw411 >>= gtGt0 []",fontsize=16,color="magenta"];175 -> 182[label="",style="dashed", color="magenta", weight=3];
174[label="gtGt0 [] xw410 ++ xw8",fontsize=16,color="black",shape="triangle"];174 -> 183[label="",style="solid", color="black", weight=3];
176 -> 56[label="",style="dashed", color="red", weight=0];
176[label="(>>) AProVE_IO xw40 foldr (>>) xw7 (take (Pos (Succ xw3000) - Pos (Succ Zero)) (repeatXs (AProVE_IO xw40)))",fontsize=16,color="magenta"];176 -> 184[label="",style="dashed", color="magenta", weight=3];
176 -> 185[label="",style="dashed", color="magenta", weight=3];
177[label="xw3000",fontsize=16,color="green",shape="box"];178[label="xw40 : xw41",fontsize=16,color="green",shape="box"];387[label="xw240 : xw241 ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="green",shape="box"];387 -> 389[label="",style="dashed", color="green", weight=3];
388[label="xw25 >>= gtGt0 (xw26 : xw27)",fontsize=16,color="burlywood",shape="box"];430[label="xw25/xw250 : xw251",fontsize=10,color="white",style="solid",shape="box"];388 -> 430[label="",style="solid", color="burlywood", weight=9];
430 -> 390[label="",style="solid", color="burlywood", weight=3];
431[label="xw25/[]",fontsize=10,color="white",style="solid",shape="box"];388 -> 431[label="",style="solid", color="burlywood", weight=9];
431 -> 391[label="",style="solid", color="burlywood", weight=3];
182[label="xw411",fontsize=16,color="green",shape="box"];183[label="[] ++ xw8",fontsize=16,color="black",shape="triangle"];183 -> 190[label="",style="solid", color="black", weight=3];
184[label="xw3000",fontsize=16,color="green",shape="box"];185[label="AProVE_IO xw40",fontsize=16,color="green",shape="box"];389 -> 348[label="",style="dashed", color="red", weight=0];
389[label="xw241 ++ (xw25 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="magenta"];389 -> 392[label="",style="dashed", color="magenta", weight=3];
390[label="xw250 : xw251 >>= gtGt0 (xw26 : xw27)",fontsize=16,color="black",shape="box"];390 -> 393[label="",style="solid", color="black", weight=3];
391[label="[] >>= gtGt0 (xw26 : xw27)",fontsize=16,color="black",shape="box"];391 -> 394[label="",style="solid", color="black", weight=3];
190[label="xw8",fontsize=16,color="green",shape="box"];392[label="xw241",fontsize=16,color="green",shape="box"];393 -> 348[label="",style="dashed", color="red", weight=0];
393[label="gtGt0 (xw26 : xw27) xw250 ++ (xw251 >>= gtGt0 (xw26 : xw27))",fontsize=16,color="magenta"];393 -> 395[label="",style="dashed", color="magenta", weight=3];
393 -> 396[label="",style="dashed", color="magenta", weight=3];
394[label="[]",fontsize=16,color="green",shape="box"];395[label="gtGt0 (xw26 : xw27) xw250",fontsize=16,color="black",shape="box"];395 -> 397[label="",style="solid", color="black", weight=3];
396[label="xw251",fontsize=16,color="green",shape="box"];397[label="xw26 : xw27",fontsize=16,color="green",shape="box"];}

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

(12)
Complex Obligation (AND)

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

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

   new_gtGt1(Just(xw40), xw5, Succ(xw3000), h) -> new_gtGt1(Just(xw40), xw5, xw3000, h)

R is empty.
Q is empty.
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_gtGt1(Just(xw40), xw5, Succ(xw3000), h) -> new_gtGt1(Just(xw40), xw5, xw3000, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4


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

(15)
YES

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

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

   new_gtGt(AProVE_IO(xw40), xw7, Succ(xw3000), h) -> new_gtGt(AProVE_IO(xw40), xw7, xw3000, h)

R is empty.
Q is empty.
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_gtGt(AProVE_IO(xw40), xw7, Succ(xw3000), h) -> new_gtGt(AProVE_IO(xw40), xw7, xw3000, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4


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

(18)
YES

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

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

   new_gtGtEs(:(xw410, xw411), h) -> new_gtGtEs(xw411, h)

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_gtGtEs(:(xw410, xw411), h) -> new_gtGtEs(xw411, h)
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_gtGt0(:(xw40, xw41), xw6, Succ(xw3000), h) -> new_gtGt0(:(xw40, xw41), xw6, xw3000, h)

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_gtGt0(:(xw40, xw41), xw6, Succ(xw3000), h) -> new_gtGt0(:(xw40, xw41), xw6, xw3000, h)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4


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

(24)
YES

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

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

   new_psPs(:(xw240, xw241), xw25, xw26, xw27, h, ba) -> new_psPs(xw241, xw25, xw26, xw27, h, ba)
   new_psPs([], :(xw250, xw251), xw26, xw27, h, ba) -> new_psPs(:(xw26, xw27), xw251, xw26, xw27, h, ba)

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_psPs(:(xw240, xw241), xw25, xw26, xw27, h, ba) -> new_psPs(xw241, xw25, xw26, xw27, h, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6


*new_psPs([], :(xw250, xw251), xw26, xw27, h, ba) -> new_psPs(:(xw26, xw27), xw251, xw26, xw27, h, ba)
The graph contains the following edges 2 > 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6


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

(27)
YES