/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 20 ms]
(4) HASKELL
(5) NumRed [SOUND, 0 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) 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;
genericLength :: Num b => [a]  ->  b;
genericLength [] = 0;
genericLength (_ : l) = 1 + genericLength l;

}
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;
genericLength :: Num a => [b]  ->  a;
genericLength [] = 0;
genericLength (vy : l) = 1 + genericLength l;

}
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;
"

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

(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;
genericLength :: Num a => [b]  ->  a;
genericLength [] = 0;
genericLength (vy : l) = 1 + genericLength l;

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

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

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

(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;
genericLength :: Num b => [a]  ->  b;
genericLength [] = fromInt (Pos Zero);
genericLength (vy : l) = fromInt (Pos (Succ Zero)) + genericLength l;

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="List.genericLength",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="List.genericLength vz3",fontsize=16,color="burlywood",shape="triangle"];294[label="vz3/vz30 : vz31",fontsize=10,color="white",style="solid",shape="box"];3 -> 294[label="",style="solid", color="burlywood", weight=9];
294 -> 4[label="",style="solid", color="burlywood", weight=3];
295[label="vz3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 295[label="",style="solid", color="burlywood", weight=9];
295 -> 5[label="",style="solid", color="burlywood", weight=3];
4[label="List.genericLength (vz30 : vz31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
5[label="List.genericLength []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
6 -> 8[label="",style="dashed", color="red", weight=0];
6[label="fromInt (Pos (Succ Zero)) + List.genericLength vz31",fontsize=16,color="magenta"];6 -> 9[label="",style="dashed", color="magenta", weight=3];
7[label="fromInt (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
9 -> 3[label="",style="dashed", color="red", weight=0];
9[label="List.genericLength vz31",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3];
8[label="fromInt (Pos (Succ Zero)) + vz4",fontsize=16,color="black",shape="triangle"];8 -> 12[label="",style="solid", color="black", weight=3];
10[label="primIntToFloat (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
11[label="vz31",fontsize=16,color="green",shape="box"];12[label="primPlusFloat (fromInt (Pos (Succ Zero))) vz4",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="Float (Pos Zero) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];14[label="primPlusFloat (primIntToFloat (Pos (Succ Zero))) vz4",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="primPlusFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vz4",fontsize=16,color="burlywood",shape="box"];296[label="vz4/Float vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];15 -> 296[label="",style="solid", color="burlywood", weight=9];
296 -> 16[label="",style="solid", color="burlywood", weight=3];
16[label="primPlusFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vz40 vz41)",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
17[label="Float (Pos (Succ Zero) * vz41 + vz40 * Pos (Succ Zero)) (Pos (Succ Zero) * vz41)",fontsize=16,color="green",shape="box"];17 -> 18[label="",style="dashed", color="green", weight=3];
17 -> 19[label="",style="dashed", color="green", weight=3];
18[label="Pos (Succ Zero) * vz41 + vz40 * Pos (Succ Zero)",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
19[label="Pos (Succ Zero) * vz41",fontsize=16,color="black",shape="triangle"];19 -> 21[label="",style="solid", color="black", weight=3];
20 -> 22[label="",style="dashed", color="red", weight=0];
20[label="primPlusInt (Pos (Succ Zero) * vz41) (vz40 * Pos (Succ Zero))",fontsize=16,color="magenta"];20 -> 23[label="",style="dashed", color="magenta", weight=3];
21[label="primMulInt (Pos (Succ Zero)) vz41",fontsize=16,color="burlywood",shape="box"];297[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];21 -> 297[label="",style="solid", color="burlywood", weight=9];
297 -> 24[label="",style="solid", color="burlywood", weight=3];
298[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];21 -> 298[label="",style="solid", color="burlywood", weight=9];
298 -> 25[label="",style="solid", color="burlywood", weight=3];
23 -> 19[label="",style="dashed", color="red", weight=0];
23[label="Pos (Succ Zero) * vz41",fontsize=16,color="magenta"];22[label="primPlusInt vz5 (vz40 * Pos (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];299[label="vz5/Pos vz50",fontsize=10,color="white",style="solid",shape="box"];22 -> 299[label="",style="solid", color="burlywood", weight=9];
299 -> 26[label="",style="solid", color="burlywood", weight=3];
300[label="vz5/Neg vz50",fontsize=10,color="white",style="solid",shape="box"];22 -> 300[label="",style="solid", color="burlywood", weight=9];
300 -> 27[label="",style="solid", color="burlywood", weight=3];
24[label="primMulInt (Pos (Succ Zero)) (Pos vz410)",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="primMulInt (Pos (Succ Zero)) (Neg vz410)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="primPlusInt (Pos vz50) (vz40 * Pos (Succ Zero))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
27[label="primPlusInt (Neg vz50) (vz40 * Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28[label="Pos (primMulNat (Succ Zero) vz410)",fontsize=16,color="green",shape="box"];28 -> 32[label="",style="dashed", color="green", weight=3];
29[label="Neg (primMulNat (Succ Zero) vz410)",fontsize=16,color="green",shape="box"];29 -> 33[label="",style="dashed", color="green", weight=3];
30[label="primPlusInt (Pos vz50) (primMulInt vz40 (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];301[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];30 -> 301[label="",style="solid", color="burlywood", weight=9];
301 -> 34[label="",style="solid", color="burlywood", weight=3];
302[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];30 -> 302[label="",style="solid", color="burlywood", weight=9];
302 -> 35[label="",style="solid", color="burlywood", weight=3];
31[label="primPlusInt (Neg vz50) (primMulInt vz40 (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];303[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];31 -> 303[label="",style="solid", color="burlywood", weight=9];
303 -> 36[label="",style="solid", color="burlywood", weight=3];
304[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];31 -> 304[label="",style="solid", color="burlywood", weight=9];
304 -> 37[label="",style="solid", color="burlywood", weight=3];
32[label="primMulNat (Succ Zero) vz410",fontsize=16,color="burlywood",shape="triangle"];305[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];32 -> 305[label="",style="solid", color="burlywood", weight=9];
305 -> 38[label="",style="solid", color="burlywood", weight=3];
306[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];32 -> 306[label="",style="solid", color="burlywood", weight=9];
306 -> 39[label="",style="solid", color="burlywood", weight=3];
33 -> 32[label="",style="dashed", color="red", weight=0];
33[label="primMulNat (Succ Zero) vz410",fontsize=16,color="magenta"];33 -> 40[label="",style="dashed", color="magenta", weight=3];
34[label="primPlusInt (Pos vz50) (primMulInt (Pos vz400) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3];
35[label="primPlusInt (Pos vz50) (primMulInt (Neg vz400) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];35 -> 42[label="",style="solid", color="black", weight=3];
36[label="primPlusInt (Neg vz50) (primMulInt (Pos vz400) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];36 -> 43[label="",style="solid", color="black", weight=3];
37[label="primPlusInt (Neg vz50) (primMulInt (Neg vz400) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];37 -> 44[label="",style="solid", color="black", weight=3];
38[label="primMulNat (Succ Zero) (Succ vz4100)",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3];
39[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];39 -> 46[label="",style="solid", color="black", weight=3];
40[label="vz410",fontsize=16,color="green",shape="box"];41[label="primPlusInt (Pos vz50) (Pos (primMulNat vz400 (Succ Zero)))",fontsize=16,color="black",shape="box"];41 -> 47[label="",style="solid", color="black", weight=3];
42[label="primPlusInt (Pos vz50) (Neg (primMulNat vz400 (Succ Zero)))",fontsize=16,color="black",shape="box"];42 -> 48[label="",style="solid", color="black", weight=3];
43[label="primPlusInt (Neg vz50) (Pos (primMulNat vz400 (Succ Zero)))",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
44[label="primPlusInt (Neg vz50) (Neg (primMulNat vz400 (Succ Zero)))",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
45 -> 192[label="",style="dashed", color="red", weight=0];
45[label="primPlusNat (primMulNat Zero (Succ vz4100)) (Succ vz4100)",fontsize=16,color="magenta"];45 -> 193[label="",style="dashed", color="magenta", weight=3];
45 -> 194[label="",style="dashed", color="magenta", weight=3];
46[label="Zero",fontsize=16,color="green",shape="box"];47[label="Pos (primPlusNat vz50 (primMulNat vz400 (Succ Zero)))",fontsize=16,color="green",shape="box"];47 -> 52[label="",style="dashed", color="green", weight=3];
48 -> 219[label="",style="dashed", color="red", weight=0];
48[label="primMinusNat vz50 (primMulNat vz400 (Succ Zero))",fontsize=16,color="magenta"];48 -> 220[label="",style="dashed", color="magenta", weight=3];
48 -> 221[label="",style="dashed", color="magenta", weight=3];
49 -> 219[label="",style="dashed", color="red", weight=0];
49[label="primMinusNat (primMulNat vz400 (Succ Zero)) vz50",fontsize=16,color="magenta"];49 -> 222[label="",style="dashed", color="magenta", weight=3];
49 -> 223[label="",style="dashed", color="magenta", weight=3];
50[label="Neg (primPlusNat vz50 (primMulNat vz400 (Succ Zero)))",fontsize=16,color="green",shape="box"];50 -> 57[label="",style="dashed", color="green", weight=3];
193[label="primMulNat Zero (Succ vz4100)",fontsize=16,color="black",shape="box"];193 -> 212[label="",style="solid", color="black", weight=3];
194[label="vz4100",fontsize=16,color="green",shape="box"];192[label="primPlusNat vz500 (Succ vz15)",fontsize=16,color="burlywood",shape="triangle"];307[label="vz500/Succ vz5000",fontsize=10,color="white",style="solid",shape="box"];192 -> 307[label="",style="solid", color="burlywood", weight=9];
307 -> 213[label="",style="solid", color="burlywood", weight=3];
308[label="vz500/Zero",fontsize=10,color="white",style="solid",shape="box"];192 -> 308[label="",style="solid", color="burlywood", weight=9];
308 -> 214[label="",style="solid", color="burlywood", weight=3];
52[label="primPlusNat vz50 (primMulNat vz400 (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];309[label="vz50/Succ vz500",fontsize=10,color="white",style="solid",shape="box"];52 -> 309[label="",style="solid", color="burlywood", weight=9];
309 -> 59[label="",style="solid", color="burlywood", weight=3];
310[label="vz50/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 310[label="",style="solid", color="burlywood", weight=9];
310 -> 60[label="",style="solid", color="burlywood", weight=3];
220[label="vz50",fontsize=16,color="green",shape="box"];221 -> 105[label="",style="dashed", color="red", weight=0];
221[label="primMulNat vz400 (Succ Zero)",fontsize=16,color="magenta"];221 -> 259[label="",style="dashed", color="magenta", weight=3];
219[label="primMinusNat vz5000 vz16",fontsize=16,color="burlywood",shape="triangle"];311[label="vz5000/Succ vz50000",fontsize=10,color="white",style="solid",shape="box"];219 -> 311[label="",style="solid", color="burlywood", weight=9];
311 -> 260[label="",style="solid", color="burlywood", weight=3];
312[label="vz5000/Zero",fontsize=10,color="white",style="solid",shape="box"];219 -> 312[label="",style="solid", color="burlywood", weight=9];
312 -> 261[label="",style="solid", color="burlywood", weight=3];
222 -> 105[label="",style="dashed", color="red", weight=0];
222[label="primMulNat vz400 (Succ Zero)",fontsize=16,color="magenta"];222 -> 262[label="",style="dashed", color="magenta", weight=3];
223[label="vz50",fontsize=16,color="green",shape="box"];57 -> 52[label="",style="dashed", color="red", weight=0];
57[label="primPlusNat vz50 (primMulNat vz400 (Succ Zero))",fontsize=16,color="magenta"];57 -> 67[label="",style="dashed", color="magenta", weight=3];
57 -> 68[label="",style="dashed", color="magenta", weight=3];
212[label="Zero",fontsize=16,color="green",shape="box"];213[label="primPlusNat (Succ vz5000) (Succ vz15)",fontsize=16,color="black",shape="box"];213 -> 263[label="",style="solid", color="black", weight=3];
214[label="primPlusNat Zero (Succ vz15)",fontsize=16,color="black",shape="box"];214 -> 264[label="",style="solid", color="black", weight=3];
59[label="primPlusNat (Succ vz500) (primMulNat vz400 (Succ Zero))",fontsize=16,color="burlywood",shape="box"];313[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];59 -> 313[label="",style="solid", color="burlywood", weight=9];
313 -> 69[label="",style="solid", color="burlywood", weight=3];
314[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 314[label="",style="solid", color="burlywood", weight=9];
314 -> 70[label="",style="solid", color="burlywood", weight=3];
60[label="primPlusNat Zero (primMulNat vz400 (Succ Zero))",fontsize=16,color="burlywood",shape="box"];315[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];60 -> 315[label="",style="solid", color="burlywood", weight=9];
315 -> 71[label="",style="solid", color="burlywood", weight=3];
316[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];60 -> 316[label="",style="solid", color="burlywood", weight=9];
316 -> 72[label="",style="solid", color="burlywood", weight=3];
259[label="vz400",fontsize=16,color="green",shape="box"];105[label="primMulNat vz4000 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];317[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];105 -> 317[label="",style="solid", color="burlywood", weight=9];
317 -> 108[label="",style="solid", color="burlywood", weight=3];
318[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];105 -> 318[label="",style="solid", color="burlywood", weight=9];
318 -> 109[label="",style="solid", color="burlywood", weight=3];
260[label="primMinusNat (Succ vz50000) vz16",fontsize=16,color="burlywood",shape="box"];319[label="vz16/Succ vz160",fontsize=10,color="white",style="solid",shape="box"];260 -> 319[label="",style="solid", color="burlywood", weight=9];
319 -> 268[label="",style="solid", color="burlywood", weight=3];
320[label="vz16/Zero",fontsize=10,color="white",style="solid",shape="box"];260 -> 320[label="",style="solid", color="burlywood", weight=9];
320 -> 269[label="",style="solid", color="burlywood", weight=3];
261[label="primMinusNat Zero vz16",fontsize=16,color="burlywood",shape="box"];321[label="vz16/Succ vz160",fontsize=10,color="white",style="solid",shape="box"];261 -> 321[label="",style="solid", color="burlywood", weight=9];
321 -> 270[label="",style="solid", color="burlywood", weight=3];
322[label="vz16/Zero",fontsize=10,color="white",style="solid",shape="box"];261 -> 322[label="",style="solid", color="burlywood", weight=9];
322 -> 271[label="",style="solid", color="burlywood", weight=3];
262[label="vz400",fontsize=16,color="green",shape="box"];67[label="vz50",fontsize=16,color="green",shape="box"];68[label="vz400",fontsize=16,color="green",shape="box"];263[label="Succ (Succ (primPlusNat vz5000 vz15))",fontsize=16,color="green",shape="box"];263 -> 272[label="",style="dashed", color="green", weight=3];
264[label="Succ vz15",fontsize=16,color="green",shape="box"];69[label="primPlusNat (Succ vz500) (primMulNat (Succ vz4000) (Succ Zero))",fontsize=16,color="black",shape="box"];69 -> 81[label="",style="solid", color="black", weight=3];
70[label="primPlusNat (Succ vz500) (primMulNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];70 -> 82[label="",style="solid", color="black", weight=3];
71[label="primPlusNat Zero (primMulNat (Succ vz4000) (Succ Zero))",fontsize=16,color="black",shape="box"];71 -> 83[label="",style="solid", color="black", weight=3];
72[label="primPlusNat Zero (primMulNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];72 -> 84[label="",style="solid", color="black", weight=3];
108[label="primMulNat (Succ vz40000) (Succ Zero)",fontsize=16,color="black",shape="box"];108 -> 123[label="",style="solid", color="black", weight=3];
109[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];109 -> 124[label="",style="solid", color="black", weight=3];
268[label="primMinusNat (Succ vz50000) (Succ vz160)",fontsize=16,color="black",shape="box"];268 -> 275[label="",style="solid", color="black", weight=3];
269[label="primMinusNat (Succ vz50000) Zero",fontsize=16,color="black",shape="box"];269 -> 276[label="",style="solid", color="black", weight=3];
270[label="primMinusNat Zero (Succ vz160)",fontsize=16,color="black",shape="box"];270 -> 277[label="",style="solid", color="black", weight=3];
271[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];271 -> 278[label="",style="solid", color="black", weight=3];
272[label="primPlusNat vz5000 vz15",fontsize=16,color="burlywood",shape="triangle"];323[label="vz5000/Succ vz50000",fontsize=10,color="white",style="solid",shape="box"];272 -> 323[label="",style="solid", color="burlywood", weight=9];
323 -> 279[label="",style="solid", color="burlywood", weight=3];
324[label="vz5000/Zero",fontsize=10,color="white",style="solid",shape="box"];272 -> 324[label="",style="solid", color="burlywood", weight=9];
324 -> 280[label="",style="solid", color="burlywood", weight=3];
81 -> 129[label="",style="dashed", color="red", weight=0];
81[label="primPlusNat (Succ vz500) (primPlusNat (primMulNat vz4000 (Succ Zero)) (Succ Zero))",fontsize=16,color="magenta"];81 -> 130[label="",style="dashed", color="magenta", weight=3];
82[label="primPlusNat (Succ vz500) Zero",fontsize=16,color="black",shape="box"];82 -> 96[label="",style="solid", color="black", weight=3];
83 -> 142[label="",style="dashed", color="red", weight=0];
83[label="primPlusNat Zero (primPlusNat (primMulNat vz4000 (Succ Zero)) (Succ Zero))",fontsize=16,color="magenta"];83 -> 143[label="",style="dashed", color="magenta", weight=3];
84[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];84 -> 99[label="",style="solid", color="black", weight=3];
123 -> 192[label="",style="dashed", color="red", weight=0];
123[label="primPlusNat (primMulNat vz40000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];123 -> 201[label="",style="dashed", color="magenta", weight=3];
123 -> 202[label="",style="dashed", color="magenta", weight=3];
124[label="Zero",fontsize=16,color="green",shape="box"];275 -> 219[label="",style="dashed", color="red", weight=0];
275[label="primMinusNat vz50000 vz160",fontsize=16,color="magenta"];275 -> 281[label="",style="dashed", color="magenta", weight=3];
275 -> 282[label="",style="dashed", color="magenta", weight=3];
276[label="Pos (Succ vz50000)",fontsize=16,color="green",shape="box"];277[label="Neg (Succ vz160)",fontsize=16,color="green",shape="box"];278[label="Pos Zero",fontsize=16,color="green",shape="box"];279[label="primPlusNat (Succ vz50000) vz15",fontsize=16,color="burlywood",shape="box"];325[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];279 -> 325[label="",style="solid", color="burlywood", weight=9];
325 -> 283[label="",style="solid", color="burlywood", weight=3];
326[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];279 -> 326[label="",style="solid", color="burlywood", weight=9];
326 -> 284[label="",style="solid", color="burlywood", weight=3];
280[label="primPlusNat Zero vz15",fontsize=16,color="burlywood",shape="box"];327[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];280 -> 327[label="",style="solid", color="burlywood", weight=9];
327 -> 285[label="",style="solid", color="burlywood", weight=3];
328[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];280 -> 328[label="",style="solid", color="burlywood", weight=9];
328 -> 286[label="",style="solid", color="burlywood", weight=3];
130 -> 105[label="",style="dashed", color="red", weight=0];
130[label="primMulNat vz4000 (Succ Zero)",fontsize=16,color="magenta"];129[label="primPlusNat (Succ vz500) (primPlusNat vz9 (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];329[label="vz9/Succ vz90",fontsize=10,color="white",style="solid",shape="box"];129 -> 329[label="",style="solid", color="burlywood", weight=9];
329 -> 133[label="",style="solid", color="burlywood", weight=3];
330[label="vz9/Zero",fontsize=10,color="white",style="solid",shape="box"];129 -> 330[label="",style="solid", color="burlywood", weight=9];
330 -> 134[label="",style="solid", color="burlywood", weight=3];
96[label="Succ vz500",fontsize=16,color="green",shape="box"];143 -> 105[label="",style="dashed", color="red", weight=0];
143[label="primMulNat vz4000 (Succ Zero)",fontsize=16,color="magenta"];142[label="primPlusNat Zero (primPlusNat vz11 (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];331[label="vz11/Succ vz110",fontsize=10,color="white",style="solid",shape="box"];142 -> 331[label="",style="solid", color="burlywood", weight=9];
331 -> 146[label="",style="solid", color="burlywood", weight=3];
332[label="vz11/Zero",fontsize=10,color="white",style="solid",shape="box"];142 -> 332[label="",style="solid", color="burlywood", weight=9];
332 -> 147[label="",style="solid", color="burlywood", weight=3];
99[label="Zero",fontsize=16,color="green",shape="box"];201 -> 105[label="",style="dashed", color="red", weight=0];
201[label="primMulNat vz40000 (Succ Zero)",fontsize=16,color="magenta"];201 -> 216[label="",style="dashed", color="magenta", weight=3];
202[label="Zero",fontsize=16,color="green",shape="box"];281[label="vz50000",fontsize=16,color="green",shape="box"];282[label="vz160",fontsize=16,color="green",shape="box"];283[label="primPlusNat (Succ vz50000) (Succ vz150)",fontsize=16,color="black",shape="box"];283 -> 287[label="",style="solid", color="black", weight=3];
284[label="primPlusNat (Succ vz50000) Zero",fontsize=16,color="black",shape="box"];284 -> 288[label="",style="solid", color="black", weight=3];
285[label="primPlusNat Zero (Succ vz150)",fontsize=16,color="black",shape="box"];285 -> 289[label="",style="solid", color="black", weight=3];
286[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];286 -> 290[label="",style="solid", color="black", weight=3];
133[label="primPlusNat (Succ vz500) (primPlusNat (Succ vz90) (Succ Zero))",fontsize=16,color="black",shape="box"];133 -> 148[label="",style="solid", color="black", weight=3];
134[label="primPlusNat (Succ vz500) (primPlusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];134 -> 149[label="",style="solid", color="black", weight=3];
146[label="primPlusNat Zero (primPlusNat (Succ vz110) (Succ Zero))",fontsize=16,color="black",shape="box"];146 -> 161[label="",style="solid", color="black", weight=3];
147[label="primPlusNat Zero (primPlusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];147 -> 162[label="",style="solid", color="black", weight=3];
216[label="vz40000",fontsize=16,color="green",shape="box"];287[label="Succ (Succ (primPlusNat vz50000 vz150))",fontsize=16,color="green",shape="box"];287 -> 291[label="",style="dashed", color="green", weight=3];
288[label="Succ vz50000",fontsize=16,color="green",shape="box"];289[label="Succ vz150",fontsize=16,color="green",shape="box"];290[label="Zero",fontsize=16,color="green",shape="box"];148 -> 192[label="",style="dashed", color="red", weight=0];
148[label="primPlusNat (Succ vz500) (Succ (Succ (primPlusNat vz90 Zero)))",fontsize=16,color="magenta"];148 -> 203[label="",style="dashed", color="magenta", weight=3];
148 -> 204[label="",style="dashed", color="magenta", weight=3];
149 -> 192[label="",style="dashed", color="red", weight=0];
149[label="primPlusNat (Succ vz500) (Succ Zero)",fontsize=16,color="magenta"];149 -> 205[label="",style="dashed", color="magenta", weight=3];
149 -> 206[label="",style="dashed", color="magenta", weight=3];
161 -> 192[label="",style="dashed", color="red", weight=0];
161[label="primPlusNat Zero (Succ (Succ (primPlusNat vz110 Zero)))",fontsize=16,color="magenta"];161 -> 207[label="",style="dashed", color="magenta", weight=3];
161 -> 208[label="",style="dashed", color="magenta", weight=3];
162 -> 192[label="",style="dashed", color="red", weight=0];
162[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="magenta"];162 -> 209[label="",style="dashed", color="magenta", weight=3];
162 -> 210[label="",style="dashed", color="magenta", weight=3];
291 -> 272[label="",style="dashed", color="red", weight=0];
291[label="primPlusNat vz50000 vz150",fontsize=16,color="magenta"];291 -> 292[label="",style="dashed", color="magenta", weight=3];
291 -> 293[label="",style="dashed", color="magenta", weight=3];
203[label="Succ vz500",fontsize=16,color="green",shape="box"];204[label="Succ (primPlusNat vz90 Zero)",fontsize=16,color="green",shape="box"];204 -> 217[label="",style="dashed", color="green", weight=3];
205[label="Succ vz500",fontsize=16,color="green",shape="box"];206[label="Zero",fontsize=16,color="green",shape="box"];207[label="Zero",fontsize=16,color="green",shape="box"];208[label="Succ (primPlusNat vz110 Zero)",fontsize=16,color="green",shape="box"];208 -> 218[label="",style="dashed", color="green", weight=3];
209[label="Zero",fontsize=16,color="green",shape="box"];210[label="Zero",fontsize=16,color="green",shape="box"];292[label="vz50000",fontsize=16,color="green",shape="box"];293[label="vz150",fontsize=16,color="green",shape="box"];217[label="primPlusNat vz90 Zero",fontsize=16,color="burlywood",shape="triangle"];333[label="vz90/Succ vz900",fontsize=10,color="white",style="solid",shape="box"];217 -> 333[label="",style="solid", color="burlywood", weight=9];
333 -> 265[label="",style="solid", color="burlywood", weight=3];
334[label="vz90/Zero",fontsize=10,color="white",style="solid",shape="box"];217 -> 334[label="",style="solid", color="burlywood", weight=9];
334 -> 266[label="",style="solid", color="burlywood", weight=3];
218 -> 217[label="",style="dashed", color="red", weight=0];
218[label="primPlusNat vz110 Zero",fontsize=16,color="magenta"];218 -> 267[label="",style="dashed", color="magenta", weight=3];
265[label="primPlusNat (Succ vz900) Zero",fontsize=16,color="black",shape="box"];265 -> 273[label="",style="solid", color="black", weight=3];
266[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];266 -> 274[label="",style="solid", color="black", weight=3];
267[label="vz110",fontsize=16,color="green",shape="box"];273[label="Succ vz900",fontsize=16,color="green",shape="box"];274[label="Zero",fontsize=16,color="green",shape="box"];}

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

(8)
Complex Obligation (AND)

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

(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_genericLength(:(vz30, vz31), ba) -> new_genericLength(vz31, ba)

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

(10) 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_genericLength(:(vz30, vz31), ba) -> new_genericLength(vz31, ba)
The graph contains the following edges 1 > 1, 2 >= 2


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

(11)
YES

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

(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMulNat(Succ(vz40000)) -> new_primMulNat(vz40000)

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

(13) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_primMulNat(Succ(vz40000)) -> new_primMulNat(vz40000)
The graph contains the following edges 1 > 1


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

(14)
YES

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

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

   new_primMinusNat(Succ(vz50000), Succ(vz160)) -> new_primMinusNat(vz50000, vz160)

R is empty.
Q is empty.
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_primMinusNat(Succ(vz50000), Succ(vz160)) -> new_primMinusNat(vz50000, vz160)
The graph contains the following edges 1 > 1, 2 > 2


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

(17)
YES

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

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

   new_primPlusNat(Succ(vz50000), Succ(vz150)) -> new_primPlusNat(vz50000, vz150)

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

(19) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*new_primPlusNat(Succ(vz50000), Succ(vz150)) -> new_primPlusNat(vz50000, vz150)
The graph contains the following edges 1 > 1, 2 > 2


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

(20)
YES