/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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="sinh",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="sinh 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 (primMinusFloat (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 (primMinusFloat vx4 vx5) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="burlywood",shape="triangle"];499[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];16 -> 499[label="",style="solid", color="burlywood", weight=9];
499 -> 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 (primMinusFloat (Float vx40 vx41) vx5) (fromInt (Pos (Succ (Succ Zero))))",fontsize=16,color="burlywood",shape="box"];500[label="vx5/Float vx50 vx51",fontsize=10,color="white",style="solid",shape="box"];22 -> 500[label="",style="solid", color="burlywood", weight=9];
500 -> 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"];501[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];24 -> 501[label="",style="solid", color="burlywood", weight=9];
501 -> 27[label="",style="solid", color="burlywood", weight=3];
25[label="primDivFloat (primMinusFloat (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"];502[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];34 -> 502[label="",style="solid", color="burlywood", weight=9];
502 -> 36[label="",style="solid", color="burlywood", weight=3];
503[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];34 -> 503[label="",style="solid", color="burlywood", weight=9];
503 -> 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 (primMinusInt (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"];504[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];45 -> 504[label="",style="solid", color="burlywood", weight=9];
504 -> 47[label="",style="solid", color="burlywood", weight=3];
505[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];45 -> 505[label="",style="solid", color="burlywood", weight=9];
505 -> 48[label="",style="solid", color="burlywood", weight=3];
46[label="primMulInt (primMinusInt (primMulInt vx40 vx51) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];506[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];46 -> 506[label="",style="solid", color="burlywood", weight=9];
506 -> 49[label="",style="solid", color="burlywood", weight=3];
507[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];46 -> 507[label="",style="solid", color="burlywood", weight=9];
507 -> 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"];508[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];47 -> 508[label="",style="solid", color="burlywood", weight=9];
508 -> 51[label="",style="solid", color="burlywood", weight=3];
509[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];47 -> 509[label="",style="solid", color="burlywood", weight=9];
509 -> 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"];510[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];48 -> 510[label="",style="solid", color="burlywood", weight=9];
510 -> 53[label="",style="solid", color="burlywood", weight=3];
511[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];48 -> 511[label="",style="solid", color="burlywood", weight=9];
511 -> 54[label="",style="solid", color="burlywood", weight=3];
49[label="primMulInt (primMinusInt (primMulInt (Pos 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"];49 -> 512[label="",style="solid", color="burlywood", weight=9];
512 -> 55[label="",style="solid", color="burlywood", weight=3];
513[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];49 -> 513[label="",style="solid", color="burlywood", weight=9];
513 -> 56[label="",style="solid", color="burlywood", weight=3];
50[label="primMulInt (primMinusInt (primMulInt (Neg vx400) vx51) (vx50 * vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];514[label="vx51/Pos vx510",fontsize=10,color="white",style="solid",shape="box"];50 -> 514[label="",style="solid", color="burlywood", weight=9];
514 -> 57[label="",style="solid", color="burlywood", weight=3];
515[label="vx51/Neg vx510",fontsize=10,color="white",style="solid",shape="box"];50 -> 515[label="",style="solid", color="burlywood", weight=9];
515 -> 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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (Pos (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"];73 -> 516[label="",style="solid", color="burlywood", weight=9];
516 -> 81[label="",style="solid", color="burlywood", weight=3];
517[label="vx50/Neg vx500",fontsize=10,color="white",style="solid",shape="box"];73 -> 517[label="",style="solid", color="burlywood", weight=9];
517 -> 82[label="",style="solid", color="burlywood", weight=3];
74[label="primMulInt (primMinusInt (Neg (primMulNat vx400 vx510)) (primMulInt vx50 vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];518[label="vx50/Pos vx500",fontsize=10,color="white",style="solid",shape="box"];74 -> 518[label="",style="solid", color="burlywood", weight=9];
518 -> 83[label="",style="solid", color="burlywood", weight=3];
519[label="vx50/Neg vx500",fontsize=10,color="white",style="solid",shape="box"];74 -> 519[label="",style="solid", color="burlywood", weight=9];
519 -> 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"];520[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];79 -> 520[label="",style="solid", color="burlywood", weight=9];
520 -> 85[label="",style="solid", color="burlywood", weight=3];
521[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 521[label="",style="solid", color="burlywood", weight=9];
521 -> 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 (primMinusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Pos vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];522[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];81 -> 522[label="",style="solid", color="burlywood", weight=9];
522 -> 88[label="",style="solid", color="burlywood", weight=3];
523[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];81 -> 523[label="",style="solid", color="burlywood", weight=9];
523 -> 89[label="",style="solid", color="burlywood", weight=3];
82[label="primMulInt (primMinusInt (Pos (primMulNat vx400 vx510)) (primMulInt (Neg vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];524[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];82 -> 524[label="",style="solid", color="burlywood", weight=9];
524 -> 90[label="",style="solid", color="burlywood", weight=3];
525[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];82 -> 525[label="",style="solid", color="burlywood", weight=9];
525 -> 91[label="",style="solid", color="burlywood", weight=3];
83[label="primMulInt (primMinusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Pos vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];526[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];83 -> 526[label="",style="solid", color="burlywood", weight=9];
526 -> 92[label="",style="solid", color="burlywood", weight=3];
527[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];83 -> 527[label="",style="solid", color="burlywood", weight=9];
527 -> 93[label="",style="solid", color="burlywood", weight=3];
84[label="primMulInt (primMinusInt (Neg (primMulNat vx400 vx510)) (primMulInt (Neg vx500) vx41)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];528[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];84 -> 528[label="",style="solid", color="burlywood", weight=9];
528 -> 94[label="",style="solid", color="burlywood", weight=3];
529[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];84 -> 529[label="",style="solid", color="burlywood", weight=9];
529 -> 95[label="",style="solid", color="burlywood", weight=3];
85[label="primMulNat (primMulNat (Succ vx4100) vx510) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];530[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];85 -> 530[label="",style="solid", color="burlywood", weight=9];
530 -> 96[label="",style="solid", color="burlywood", weight=3];
531[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];85 -> 531[label="",style="solid", color="burlywood", weight=9];
531 -> 97[label="",style="solid", color="burlywood", weight=3];
86[label="primMulNat (primMulNat Zero vx510) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];532[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];86 -> 532[label="",style="solid", color="burlywood", weight=9];
532 -> 98[label="",style="solid", color="burlywood", weight=3];
533[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];86 -> 533[label="",style="solid", color="burlywood", weight=9];
533 -> 99[label="",style="solid", color="burlywood", weight=3];
87[label="vx510",fontsize=16,color="green",shape="box"];88[label="primMulInt (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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];
102[label="primMulInt (primMinusInt (Pos (primMulNat vx400 vx510)) (Neg (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="magenta"];102 -> 114[label="",style="dashed", color="magenta", weight=3];
102 -> 115[label="",style="dashed", color="magenta", weight=3];
103 -> 100[label="",style="dashed", color="red", weight=0];
103[label="primMulInt (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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 (primMinusInt (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"];534[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];108 -> 534[label="",style="solid", color="burlywood", weight=9];
534 -> 124[label="",style="solid", color="burlywood", weight=3];
535[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 535[label="",style="solid", color="burlywood", weight=9];
535 -> 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 -> 274[label="",style="dashed", color="red", weight=0];
112[label="primMulInt (primMinusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Pos (Succ Zero))",fontsize=16,color="magenta"];112 -> 275[label="",style="dashed", color="magenta", weight=3];
112 -> 276[label="",style="dashed", color="magenta", weight=3];
113[label="primMulInt (Pos (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];113 -> 129[label="",style="solid", color="black", 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[label="primMulInt (Neg (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];118 -> 130[label="",style="solid", color="black", weight=3];
119 -> 274[label="",style="dashed", color="red", weight=0];
119[label="primMulInt (primMinusNat (primMulNat vx500 vx410) (primMulNat vx400 vx510)) (Pos (Succ Zero))",fontsize=16,color="magenta"];119 -> 277[label="",style="dashed", color="magenta", weight=3];
119 -> 278[label="",style="dashed", color="magenta", 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"];275[label="primMulNat vx500 vx410",fontsize=16,color="burlywood",shape="triangle"];536[label="vx500/Succ vx5000",fontsize=10,color="white",style="solid",shape="box"];275 -> 536[label="",style="solid", color="burlywood", weight=9];
536 -> 280[label="",style="solid", color="burlywood", weight=3];
537[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];275 -> 537[label="",style="solid", color="burlywood", weight=9];
537 -> 281[label="",style="solid", color="burlywood", weight=3];
276 -> 275[label="",style="dashed", color="red", weight=0];
276[label="primMulNat vx400 vx510",fontsize=16,color="magenta"];276 -> 282[label="",style="dashed", color="magenta", weight=3];
276 -> 283[label="",style="dashed", color="magenta", weight=3];
274[label="primMulInt (primMinusNat vx7 vx8) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="triangle"];538[label="vx7/Succ vx70",fontsize=10,color="white",style="solid",shape="box"];274 -> 538[label="",style="solid", color="burlywood", weight=9];
538 -> 284[label="",style="solid", color="burlywood", weight=3];
539[label="vx7/Zero",fontsize=10,color="white",style="solid",shape="box"];274 -> 539[label="",style="solid", color="burlywood", weight=9];
539 -> 285[label="",style="solid", color="burlywood", weight=3];
129[label="Pos (primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero))",fontsize=16,color="green",shape="box"];129 -> 141[label="",style="dashed", color="green", weight=3];
130[label="Neg (primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero))",fontsize=16,color="green",shape="box"];130 -> 142[label="",style="dashed", color="green", weight=3];
277 -> 275[label="",style="dashed", color="red", weight=0];
277[label="primMulNat vx400 vx510",fontsize=16,color="magenta"];277 -> 286[label="",style="dashed", color="magenta", weight=3];
277 -> 287[label="",style="dashed", color="magenta", weight=3];
278 -> 275[label="",style="dashed", color="red", weight=0];
278[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];278 -> 288[label="",style="dashed", color="magenta", weight=3];
135[label="primMulNat (primPlusNat (primPlusNat (primMulNat vx41000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ (Succ Zero))",fontsize=16,color="burlywood",shape="box"];540[label="vx41000/Succ vx410000",fontsize=10,color="white",style="solid",shape="box"];135 -> 540[label="",style="solid", color="burlywood", weight=9];
540 -> 143[label="",style="solid", color="burlywood", weight=3];
541[label="vx41000/Zero",fontsize=10,color="white",style="solid",shape="box"];135 -> 541[label="",style="solid", color="burlywood", weight=9];
541 -> 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];
280[label="primMulNat (Succ vx5000) vx410",fontsize=16,color="burlywood",shape="box"];542[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];280 -> 542[label="",style="solid", color="burlywood", weight=9];
542 -> 307[label="",style="solid", color="burlywood", weight=3];
543[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];280 -> 543[label="",style="solid", color="burlywood", weight=9];
543 -> 308[label="",style="solid", color="burlywood", weight=3];
281[label="primMulNat Zero vx410",fontsize=16,color="burlywood",shape="box"];544[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];281 -> 544[label="",style="solid", color="burlywood", weight=9];
544 -> 309[label="",style="solid", color="burlywood", weight=3];
545[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];281 -> 545[label="",style="solid", color="burlywood", weight=9];
545 -> 310[label="",style="solid", color="burlywood", weight=3];
282[label="vx400",fontsize=16,color="green",shape="box"];283[label="vx510",fontsize=16,color="green",shape="box"];284[label="primMulInt (primMinusNat (Succ vx70) vx8) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];546[label="vx8/Succ vx80",fontsize=10,color="white",style="solid",shape="box"];284 -> 546[label="",style="solid", color="burlywood", weight=9];
546 -> 311[label="",style="solid", color="burlywood", weight=3];
547[label="vx8/Zero",fontsize=10,color="white",style="solid",shape="box"];284 -> 547[label="",style="solid", color="burlywood", weight=9];
547 -> 312[label="",style="solid", color="burlywood", weight=3];
285[label="primMulInt (primMinusNat Zero vx8) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];548[label="vx8/Succ vx80",fontsize=10,color="white",style="solid",shape="box"];285 -> 548[label="",style="solid", color="burlywood", weight=9];
548 -> 313[label="",style="solid", color="burlywood", weight=3];
549[label="vx8/Zero",fontsize=10,color="white",style="solid",shape="box"];285 -> 549[label="",style="solid", color="burlywood", weight=9];
549 -> 314[label="",style="solid", color="burlywood", weight=3];
141[label="primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];550[label="vx400/Succ vx4000",fontsize=10,color="white",style="solid",shape="box"];141 -> 550[label="",style="solid", color="burlywood", weight=9];
550 -> 150[label="",style="solid", color="burlywood", weight=3];
551[label="vx400/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 551[label="",style="solid", color="burlywood", weight=9];
551 -> 151[label="",style="solid", color="burlywood", weight=3];
142 -> 141[label="",style="dashed", color="red", weight=0];
142[label="primMulNat (primPlusNat (primMulNat vx400 vx510) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="magenta"];142 -> 152[label="",style="dashed", color="magenta", weight=3];
142 -> 153[label="",style="dashed", color="magenta", weight=3];
286[label="vx400",fontsize=16,color="green",shape="box"];287[label="vx510",fontsize=16,color="green",shape="box"];288[label="vx410",fontsize=16,color="green",shape="box"];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];
307[label="primMulNat (Succ vx5000) (Succ vx4100)",fontsize=16,color="black",shape="box"];307 -> 318[label="",style="solid", color="black", weight=3];
308[label="primMulNat (Succ vx5000) Zero",fontsize=16,color="black",shape="box"];308 -> 319[label="",style="solid", color="black", weight=3];
309[label="primMulNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];309 -> 320[label="",style="solid", color="black", weight=3];
310[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];310 -> 321[label="",style="solid", color="black", weight=3];
311[label="primMulInt (primMinusNat (Succ vx70) (Succ vx80)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];311 -> 322[label="",style="solid", color="black", weight=3];
312[label="primMulInt (primMinusNat (Succ vx70) Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];312 -> 323[label="",style="solid", color="black", weight=3];
313[label="primMulInt (primMinusNat Zero (Succ vx80)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];313 -> 324[label="",style="solid", color="black", weight=3];
314[label="primMulInt (primMinusNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];314 -> 325[label="",style="solid", color="black", weight=3];
150[label="primMulNat (primPlusNat (primMulNat (Succ vx4000) vx510) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];552[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];150 -> 552[label="",style="solid", color="burlywood", weight=9];
552 -> 161[label="",style="solid", color="burlywood", weight=3];
553[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];150 -> 553[label="",style="solid", color="burlywood", weight=9];
553 -> 162[label="",style="solid", color="burlywood", weight=3];
151[label="primMulNat (primPlusNat (primMulNat Zero vx510) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];554[label="vx510/Succ vx5100",fontsize=10,color="white",style="solid",shape="box"];151 -> 554[label="",style="solid", color="burlywood", weight=9];
554 -> 163[label="",style="solid", color="burlywood", weight=3];
555[label="vx510/Zero",fontsize=10,color="white",style="solid",shape="box"];151 -> 555[label="",style="solid", color="burlywood", weight=9];
555 -> 164[label="",style="solid", color="burlywood", weight=3];
152[label="vx510",fontsize=16,color="green",shape="box"];153[label="vx410",fontsize=16,color="green",shape="box"];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"];556[label="vx410000/Succ vx4100000",fontsize=10,color="white",style="solid",shape="box"];154 -> 556[label="",style="solid", color="burlywood", weight=9];
556 -> 165[label="",style="solid", color="burlywood", weight=3];
557[label="vx410000/Zero",fontsize=10,color="white",style="solid",shape="box"];154 -> 557[label="",style="solid", color="burlywood", weight=9];
557 -> 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 -> 389[label="",style="dashed", color="red", weight=0];
156[label="primPlusNat (primMulNat vx5100 (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];156 -> 390[label="",style="dashed", color="magenta", weight=3];
156 -> 391[label="",style="dashed", color="magenta", weight=3];
318 -> 389[label="",style="dashed", color="red", weight=0];
318[label="primPlusNat (primMulNat vx5000 (Succ vx4100)) (Succ vx4100)",fontsize=16,color="magenta"];318 -> 392[label="",style="dashed", color="magenta", weight=3];
318 -> 393[label="",style="dashed", color="magenta", weight=3];
319[label="Zero",fontsize=16,color="green",shape="box"];320[label="Zero",fontsize=16,color="green",shape="box"];321[label="Zero",fontsize=16,color="green",shape="box"];322 -> 274[label="",style="dashed", color="red", weight=0];
322[label="primMulInt (primMinusNat vx70 vx80) (Pos (Succ Zero))",fontsize=16,color="magenta"];322 -> 362[label="",style="dashed", color="magenta", weight=3];
322 -> 363[label="",style="dashed", color="magenta", weight=3];
323[label="primMulInt (Pos (Succ vx70)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];323 -> 364[label="",style="solid", color="black", weight=3];
324[label="primMulInt (Neg (Succ vx80)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];324 -> 365[label="",style="solid", color="black", weight=3];
325[label="primMulInt (Pos Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];325 -> 366[label="",style="solid", color="black", weight=3];
161[label="primMulNat (primPlusNat (primMulNat (Succ vx4000) (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];161 -> 176[label="",style="solid", color="black", weight=3];
162[label="primMulNat (primPlusNat (primMulNat (Succ vx4000) Zero) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];162 -> 177[label="",style="solid", color="black", weight=3];
163[label="primMulNat (primPlusNat (primMulNat Zero (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];163 -> 178[label="",style="solid", color="black", weight=3];
164[label="primMulNat (primPlusNat (primMulNat Zero Zero) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];164 -> 179[label="",style="solid", color="black", 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];
390[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];391 -> 275[label="",style="dashed", color="red", weight=0];
391[label="primMulNat vx5100 (Succ (Succ Zero))",fontsize=16,color="magenta"];391 -> 438[label="",style="dashed", color="magenta", weight=3];
391 -> 439[label="",style="dashed", color="magenta", weight=3];
389[label="primPlusNat vx16 vx15",fontsize=16,color="burlywood",shape="triangle"];558[label="vx16/Succ vx160",fontsize=10,color="white",style="solid",shape="box"];389 -> 558[label="",style="solid", color="burlywood", weight=9];
558 -> 440[label="",style="solid", color="burlywood", weight=3];
559[label="vx16/Zero",fontsize=10,color="white",style="solid",shape="box"];389 -> 559[label="",style="solid", color="burlywood", weight=9];
559 -> 441[label="",style="solid", color="burlywood", weight=3];
392[label="Succ vx4100",fontsize=16,color="green",shape="box"];393 -> 275[label="",style="dashed", color="red", weight=0];
393[label="primMulNat vx5000 (Succ vx4100)",fontsize=16,color="magenta"];393 -> 442[label="",style="dashed", color="magenta", weight=3];
393 -> 443[label="",style="dashed", color="magenta", weight=3];
362[label="vx80",fontsize=16,color="green",shape="box"];363[label="vx70",fontsize=16,color="green",shape="box"];364[label="Pos (primMulNat (Succ vx70) (Succ Zero))",fontsize=16,color="green",shape="box"];364 -> 379[label="",style="dashed", color="green", weight=3];
365[label="Neg (primMulNat (Succ vx80) (Succ Zero))",fontsize=16,color="green",shape="box"];365 -> 380[label="",style="dashed", color="green", weight=3];
366[label="Pos (primMulNat Zero (Succ Zero))",fontsize=16,color="green",shape="box"];366 -> 381[label="",style="dashed", color="green", weight=3];
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560 -> 192[label="",style="solid", color="burlywood", weight=3];
561[label="vx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];176 -> 561[label="",style="solid", color="burlywood", weight=9];
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563[label="vx500/Zero",fontsize=10,color="white",style="solid",shape="box"];177 -> 563[label="",style="solid", color="burlywood", weight=9];
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565[label="vx4100000/Zero",fontsize=10,color="white",style="solid",shape="box"];180 -> 565[label="",style="solid", color="burlywood", weight=9];
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182 -> 145[label="",style="dashed", color="red", weight=0];
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438[label="vx5100",fontsize=16,color="green",shape="box"];439[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];440[label="primPlusNat (Succ vx160) vx15",fontsize=16,color="burlywood",shape="box"];566[label="vx15/Succ vx150",fontsize=10,color="white",style="solid",shape="box"];440 -> 566[label="",style="solid", color="burlywood", weight=9];
566 -> 466[label="",style="solid", color="burlywood", weight=3];
567[label="vx15/Zero",fontsize=10,color="white",style="solid",shape="box"];440 -> 567[label="",style="solid", color="burlywood", weight=9];
567 -> 467[label="",style="solid", color="burlywood", weight=3];
441[label="primPlusNat Zero vx15",fontsize=16,color="burlywood",shape="box"];568[label="vx15/Succ vx150",fontsize=10,color="white",style="solid",shape="box"];441 -> 568[label="",style="solid", color="burlywood", weight=9];
568 -> 468[label="",style="solid", color="burlywood", weight=3];
569[label="vx15/Zero",fontsize=10,color="white",style="solid",shape="box"];441 -> 569[label="",style="solid", color="burlywood", weight=9];
569 -> 469[label="",style="solid", color="burlywood", weight=3];
442[label="vx5000",fontsize=16,color="green",shape="box"];443[label="Succ vx4100",fontsize=16,color="green",shape="box"];379 -> 275[label="",style="dashed", color="red", weight=0];
379[label="primMulNat (Succ vx70) (Succ Zero)",fontsize=16,color="magenta"];379 -> 444[label="",style="dashed", color="magenta", weight=3];
379 -> 445[label="",style="dashed", color="magenta", weight=3];
380 -> 275[label="",style="dashed", color="red", weight=0];
380[label="primMulNat (Succ vx80) (Succ Zero)",fontsize=16,color="magenta"];380 -> 446[label="",style="dashed", color="magenta", weight=3];
380 -> 447[label="",style="dashed", color="magenta", weight=3];
381 -> 275[label="",style="dashed", color="red", weight=0];
381[label="primMulNat Zero (Succ Zero)",fontsize=16,color="magenta"];381 -> 448[label="",style="dashed", color="magenta", weight=3];
381 -> 449[label="",style="dashed", color="magenta", weight=3];
192[label="primMulNat (primPlusNat (primPlusNat (primMulNat (Succ vx40000) (Succ vx5100)) (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];192 -> 215[label="",style="solid", color="black", weight=3];
193[label="primMulNat (primPlusNat (primPlusNat (primMulNat Zero (Succ vx5100)) (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];193 -> 216[label="",style="solid", color="black", weight=3];
194[label="primMulNat (primPlusNat Zero (primMulNat (Succ vx5000) vx410)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];570[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];194 -> 570[label="",style="solid", color="burlywood", weight=9];
570 -> 217[label="",style="solid", color="burlywood", weight=3];
571[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];194 -> 571[label="",style="solid", color="burlywood", weight=9];
571 -> 218[label="",style="solid", color="burlywood", weight=3];
195[label="primMulNat (primPlusNat Zero (primMulNat Zero vx410)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];572[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];195 -> 572[label="",style="solid", color="burlywood", weight=9];
572 -> 219[label="",style="solid", color="burlywood", weight=3];
573[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];195 -> 573[label="",style="solid", color="burlywood", weight=9];
573 -> 220[label="",style="solid", color="burlywood", weight=3];
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199[label="Succ (primPlusNat vx5100 vx5100)",fontsize=16,color="green",shape="box"];199 -> 224[label="",style="dashed", color="green", weight=3];
466[label="primPlusNat (Succ vx160) (Succ vx150)",fontsize=16,color="black",shape="box"];466 -> 480[label="",style="solid", color="black", weight=3];
467[label="primPlusNat (Succ vx160) Zero",fontsize=16,color="black",shape="box"];467 -> 481[label="",style="solid", color="black", weight=3];
468[label="primPlusNat Zero (Succ vx150)",fontsize=16,color="black",shape="box"];468 -> 482[label="",style="solid", color="black", weight=3];
469[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];469 -> 483[label="",style="solid", color="black", weight=3];
444[label="Succ vx70",fontsize=16,color="green",shape="box"];445[label="Succ Zero",fontsize=16,color="green",shape="box"];446[label="Succ vx80",fontsize=16,color="green",shape="box"];447[label="Succ Zero",fontsize=16,color="green",shape="box"];448[label="Zero",fontsize=16,color="green",shape="box"];449[label="Succ Zero",fontsize=16,color="green",shape="box"];215[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx40000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];574[label="vx40000/Succ vx400000",fontsize=10,color="white",style="solid",shape="box"];215 -> 574[label="",style="solid", color="burlywood", weight=9];
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575[label="vx40000/Zero",fontsize=10,color="white",style="solid",shape="box"];215 -> 575[label="",style="solid", color="burlywood", weight=9];
575 -> 240[label="",style="solid", color="burlywood", weight=3];
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220[label="primMulNat (primPlusNat Zero (primMulNat Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];220 -> 245[label="",style="solid", color="black", weight=3];
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223 -> 397[label="",style="dashed", color="magenta", weight=3];
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576 -> 204[label="",style="solid", color="burlywood", weight=3];
577[label="vx5100/Zero",fontsize=10,color="white",style="solid",shape="box"];201 -> 577[label="",style="solid", color="burlywood", weight=9];
577 -> 205[label="",style="solid", color="burlywood", weight=3];
224 -> 389[label="",style="dashed", color="red", weight=0];
224[label="primPlusNat vx5100 vx5100",fontsize=16,color="magenta"];224 -> 398[label="",style="dashed", color="magenta", weight=3];
224 -> 399[label="",style="dashed", color="magenta", weight=3];
480[label="Succ (Succ (primPlusNat vx160 vx150))",fontsize=16,color="green",shape="box"];480 -> 490[label="",style="dashed", color="green", weight=3];
481[label="Succ vx160",fontsize=16,color="green",shape="box"];482[label="Succ vx150",fontsize=16,color="green",shape="box"];483[label="Zero",fontsize=16,color="green",shape="box"];239[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ vx400000) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];239 -> 293[label="",style="solid", color="black", weight=3];
240[label="primMulNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (primMulNat vx500 vx410)) (Succ Zero)",fontsize=16,color="black",shape="box"];240 -> 294[label="",style="solid", color="black", weight=3];
241 -> 275[label="",style="dashed", color="red", weight=0];
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242 -> 275[label="",style="dashed", color="red", weight=0];
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242 -> 298[label="",style="dashed", color="magenta", weight=3];
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243[label="primMulNat (primPlusNat Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];243 -> 299[label="",style="dashed", color="magenta", weight=3];
243 -> 300[label="",style="dashed", color="magenta", weight=3];
244 -> 275[label="",style="dashed", color="red", weight=0];
244[label="primMulNat (primPlusNat Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];244 -> 301[label="",style="dashed", color="magenta", weight=3];
244 -> 302[label="",style="dashed", color="magenta", weight=3];
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245[label="primMulNat (primPlusNat Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];245 -> 303[label="",style="dashed", color="magenta", weight=3];
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246 -> 389[label="",style="dashed", color="red", weight=0];
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396[label="Succ vx5100",fontsize=16,color="green",shape="box"];397 -> 224[label="",style="dashed", color="red", weight=0];
397[label="primPlusNat (Succ vx5100) (Succ vx5100)",fontsize=16,color="magenta"];397 -> 450[label="",style="dashed", color="magenta", weight=3];
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];
398[label="vx5100",fontsize=16,color="green",shape="box"];399[label="vx5100",fontsize=16,color="green",shape="box"];490 -> 389[label="",style="dashed", color="red", weight=0];
490[label="primPlusNat vx160 vx150",fontsize=16,color="magenta"];490 -> 495[label="",style="dashed", color="magenta", weight=3];
490 -> 496[label="",style="dashed", color="magenta", weight=3];
293 -> 275[label="",style="dashed", color="red", weight=0];
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294 -> 333[label="",style="dashed", color="magenta", weight=3];
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295 -> 407[label="",style="dashed", color="magenta", weight=3];
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297 -> 409[label="",style="dashed", color="magenta", weight=3];
298[label="Succ Zero",fontsize=16,color="green",shape="box"];299 -> 389[label="",style="dashed", color="red", weight=0];
299[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];299 -> 410[label="",style="dashed", color="magenta", weight=3];
299 -> 411[label="",style="dashed", color="magenta", weight=3];
300[label="Succ Zero",fontsize=16,color="green",shape="box"];301 -> 389[label="",style="dashed", color="red", weight=0];
301[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];301 -> 412[label="",style="dashed", color="magenta", weight=3];
301 -> 413[label="",style="dashed", color="magenta", weight=3];
302[label="Succ Zero",fontsize=16,color="green",shape="box"];303 -> 389[label="",style="dashed", color="red", weight=0];
303[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];303 -> 414[label="",style="dashed", color="magenta", weight=3];
303 -> 415[label="",style="dashed", color="magenta", weight=3];
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401[label="primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];401 -> 451[label="",style="dashed", color="magenta", weight=3];
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450[label="Succ vx5100",fontsize=16,color="green",shape="box"];225 -> 389[label="",style="dashed", color="red", weight=0];
225[label="primPlusNat (primMulNat vx51000 (Succ (Succ Zero))) (Succ (Succ Zero))",fontsize=16,color="magenta"];225 -> 420[label="",style="dashed", color="magenta", weight=3];
225 -> 421[label="",style="dashed", color="magenta", weight=3];
226[label="Zero",fontsize=16,color="green",shape="box"];495[label="vx150",fontsize=16,color="green",shape="box"];496[label="vx160",fontsize=16,color="green",shape="box"];330 -> 389[label="",style="dashed", color="red", weight=0];
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330 -> 423[label="",style="dashed", color="magenta", weight=3];
331[label="Succ Zero",fontsize=16,color="green",shape="box"];332 -> 389[label="",style="dashed", color="red", weight=0];
332[label="primPlusNat (primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)) (primMulNat vx500 vx410)",fontsize=16,color="magenta"];332 -> 424[label="",style="dashed", color="magenta", weight=3];
332 -> 425[label="",style="dashed", color="magenta", weight=3];
333[label="Succ Zero",fontsize=16,color="green",shape="box"];406 -> 275[label="",style="dashed", color="red", weight=0];
406[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];406 -> 455[label="",style="dashed", color="magenta", weight=3];
407[label="Succ vx5100",fontsize=16,color="green",shape="box"];408 -> 389[label="",style="dashed", color="red", weight=0];
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409[label="Zero",fontsize=16,color="green",shape="box"];410[label="Zero",fontsize=16,color="green",shape="box"];411[label="Zero",fontsize=16,color="green",shape="box"];412[label="Zero",fontsize=16,color="green",shape="box"];413[label="Zero",fontsize=16,color="green",shape="box"];414[label="Zero",fontsize=16,color="green",shape="box"];415[label="Zero",fontsize=16,color="green",shape="box"];451[label="Succ vx5100",fontsize=16,color="green",shape="box"];452 -> 389[label="",style="dashed", color="red", weight=0];
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452 -> 471[label="",style="dashed", color="magenta", weight=3];
453[label="Succ vx5100",fontsize=16,color="green",shape="box"];454 -> 389[label="",style="dashed", color="red", weight=0];
454[label="primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];454 -> 472[label="",style="dashed", color="magenta", weight=3];
454 -> 473[label="",style="dashed", color="magenta", weight=3];
420[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];421 -> 275[label="",style="dashed", color="red", weight=0];
421[label="primMulNat vx51000 (Succ (Succ Zero))",fontsize=16,color="magenta"];421 -> 458[label="",style="dashed", color="magenta", weight=3];
421 -> 459[label="",style="dashed", color="magenta", weight=3];
422 -> 275[label="",style="dashed", color="red", weight=0];
422[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];422 -> 460[label="",style="dashed", color="magenta", weight=3];
423 -> 389[label="",style="dashed", color="red", weight=0];
423[label="primPlusNat (primPlusNat (primPlusNat (primMulNat vx400000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];423 -> 461[label="",style="dashed", color="magenta", weight=3];
423 -> 462[label="",style="dashed", color="magenta", weight=3];
424 -> 275[label="",style="dashed", color="red", weight=0];
424[label="primMulNat vx500 vx410",fontsize=16,color="magenta"];424 -> 463[label="",style="dashed", color="magenta", weight=3];
425 -> 389[label="",style="dashed", color="red", weight=0];
425[label="primPlusNat (primPlusNat Zero (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];425 -> 464[label="",style="dashed", color="magenta", weight=3];
425 -> 465[label="",style="dashed", color="magenta", weight=3];
455[label="vx410",fontsize=16,color="green",shape="box"];456[label="Succ vx4100",fontsize=16,color="green",shape="box"];457 -> 275[label="",style="dashed", color="red", weight=0];
457[label="primMulNat vx5000 (Succ vx4100)",fontsize=16,color="magenta"];457 -> 474[label="",style="dashed", color="magenta", weight=3];
457 -> 475[label="",style="dashed", color="magenta", weight=3];
470[label="Succ vx5100",fontsize=16,color="green",shape="box"];471 -> 389[label="",style="dashed", color="red", weight=0];
471[label="primPlusNat (primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];471 -> 484[label="",style="dashed", color="magenta", weight=3];
471 -> 485[label="",style="dashed", color="magenta", weight=3];
472[label="Succ vx5100",fontsize=16,color="green",shape="box"];473 -> 389[label="",style="dashed", color="red", weight=0];
473[label="primPlusNat Zero (Succ vx5100)",fontsize=16,color="magenta"];473 -> 486[label="",style="dashed", color="magenta", weight=3];
473 -> 487[label="",style="dashed", color="magenta", weight=3];
458[label="vx51000",fontsize=16,color="green",shape="box"];459[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];460[label="vx410",fontsize=16,color="green",shape="box"];461[label="Succ vx5100",fontsize=16,color="green",shape="box"];462 -> 389[label="",style="dashed", color="red", weight=0];
462[label="primPlusNat (primPlusNat (primMulNat vx400000 (Succ vx5100)) (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];462 -> 476[label="",style="dashed", color="magenta", weight=3];
462 -> 477[label="",style="dashed", color="magenta", weight=3];
463[label="vx410",fontsize=16,color="green",shape="box"];464[label="Succ vx5100",fontsize=16,color="green",shape="box"];465 -> 389[label="",style="dashed", color="red", weight=0];
465[label="primPlusNat Zero (Succ vx5100)",fontsize=16,color="magenta"];465 -> 478[label="",style="dashed", color="magenta", weight=3];
465 -> 479[label="",style="dashed", color="magenta", weight=3];
474[label="vx5000",fontsize=16,color="green",shape="box"];475[label="Succ vx4100",fontsize=16,color="green",shape="box"];484[label="Succ vx5100",fontsize=16,color="green",shape="box"];485 -> 389[label="",style="dashed", color="red", weight=0];
485[label="primPlusNat (primMulNat vx41000000 (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];485 -> 491[label="",style="dashed", color="magenta", weight=3];
485 -> 492[label="",style="dashed", color="magenta", weight=3];
486[label="Succ vx5100",fontsize=16,color="green",shape="box"];487[label="Zero",fontsize=16,color="green",shape="box"];476[label="Succ vx5100",fontsize=16,color="green",shape="box"];477 -> 389[label="",style="dashed", color="red", weight=0];
477[label="primPlusNat (primMulNat vx400000 (Succ vx5100)) (Succ vx5100)",fontsize=16,color="magenta"];477 -> 488[label="",style="dashed", color="magenta", weight=3];
477 -> 489[label="",style="dashed", color="magenta", weight=3];
478[label="Succ vx5100",fontsize=16,color="green",shape="box"];479[label="Zero",fontsize=16,color="green",shape="box"];491[label="Succ vx5100",fontsize=16,color="green",shape="box"];492 -> 275[label="",style="dashed", color="red", weight=0];
492[label="primMulNat vx41000000 (Succ vx5100)",fontsize=16,color="magenta"];492 -> 497[label="",style="dashed", color="magenta", weight=3];
492 -> 498[label="",style="dashed", color="magenta", weight=3];
488[label="Succ vx5100",fontsize=16,color="green",shape="box"];489 -> 275[label="",style="dashed", color="red", weight=0];
489[label="primMulNat vx400000 (Succ vx5100)",fontsize=16,color="magenta"];489 -> 493[label="",style="dashed", color="magenta", weight=3];
489 -> 494[label="",style="dashed", color="magenta", weight=3];
497[label="vx41000000",fontsize=16,color="green",shape="box"];498[label="Succ vx5100",fontsize=16,color="green",shape="box"];493[label="vx400000",fontsize=16,color="green",shape="box"];494[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(vx70), Succ(vx80)) -> new_primMulInt(vx70, vx80)

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(vx70), Succ(vx80)) -> new_primMulInt(vx70, vx80)
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(vx5000), Succ(vx4100)) -> new_primMulNat(vx5000, Succ(vx4100))

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(vx5000), Succ(vx4100)) -> new_primMulNat(vx5000, Succ(vx4100))
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(vx150)) -> new_primPlusNat(vx160, vx150)

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(vx150)) -> new_primPlusNat(vx160, vx150)
The graph contains the following edges 1 > 1, 2 > 2


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

(17)
YES