/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 4 ms]
(4) HASKELL
(5) LetRed [EQUIVALENT, 0 ms]
(6) HASKELL
(7) NumRed [SOUND, 10 ms]
(8) HASKELL
(9) Narrow [SOUND, 0 ms]
(10) QDP
(11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(12) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
genericReplicate :: Integral a => a  ->  b  ->  [b];
genericReplicate n x = genericTake n (repeat x);

genericTake :: Integral b => b  ->  [a]  ->  [a];
genericTake 0 _ = [];
genericTake _ [] = [];
genericTake n (x : xs)  | n > 0 = x : genericTake (n - 1) xs;
genericTake _ _ = error [];

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

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

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
genericReplicate :: Integral a => a  ->  b  ->  [b];
genericReplicate n x = genericTake n (repeat x);

genericTake :: Integral a => a  ->  [b]  ->  [b];
genericTake 0 xw = [];
genericTake xx [] = [];
genericTake n (x : xs)  | n > 0 = x : genericTake (n - 1) xs;
genericTake xy xz = error [];

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

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

(3) 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
"genericTake 0 xw = [];
genericTake xx [] = [];
genericTake n (x : xs)|n > 0x : genericTake (n - 1) xs;
genericTake xy xz = error [];
"
is transformed to
"genericTake zu xw = genericTake5 zu xw;
genericTake xx [] = genericTake3 xx [];
genericTake n (x : xs) = genericTake2 n (x : xs);
genericTake xy xz = genericTake0 xy xz;
"
"genericTake0 xy xz = error [];
"
"genericTake1 n x xs True = x : genericTake (n - 1) xs;
genericTake1 n x xs False = genericTake0 n (x : xs);
"
"genericTake2 n (x : xs) = genericTake1 n x xs (n > 0);
genericTake2 yv yw = genericTake0 yv yw;
"
"genericTake3 xx [] = [];
genericTake3 yy yz = genericTake2 yy yz;
"
"genericTake4 True zu xw = [];
genericTake4 zv zw zx = genericTake3 zw zx;
"
"genericTake5 zu xw = genericTake4 (zu == 0) zu xw;
genericTake5 zy zz = genericTake3 zy zz;
"

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

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
genericReplicate :: Integral a => a  ->  b  ->  [b];
genericReplicate n x = genericTake n (repeat x);

genericTake :: Integral b => b  ->  [a]  ->  [a];
genericTake zu xw = genericTake5 zu xw;
genericTake xx [] = genericTake3 xx [];
genericTake n (x : xs) = genericTake2 n (x : xs);
genericTake xy xz = genericTake0 xy xz;

genericTake0 xy xz = error [];

genericTake1 n x xs True = x : genericTake (n - 1) xs;
genericTake1 n x xs False = genericTake0 n (x : xs);

genericTake2 n (x : xs) = genericTake1 n x xs (n > 0);
genericTake2 yv yw = genericTake0 yv yw;

genericTake3 xx [] = [];
genericTake3 yy yz = genericTake2 yy yz;

genericTake4 True zu xw = [];
genericTake4 zv zw zx = genericTake3 zw zx;

genericTake5 zu xw = genericTake4 (zu == 0) zu xw;
genericTake5 zy zz = genericTake3 zy zz;

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

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

(5) 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 vuu = vuu : repeatXs vuu;
"

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

(6)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
genericReplicate :: Integral b => b  ->  a  ->  [a];
genericReplicate n x = genericTake n (repeat x);

genericTake :: Integral b => b  ->  [a]  ->  [a];
genericTake zu xw = genericTake5 zu xw;
genericTake xx [] = genericTake3 xx [];
genericTake n (x : xs) = genericTake2 n (x : xs);
genericTake xy xz = genericTake0 xy xz;

genericTake0 xy xz = error [];

genericTake1 n x xs True = x : genericTake (n - 1) xs;
genericTake1 n x xs False = genericTake0 n (x : xs);

genericTake2 n (x : xs) = genericTake1 n x xs (n > 0);
genericTake2 yv yw = genericTake0 yv yw;

genericTake3 xx [] = [];
genericTake3 yy yz = genericTake2 yy yz;

genericTake4 True zu xw = [];
genericTake4 zv zw zx = genericTake3 zw zx;

genericTake5 zu xw = genericTake4 (zu == 0) zu xw;
genericTake5 zy zz = genericTake3 zy zz;

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

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

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

(8)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
genericReplicate :: Integral b => b  ->  a  ->  [a];
genericReplicate n x = genericTake n (repeat x);

genericTake :: Integral b => b  ->  [a]  ->  [a];
genericTake zu xw = genericTake5 zu xw;
genericTake xx [] = genericTake3 xx [];
genericTake n (x : xs) = genericTake2 n (x : xs);
genericTake xy xz = genericTake0 xy xz;

genericTake0 xy xz = error [];

genericTake1 n x xs True = x : genericTake (n - fromInt (Pos (Succ Zero))) xs;
genericTake1 n x xs False = genericTake0 n (x : xs);

genericTake2 n (x : xs) = genericTake1 n x xs (n > fromInt (Pos Zero));
genericTake2 yv yw = genericTake0 yv yw;

genericTake3 xx [] = [];
genericTake3 yy yz = genericTake2 yy yz;

genericTake4 True zu xw = [];
genericTake4 zv zw zx = genericTake3 zw zx;

genericTake5 zu xw = genericTake4 (zu == fromInt (Pos Zero)) zu xw;
genericTake5 zy zz = genericTake3 zy zz;

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

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

(9) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="List.genericReplicate",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="List.genericReplicate vuv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="List.genericReplicate vuv3 vuv4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="List.genericTake vuv3 (repeat vuv4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="List.genericTake5 vuv3 (repeat vuv4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="List.genericTake4 (vuv3 == fromInt (Pos Zero)) vuv3 (repeat vuv4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="List.genericTake4 (primEqInt vuv3 (fromInt (Pos Zero))) vuv3 (repeat vuv4)",fontsize=16,color="burlywood",shape="box"];69[label="vuv3/Pos vuv30",fontsize=10,color="white",style="solid",shape="box"];8 -> 69[label="",style="solid", color="burlywood", weight=9];
69 -> 9[label="",style="solid", color="burlywood", weight=3];
70[label="vuv3/Neg vuv30",fontsize=10,color="white",style="solid",shape="box"];8 -> 70[label="",style="solid", color="burlywood", weight=9];
70 -> 10[label="",style="solid", color="burlywood", weight=3];
9[label="List.genericTake4 (primEqInt (Pos vuv30) (fromInt (Pos Zero))) (Pos vuv30) (repeat vuv4)",fontsize=16,color="burlywood",shape="box"];71[label="vuv30/Succ vuv300",fontsize=10,color="white",style="solid",shape="box"];9 -> 71[label="",style="solid", color="burlywood", weight=9];
71 -> 11[label="",style="solid", color="burlywood", weight=3];
72[label="vuv30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 72[label="",style="solid", color="burlywood", weight=9];
72 -> 12[label="",style="solid", color="burlywood", weight=3];
10[label="List.genericTake4 (primEqInt (Neg vuv30) (fromInt (Pos Zero))) (Neg vuv30) (repeat vuv4)",fontsize=16,color="burlywood",shape="box"];73[label="vuv30/Succ vuv300",fontsize=10,color="white",style="solid",shape="box"];10 -> 73[label="",style="solid", color="burlywood", weight=9];
73 -> 13[label="",style="solid", color="burlywood", weight=3];
74[label="vuv30/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 74[label="",style="solid", color="burlywood", weight=9];
74 -> 14[label="",style="solid", color="burlywood", weight=3];
11[label="List.genericTake4 (primEqInt (Pos (Succ vuv300)) (fromInt (Pos Zero))) (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="List.genericTake4 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="List.genericTake4 (primEqInt (Neg (Succ vuv300)) (fromInt (Pos Zero))) (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="List.genericTake4 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="List.genericTake4 (primEqInt (Pos (Succ vuv300)) (Pos Zero)) (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="List.genericTake4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="List.genericTake4 (primEqInt (Neg (Succ vuv300)) (Pos Zero)) (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="List.genericTake4 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="List.genericTake4 False (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="List.genericTake4 True (Pos Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="List.genericTake4 False (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="List.genericTake4 True (Neg Zero) (repeat vuv4)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="List.genericTake3 (Pos (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="[]",fontsize=16,color="green",shape="box"];25[label="List.genericTake3 (Neg (Succ vuv300)) (repeat vuv4)",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
26[label="[]",fontsize=16,color="green",shape="box"];27[label="List.genericTake3 (Pos (Succ vuv300)) (repeatXs vuv4)",fontsize=16,color="black",shape="triangle"];27 -> 29[label="",style="solid", color="black", weight=3];
28[label="List.genericTake3 (Neg (Succ vuv300)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
29[label="List.genericTake3 (Pos (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
30[label="List.genericTake3 (Neg (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
31[label="List.genericTake2 (Pos (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
32[label="List.genericTake2 (Neg (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
33[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (Pos (Succ vuv300) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
34[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (Neg (Succ vuv300) > fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
35[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (compare (Pos (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
36[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (compare (Neg (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3];
37[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Pos (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
38[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Neg (Succ vuv300)) (fromInt (Pos Zero)) == GT)",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
39[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Pos (Succ vuv300)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3];
40[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpInt (Neg (Succ vuv300)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];40 -> 42[label="",style="solid", color="black", weight=3];
41[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (primCmpNat (Succ vuv300) Zero == GT)",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3];
42[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) (LT == GT)",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
43[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) (GT == GT)",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
44[label="List.genericTake1 (Neg (Succ vuv300)) vuv4 (repeatXs vuv4) False",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
45[label="List.genericTake1 (Pos (Succ vuv300)) vuv4 (repeatXs vuv4) True",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3];
46[label="List.genericTake0 (Neg (Succ vuv300)) (vuv4 : repeatXs vuv4)",fontsize=16,color="black",shape="box"];46 -> 48[label="",style="solid", color="black", weight=3];
47[label="vuv4 : List.genericTake (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="green",shape="box"];47 -> 49[label="",style="dashed", color="green", weight=3];
48[label="error []",fontsize=16,color="black",shape="box"];48 -> 50[label="",style="solid", color="black", weight=3];
49[label="List.genericTake (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];49 -> 51[label="",style="solid", color="black", weight=3];
50[label="error []",fontsize=16,color="red",shape="box"];51[label="List.genericTake5 (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];51 -> 52[label="",style="solid", color="black", weight=3];
52[label="List.genericTake4 (Pos (Succ vuv300) - fromInt (Pos (Succ Zero)) == fromInt (Pos Zero)) (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];52 -> 53[label="",style="solid", color="black", weight=3];
53[label="List.genericTake4 (primEqInt (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (fromInt (Pos Zero))) (Pos (Succ vuv300) - fromInt (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];53 -> 54[label="",style="solid", color="black", weight=3];
54[label="List.genericTake4 (primEqInt (primMinusInt (Pos (Succ vuv300)) (fromInt (Pos (Succ Zero)))) (fromInt (Pos Zero))) (primMinusInt (Pos (Succ vuv300)) (fromInt (Pos (Succ Zero)))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];54 -> 55[label="",style="solid", color="black", weight=3];
55[label="List.genericTake4 (primEqInt (primMinusInt (Pos (Succ vuv300)) (Pos (Succ Zero))) (fromInt (Pos Zero))) (primMinusInt (Pos (Succ vuv300)) (Pos (Succ Zero))) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];55 -> 56[label="",style="solid", color="black", weight=3];
56[label="List.genericTake4 (primEqInt (primMinusNat (Succ vuv300) (Succ Zero)) (fromInt (Pos Zero))) (primMinusNat (Succ vuv300) (Succ Zero)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];56 -> 57[label="",style="solid", color="black", weight=3];
57[label="List.genericTake4 (primEqInt (primMinusNat vuv300 Zero) (fromInt (Pos Zero))) (primMinusNat vuv300 Zero) (repeatXs vuv4)",fontsize=16,color="burlywood",shape="box"];75[label="vuv300/Succ vuv3000",fontsize=10,color="white",style="solid",shape="box"];57 -> 75[label="",style="solid", color="burlywood", weight=9];
75 -> 58[label="",style="solid", color="burlywood", weight=3];
76[label="vuv300/Zero",fontsize=10,color="white",style="solid",shape="box"];57 -> 76[label="",style="solid", color="burlywood", weight=9];
76 -> 59[label="",style="solid", color="burlywood", weight=3];
58[label="List.genericTake4 (primEqInt (primMinusNat (Succ vuv3000) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuv3000) Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];58 -> 60[label="",style="solid", color="black", weight=3];
59[label="List.genericTake4 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];59 -> 61[label="",style="solid", color="black", weight=3];
60[label="List.genericTake4 (primEqInt (Pos (Succ vuv3000)) (fromInt (Pos Zero))) (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
61[label="List.genericTake4 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];61 -> 63[label="",style="solid", color="black", weight=3];
62[label="List.genericTake4 (primEqInt (Pos (Succ vuv3000)) (Pos Zero)) (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];62 -> 64[label="",style="solid", color="black", weight=3];
63[label="List.genericTake4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];63 -> 65[label="",style="solid", color="black", weight=3];
64[label="List.genericTake4 False (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];64 -> 66[label="",style="solid", color="black", weight=3];
65[label="List.genericTake4 True (Pos Zero) (repeatXs vuv4)",fontsize=16,color="black",shape="box"];65 -> 67[label="",style="solid", color="black", weight=3];
66 -> 27[label="",style="dashed", color="red", weight=0];
66[label="List.genericTake3 (Pos (Succ vuv3000)) (repeatXs vuv4)",fontsize=16,color="magenta"];66 -> 68[label="",style="dashed", color="magenta", weight=3];
67[label="[]",fontsize=16,color="green",shape="box"];68[label="vuv3000",fontsize=16,color="green",shape="box"];}

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

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

   new_genericTake3(Succ(vuv3000), vuv4, ba) -> new_genericTake3(vuv3000, vuv4, ba)

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

(11) 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_genericTake3(Succ(vuv3000), vuv4, ba) -> new_genericTake3(vuv3000, vuv4, ba)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3


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

(12)
YES