/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 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


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

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

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

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

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

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

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

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

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="cosh",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="cosh vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="(exp vx3 + exp (`negate` vx3)) / fromInt (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="primDivFloat (exp vx3 + exp (`negate` vx3)) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6 -> 16[label="",style="dashed", color="red", weight=0];
6[label="primDivFloat (primPlusFloat (exp vx3) (exp (`negate` vx3))) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="magenta"];6 -> 17[label="",style="dashed", color="magenta", weight=3];
6 -> 18[label="",style="dashed", color="magenta", weight=3];
17[label="exp vx3",fontsize=16,color="black",shape="triangle"];17 -> 20[label="",style="solid", color="black", weight=3];
18 -> 17[label="",style="dashed", color="red", weight=0];
18[label="exp (`negate` vx3)",fontsize=16,color="magenta"];18 -> 21[label="",style="dashed", color="magenta", weight=3];
16[label="primDivFloat (primPlusFloat vx4 vx5) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="burlywood",shape="triangle"];497[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];16 -> 497[label="",style="solid", color="burlywood", weight=9];
497 -> 22[label="",style="solid", color="burlywood", weight=3];
20[label="primExpFloat vx3",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
21[label="`negate` vx3",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
22[label="primDivFloat (primPlusFloat (Float vx40 vx41) vx5) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];498[label="vx5/Float vx50 vx51",fontsize=10,color="white",style="solid",shape="box"];22 -> 498[label="",style="solid", color="burlywood", weight=9];
498 -> 25[label="",style="solid", color="burlywood", weight=3];
23[label="terminator vx3",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3];
24[label="primNegFloat vx3",fontsize=16,color="burlywood",shape="box"];499[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];24 -> 499[label="",style="solid", color="burlywood", weight=9];
499 -> 27[label="",style="solid", color="burlywood", weight=3];
25[label="primDivFloat (primPlusFloat (Float vx40 vx41) (Float vx50 vx51)) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
26[label="ter1m vx3",fontsize=16,color="green",shape="box"];26 -> 29[label="",style="dashed", color="green", weight=3];
27[label="primNegFloat (Float vx30 vx31)",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
28[label="primDivFloat (Float (vx40 * vx51 + vx50 * vx41) (vx41 * vx51)) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
29[label="vx3",fontsize=16,color="green",shape="box"];30[label="Float (`negate` vx30) vx31",fontsize=16,color="green",shape="box"];30 -> 32[label="",style="dashed", color="green", weight=3];
31[label="primDivFloat (Float (vx40 * vx51 + vx50 * vx41) (vx41 * vx51)) (primIntToFloat (Pos (Succ (Succ Zero))))",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3];
32[label="`negate` vx30",fontsize=16,color="black",shape="box"];32 -> 34[label="",style="solid", color="black", weight=3];
33[label="primDivFloat (Float (vx40 * vx51 + vx50 * vx41) (vx41 * vx51)) (Float (Pos (Succ (Succ Zero))) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
34[label="primNegInt vx30",fontsize=16,color="burlywood",shape="box"];500[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];34 -> 500[label="",style="solid", color="burlywood", weight=9];
500 -> 36[label="",style="solid", color="burlywood", weight=3];
501[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];34 -> 501[label="",style="solid", color="burlywood", weight=9];
501 -> 37[label="",style="solid", color="burlywood", weight=3];
35[label="Float ((vx40 * vx51 + vx50 * vx41) * Pos (Succ Zero)) (vx41 * vx51 * Pos (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];35 -> 38[label="",style="dashed", color="green", weight=3];
35 -> 39[label="",style="dashed", color="green", weight=3];
36[label="primNegInt (Pos vx300)",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3];
37[label="primNegInt (Neg vx300)",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3];
38[label="(vx40 * vx51 + vx50 * vx41) * Pos (Succ Zero)",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3];
39[label="vx41 * vx51 * Pos (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];39 -> 43[label="",style="solid", color="black", weight=3];
40[label="Neg vx300",fontsize=16,color="green",shape="box"];41[label="Pos vx300",fontsize=16,color="green",shape="box"];42[label="primMulInt (vx40 * vx51 + vx50 * vx41) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
43[label="primMulInt (vx41 * vx51) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3];
44[label="primMulInt (primPlusInt (vx40 * vx51) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3];
45[label="primMulInt (primMulInt vx41 vx51) (Pos (Succ (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];502[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];45 -> 502[label="",style="solid", color="burlywood", weight=9];
502 -> 47[label="",style="solid", color="burlywood", weight=3];
503[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];45 -> 503[label="",style="solid", color="burlywood", weight=9];
503 -> 48[label="",style="solid", color="burlywood", weight=3];
46[label="primMulInt (primPlusInt (primMulInt vx40 vx51) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];504[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];46 -> 504[label="",style="solid", color="burlywood", weight=9];
504 -> 49[label="",style="solid", color="burlywood", weight=3];
505[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];46 -> 505[label="",style="solid", color="burlywood", weight=9];
505 -> 50[label="",style="solid", color="burlywood", weight=3];
47[label="primMulInt (primMulInt (Pos vx410) vx51) (Pos (Succ (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];506[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];47 -> 506[label="",style="solid", color="burlywood", weight=9];
506 -> 51[label="",style="solid", color="burlywood", weight=3];
507[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];47 -> 507[label="",style="solid", color="burlywood", weight=9];
507 -> 52[label="",style="solid", color="burlywood", weight=3];
48[label="primMulInt (primMulInt (Neg vx410) vx51) (Pos (Succ (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];508[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];48 -> 508[label="",style="solid", color="burlywood", weight=9];
508 -> 53[label="",style="solid", color="burlywood", weight=3];
509[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];48 -> 509[label="",style="solid", color="burlywood", weight=9];
509 -> 54[label="",style="solid", color="burlywood", weight=3];
49[label="primMulInt (primPlusInt (primMulInt (Pos vx400) vx51) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];510[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];49 -> 510[label="",style="solid", color="burlywood", weight=9];
510 -> 55[label="",style="solid", color="burlywood", weight=3];
511[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];49 -> 511[label="",style="solid", color="burlywood", weight=9];
511 -> 56[label="",style="solid", color="burlywood", weight=3];
50[label="primMulInt (primPlusInt (primMulInt (Neg vx400) vx51) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];512[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];50 -> 512[label="",style="solid", color="burlywood", weight=9];
512 -> 57[label="",style="solid", color="burlywood", weight=3];
513[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];50 -> 513[label="",style="solid", color="burlywood", weight=9];
513 -> 58[label="",style="solid", color="burlywood", weight=3];
51[label="primMulInt (primMulInt (Pos vx410) (Pos vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];51 -> 59[label="",style="solid", color="black", weight=3];
52[label="primMulInt (primMulInt (Pos vx410) (Neg vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];52 -> 60[label="",style="solid", color="black", weight=3];
53[label="primMulInt (primMulInt (Neg vx410) (Pos vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];53 -> 61[label="",style="solid", color="black", weight=3];
54[label="primMulInt (primMulInt (Neg vx410) (Neg vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];54 -> 62[label="",style="solid", color="black", weight=3];
55[label="primMulInt (primPlusInt (primMulInt (Pos vx400) (Pos vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];55 -> 63[label="",style="solid", color="black", weight=3];
56[label="primMulInt (primPlusInt (primMulInt (Pos vx400) (Neg vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];56 -> 64[label="",style="solid", color="black", weight=3];
57[label="primMulInt (primPlusInt (primMulInt (Neg vx400) (Pos vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];57 -> 65[label="",style="solid", color="black", weight=3];
58[label="primMulInt (primPlusInt (primMulInt (Neg vx400) (Neg vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];58 -> 66[label="",style="solid", color="black", weight=3];
59[label="primMulInt (Pos (primMulNat vx410 vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="triangle"];59 -> 67[label="",style="solid", color="black", weight=3];
60[label="primMulInt (Neg (primMulNat vx410 vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="triangle"];60 -> 68[label="",style="solid", color="black", weight=3];
61 -> 60[label="",style="dashed", color="red", weight=0];
61[label="primMulInt (Neg (primMulNat vx410 vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];61 -> 69[label="",style="dashed", color="magenta", weight=3];
61 -> 70[label="",style="dashed", color="magenta", weight=3];
62 -> 59[label="",style="dashed", color="red", weight=0];
62[label="primMulInt (Pos (primMulNat vx410 vx510)) (Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];62 -> 71[label="",style="dashed", color="magenta", weight=3];
62 -> 72[label="",style="dashed", color="magenta", weight=3];
63[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];63 -> 73[label="",style="solid", color="black", weight=3];
64[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];64 -> 74[label="",style="solid", color="black", weight=3];
65 -> 64[label="",style="dashed", color="red", weight=0];
65[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="magenta"];65 -> 75[label="",style="dashed", color="magenta", weight=3];
65 -> 76[label="",style="dashed", color="magenta", weight=3];
66 -> 63[label="",style="dashed", color="red", weight=0];
66[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="magenta"];66 -> 77[label="",style="dashed", color="magenta", weight=3];
66 -> 78[label="",style="dashed", color="magenta", weight=3];
67[label="Pos (primMulNat (primMulNat vx410 vx510) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];67 -> 79[label="",style="dashed", color="green", weight=3];
68[label="Neg (primMulNat (primMulNat vx410 vx510) (Succ (Succ Zero)))",fontsize=16,color="green",shape="box"];68 -> 80[label="",style="dashed", color="green", weight=3];
69[label="vx510",fontsize=16,color="green",shape="box"];70[label="vx410",fontsize=16,color="green",shape="box"];71[label="vx510",fontsize=16,color="green",shape="box"];72[label="vx410",fontsize=16,color="green",shape="box"];73[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt vx50 vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];514[label="vx50/Pos vx500",fontsize=10,color="white",style="solid",shape="box"];73 -> 514[label="",style="solid", color="burlywood", weight=9];
514 -> 81[label="",style="solid", color="burlywood", weight=3];
515[label="vx50/Neg vx500",fontsize=10,color="white",style="solid",shape="box"];73 -> 515[label="",style="solid", color="burlywood", weight=9];
515 -> 82[label="",style="solid", color="burlywood", weight=3];
74[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt vx50 vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];516[label="vx50/Pos vx500",fontsize=10,color="white",style="solid",shape="box"];74 -> 516[label="",style="solid", color="burlywood", weight=9];
516 -> 83[label="",style="solid", color="burlywood", weight=3];
517[label="vx50/Neg vx500",fontsize=10,color="white",style="solid",shape="box"];74 -> 517[label="",style="solid", color="burlywood", weight=9];
517 -> 84[label="",style="solid", color="burlywood", weight=3];
75[label="vx510",fontsize=16,color="green",shape="box"];76[label="vx400",fontsize=16,color="green",shape="box"];77[label="vx400",fontsize=16,color="green",shape="box"];78[label="vx510",fontsize=16,color="green",shape="box"];79[label="primMulNat (primMulNat vx410 vx510) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];518[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];79 -> 518[label="",style="solid", color="burlywood", weight=9];
518 -> 85[label="",style="solid", color="burlywood", weight=3];
519[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 519[label="",style="solid", color="burlywood", weight=9];
519 -> 86[label="",style="solid", color="burlywood", weight=3];
80 -> 79[label="",style="dashed", color="red", weight=0];
80[label="primMulNat (primMulNat vx410 vx510) (Succ (Succ Zero))",fontsize=16,color="magenta"];80 -> 87[label="",style="dashed", color="magenta", weight=3];
81[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Pos vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];520[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];81 -> 520[label="",style="solid", color="burlywood", weight=9];
520 -> 88[label="",style="solid", color="burlywood", weight=3];
521[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];81 -> 521[label="",style="solid", color="burlywood", weight=9];
521 -> 89[label="",style="solid", color="burlywood", weight=3];
82[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Neg vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];522[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];82 -> 522[label="",style="solid", color="burlywood", weight=9];
522 -> 90[label="",style="solid", color="burlywood", weight=3];
523[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];82 -> 523[label="",style="solid", color="burlywood", weight=9];
523 -> 91[label="",style="solid", color="burlywood", weight=3];
83[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Pos vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];524[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];83 -> 524[label="",style="solid", color="burlywood", weight=9];
524 -> 92[label="",style="solid", color="burlywood", weight=3];
525[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];83 -> 525[label="",style="solid", color="burlywood", weight=9];
525 -> 93[label="",style="solid", color="burlywood", weight=3];
84[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Neg vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];526[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];84 -> 526[label="",style="solid", color="burlywood", weight=9];
526 -> 94[label="",style="solid", color="burlywood", weight=3];
527[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];84 -> 527[label="",style="solid", color="burlywood", weight=9];
527 -> 95[label="",style="solid", color="burlywood", weight=3];
85[label="primMulNat (primMulNat (Succ vx4100) vx510) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];528[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];85 -> 528[label="",style="solid", color="burlywood", weight=9];
528 -> 96[label="",style="solid", color="burlywood", weight=3];
529[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];85 -> 529[label="",style="solid", color="burlywood", weight=9];
529 -> 97[label="",style="solid", color="burlywood", weight=3];
86[label="primMulNat (primMulNat Zero vx510) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];530[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];86 -> 530[label="",style="solid", color="burlywood", weight=9];
530 -> 98[label="",style="solid", color="burlywood", weight=3];
531[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];86 -> 531[label="",style="solid", color="burlywood", weight=9];
531 -> 99[label="",style="solid", color="burlywood", weight=3];
87[label="vx510",fontsize=16,color="green",shape="box"];88[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Pos vx500) (Pos vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];88 -> 100[label="",style="solid", color="black", weight=3];
89[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Pos vx500) (Neg vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];89 -> 101[label="",style="solid", color="black", weight=3];
90[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Neg vx500) (Pos vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];90 -> 102[label="",style="solid", color="black", weight=3];
91[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Neg vx500) (Neg vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];91 -> 103[label="",style="solid", color="black", weight=3];
92[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Pos vx500) (Pos vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];92 -> 104[label="",style="solid", color="black", weight=3];
93[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Pos vx500) (Neg vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];93 -> 105[label="",style="solid", color="black", weight=3];
94[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Neg vx500) (Pos vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];94 -> 106[label="",style="solid", color="black", weight=3];
95[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Neg vx500) (Neg vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];95 -> 107[label="",style="solid", color="black", weight=3];
96[label="primMulNat (primMulNat (Succ vx4100) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];96 -> 108[label="",style="solid", color="black", weight=3];
97[label="primMulNat (primMulNat (Succ vx4100) Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];97 -> 109[label="",style="solid", color="black", weight=3];
98[label="primMulNat (primMulNat Zero (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];98 -> 110[label="",style="solid", color="black", weight=3];
99[label="primMulNat (primMulNat Zero Zero) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];99 -> 111[label="",style="solid", color="black", weight=3];
100[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (Pos (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];100 -> 112[label="",style="solid", color="black", weight=3];
101[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (Neg (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];101 -> 113[label="",style="solid", color="black", weight=3];
102 -> 101[label="",style="dashed", color="red", weight=0];
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102 -> 115[label="",style="dashed", color="magenta", weight=3];
103 -> 100[label="",style="dashed", color="red", weight=0];
103[label="primMulInt (primPlusInt (Pos (primMulNat vx400 vx510)) (Pos (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="magenta"];103 -> 116[label="",style="dashed", color="magenta", weight=3];
103 -> 117[label="",style="dashed", color="magenta", weight=3];
104[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (Pos (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];104 -> 118[label="",style="solid", color="black", weight=3];
105[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (Neg (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];105 -> 119[label="",style="solid", color="black", weight=3];
106 -> 105[label="",style="dashed", color="red", weight=0];
106[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (Neg (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="magenta"];106 -> 120[label="",style="dashed", color="magenta", weight=3];
106 -> 121[label="",style="dashed", color="magenta", weight=3];
107 -> 104[label="",style="dashed", color="red", weight=0];
107[label="primMulInt (primPlusInt (Neg (primMulNat vx400 vx510)) (Pos (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="magenta"];107 -> 122[label="",style="dashed", color="magenta", weight=3];
107 -> 123[label="",style="dashed", color="magenta", weight=3];
108[label="primMulNat (primPlusNat (primMulNat vx4100 (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];532[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];108 -> 532[label="",style="solid", color="burlywood", weight=9];
532 -> 124[label="",style="solid", color="burlywood", weight=3];
533[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 533[label="",style="solid", color="burlywood", weight=9];
533 -> 125[label="",style="solid", color="burlywood", weight=3];
109[label="primMulNat Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];109 -> 126[label="",style="solid", color="black", weight=3];
110 -> 109[label="",style="dashed", color="red", weight=0];
110[label="primMulNat Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];111 -> 109[label="",style="dashed", color="red", weight=0];
111[label="primMulNat Zero (Succ (Succ Zero))",fontsize=16,color="magenta"];112[label="primMulInt (Pos (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];112 -> 127[label="",style="solid", color="black", weight=3];
113 -> 305[label="",style="dashed", color="red", weight=0];
113[label="primMulInt (primMinusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Pos (Succ Zero))",fontsize=16,color="magenta"];113 -> 306[label="",style="dashed", color="magenta", weight=3];
113 -> 307[label="",style="dashed", color="magenta", weight=3];
114[label="vx500",fontsize=16,color="green",shape="box"];115[label="vx410",fontsize=16,color="green",shape="box"];116[label="vx500",fontsize=16,color="green",shape="box"];117[label="vx410",fontsize=16,color="green",shape="box"];118 -> 305[label="",style="dashed", color="red", weight=0];
118[label="primMulInt (primMinusNat (primMulNat vx500 vx410) (primMulNat vx400 vx510)) (Pos (Succ Zero))",fontsize=16,color="magenta"];118 -> 308[label="",style="dashed", color="magenta", weight=3];
118 -> 309[label="",style="dashed", color="magenta", weight=3];
119[label="primMulInt (Neg (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];119 -> 134[label="",style="solid", color="black", weight=3];
120[label="vx500",fontsize=16,color="green",shape="box"];121[label="vx410",fontsize=16,color="green",shape="box"];122[label="vx500",fontsize=16,color="green",shape="box"];123[label="vx410",fontsize=16,color="green",shape="box"];124[label="primMulNat (primPlusNat (primMulNat (Succ vx41000) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];124 -> 135[label="",style="solid", color="black", weight=3];
125[label="primMulNat (primPlusNat (primMulNat Zero (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];125 -> 136[label="",style="solid", color="black", weight=3];
126[label="Zero",fontsize=16,color="green",shape="box"];127[label="Pos (primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero))",fontsize=16,color="green",shape="box"];127 -> 137[label="",style="dashed", color="green", weight=3];
306[label="primMulNat vx400 vx510",fontsize=16,color="burlywood",shape="triangle"];534[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];306 -> 534[label="",style="solid", color="burlywood", weight=9];
534 -> 311[label="",style="solid", color="burlywood", weight=3];
535[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];306 -> 535[label="",style="solid", color="burlywood", weight=9];
535 -> 312[label="",style="solid", color="burlywood", weight=3];
307 -> 306[label="",style="dashed", color="red", weight=0];
307[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];307 -> 313[label="",style="dashed", color="magenta", weight=3];
307 -> 314[label="",style="dashed", color="magenta", weight=3];
305[label="primMulInt (primMinusNat vx8 vx9) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];536[label="vx8/Succ vx80",fontsize=10,color="white",style="solid",shape="box"];305 -> 536[label="",style="solid", color="burlywood", weight=9];
536 -> 315[label="",style="solid", color="burlywood", weight=3];
537[label="vx8/Zero",fontsize=10,color="white",style="solid",shape="box"];305 -> 537[label="",style="solid", color="burlywood", weight=9];
537 -> 316[label="",style="solid", color="burlywood", weight=3];
308 -> 306[label="",style="dashed", color="red", weight=0];
308[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];308 -> 317[label="",style="dashed", color="magenta", weight=3];
308 -> 318[label="",style="dashed", color="magenta", weight=3];
309 -> 306[label="",style="dashed", color="red", weight=0];
309[label="primMulNat vx400 vx510",fontsize=16,color="magenta"];309 -> 319[label="",style="dashed", color="magenta", weight=3];
134[label="Neg (primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero))",fontsize=16,color="green",shape="box"];134 -> 142[label="",style="dashed", color="green", weight=3];
135[label="primMulNat (primPlusNat (primPlusNat (primMulNat vx41000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];538[label="vx41000/Succ vx410000",fontsize=10,color="white",style="solid",shape="box"];135 -> 538[label="",style="solid", color="burlywood", weight=9];
538 -> 143[label="",style="solid", color="burlywood", weight=3];
539[label="vx41000/Zero",fontsize=10,color="white",style="solid",shape="box"];135 -> 539[label="",style="solid", color="burlywood", weight=9];
539 -> 144[label="",style="solid", color="burlywood", weight=3];
136[label="primMulNat (primPlusNat Zero (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];136 -> 145[label="",style="solid", color="black", weight=3];
137 -> 259[label="",style="dashed", color="red", weight=0];
137[label="primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="magenta"];137 -> 260[label="",style="dashed", color="magenta", weight=3];
311[label="primMulNat (Succ vx4000) vx510",fontsize=16,color="burlywood",shape="box"];540[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];311 -> 540[label="",style="solid", color="burlywood", weight=9];
540 -> 328[label="",style="solid", color="burlywood", weight=3];
541[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];311 -> 541[label="",style="solid", color="burlywood", weight=9];
541 -> 329[label="",style="solid", color="burlywood", weight=3];
312[label="primMulNat Zero vx510",fontsize=16,color="burlywood",shape="box"];542[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];312 -> 542[label="",style="solid", color="burlywood", weight=9];
542 -> 330[label="",style="solid", color="burlywood", weight=3];
543[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];312 -> 543[label="",style="solid", color="burlywood", weight=9];
543 -> 331[label="",style="solid", color="burlywood", weight=3];
313[label="vx500",fontsize=16,color="green",shape="box"];314[label="vx410",fontsize=16,color="green",shape="box"];315[label="primMulInt (primMinusNat (Succ vx80) vx9) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];544[label="vx9/Succ vx90",fontsize=10,color="white",style="solid",shape="box"];315 -> 544[label="",style="solid", color="burlywood", weight=9];
544 -> 332[label="",style="solid", color="burlywood", weight=3];
545[label="vx9/Zero",fontsize=10,color="white",style="solid",shape="box"];315 -> 545[label="",style="solid", color="burlywood", weight=9];
545 -> 333[label="",style="solid", color="burlywood", weight=3];
316[label="primMulInt (primMinusNat Zero vx9) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];546[label="vx9/Succ vx90",fontsize=10,color="white",style="solid",shape="box"];316 -> 546[label="",style="solid", color="burlywood", weight=9];
546 -> 334[label="",style="solid", color="burlywood", weight=3];
547[label="vx9/Zero",fontsize=10,color="white",style="solid",shape="box"];316 -> 547[label="",style="solid", color="burlywood", weight=9];
547 -> 335[label="",style="solid", color="burlywood", weight=3];
317[label="vx500",fontsize=16,color="green",shape="box"];318[label="vx410",fontsize=16,color="green",shape="box"];319[label="vx510",fontsize=16,color="green",shape="box"];142 -> 259[label="",style="dashed", color="red", weight=0];
142[label="primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="magenta"];142 -> 261[label="",style="dashed", color="magenta", weight=3];
143[label="primMulNat (primPlusNat (primPlusNat (primMulNat (Succ vx410000) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];143 -> 154[label="",style="solid", color="black", weight=3];
144[label="primMulNat (primPlusNat (primPlusNat (primMulNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];144 -> 155[label="",style="solid", color="black", weight=3];
145[label="primMulNat (Succ vx5100) (Succ (Succ Zero))",fontsize=16,color="black",shape="triangle"];145 -> 156[label="",style="solid", color="black", weight=3];
260 -> 408[label="",style="dashed", color="red", weight=0];
260[label="primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)",fontsize=16,color="magenta"];260 -> 409[label="",style="dashed", color="magenta", weight=3];
260 -> 410[label="",style="dashed", color="magenta", weight=3];
259[label="primMulNat vx7 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];548[label="vx7/Succ vx70",fontsize=10,color="white",style="solid",shape="box"];259 -> 548[label="",style="solid", color="burlywood", weight=9];
548 -> 277[label="",style="solid", color="burlywood", weight=3];
549[label="vx7/Zero",fontsize=10,color="white",style="solid",shape="box"];259 -> 549[label="",style="solid", color="burlywood", weight=9];
549 -> 278[label="",style="solid", color="burlywood", weight=3];
328[label="primMulNat (Succ vx4000) (Succ vx5100)",fontsize=16,color="black",shape="box"];328 -> 344[label="",style="solid", color="black", weight=3];
329[label="primMulNat (Succ vx4000) Zero",fontsize=16,color="black",shape="box"];329 -> 345[label="",style="solid", color="black", weight=3];
330[label="primMulNat Zero (Succ vx5100)",fontsize=16,color="black",shape="box"];330 -> 346[label="",style="solid", color="black", weight=3];
331[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];331 -> 347[label="",style="solid", color="black", weight=3];
332[label="primMulInt (primMinusNat (Succ vx80) (Succ vx90)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];332 -> 348[label="",style="solid", color="black", weight=3];
333[label="primMulInt (primMinusNat (Succ vx80) Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];333 -> 349[label="",style="solid", color="black", weight=3];
334[label="primMulInt (primMinusNat Zero (Succ vx90)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];334 -> 350[label="",style="solid", color="black", weight=3];
335[label="primMulInt (primMinusNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];335 -> 351[label="",style="solid", color="black", weight=3];
261 -> 408[label="",style="dashed", color="red", weight=0];
261[label="primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)",fontsize=16,color="magenta"];261 -> 411[label="",style="dashed", color="magenta", weight=3];
261 -> 412[label="",style="dashed", color="magenta", weight=3];
154[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx410000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];550[label="vx410000/Succ vx4100000",fontsize=10,color="white",style="solid",shape="box"];154 -> 550[label="",style="solid", color="burlywood", weight=9];
550 -> 165[label="",style="solid", color="burlywood", weight=3];
551[label="vx410000/Zero",fontsize=10,color="white",style="solid",shape="box"];154 -> 551[label="",style="solid", color="burlywood", weight=9];
551 -> 166[label="",style="solid", color="burlywood", weight=3];
155[label="primMulNat (primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];155 -> 167[label="",style="solid", color="black", weight=3];
156 -> 408[label="",style="dashed", color="red", weight=0];
156[label="primPlusNat (primMulNat vx5100 (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];156 -> 413[label="",style="dashed", color="magenta", weight=3];
156 -> 414[label="",style="dashed", color="magenta", weight=3];
409 -> 306[label="",style="dashed", color="red", weight=0];
409[label="primMulNat vx400 vx510",fontsize=16,color="magenta"];410 -> 306[label="",style="dashed", color="red", weight=0];
410[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];410 -> 448[label="",style="dashed", color="magenta", weight=3];
410 -> 449[label="",style="dashed", color="magenta", weight=3];
408[label="primPlusNat vx16 vx12",fontsize=16,color="burlywood",shape="triangle"];552[label="vx16/Succ vx160",fontsize=10,color="white",style="solid",shape="box"];408 -> 552[label="",style="solid", color="burlywood", weight=9];
552 -> 450[label="",style="solid", color="burlywood", weight=3];
553[label="vx16/Zero",fontsize=10,color="white",style="solid",shape="box"];408 -> 553[label="",style="solid", color="burlywood", weight=9];
553 -> 451[label="",style="solid", color="burlywood", weight=3];
277[label="primMulNat (Succ vx70) (Succ Zero)",fontsize=16,color="black",shape="box"];277 -> 324[label="",style="solid", color="black", weight=3];
278[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];278 -> 325[label="",style="solid", color="black", weight=3];
344 -> 408[label="",style="dashed", color="red", weight=0];
344[label="primPlusNat (primMulNat vx4000 (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];344 -> 415[label="",style="dashed", color="magenta", weight=3];
344 -> 416[label="",style="dashed", color="magenta", weight=3];
345[label="Zero",fontsize=16,color="green",shape="box"];346[label="Zero",fontsize=16,color="green",shape="box"];347[label="Zero",fontsize=16,color="green",shape="box"];348 -> 305[label="",style="dashed", color="red", weight=0];
348[label="primMulInt (primMinusNat vx80 vx90) (Pos (Succ Zero))",fontsize=16,color="magenta"];348 -> 382[label="",style="dashed", color="magenta", weight=3];
348 -> 383[label="",style="dashed", color="magenta", weight=3];
349[label="primMulInt (Pos (Succ vx80)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];349 -> 384[label="",style="solid", color="black", weight=3];
350[label="primMulInt (Neg (Succ vx90)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];350 -> 385[label="",style="solid", color="black", weight=3];
351[label="primMulInt (Pos Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];351 -> 386[label="",style="solid", color="black", weight=3];
411 -> 306[label="",style="dashed", color="red", weight=0];
411[label="primMulNat vx400 vx510",fontsize=16,color="magenta"];411 -> 452[label="",style="dashed", color="magenta", weight=3];
412 -> 306[label="",style="dashed", color="red", weight=0];
412[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];412 -> 453[label="",style="dashed", color="magenta", weight=3];
412 -> 454[label="",style="dashed", color="magenta", weight=3];
165[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ vx4100000) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];165 -> 180[label="",style="solid", color="black", weight=3];
166[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];166 -> 181[label="",style="solid", color="black", weight=3];
167[label="primMulNat (primPlusNat (Succ vx5100) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];167 -> 182[label="",style="solid", color="black", weight=3];
413 -> 306[label="",style="dashed", color="red", weight=0];
413[label="primMulNat vx5100 (Succ (Succ Zero))",fontsize=16,color="magenta"];413 -> 455[label="",style="dashed", color="magenta", weight=3];
413 -> 456[label="",style="dashed", color="magenta", weight=3];
414[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];448[label="vx500",fontsize=16,color="green",shape="box"];449[label="vx410",fontsize=16,color="green",shape="box"];450[label="primPlusNat (Succ vx160) vx12",fontsize=16,color="burlywood",shape="box"];554[label="vx12/Succ vx120",fontsize=10,color="white",style="solid",shape="box"];450 -> 554[label="",style="solid", color="burlywood", weight=9];
554 -> 474[label="",style="solid", color="burlywood", weight=3];
555[label="vx12/Zero",fontsize=10,color="white",style="solid",shape="box"];450 -> 555[label="",style="solid", color="burlywood", weight=9];
555 -> 475[label="",style="solid", color="burlywood", weight=3];
451[label="primPlusNat Zero vx12",fontsize=16,color="burlywood",shape="box"];556[label="vx12/Succ vx120",fontsize=10,color="white",style="solid",shape="box"];451 -> 556[label="",style="solid", color="burlywood", weight=9];
556 -> 476[label="",style="solid", color="burlywood", weight=3];
557[label="vx12/Zero",fontsize=10,color="white",style="solid",shape="box"];451 -> 557[label="",style="solid", color="burlywood", weight=9];
557 -> 477[label="",style="solid", color="burlywood", weight=3];
324 -> 408[label="",style="dashed", color="red", weight=0];
324[label="primPlusNat (primMulNat vx70 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];324 -> 419[label="",style="dashed", color="magenta", weight=3];
324 -> 420[label="",style="dashed", color="magenta", weight=3];
325[label="Zero",fontsize=16,color="green",shape="box"];415 -> 306[label="",style="dashed", color="red", weight=0];
415[label="primMulNat vx4000 (Succ vx5100)",fontsize=16,color="magenta"];415 -> 457[label="",style="dashed", color="magenta", weight=3];
415 -> 458[label="",style="dashed", color="magenta", weight=3];
416[label="Succ vx5100",fontsize=16,color="green",shape="box"];382[label="vx80",fontsize=16,color="green",shape="box"];383[label="vx90",fontsize=16,color="green",shape="box"];384[label="Pos (primMulNat (Succ vx80) (Succ Zero))",fontsize=16,color="green",shape="box"];384 -> 397[label="",style="dashed", color="green", weight=3];
385[label="Neg (primMulNat (Succ vx90) (Succ Zero))",fontsize=16,color="green",shape="box"];385 -> 398[label="",style="dashed", color="green", weight=3];
386[label="Pos (primMulNat Zero (Succ Zero))",fontsize=16,color="green",shape="box"];386 -> 399[label="",style="dashed", color="green", weight=3];
452[label="vx510",fontsize=16,color="green",shape="box"];453[label="vx500",fontsize=16,color="green",shape="box"];454[label="vx410",fontsize=16,color="green",shape="box"];180[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx4100000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];558[label="vx4100000/Succ vx41000000",fontsize=10,color="white",style="solid",shape="box"];180 -> 558[label="",style="solid", color="burlywood", weight=9];
558 -> 196[label="",style="solid", color="burlywood", weight=3];
559[label="vx4100000/Zero",fontsize=10,color="white",style="solid",shape="box"];180 -> 559[label="",style="solid", color="burlywood", weight=9];
559 -> 197[label="",style="solid", color="burlywood", weight=3];
181[label="primMulNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];181 -> 198[label="",style="solid", color="black", weight=3];
182 -> 145[label="",style="dashed", color="red", weight=0];
182[label="primMulNat (Succ (Succ (primPlusNat vx5100 vx5100))) (Succ (Succ Zero))",fontsize=16,color="magenta"];182 -> 199[label="",style="dashed", color="magenta", weight=3];
455[label="vx5100",fontsize=16,color="green",shape="box"];456[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];474[label="primPlusNat (Succ vx160) (Succ vx120)",fontsize=16,color="black",shape="box"];474 -> 482[label="",style="solid", color="black", weight=3];
475[label="primPlusNat (Succ vx160) Zero",fontsize=16,color="black",shape="box"];475 -> 483[label="",style="solid", color="black", weight=3];
476[label="primPlusNat Zero (Succ vx120)",fontsize=16,color="black",shape="box"];476 -> 484[label="",style="solid", color="black", weight=3];
477[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];477 -> 485[label="",style="solid", color="black", weight=3];
419 -> 306[label="",style="dashed", color="red", weight=0];
419[label="primMulNat vx70 (Succ Zero)",fontsize=16,color="magenta"];419 -> 459[label="",style="dashed", color="magenta", weight=3];
419 -> 460[label="",style="dashed", color="magenta", weight=3];
420[label="Succ Zero",fontsize=16,color="green",shape="box"];457[label="vx4000",fontsize=16,color="green",shape="box"];458[label="Succ vx5100",fontsize=16,color="green",shape="box"];397 -> 306[label="",style="dashed", color="red", weight=0];
397[label="primMulNat (Succ vx80) (Succ Zero)",fontsize=16,color="magenta"];397 -> 461[label="",style="dashed", color="magenta", weight=3];
397 -> 462[label="",style="dashed", color="magenta", weight=3];
398 -> 306[label="",style="dashed", color="red", weight=0];
398[label="primMulNat (Succ vx90) (Succ Zero)",fontsize=16,color="magenta"];398 -> 463[label="",style="dashed", color="magenta", weight=3];
398 -> 464[label="",style="dashed", color="magenta", weight=3];
399 -> 306[label="",style="dashed", color="red", weight=0];
399[label="primMulNat Zero (Succ Zero)",fontsize=16,color="magenta"];399 -> 465[label="",style="dashed", color="magenta", weight=3];
399 -> 466[label="",style="dashed", color="magenta", weight=3];
196[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ vx41000000) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];196 -> 221[label="",style="solid", color="black", weight=3];
197[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];197 -> 222[label="",style="solid", color="black", weight=3];
198 -> 201[label="",style="dashed", color="red", weight=0];
198[label="primMulNat (primPlusNat (primPlusNat (Succ vx5100) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="magenta"];198 -> 223[label="",style="dashed", color="magenta", weight=3];
199[label="Succ (primPlusNat vx5100 vx5100)",fontsize=16,color="green",shape="box"];199 -> 224[label="",style="dashed", color="green", weight=3];
482[label="Succ (Succ (primPlusNat vx160 vx120))",fontsize=16,color="green",shape="box"];482 -> 490[label="",style="dashed", color="green", weight=3];
483[label="Succ vx160",fontsize=16,color="green",shape="box"];484[label="Succ vx120",fontsize=16,color="green",shape="box"];485[label="Zero",fontsize=16,color="green",shape="box"];459[label="vx70",fontsize=16,color="green",shape="box"];460[label="Succ Zero",fontsize=16,color="green",shape="box"];461[label="Succ vx80",fontsize=16,color="green",shape="box"];462[label="Succ Zero",fontsize=16,color="green",shape="box"];463[label="Succ vx90",fontsize=16,color="green",shape="box"];464[label="Succ Zero",fontsize=16,color="green",shape="box"];465[label="Zero",fontsize=16,color="green",shape="box"];466[label="Succ Zero",fontsize=16,color="green",shape="box"];221 -> 201[label="",style="dashed", color="red", weight=0];
221[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="magenta"];221 -> 246[label="",style="dashed", color="magenta", weight=3];
222 -> 201[label="",style="dashed", color="red", weight=0];
222[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="magenta"];222 -> 247[label="",style="dashed", color="magenta", weight=3];
223 -> 408[label="",style="dashed", color="red", weight=0];
223[label="primPlusNat (primPlusNat (Succ vx5100) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];223 -> 432[label="",style="dashed", color="magenta", weight=3];
223 -> 433[label="",style="dashed", color="magenta", weight=3];
201[label="primMulNat vx5100 (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];560[label="vx5100/Succ vx51000",fontsize=10,color="white",style="solid",shape="box"];201 -> 560[label="",style="solid", color="burlywood", weight=9];
560 -> 204[label="",style="solid", color="burlywood", weight=3];
561[label="vx5100/Zero",fontsize=10,color="white",style="solid",shape="box"];201 -> 561[label="",style="solid", color="burlywood", weight=9];
561 -> 205[label="",style="solid", color="burlywood", weight=3];
224 -> 408[label="",style="dashed", color="red", weight=0];
224[label="primPlusNat vx5100 vx5100",fontsize=16,color="magenta"];224 -> 434[label="",style="dashed", color="magenta", weight=3];
224 -> 435[label="",style="dashed", color="magenta", weight=3];
490 -> 408[label="",style="dashed", color="red", weight=0];
490[label="primPlusNat vx160 vx120",fontsize=16,color="magenta"];490 -> 493[label="",style="dashed", color="magenta", weight=3];
490 -> 494[label="",style="dashed", color="magenta", weight=3];
246 -> 408[label="",style="dashed", color="red", weight=0];
246[label="primPlusNat (primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];246 -> 436[label="",style="dashed", color="magenta", weight=3];
246 -> 437[label="",style="dashed", color="magenta", weight=3];
247 -> 408[label="",style="dashed", color="red", weight=0];
247[label="primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];247 -> 438[label="",style="dashed", color="magenta", weight=3];
247 -> 439[label="",style="dashed", color="magenta", weight=3];
432 -> 224[label="",style="dashed", color="red", weight=0];
432[label="primPlusNat (Succ vx5100) (Succ vx5100)",fontsize=16,color="magenta"];432 -> 467[label="",style="dashed", color="magenta", weight=3];
433[label="Succ vx5100",fontsize=16,color="green",shape="box"];204[label="primMulNat (Succ vx51000) (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];204 -> 225[label="",style="solid", color="black", weight=3];
205[label="primMulNat Zero (Succ (Succ Zero))",fontsize=16,color="black",shape="box"];205 -> 226[label="",style="solid", color="black", weight=3];
434[label="vx5100",fontsize=16,color="green",shape="box"];435[label="vx5100",fontsize=16,color="green",shape="box"];493[label="vx160",fontsize=16,color="green",shape="box"];494[label="vx120",fontsize=16,color="green",shape="box"];436 -> 408[label="",style="dashed", color="red", weight=0];
436[label="primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];436 -> 468[label="",style="dashed", color="magenta", weight=3];
436 -> 469[label="",style="dashed", color="magenta", weight=3];
437[label="Succ vx5100",fontsize=16,color="green",shape="box"];438 -> 408[label="",style="dashed", color="red", weight=0];
438[label="primPlusNat (primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];438 -> 470[label="",style="dashed", color="magenta", weight=3];
438 -> 471[label="",style="dashed", color="magenta", weight=3];
439[label="Succ vx5100",fontsize=16,color="green",shape="box"];467[label="Succ vx5100",fontsize=16,color="green",shape="box"];225 -> 408[label="",style="dashed", color="red", weight=0];
225[label="primPlusNat (primMulNat vx51000 (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];225 -> 446[label="",style="dashed", color="magenta", weight=3];
225 -> 447[label="",style="dashed", color="magenta", weight=3];
226[label="Zero",fontsize=16,color="green",shape="box"];468 -> 408[label="",style="dashed", color="red", weight=0];
468[label="primPlusNat (primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];468 -> 478[label="",style="dashed", color="magenta", weight=3];
468 -> 479[label="",style="dashed", color="magenta", weight=3];
469[label="Succ vx5100",fontsize=16,color="green",shape="box"];470 -> 408[label="",style="dashed", color="red", weight=0];
470[label="primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];470 -> 480[label="",style="dashed", color="magenta", weight=3];
470 -> 481[label="",style="dashed", color="magenta", weight=3];
471[label="Succ vx5100",fontsize=16,color="green",shape="box"];446 -> 306[label="",style="dashed", color="red", weight=0];
446[label="primMulNat vx51000 (Succ (Succ Zero))",fontsize=16,color="magenta"];446 -> 472[label="",style="dashed", color="magenta", weight=3];
446 -> 473[label="",style="dashed", color="magenta", weight=3];
447[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];478 -> 408[label="",style="dashed", color="red", weight=0];
478[label="primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];478 -> 486[label="",style="dashed", color="magenta", weight=3];
478 -> 487[label="",style="dashed", color="magenta", weight=3];
479[label="Succ vx5100",fontsize=16,color="green",shape="box"];480 -> 408[label="",style="dashed", color="red", weight=0];
480[label="primPlusNat Zero (Succ vx5100)",fontsize=16,color="magenta"];480 -> 488[label="",style="dashed", color="magenta", weight=3];
480 -> 489[label="",style="dashed", color="magenta", weight=3];
481[label="Succ vx5100",fontsize=16,color="green",shape="box"];472[label="vx51000",fontsize=16,color="green",shape="box"];473[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];486 -> 408[label="",style="dashed", color="red", weight=0];
486[label="primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];486 -> 491[label="",style="dashed", color="magenta", weight=3];
486 -> 492[label="",style="dashed", color="magenta", weight=3];
487[label="Succ vx5100",fontsize=16,color="green",shape="box"];488[label="Zero",fontsize=16,color="green",shape="box"];489[label="Succ vx5100",fontsize=16,color="green",shape="box"];491 -> 306[label="",style="dashed", color="red", weight=0];
491[label="primMulNat vx41000000 (Succ vx5100)",fontsize=16,color="magenta"];491 -> 495[label="",style="dashed", color="magenta", weight=3];
491 -> 496[label="",style="dashed", color="magenta", weight=3];
492[label="Succ vx5100",fontsize=16,color="green",shape="box"];495[label="vx41000000",fontsize=16,color="green",shape="box"];496[label="Succ vx5100",fontsize=16,color="green",shape="box"];}

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

(8)
Complex Obligation (AND)

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

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

   new_primMulInt(Succ(vx80), Succ(vx90)) -> new_primMulInt(vx80, vx90)

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_primMulInt(Succ(vx80), Succ(vx90)) -> new_primMulInt(vx80, vx90)
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(vx4000), Succ(vx5100)) -> new_primMulNat(vx4000, Succ(vx5100))

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(vx4000), Succ(vx5100)) -> new_primMulNat(vx4000, Succ(vx5100))
The graph contains the following edges 1 > 1, 2 >= 2


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

(14)
YES

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

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

   new_primPlusNat(Succ(vx160), Succ(vx120)) -> new_primPlusNat(vx160, vx120)

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_primPlusNat(Succ(vx160), Succ(vx120)) -> new_primPlusNat(vx160, vx120)
The graph contains the following edges 1 > 1, 2 > 2


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

(17)
YES