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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) Narrow [SOUND, 0 ms]
(6) AND
    (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (12) YES
    (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) 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) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="compare",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="compare vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="compare vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="primCmpFloat vx3 vx4",fontsize=16,color="burlywood",shape="box"];692[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 692[label="",style="solid", color="burlywood", weight=9];
692 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="primCmpFloat (Float vx30 vx31) vx4",fontsize=16,color="burlywood",shape="box"];693[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];6 -> 693[label="",style="solid", color="burlywood", weight=9];
693 -> 7[label="",style="solid", color="burlywood", weight=3];
694[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];6 -> 694[label="",style="solid", color="burlywood", weight=9];
694 -> 8[label="",style="solid", color="burlywood", weight=3];
7[label="primCmpFloat (Float vx30 (Pos vx310)) vx4",fontsize=16,color="burlywood",shape="box"];695[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];7 -> 695[label="",style="solid", color="burlywood", weight=9];
695 -> 9[label="",style="solid", color="burlywood", weight=3];
8[label="primCmpFloat (Float vx30 (Neg vx310)) vx4",fontsize=16,color="burlywood",shape="box"];696[label="vx4/Float vx40 vx41",fontsize=10,color="white",style="solid",shape="box"];8 -> 696[label="",style="solid", color="burlywood", weight=9];
696 -> 10[label="",style="solid", color="burlywood", weight=3];
9[label="primCmpFloat (Float vx30 (Pos vx310)) (Float vx40 vx41)",fontsize=16,color="burlywood",shape="box"];697[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];9 -> 697[label="",style="solid", color="burlywood", weight=9];
697 -> 11[label="",style="solid", color="burlywood", weight=3];
698[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];9 -> 698[label="",style="solid", color="burlywood", weight=9];
698 -> 12[label="",style="solid", color="burlywood", weight=3];
10[label="primCmpFloat (Float vx30 (Neg vx310)) (Float vx40 vx41)",fontsize=16,color="burlywood",shape="box"];699[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];10 -> 699[label="",style="solid", color="burlywood", weight=9];
699 -> 13[label="",style="solid", color="burlywood", weight=3];
700[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];10 -> 700[label="",style="solid", color="burlywood", weight=9];
700 -> 14[label="",style="solid", color="burlywood", weight=3];
11[label="primCmpFloat (Float vx30 (Pos vx310)) (Float vx40 (Pos vx410))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
12[label="primCmpFloat (Float vx30 (Pos vx310)) (Float vx40 (Neg vx410))",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
13[label="primCmpFloat (Float vx30 (Neg vx310)) (Float vx40 (Pos vx410))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="primCmpFloat (Float vx30 (Neg vx310)) (Float vx40 (Neg vx410))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="compare (vx30 * Pos vx410) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="compare (vx30 * Pos vx410) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="compare (vx30 * Neg vx410) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="compare (vx30 * Neg vx410) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="primCmpInt (vx30 * Pos vx410) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="primCmpInt (vx30 * Pos vx410) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="primCmpInt (vx30 * Neg vx410) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="primCmpInt (vx30 * Neg vx410) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="primCmpInt (primMulInt vx30 (Pos vx410)) (Pos vx310 * vx40)",fontsize=16,color="burlywood",shape="box"];701[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];23 -> 701[label="",style="solid", color="burlywood", weight=9];
701 -> 27[label="",style="solid", color="burlywood", weight=3];
702[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];23 -> 702[label="",style="solid", color="burlywood", weight=9];
702 -> 28[label="",style="solid", color="burlywood", weight=3];
24[label="primCmpInt (primMulInt vx30 (Pos vx410)) (Neg vx310 * vx40)",fontsize=16,color="burlywood",shape="box"];703[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];24 -> 703[label="",style="solid", color="burlywood", weight=9];
703 -> 29[label="",style="solid", color="burlywood", weight=3];
704[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];24 -> 704[label="",style="solid", color="burlywood", weight=9];
704 -> 30[label="",style="solid", color="burlywood", weight=3];
25[label="primCmpInt (primMulInt vx30 (Neg vx410)) (Pos vx310 * vx40)",fontsize=16,color="burlywood",shape="box"];705[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];25 -> 705[label="",style="solid", color="burlywood", weight=9];
705 -> 31[label="",style="solid", color="burlywood", weight=3];
706[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];25 -> 706[label="",style="solid", color="burlywood", weight=9];
706 -> 32[label="",style="solid", color="burlywood", weight=3];
26[label="primCmpInt (primMulInt vx30 (Neg vx410)) (Neg vx310 * vx40)",fontsize=16,color="burlywood",shape="box"];707[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];26 -> 707[label="",style="solid", color="burlywood", weight=9];
707 -> 33[label="",style="solid", color="burlywood", weight=3];
708[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];26 -> 708[label="",style="solid", color="burlywood", weight=9];
708 -> 34[label="",style="solid", color="burlywood", weight=3];
27[label="primCmpInt (primMulInt (Pos vx300) (Pos vx410)) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];27 -> 35[label="",style="solid", color="black", weight=3];
28[label="primCmpInt (primMulInt (Neg vx300) (Pos vx410)) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];28 -> 36[label="",style="solid", color="black", weight=3];
29[label="primCmpInt (primMulInt (Pos vx300) (Pos vx410)) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3];
30[label="primCmpInt (primMulInt (Neg vx300) (Pos vx410)) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3];
31[label="primCmpInt (primMulInt (Pos vx300) (Neg vx410)) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3];
32[label="primCmpInt (primMulInt (Neg vx300) (Neg vx410)) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3];
33[label="primCmpInt (primMulInt (Pos vx300) (Neg vx410)) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3];
34[label="primCmpInt (primMulInt (Neg vx300) (Neg vx410)) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3];
35 -> 428[label="",style="dashed", color="red", weight=0];
35[label="primCmpInt (Pos (primMulNat vx300 vx410)) (Pos vx310 * vx40)",fontsize=16,color="magenta"];35 -> 429[label="",style="dashed", color="magenta", weight=3];
36 -> 447[label="",style="dashed", color="red", weight=0];
36[label="primCmpInt (Neg (primMulNat vx300 vx410)) (Pos vx310 * vx40)",fontsize=16,color="magenta"];36 -> 448[label="",style="dashed", color="magenta", weight=3];
37 -> 470[label="",style="dashed", color="red", weight=0];
37[label="primCmpInt (Pos (primMulNat vx300 vx410)) (Neg vx310 * vx40)",fontsize=16,color="magenta"];37 -> 471[label="",style="dashed", color="magenta", weight=3];
38 -> 539[label="",style="dashed", color="red", weight=0];
38[label="primCmpInt (Neg (primMulNat vx300 vx410)) (Neg vx310 * vx40)",fontsize=16,color="magenta"];38 -> 540[label="",style="dashed", color="magenta", weight=3];
39 -> 447[label="",style="dashed", color="red", weight=0];
39[label="primCmpInt (Neg (primMulNat vx300 vx410)) (Pos vx310 * vx40)",fontsize=16,color="magenta"];39 -> 449[label="",style="dashed", color="magenta", weight=3];
39 -> 450[label="",style="dashed", color="magenta", weight=3];
40 -> 428[label="",style="dashed", color="red", weight=0];
40[label="primCmpInt (Pos (primMulNat vx300 vx410)) (Pos vx310 * vx40)",fontsize=16,color="magenta"];40 -> 430[label="",style="dashed", color="magenta", weight=3];
40 -> 431[label="",style="dashed", color="magenta", weight=3];
41 -> 539[label="",style="dashed", color="red", weight=0];
41[label="primCmpInt (Neg (primMulNat vx300 vx410)) (Neg vx310 * vx40)",fontsize=16,color="magenta"];41 -> 541[label="",style="dashed", color="magenta", weight=3];
41 -> 542[label="",style="dashed", color="magenta", weight=3];
42 -> 470[label="",style="dashed", color="red", weight=0];
42[label="primCmpInt (Pos (primMulNat vx300 vx410)) (Neg vx310 * vx40)",fontsize=16,color="magenta"];42 -> 472[label="",style="dashed", color="magenta", weight=3];
42 -> 473[label="",style="dashed", color="magenta", weight=3];
429[label="primMulNat vx300 vx410",fontsize=16,color="burlywood",shape="triangle"];709[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];429 -> 709[label="",style="solid", color="burlywood", weight=9];
709 -> 442[label="",style="solid", color="burlywood", weight=3];
710[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];429 -> 710[label="",style="solid", color="burlywood", weight=9];
710 -> 443[label="",style="solid", color="burlywood", weight=3];
428[label="primCmpInt (Pos vx12) (Pos vx310 * vx40)",fontsize=16,color="burlywood",shape="triangle"];711[label="vx12/Succ vx120",fontsize=10,color="white",style="solid",shape="box"];428 -> 711[label="",style="solid", color="burlywood", weight=9];
711 -> 444[label="",style="solid", color="burlywood", weight=3];
712[label="vx12/Zero",fontsize=10,color="white",style="solid",shape="box"];428 -> 712[label="",style="solid", color="burlywood", weight=9];
712 -> 445[label="",style="solid", color="burlywood", weight=3];
448 -> 429[label="",style="dashed", color="red", weight=0];
448[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];448 -> 461[label="",style="dashed", color="magenta", weight=3];
447[label="primCmpInt (Neg vx13) (Pos vx310 * vx40)",fontsize=16,color="burlywood",shape="triangle"];713[label="vx13/Succ vx130",fontsize=10,color="white",style="solid",shape="box"];447 -> 713[label="",style="solid", color="burlywood", weight=9];
713 -> 462[label="",style="solid", color="burlywood", weight=3];
714[label="vx13/Zero",fontsize=10,color="white",style="solid",shape="box"];447 -> 714[label="",style="solid", color="burlywood", weight=9];
714 -> 463[label="",style="solid", color="burlywood", weight=3];
471 -> 429[label="",style="dashed", color="red", weight=0];
471[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];471 -> 484[label="",style="dashed", color="magenta", weight=3];
470[label="primCmpInt (Pos vx14) (Neg vx310 * vx40)",fontsize=16,color="burlywood",shape="triangle"];715[label="vx14/Succ vx140",fontsize=10,color="white",style="solid",shape="box"];470 -> 715[label="",style="solid", color="burlywood", weight=9];
715 -> 485[label="",style="solid", color="burlywood", weight=3];
716[label="vx14/Zero",fontsize=10,color="white",style="solid",shape="box"];470 -> 716[label="",style="solid", color="burlywood", weight=9];
716 -> 486[label="",style="solid", color="burlywood", weight=3];
540 -> 429[label="",style="dashed", color="red", weight=0];
540[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];540 -> 551[label="",style="dashed", color="magenta", weight=3];
540 -> 552[label="",style="dashed", color="magenta", weight=3];
539[label="primCmpInt (Neg vx17) (Neg vx310 * vx40)",fontsize=16,color="burlywood",shape="triangle"];717[label="vx17/Succ vx170",fontsize=10,color="white",style="solid",shape="box"];539 -> 717[label="",style="solid", color="burlywood", weight=9];
717 -> 553[label="",style="solid", color="burlywood", weight=3];
718[label="vx17/Zero",fontsize=10,color="white",style="solid",shape="box"];539 -> 718[label="",style="solid", color="burlywood", weight=9];
718 -> 554[label="",style="solid", color="burlywood", weight=3];
449 -> 429[label="",style="dashed", color="red", weight=0];
449[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];450[label="vx310",fontsize=16,color="green",shape="box"];430 -> 429[label="",style="dashed", color="red", weight=0];
430[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];430 -> 446[label="",style="dashed", color="magenta", weight=3];
431[label="vx310",fontsize=16,color="green",shape="box"];541 -> 429[label="",style="dashed", color="red", weight=0];
541[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];541 -> 555[label="",style="dashed", color="magenta", weight=3];
542[label="vx310",fontsize=16,color="green",shape="box"];472 -> 429[label="",style="dashed", color="red", weight=0];
472[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];472 -> 487[label="",style="dashed", color="magenta", weight=3];
472 -> 488[label="",style="dashed", color="magenta", weight=3];
473[label="vx310",fontsize=16,color="green",shape="box"];442[label="primMulNat (Succ vx3000) vx410",fontsize=16,color="burlywood",shape="box"];719[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];442 -> 719[label="",style="solid", color="burlywood", weight=9];
719 -> 464[label="",style="solid", color="burlywood", weight=3];
720[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];442 -> 720[label="",style="solid", color="burlywood", weight=9];
720 -> 465[label="",style="solid", color="burlywood", weight=3];
443[label="primMulNat Zero vx410",fontsize=16,color="burlywood",shape="box"];721[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];443 -> 721[label="",style="solid", color="burlywood", weight=9];
721 -> 466[label="",style="solid", color="burlywood", weight=3];
722[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];443 -> 722[label="",style="solid", color="burlywood", weight=9];
722 -> 467[label="",style="solid", color="burlywood", weight=3];
444[label="primCmpInt (Pos (Succ vx120)) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];444 -> 468[label="",style="solid", color="black", weight=3];
445[label="primCmpInt (Pos Zero) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];445 -> 469[label="",style="solid", color="black", weight=3];
461[label="vx300",fontsize=16,color="green",shape="box"];462[label="primCmpInt (Neg (Succ vx130)) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];462 -> 489[label="",style="solid", color="black", weight=3];
463[label="primCmpInt (Neg Zero) (Pos vx310 * vx40)",fontsize=16,color="black",shape="box"];463 -> 490[label="",style="solid", color="black", weight=3];
484[label="vx410",fontsize=16,color="green",shape="box"];485[label="primCmpInt (Pos (Succ vx140)) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];485 -> 513[label="",style="solid", color="black", weight=3];
486[label="primCmpInt (Pos Zero) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];486 -> 514[label="",style="solid", color="black", weight=3];
551[label="vx300",fontsize=16,color="green",shape="box"];552[label="vx410",fontsize=16,color="green",shape="box"];553[label="primCmpInt (Neg (Succ vx170)) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];553 -> 564[label="",style="solid", color="black", weight=3];
554[label="primCmpInt (Neg Zero) (Neg vx310 * vx40)",fontsize=16,color="black",shape="box"];554 -> 565[label="",style="solid", color="black", weight=3];
446[label="vx300",fontsize=16,color="green",shape="box"];555[label="vx410",fontsize=16,color="green",shape="box"];487[label="vx300",fontsize=16,color="green",shape="box"];488[label="vx410",fontsize=16,color="green",shape="box"];464[label="primMulNat (Succ vx3000) (Succ vx4100)",fontsize=16,color="black",shape="box"];464 -> 491[label="",style="solid", color="black", weight=3];
465[label="primMulNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];465 -> 492[label="",style="solid", color="black", weight=3];
466[label="primMulNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];466 -> 493[label="",style="solid", color="black", weight=3];
467[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];467 -> 494[label="",style="solid", color="black", weight=3];
468[label="primCmpInt (Pos (Succ vx120)) (primMulInt (Pos vx310) vx40)",fontsize=16,color="burlywood",shape="box"];723[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];468 -> 723[label="",style="solid", color="burlywood", weight=9];
723 -> 495[label="",style="solid", color="burlywood", weight=3];
724[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];468 -> 724[label="",style="solid", color="burlywood", weight=9];
724 -> 496[label="",style="solid", color="burlywood", weight=3];
469[label="primCmpInt (Pos Zero) (primMulInt (Pos vx310) vx40)",fontsize=16,color="burlywood",shape="box"];725[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];469 -> 725[label="",style="solid", color="burlywood", weight=9];
725 -> 497[label="",style="solid", color="burlywood", weight=3];
726[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];469 -> 726[label="",style="solid", color="burlywood", weight=9];
726 -> 498[label="",style="solid", color="burlywood", weight=3];
489[label="primCmpInt (Neg (Succ vx130)) (primMulInt (Pos vx310) vx40)",fontsize=16,color="burlywood",shape="box"];727[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];489 -> 727[label="",style="solid", color="burlywood", weight=9];
727 -> 515[label="",style="solid", color="burlywood", weight=3];
728[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];489 -> 728[label="",style="solid", color="burlywood", weight=9];
728 -> 516[label="",style="solid", color="burlywood", weight=3];
490[label="primCmpInt (Neg Zero) (primMulInt (Pos vx310) vx40)",fontsize=16,color="burlywood",shape="box"];729[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];490 -> 729[label="",style="solid", color="burlywood", weight=9];
729 -> 517[label="",style="solid", color="burlywood", weight=3];
730[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];490 -> 730[label="",style="solid", color="burlywood", weight=9];
730 -> 518[label="",style="solid", color="burlywood", weight=3];
513[label="primCmpInt (Pos (Succ vx140)) (primMulInt (Neg vx310) vx40)",fontsize=16,color="burlywood",shape="box"];731[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];513 -> 731[label="",style="solid", color="burlywood", weight=9];
731 -> 521[label="",style="solid", color="burlywood", weight=3];
732[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];513 -> 732[label="",style="solid", color="burlywood", weight=9];
732 -> 522[label="",style="solid", color="burlywood", weight=3];
514[label="primCmpInt (Pos Zero) (primMulInt (Neg vx310) vx40)",fontsize=16,color="burlywood",shape="box"];733[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];514 -> 733[label="",style="solid", color="burlywood", weight=9];
733 -> 523[label="",style="solid", color="burlywood", weight=3];
734[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];514 -> 734[label="",style="solid", color="burlywood", weight=9];
734 -> 524[label="",style="solid", color="burlywood", weight=3];
564[label="primCmpInt (Neg (Succ vx170)) (primMulInt (Neg vx310) vx40)",fontsize=16,color="burlywood",shape="box"];735[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];564 -> 735[label="",style="solid", color="burlywood", weight=9];
735 -> 570[label="",style="solid", color="burlywood", weight=3];
736[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];564 -> 736[label="",style="solid", color="burlywood", weight=9];
736 -> 571[label="",style="solid", color="burlywood", weight=3];
565[label="primCmpInt (Neg Zero) (primMulInt (Neg vx310) vx40)",fontsize=16,color="burlywood",shape="box"];737[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];565 -> 737[label="",style="solid", color="burlywood", weight=9];
737 -> 572[label="",style="solid", color="burlywood", weight=3];
738[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];565 -> 738[label="",style="solid", color="burlywood", weight=9];
738 -> 573[label="",style="solid", color="burlywood", weight=3];
491 -> 519[label="",style="dashed", color="red", weight=0];
491[label="primPlusNat (primMulNat vx3000 (Succ vx4100)) (Succ vx4100)",fontsize=16,color="magenta"];491 -> 520[label="",style="dashed", color="magenta", weight=3];
492[label="Zero",fontsize=16,color="green",shape="box"];493[label="Zero",fontsize=16,color="green",shape="box"];494[label="Zero",fontsize=16,color="green",shape="box"];495[label="primCmpInt (Pos (Succ vx120)) (primMulInt (Pos vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];495 -> 525[label="",style="solid", color="black", weight=3];
496[label="primCmpInt (Pos (Succ vx120)) (primMulInt (Pos vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];496 -> 526[label="",style="solid", color="black", weight=3];
497[label="primCmpInt (Pos Zero) (primMulInt (Pos vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];497 -> 527[label="",style="solid", color="black", weight=3];
498[label="primCmpInt (Pos Zero) (primMulInt (Pos vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];498 -> 528[label="",style="solid", color="black", weight=3];
515[label="primCmpInt (Neg (Succ vx130)) (primMulInt (Pos vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];515 -> 529[label="",style="solid", color="black", weight=3];
516[label="primCmpInt (Neg (Succ vx130)) (primMulInt (Pos vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];516 -> 530[label="",style="solid", color="black", weight=3];
517[label="primCmpInt (Neg Zero) (primMulInt (Pos vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];517 -> 531[label="",style="solid", color="black", weight=3];
518[label="primCmpInt (Neg Zero) (primMulInt (Pos vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];518 -> 532[label="",style="solid", color="black", weight=3];
521[label="primCmpInt (Pos (Succ vx140)) (primMulInt (Neg vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];521 -> 556[label="",style="solid", color="black", weight=3];
522[label="primCmpInt (Pos (Succ vx140)) (primMulInt (Neg vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];522 -> 557[label="",style="solid", color="black", weight=3];
523[label="primCmpInt (Pos Zero) (primMulInt (Neg vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];523 -> 558[label="",style="solid", color="black", weight=3];
524[label="primCmpInt (Pos Zero) (primMulInt (Neg vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];524 -> 559[label="",style="solid", color="black", weight=3];
570[label="primCmpInt (Neg (Succ vx170)) (primMulInt (Neg vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];570 -> 577[label="",style="solid", color="black", weight=3];
571[label="primCmpInt (Neg (Succ vx170)) (primMulInt (Neg vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];571 -> 578[label="",style="solid", color="black", weight=3];
572[label="primCmpInt (Neg Zero) (primMulInt (Neg vx310) (Pos vx400))",fontsize=16,color="black",shape="box"];572 -> 579[label="",style="solid", color="black", weight=3];
573[label="primCmpInt (Neg Zero) (primMulInt (Neg vx310) (Neg vx400))",fontsize=16,color="black",shape="box"];573 -> 580[label="",style="solid", color="black", weight=3];
520 -> 429[label="",style="dashed", color="red", weight=0];
520[label="primMulNat vx3000 (Succ vx4100)",fontsize=16,color="magenta"];520 -> 533[label="",style="dashed", color="magenta", weight=3];
520 -> 534[label="",style="dashed", color="magenta", weight=3];
519[label="primPlusNat vx16 (Succ vx4100)",fontsize=16,color="burlywood",shape="triangle"];739[label="vx16/Succ vx160",fontsize=10,color="white",style="solid",shape="box"];519 -> 739[label="",style="solid", color="burlywood", weight=9];
739 -> 535[label="",style="solid", color="burlywood", weight=3];
740[label="vx16/Zero",fontsize=10,color="white",style="solid",shape="box"];519 -> 740[label="",style="solid", color="burlywood", weight=9];
740 -> 536[label="",style="solid", color="burlywood", weight=3];
525 -> 560[label="",style="dashed", color="red", weight=0];
525[label="primCmpInt (Pos (Succ vx120)) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];525 -> 561[label="",style="dashed", color="magenta", weight=3];
526 -> 566[label="",style="dashed", color="red", weight=0];
526[label="primCmpInt (Pos (Succ vx120)) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];526 -> 567[label="",style="dashed", color="magenta", weight=3];
527 -> 574[label="",style="dashed", color="red", weight=0];
527[label="primCmpInt (Pos Zero) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];527 -> 575[label="",style="dashed", color="magenta", weight=3];
528 -> 581[label="",style="dashed", color="red", weight=0];
528[label="primCmpInt (Pos Zero) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];528 -> 582[label="",style="dashed", color="magenta", weight=3];
529 -> 584[label="",style="dashed", color="red", weight=0];
529[label="primCmpInt (Neg (Succ vx130)) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];529 -> 585[label="",style="dashed", color="magenta", weight=3];
530 -> 588[label="",style="dashed", color="red", weight=0];
530[label="primCmpInt (Neg (Succ vx130)) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];530 -> 589[label="",style="dashed", color="magenta", weight=3];
531 -> 592[label="",style="dashed", color="red", weight=0];
531[label="primCmpInt (Neg Zero) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];531 -> 593[label="",style="dashed", color="magenta", weight=3];
532 -> 595[label="",style="dashed", color="red", weight=0];
532[label="primCmpInt (Neg Zero) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];532 -> 596[label="",style="dashed", color="magenta", weight=3];
556 -> 566[label="",style="dashed", color="red", weight=0];
556[label="primCmpInt (Pos (Succ vx140)) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];556 -> 568[label="",style="dashed", color="magenta", weight=3];
556 -> 569[label="",style="dashed", color="magenta", weight=3];
557 -> 560[label="",style="dashed", color="red", weight=0];
557[label="primCmpInt (Pos (Succ vx140)) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];557 -> 562[label="",style="dashed", color="magenta", weight=3];
557 -> 563[label="",style="dashed", color="magenta", weight=3];
558 -> 581[label="",style="dashed", color="red", weight=0];
558[label="primCmpInt (Pos Zero) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];558 -> 583[label="",style="dashed", color="magenta", weight=3];
559 -> 574[label="",style="dashed", color="red", weight=0];
559[label="primCmpInt (Pos Zero) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];559 -> 576[label="",style="dashed", color="magenta", weight=3];
577 -> 588[label="",style="dashed", color="red", weight=0];
577[label="primCmpInt (Neg (Succ vx170)) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];577 -> 590[label="",style="dashed", color="magenta", weight=3];
577 -> 591[label="",style="dashed", color="magenta", weight=3];
578 -> 584[label="",style="dashed", color="red", weight=0];
578[label="primCmpInt (Neg (Succ vx170)) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];578 -> 586[label="",style="dashed", color="magenta", weight=3];
578 -> 587[label="",style="dashed", color="magenta", weight=3];
579 -> 595[label="",style="dashed", color="red", weight=0];
579[label="primCmpInt (Neg Zero) (Neg (primMulNat vx310 vx400))",fontsize=16,color="magenta"];579 -> 597[label="",style="dashed", color="magenta", weight=3];
580 -> 592[label="",style="dashed", color="red", weight=0];
580[label="primCmpInt (Neg Zero) (Pos (primMulNat vx310 vx400))",fontsize=16,color="magenta"];580 -> 594[label="",style="dashed", color="magenta", weight=3];
533[label="vx3000",fontsize=16,color="green",shape="box"];534[label="Succ vx4100",fontsize=16,color="green",shape="box"];535[label="primPlusNat (Succ vx160) (Succ vx4100)",fontsize=16,color="black",shape="box"];535 -> 598[label="",style="solid", color="black", weight=3];
536[label="primPlusNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];536 -> 599[label="",style="solid", color="black", weight=3];
561 -> 429[label="",style="dashed", color="red", weight=0];
561[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];561 -> 600[label="",style="dashed", color="magenta", weight=3];
561 -> 601[label="",style="dashed", color="magenta", weight=3];
560[label="primCmpInt (Pos (Succ vx120)) (Pos vx19)",fontsize=16,color="black",shape="triangle"];560 -> 602[label="",style="solid", color="black", weight=3];
567 -> 429[label="",style="dashed", color="red", weight=0];
567[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];567 -> 603[label="",style="dashed", color="magenta", weight=3];
567 -> 604[label="",style="dashed", color="magenta", weight=3];
566[label="primCmpInt (Pos (Succ vx120)) (Neg vx20)",fontsize=16,color="black",shape="triangle"];566 -> 605[label="",style="solid", color="black", weight=3];
575 -> 429[label="",style="dashed", color="red", weight=0];
575[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];575 -> 606[label="",style="dashed", color="magenta", weight=3];
575 -> 607[label="",style="dashed", color="magenta", weight=3];
574[label="primCmpInt (Pos Zero) (Pos vx21)",fontsize=16,color="burlywood",shape="triangle"];741[label="vx21/Succ vx210",fontsize=10,color="white",style="solid",shape="box"];574 -> 741[label="",style="solid", color="burlywood", weight=9];
741 -> 608[label="",style="solid", color="burlywood", weight=3];
742[label="vx21/Zero",fontsize=10,color="white",style="solid",shape="box"];574 -> 742[label="",style="solid", color="burlywood", weight=9];
742 -> 609[label="",style="solid", color="burlywood", weight=3];
582 -> 429[label="",style="dashed", color="red", weight=0];
582[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];582 -> 610[label="",style="dashed", color="magenta", weight=3];
582 -> 611[label="",style="dashed", color="magenta", weight=3];
581[label="primCmpInt (Pos Zero) (Neg vx22)",fontsize=16,color="burlywood",shape="triangle"];743[label="vx22/Succ vx220",fontsize=10,color="white",style="solid",shape="box"];581 -> 743[label="",style="solid", color="burlywood", weight=9];
743 -> 612[label="",style="solid", color="burlywood", weight=3];
744[label="vx22/Zero",fontsize=10,color="white",style="solid",shape="box"];581 -> 744[label="",style="solid", color="burlywood", weight=9];
744 -> 613[label="",style="solid", color="burlywood", weight=3];
585 -> 429[label="",style="dashed", color="red", weight=0];
585[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];585 -> 614[label="",style="dashed", color="magenta", weight=3];
585 -> 615[label="",style="dashed", color="magenta", weight=3];
584[label="primCmpInt (Neg (Succ vx130)) (Pos vx23)",fontsize=16,color="black",shape="triangle"];584 -> 616[label="",style="solid", color="black", weight=3];
589 -> 429[label="",style="dashed", color="red", weight=0];
589[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];589 -> 617[label="",style="dashed", color="magenta", weight=3];
589 -> 618[label="",style="dashed", color="magenta", weight=3];
588[label="primCmpInt (Neg (Succ vx130)) (Neg vx24)",fontsize=16,color="black",shape="triangle"];588 -> 619[label="",style="solid", color="black", weight=3];
593 -> 429[label="",style="dashed", color="red", weight=0];
593[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];593 -> 620[label="",style="dashed", color="magenta", weight=3];
593 -> 621[label="",style="dashed", color="magenta", weight=3];
592[label="primCmpInt (Neg Zero) (Pos vx25)",fontsize=16,color="burlywood",shape="triangle"];745[label="vx25/Succ vx250",fontsize=10,color="white",style="solid",shape="box"];592 -> 745[label="",style="solid", color="burlywood", weight=9];
745 -> 622[label="",style="solid", color="burlywood", weight=3];
746[label="vx25/Zero",fontsize=10,color="white",style="solid",shape="box"];592 -> 746[label="",style="solid", color="burlywood", weight=9];
746 -> 623[label="",style="solid", color="burlywood", weight=3];
596 -> 429[label="",style="dashed", color="red", weight=0];
596[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];596 -> 624[label="",style="dashed", color="magenta", weight=3];
596 -> 625[label="",style="dashed", color="magenta", weight=3];
595[label="primCmpInt (Neg Zero) (Neg vx26)",fontsize=16,color="burlywood",shape="triangle"];747[label="vx26/Succ vx260",fontsize=10,color="white",style="solid",shape="box"];595 -> 747[label="",style="solid", color="burlywood", weight=9];
747 -> 626[label="",style="solid", color="burlywood", weight=3];
748[label="vx26/Zero",fontsize=10,color="white",style="solid",shape="box"];595 -> 748[label="",style="solid", color="burlywood", weight=9];
748 -> 627[label="",style="solid", color="burlywood", weight=3];
568 -> 429[label="",style="dashed", color="red", weight=0];
568[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];568 -> 628[label="",style="dashed", color="magenta", weight=3];
568 -> 629[label="",style="dashed", color="magenta", weight=3];
569[label="vx140",fontsize=16,color="green",shape="box"];562[label="vx140",fontsize=16,color="green",shape="box"];563 -> 429[label="",style="dashed", color="red", weight=0];
563[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];563 -> 630[label="",style="dashed", color="magenta", weight=3];
563 -> 631[label="",style="dashed", color="magenta", weight=3];
583 -> 429[label="",style="dashed", color="red", weight=0];
583[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];583 -> 632[label="",style="dashed", color="magenta", weight=3];
583 -> 633[label="",style="dashed", color="magenta", weight=3];
576 -> 429[label="",style="dashed", color="red", weight=0];
576[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];576 -> 634[label="",style="dashed", color="magenta", weight=3];
576 -> 635[label="",style="dashed", color="magenta", weight=3];
590[label="vx170",fontsize=16,color="green",shape="box"];591 -> 429[label="",style="dashed", color="red", weight=0];
591[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];591 -> 636[label="",style="dashed", color="magenta", weight=3];
591 -> 637[label="",style="dashed", color="magenta", weight=3];
586[label="vx170",fontsize=16,color="green",shape="box"];587 -> 429[label="",style="dashed", color="red", weight=0];
587[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];587 -> 638[label="",style="dashed", color="magenta", weight=3];
587 -> 639[label="",style="dashed", color="magenta", weight=3];
597 -> 429[label="",style="dashed", color="red", weight=0];
597[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];597 -> 640[label="",style="dashed", color="magenta", weight=3];
597 -> 641[label="",style="dashed", color="magenta", weight=3];
594 -> 429[label="",style="dashed", color="red", weight=0];
594[label="primMulNat vx310 vx400",fontsize=16,color="magenta"];594 -> 642[label="",style="dashed", color="magenta", weight=3];
594 -> 643[label="",style="dashed", color="magenta", weight=3];
598[label="Succ (Succ (primPlusNat vx160 vx4100))",fontsize=16,color="green",shape="box"];598 -> 644[label="",style="dashed", color="green", weight=3];
599[label="Succ vx4100",fontsize=16,color="green",shape="box"];600[label="vx310",fontsize=16,color="green",shape="box"];601[label="vx400",fontsize=16,color="green",shape="box"];602[label="primCmpNat (Succ vx120) vx19",fontsize=16,color="burlywood",shape="triangle"];749[label="vx19/Succ vx190",fontsize=10,color="white",style="solid",shape="box"];602 -> 749[label="",style="solid", color="burlywood", weight=9];
749 -> 645[label="",style="solid", color="burlywood", weight=3];
750[label="vx19/Zero",fontsize=10,color="white",style="solid",shape="box"];602 -> 750[label="",style="solid", color="burlywood", weight=9];
750 -> 646[label="",style="solid", color="burlywood", weight=3];
603[label="vx310",fontsize=16,color="green",shape="box"];604[label="vx400",fontsize=16,color="green",shape="box"];605[label="GT",fontsize=16,color="green",shape="box"];606[label="vx310",fontsize=16,color="green",shape="box"];607[label="vx400",fontsize=16,color="green",shape="box"];608[label="primCmpInt (Pos Zero) (Pos (Succ vx210))",fontsize=16,color="black",shape="box"];608 -> 647[label="",style="solid", color="black", weight=3];
609[label="primCmpInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];609 -> 648[label="",style="solid", color="black", weight=3];
610[label="vx310",fontsize=16,color="green",shape="box"];611[label="vx400",fontsize=16,color="green",shape="box"];612[label="primCmpInt (Pos Zero) (Neg (Succ vx220))",fontsize=16,color="black",shape="box"];612 -> 649[label="",style="solid", color="black", weight=3];
613[label="primCmpInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];613 -> 650[label="",style="solid", color="black", weight=3];
614[label="vx310",fontsize=16,color="green",shape="box"];615[label="vx400",fontsize=16,color="green",shape="box"];616[label="LT",fontsize=16,color="green",shape="box"];617[label="vx310",fontsize=16,color="green",shape="box"];618[label="vx400",fontsize=16,color="green",shape="box"];619[label="primCmpNat vx24 (Succ vx130)",fontsize=16,color="burlywood",shape="triangle"];751[label="vx24/Succ vx240",fontsize=10,color="white",style="solid",shape="box"];619 -> 751[label="",style="solid", color="burlywood", weight=9];
751 -> 651[label="",style="solid", color="burlywood", weight=3];
752[label="vx24/Zero",fontsize=10,color="white",style="solid",shape="box"];619 -> 752[label="",style="solid", color="burlywood", weight=9];
752 -> 652[label="",style="solid", color="burlywood", weight=3];
620[label="vx310",fontsize=16,color="green",shape="box"];621[label="vx400",fontsize=16,color="green",shape="box"];622[label="primCmpInt (Neg Zero) (Pos (Succ vx250))",fontsize=16,color="black",shape="box"];622 -> 653[label="",style="solid", color="black", weight=3];
623[label="primCmpInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];623 -> 654[label="",style="solid", color="black", weight=3];
624[label="vx310",fontsize=16,color="green",shape="box"];625[label="vx400",fontsize=16,color="green",shape="box"];626[label="primCmpInt (Neg Zero) (Neg (Succ vx260))",fontsize=16,color="black",shape="box"];626 -> 655[label="",style="solid", color="black", weight=3];
627[label="primCmpInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];627 -> 656[label="",style="solid", color="black", weight=3];
628[label="vx310",fontsize=16,color="green",shape="box"];629[label="vx400",fontsize=16,color="green",shape="box"];630[label="vx310",fontsize=16,color="green",shape="box"];631[label="vx400",fontsize=16,color="green",shape="box"];632[label="vx310",fontsize=16,color="green",shape="box"];633[label="vx400",fontsize=16,color="green",shape="box"];634[label="vx310",fontsize=16,color="green",shape="box"];635[label="vx400",fontsize=16,color="green",shape="box"];636[label="vx310",fontsize=16,color="green",shape="box"];637[label="vx400",fontsize=16,color="green",shape="box"];638[label="vx310",fontsize=16,color="green",shape="box"];639[label="vx400",fontsize=16,color="green",shape="box"];640[label="vx310",fontsize=16,color="green",shape="box"];641[label="vx400",fontsize=16,color="green",shape="box"];642[label="vx310",fontsize=16,color="green",shape="box"];643[label="vx400",fontsize=16,color="green",shape="box"];644[label="primPlusNat vx160 vx4100",fontsize=16,color="burlywood",shape="triangle"];753[label="vx160/Succ vx1600",fontsize=10,color="white",style="solid",shape="box"];644 -> 753[label="",style="solid", color="burlywood", weight=9];
753 -> 657[label="",style="solid", color="burlywood", weight=3];
754[label="vx160/Zero",fontsize=10,color="white",style="solid",shape="box"];644 -> 754[label="",style="solid", color="burlywood", weight=9];
754 -> 658[label="",style="solid", color="burlywood", weight=3];
645[label="primCmpNat (Succ vx120) (Succ vx190)",fontsize=16,color="black",shape="box"];645 -> 659[label="",style="solid", color="black", weight=3];
646[label="primCmpNat (Succ vx120) Zero",fontsize=16,color="black",shape="box"];646 -> 660[label="",style="solid", color="black", weight=3];
647 -> 619[label="",style="dashed", color="red", weight=0];
647[label="primCmpNat Zero (Succ vx210)",fontsize=16,color="magenta"];647 -> 661[label="",style="dashed", color="magenta", weight=3];
647 -> 662[label="",style="dashed", color="magenta", weight=3];
648[label="EQ",fontsize=16,color="green",shape="box"];649[label="GT",fontsize=16,color="green",shape="box"];650[label="EQ",fontsize=16,color="green",shape="box"];651[label="primCmpNat (Succ vx240) (Succ vx130)",fontsize=16,color="black",shape="box"];651 -> 663[label="",style="solid", color="black", weight=3];
652[label="primCmpNat Zero (Succ vx130)",fontsize=16,color="black",shape="box"];652 -> 664[label="",style="solid", color="black", weight=3];
653[label="LT",fontsize=16,color="green",shape="box"];654[label="EQ",fontsize=16,color="green",shape="box"];655 -> 602[label="",style="dashed", color="red", weight=0];
655[label="primCmpNat (Succ vx260) Zero",fontsize=16,color="magenta"];655 -> 665[label="",style="dashed", color="magenta", weight=3];
655 -> 666[label="",style="dashed", color="magenta", weight=3];
656[label="EQ",fontsize=16,color="green",shape="box"];657[label="primPlusNat (Succ vx1600) vx4100",fontsize=16,color="burlywood",shape="box"];755[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];657 -> 755[label="",style="solid", color="burlywood", weight=9];
755 -> 667[label="",style="solid", color="burlywood", weight=3];
756[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];657 -> 756[label="",style="solid", color="burlywood", weight=9];
756 -> 668[label="",style="solid", color="burlywood", weight=3];
658[label="primPlusNat Zero vx4100",fontsize=16,color="burlywood",shape="box"];757[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];658 -> 757[label="",style="solid", color="burlywood", weight=9];
757 -> 669[label="",style="solid", color="burlywood", weight=3];
758[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];658 -> 758[label="",style="solid", color="burlywood", weight=9];
758 -> 670[label="",style="solid", color="burlywood", weight=3];
659[label="primCmpNat vx120 vx190",fontsize=16,color="burlywood",shape="triangle"];759[label="vx120/Succ vx1200",fontsize=10,color="white",style="solid",shape="box"];659 -> 759[label="",style="solid", color="burlywood", weight=9];
759 -> 671[label="",style="solid", color="burlywood", weight=3];
760[label="vx120/Zero",fontsize=10,color="white",style="solid",shape="box"];659 -> 760[label="",style="solid", color="burlywood", weight=9];
760 -> 672[label="",style="solid", color="burlywood", weight=3];
660[label="GT",fontsize=16,color="green",shape="box"];661[label="vx210",fontsize=16,color="green",shape="box"];662[label="Zero",fontsize=16,color="green",shape="box"];663 -> 659[label="",style="dashed", color="red", weight=0];
663[label="primCmpNat vx240 vx130",fontsize=16,color="magenta"];663 -> 673[label="",style="dashed", color="magenta", weight=3];
663 -> 674[label="",style="dashed", color="magenta", weight=3];
664[label="LT",fontsize=16,color="green",shape="box"];665[label="vx260",fontsize=16,color="green",shape="box"];666[label="Zero",fontsize=16,color="green",shape="box"];667[label="primPlusNat (Succ vx1600) (Succ vx41000)",fontsize=16,color="black",shape="box"];667 -> 675[label="",style="solid", color="black", weight=3];
668[label="primPlusNat (Succ vx1600) Zero",fontsize=16,color="black",shape="box"];668 -> 676[label="",style="solid", color="black", weight=3];
669[label="primPlusNat Zero (Succ vx41000)",fontsize=16,color="black",shape="box"];669 -> 677[label="",style="solid", color="black", weight=3];
670[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];670 -> 678[label="",style="solid", color="black", weight=3];
671[label="primCmpNat (Succ vx1200) vx190",fontsize=16,color="burlywood",shape="box"];761[label="vx190/Succ vx1900",fontsize=10,color="white",style="solid",shape="box"];671 -> 761[label="",style="solid", color="burlywood", weight=9];
761 -> 679[label="",style="solid", color="burlywood", weight=3];
762[label="vx190/Zero",fontsize=10,color="white",style="solid",shape="box"];671 -> 762[label="",style="solid", color="burlywood", weight=9];
762 -> 680[label="",style="solid", color="burlywood", weight=3];
672[label="primCmpNat Zero vx190",fontsize=16,color="burlywood",shape="box"];763[label="vx190/Succ vx1900",fontsize=10,color="white",style="solid",shape="box"];672 -> 763[label="",style="solid", color="burlywood", weight=9];
763 -> 681[label="",style="solid", color="burlywood", weight=3];
764[label="vx190/Zero",fontsize=10,color="white",style="solid",shape="box"];672 -> 764[label="",style="solid", color="burlywood", weight=9];
764 -> 682[label="",style="solid", color="burlywood", weight=3];
673[label="vx130",fontsize=16,color="green",shape="box"];674[label="vx240",fontsize=16,color="green",shape="box"];675[label="Succ (Succ (primPlusNat vx1600 vx41000))",fontsize=16,color="green",shape="box"];675 -> 683[label="",style="dashed", color="green", weight=3];
676[label="Succ vx1600",fontsize=16,color="green",shape="box"];677[label="Succ vx41000",fontsize=16,color="green",shape="box"];678[label="Zero",fontsize=16,color="green",shape="box"];679[label="primCmpNat (Succ vx1200) (Succ vx1900)",fontsize=16,color="black",shape="box"];679 -> 684[label="",style="solid", color="black", weight=3];
680[label="primCmpNat (Succ vx1200) Zero",fontsize=16,color="black",shape="box"];680 -> 685[label="",style="solid", color="black", weight=3];
681[label="primCmpNat Zero (Succ vx1900)",fontsize=16,color="black",shape="box"];681 -> 686[label="",style="solid", color="black", weight=3];
682[label="primCmpNat Zero Zero",fontsize=16,color="black",shape="box"];682 -> 687[label="",style="solid", color="black", weight=3];
683 -> 644[label="",style="dashed", color="red", weight=0];
683[label="primPlusNat vx1600 vx41000",fontsize=16,color="magenta"];683 -> 688[label="",style="dashed", color="magenta", weight=3];
683 -> 689[label="",style="dashed", color="magenta", weight=3];
684 -> 659[label="",style="dashed", color="red", weight=0];
684[label="primCmpNat vx1200 vx1900",fontsize=16,color="magenta"];684 -> 690[label="",style="dashed", color="magenta", weight=3];
684 -> 691[label="",style="dashed", color="magenta", weight=3];
685[label="GT",fontsize=16,color="green",shape="box"];686[label="LT",fontsize=16,color="green",shape="box"];687[label="EQ",fontsize=16,color="green",shape="box"];688[label="vx41000",fontsize=16,color="green",shape="box"];689[label="vx1600",fontsize=16,color="green",shape="box"];690[label="vx1900",fontsize=16,color="green",shape="box"];691[label="vx1200",fontsize=16,color="green",shape="box"];}

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

(6)
Complex Obligation (AND)

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

(7)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primCmpNat(Succ(vx1200), Succ(vx1900)) -> new_primCmpNat(vx1200, vx1900)

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

(8) 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_primCmpNat(Succ(vx1200), Succ(vx1900)) -> new_primCmpNat(vx1200, vx1900)
The graph contains the following edges 1 > 1, 2 > 2


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

(9)
YES

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

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

   new_primMulNat(Succ(vx3000), Succ(vx4100)) -> new_primMulNat(vx3000, Succ(vx4100))

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

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

From the DPs we obtained the following set of size-change graphs:
*new_primMulNat(Succ(vx3000), Succ(vx4100)) -> new_primMulNat(vx3000, Succ(vx4100))
The graph contains the following edges 1 > 1, 2 >= 2


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

(12)
YES

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

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

   new_primPlusNat(Succ(vx1600), Succ(vx41000)) -> new_primPlusNat(vx1600, vx41000)

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

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

From the DPs we obtained the following set of size-change graphs:
*new_primPlusNat(Succ(vx1600), Succ(vx41000)) -> new_primPlusNat(vx1600, vx41000)
The graph contains the following edges 1 > 1, 2 > 2


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

(15)
YES