/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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="(<)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="(<) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="(<) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="compare vx3 vx4 == LT",fontsize=16,color="burlywood",shape="box"];511[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 511[label="",style="solid", color="burlywood", weight=9];
511 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="compare (vx30 :% vx31) vx4 == LT",fontsize=16,color="burlywood",shape="box"];512[label="vx4/vx40 :% vx41",fontsize=10,color="white",style="solid",shape="box"];6 -> 512[label="",style="solid", color="burlywood", weight=9];
512 -> 7[label="",style="solid", color="burlywood", weight=3];
7[label="compare (vx30 :% vx31) (vx40 :% vx41) == LT",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="compare (vx30 * vx41) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="primCmpInt (vx30 * vx41) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="primCmpInt (primMulInt vx30 vx41) (vx40 * vx31) == LT",fontsize=16,color="burlywood",shape="box"];513[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 513[label="",style="solid", color="burlywood", weight=9];
513 -> 11[label="",style="solid", color="burlywood", weight=3];
514[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];10 -> 514[label="",style="solid", color="burlywood", weight=9];
514 -> 12[label="",style="solid", color="burlywood", weight=3];
11[label="primCmpInt (primMulInt (Pos vx300) vx41) (vx40 * vx31) == LT",fontsize=16,color="burlywood",shape="box"];515[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];11 -> 515[label="",style="solid", color="burlywood", weight=9];
515 -> 13[label="",style="solid", color="burlywood", weight=3];
516[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];11 -> 516[label="",style="solid", color="burlywood", weight=9];
516 -> 14[label="",style="solid", color="burlywood", weight=3];
12[label="primCmpInt (primMulInt (Neg vx300) vx41) (vx40 * vx31) == LT",fontsize=16,color="burlywood",shape="box"];517[label="vx41/Pos vx410",fontsize=10,color="white",style="solid",shape="box"];12 -> 517[label="",style="solid", color="burlywood", weight=9];
517 -> 15[label="",style="solid", color="burlywood", weight=3];
518[label="vx41/Neg vx410",fontsize=10,color="white",style="solid",shape="box"];12 -> 518[label="",style="solid", color="burlywood", weight=9];
518 -> 16[label="",style="solid", color="burlywood", weight=3];
13[label="primCmpInt (primMulInt (Pos vx300) (Pos vx410)) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
14[label="primCmpInt (primMulInt (Pos vx300) (Neg vx410)) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="primCmpInt (primMulInt (Neg vx300) (Pos vx410)) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="primCmpInt (primMulInt (Neg vx300) (Neg vx410)) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17 -> 267[label="",style="dashed", color="red", weight=0];
17[label="primCmpInt (Pos (primMulNat vx300 vx410)) (vx40 * vx31) == LT",fontsize=16,color="magenta"];17 -> 268[label="",style="dashed", color="magenta", weight=3];
18 -> 343[label="",style="dashed", color="red", weight=0];
18[label="primCmpInt (Neg (primMulNat vx300 vx410)) (vx40 * vx31) == LT",fontsize=16,color="magenta"];18 -> 344[label="",style="dashed", color="magenta", weight=3];
19 -> 343[label="",style="dashed", color="red", weight=0];
19[label="primCmpInt (Neg (primMulNat vx300 vx410)) (vx40 * vx31) == LT",fontsize=16,color="magenta"];19 -> 345[label="",style="dashed", color="magenta", weight=3];
20 -> 267[label="",style="dashed", color="red", weight=0];
20[label="primCmpInt (Pos (primMulNat vx300 vx410)) (vx40 * vx31) == LT",fontsize=16,color="magenta"];20 -> 269[label="",style="dashed", color="magenta", weight=3];
268[label="primMulNat vx300 vx410",fontsize=16,color="burlywood",shape="triangle"];519[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];268 -> 519[label="",style="solid", color="burlywood", weight=9];
519 -> 280[label="",style="solid", color="burlywood", weight=3];
520[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];268 -> 520[label="",style="solid", color="burlywood", weight=9];
520 -> 281[label="",style="solid", color="burlywood", weight=3];
267[label="primCmpInt (Pos vx10) (vx40 * vx31) == LT",fontsize=16,color="burlywood",shape="triangle"];521[label="vx10/Succ vx100",fontsize=10,color="white",style="solid",shape="box"];267 -> 521[label="",style="solid", color="burlywood", weight=9];
521 -> 282[label="",style="solid", color="burlywood", weight=3];
522[label="vx10/Zero",fontsize=10,color="white",style="solid",shape="box"];267 -> 522[label="",style="solid", color="burlywood", weight=9];
522 -> 283[label="",style="solid", color="burlywood", weight=3];
344 -> 268[label="",style="dashed", color="red", weight=0];
344[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];344 -> 356[label="",style="dashed", color="magenta", weight=3];
343[label="primCmpInt (Neg vx15) (vx40 * vx31) == LT",fontsize=16,color="burlywood",shape="triangle"];523[label="vx15/Succ vx150",fontsize=10,color="white",style="solid",shape="box"];343 -> 523[label="",style="solid", color="burlywood", weight=9];
523 -> 357[label="",style="solid", color="burlywood", weight=3];
524[label="vx15/Zero",fontsize=10,color="white",style="solid",shape="box"];343 -> 524[label="",style="solid", color="burlywood", weight=9];
524 -> 358[label="",style="solid", color="burlywood", weight=3];
345 -> 268[label="",style="dashed", color="red", weight=0];
345[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];345 -> 359[label="",style="dashed", color="magenta", weight=3];
269 -> 268[label="",style="dashed", color="red", weight=0];
269[label="primMulNat vx300 vx410",fontsize=16,color="magenta"];269 -> 284[label="",style="dashed", color="magenta", weight=3];
269 -> 285[label="",style="dashed", color="magenta", weight=3];
280[label="primMulNat (Succ vx3000) vx410",fontsize=16,color="burlywood",shape="box"];525[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];280 -> 525[label="",style="solid", color="burlywood", weight=9];
525 -> 300[label="",style="solid", color="burlywood", weight=3];
526[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];280 -> 526[label="",style="solid", color="burlywood", weight=9];
526 -> 301[label="",style="solid", color="burlywood", weight=3];
281[label="primMulNat Zero vx410",fontsize=16,color="burlywood",shape="box"];527[label="vx410/Succ vx4100",fontsize=10,color="white",style="solid",shape="box"];281 -> 527[label="",style="solid", color="burlywood", weight=9];
527 -> 302[label="",style="solid", color="burlywood", weight=3];
528[label="vx410/Zero",fontsize=10,color="white",style="solid",shape="box"];281 -> 528[label="",style="solid", color="burlywood", weight=9];
528 -> 303[label="",style="solid", color="burlywood", weight=3];
282[label="primCmpInt (Pos (Succ vx100)) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];282 -> 304[label="",style="solid", color="black", weight=3];
283[label="primCmpInt (Pos Zero) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];283 -> 305[label="",style="solid", color="black", weight=3];
356[label="vx410",fontsize=16,color="green",shape="box"];357[label="primCmpInt (Neg (Succ vx150)) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];357 -> 370[label="",style="solid", color="black", weight=3];
358[label="primCmpInt (Neg Zero) (vx40 * vx31) == LT",fontsize=16,color="black",shape="box"];358 -> 371[label="",style="solid", color="black", weight=3];
359[label="vx300",fontsize=16,color="green",shape="box"];284[label="vx300",fontsize=16,color="green",shape="box"];285[label="vx410",fontsize=16,color="green",shape="box"];300[label="primMulNat (Succ vx3000) (Succ vx4100)",fontsize=16,color="black",shape="box"];300 -> 316[label="",style="solid", color="black", weight=3];
301[label="primMulNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];301 -> 317[label="",style="solid", color="black", weight=3];
302[label="primMulNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];302 -> 318[label="",style="solid", color="black", weight=3];
303[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];303 -> 319[label="",style="solid", color="black", weight=3];
304[label="primCmpInt (Pos (Succ vx100)) (primMulInt vx40 vx31) == LT",fontsize=16,color="burlywood",shape="box"];529[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];304 -> 529[label="",style="solid", color="burlywood", weight=9];
529 -> 320[label="",style="solid", color="burlywood", weight=3];
530[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];304 -> 530[label="",style="solid", color="burlywood", weight=9];
530 -> 321[label="",style="solid", color="burlywood", weight=3];
305[label="primCmpInt (Pos Zero) (primMulInt vx40 vx31) == LT",fontsize=16,color="burlywood",shape="box"];531[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];305 -> 531[label="",style="solid", color="burlywood", weight=9];
531 -> 322[label="",style="solid", color="burlywood", weight=3];
532[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];305 -> 532[label="",style="solid", color="burlywood", weight=9];
532 -> 323[label="",style="solid", color="burlywood", weight=3];
370[label="primCmpInt (Neg (Succ vx150)) (primMulInt vx40 vx31) == LT",fontsize=16,color="burlywood",shape="box"];533[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];370 -> 533[label="",style="solid", color="burlywood", weight=9];
533 -> 375[label="",style="solid", color="burlywood", weight=3];
534[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];370 -> 534[label="",style="solid", color="burlywood", weight=9];
534 -> 376[label="",style="solid", color="burlywood", weight=3];
371[label="primCmpInt (Neg Zero) (primMulInt vx40 vx31) == LT",fontsize=16,color="burlywood",shape="box"];535[label="vx40/Pos vx400",fontsize=10,color="white",style="solid",shape="box"];371 -> 535[label="",style="solid", color="burlywood", weight=9];
535 -> 377[label="",style="solid", color="burlywood", weight=3];
536[label="vx40/Neg vx400",fontsize=10,color="white",style="solid",shape="box"];371 -> 536[label="",style="solid", color="burlywood", weight=9];
536 -> 378[label="",style="solid", color="burlywood", weight=3];
316 -> 329[label="",style="dashed", color="red", weight=0];
316[label="primPlusNat (primMulNat vx3000 (Succ vx4100)) (Succ vx4100)",fontsize=16,color="magenta"];316 -> 330[label="",style="dashed", color="magenta", weight=3];
317[label="Zero",fontsize=16,color="green",shape="box"];318[label="Zero",fontsize=16,color="green",shape="box"];319[label="Zero",fontsize=16,color="green",shape="box"];320[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Pos vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];537[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];320 -> 537[label="",style="solid", color="burlywood", weight=9];
537 -> 331[label="",style="solid", color="burlywood", weight=3];
538[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];320 -> 538[label="",style="solid", color="burlywood", weight=9];
538 -> 332[label="",style="solid", color="burlywood", weight=3];
321[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Neg vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];539[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];321 -> 539[label="",style="solid", color="burlywood", weight=9];
539 -> 333[label="",style="solid", color="burlywood", weight=3];
540[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];321 -> 540[label="",style="solid", color="burlywood", weight=9];
540 -> 334[label="",style="solid", color="burlywood", weight=3];
322[label="primCmpInt (Pos Zero) (primMulInt (Pos vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];541[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];322 -> 541[label="",style="solid", color="burlywood", weight=9];
541 -> 335[label="",style="solid", color="burlywood", weight=3];
542[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];322 -> 542[label="",style="solid", color="burlywood", weight=9];
542 -> 336[label="",style="solid", color="burlywood", weight=3];
323[label="primCmpInt (Pos Zero) (primMulInt (Neg vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];543[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];323 -> 543[label="",style="solid", color="burlywood", weight=9];
543 -> 337[label="",style="solid", color="burlywood", weight=3];
544[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];323 -> 544[label="",style="solid", color="burlywood", weight=9];
544 -> 338[label="",style="solid", color="burlywood", weight=3];
375[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Pos vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];545[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];375 -> 545[label="",style="solid", color="burlywood", weight=9];
545 -> 382[label="",style="solid", color="burlywood", weight=3];
546[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];375 -> 546[label="",style="solid", color="burlywood", weight=9];
546 -> 383[label="",style="solid", color="burlywood", weight=3];
376[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Neg vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];547[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];376 -> 547[label="",style="solid", color="burlywood", weight=9];
547 -> 384[label="",style="solid", color="burlywood", weight=3];
548[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];376 -> 548[label="",style="solid", color="burlywood", weight=9];
548 -> 385[label="",style="solid", color="burlywood", weight=3];
377[label="primCmpInt (Neg Zero) (primMulInt (Pos vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];549[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];377 -> 549[label="",style="solid", color="burlywood", weight=9];
549 -> 386[label="",style="solid", color="burlywood", weight=3];
550[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];377 -> 550[label="",style="solid", color="burlywood", weight=9];
550 -> 387[label="",style="solid", color="burlywood", weight=3];
378[label="primCmpInt (Neg Zero) (primMulInt (Neg vx400) vx31) == LT",fontsize=16,color="burlywood",shape="box"];551[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];378 -> 551[label="",style="solid", color="burlywood", weight=9];
551 -> 388[label="",style="solid", color="burlywood", weight=3];
552[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];378 -> 552[label="",style="solid", color="burlywood", weight=9];
552 -> 389[label="",style="solid", color="burlywood", weight=3];
330 -> 268[label="",style="dashed", color="red", weight=0];
330[label="primMulNat vx3000 (Succ vx4100)",fontsize=16,color="magenta"];330 -> 339[label="",style="dashed", color="magenta", weight=3];
330 -> 340[label="",style="dashed", color="magenta", weight=3];
329[label="primPlusNat vx14 (Succ vx4100)",fontsize=16,color="burlywood",shape="triangle"];553[label="vx14/Succ vx140",fontsize=10,color="white",style="solid",shape="box"];329 -> 553[label="",style="solid", color="burlywood", weight=9];
553 -> 341[label="",style="solid", color="burlywood", weight=3];
554[label="vx14/Zero",fontsize=10,color="white",style="solid",shape="box"];329 -> 554[label="",style="solid", color="burlywood", weight=9];
554 -> 342[label="",style="solid", color="burlywood", weight=3];
331[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Pos vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];331 -> 360[label="",style="solid", color="black", weight=3];
332[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Pos vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];332 -> 361[label="",style="solid", color="black", weight=3];
333[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Neg vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];333 -> 362[label="",style="solid", color="black", weight=3];
334[label="primCmpInt (Pos (Succ vx100)) (primMulInt (Neg vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];334 -> 363[label="",style="solid", color="black", weight=3];
335[label="primCmpInt (Pos Zero) (primMulInt (Pos vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];335 -> 364[label="",style="solid", color="black", weight=3];
336[label="primCmpInt (Pos Zero) (primMulInt (Pos vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];336 -> 365[label="",style="solid", color="black", weight=3];
337[label="primCmpInt (Pos Zero) (primMulInt (Neg vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];337 -> 366[label="",style="solid", color="black", weight=3];
338[label="primCmpInt (Pos Zero) (primMulInt (Neg vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];338 -> 367[label="",style="solid", color="black", weight=3];
382[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Pos vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];382 -> 393[label="",style="solid", color="black", weight=3];
383[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Pos vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];383 -> 394[label="",style="solid", color="black", weight=3];
384[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Neg vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];384 -> 395[label="",style="solid", color="black", weight=3];
385[label="primCmpInt (Neg (Succ vx150)) (primMulInt (Neg vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];385 -> 396[label="",style="solid", color="black", weight=3];
386[label="primCmpInt (Neg Zero) (primMulInt (Pos vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];386 -> 397[label="",style="solid", color="black", weight=3];
387[label="primCmpInt (Neg Zero) (primMulInt (Pos vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];387 -> 398[label="",style="solid", color="black", weight=3];
388[label="primCmpInt (Neg Zero) (primMulInt (Neg vx400) (Pos vx310)) == LT",fontsize=16,color="black",shape="box"];388 -> 399[label="",style="solid", color="black", weight=3];
389[label="primCmpInt (Neg Zero) (primMulInt (Neg vx400) (Neg vx310)) == LT",fontsize=16,color="black",shape="box"];389 -> 400[label="",style="solid", color="black", weight=3];
339[label="vx3000",fontsize=16,color="green",shape="box"];340[label="Succ vx4100",fontsize=16,color="green",shape="box"];341[label="primPlusNat (Succ vx140) (Succ vx4100)",fontsize=16,color="black",shape="box"];341 -> 368[label="",style="solid", color="black", weight=3];
342[label="primPlusNat Zero (Succ vx4100)",fontsize=16,color="black",shape="box"];342 -> 369[label="",style="solid", color="black", weight=3];
360 -> 372[label="",style="dashed", color="red", weight=0];
360[label="primCmpInt (Pos (Succ vx100)) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];360 -> 373[label="",style="dashed", color="magenta", weight=3];
361 -> 379[label="",style="dashed", color="red", weight=0];
361[label="primCmpInt (Pos (Succ vx100)) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];361 -> 380[label="",style="dashed", color="magenta", weight=3];
362 -> 379[label="",style="dashed", color="red", weight=0];
362[label="primCmpInt (Pos (Succ vx100)) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];362 -> 381[label="",style="dashed", color="magenta", weight=3];
363 -> 372[label="",style="dashed", color="red", weight=0];
363[label="primCmpInt (Pos (Succ vx100)) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];363 -> 374[label="",style="dashed", color="magenta", weight=3];
364 -> 390[label="",style="dashed", color="red", weight=0];
364[label="primCmpInt (Pos Zero) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];364 -> 391[label="",style="dashed", color="magenta", weight=3];
365 -> 401[label="",style="dashed", color="red", weight=0];
365[label="primCmpInt (Pos Zero) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];365 -> 402[label="",style="dashed", color="magenta", weight=3];
366 -> 401[label="",style="dashed", color="red", weight=0];
366[label="primCmpInt (Pos Zero) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];366 -> 403[label="",style="dashed", color="magenta", weight=3];
367 -> 390[label="",style="dashed", color="red", weight=0];
367[label="primCmpInt (Pos Zero) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];367 -> 392[label="",style="dashed", color="magenta", weight=3];
393 -> 404[label="",style="dashed", color="red", weight=0];
393[label="primCmpInt (Neg (Succ vx150)) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];393 -> 405[label="",style="dashed", color="magenta", weight=3];
394 -> 407[label="",style="dashed", color="red", weight=0];
394[label="primCmpInt (Neg (Succ vx150)) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];394 -> 408[label="",style="dashed", color="magenta", weight=3];
395 -> 407[label="",style="dashed", color="red", weight=0];
395[label="primCmpInt (Neg (Succ vx150)) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];395 -> 409[label="",style="dashed", color="magenta", weight=3];
396 -> 404[label="",style="dashed", color="red", weight=0];
396[label="primCmpInt (Neg (Succ vx150)) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];396 -> 406[label="",style="dashed", color="magenta", weight=3];
397 -> 410[label="",style="dashed", color="red", weight=0];
397[label="primCmpInt (Neg Zero) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];397 -> 411[label="",style="dashed", color="magenta", weight=3];
398 -> 413[label="",style="dashed", color="red", weight=0];
398[label="primCmpInt (Neg Zero) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];398 -> 414[label="",style="dashed", color="magenta", weight=3];
399 -> 413[label="",style="dashed", color="red", weight=0];
399[label="primCmpInt (Neg Zero) (Neg (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];399 -> 415[label="",style="dashed", color="magenta", weight=3];
400 -> 410[label="",style="dashed", color="red", weight=0];
400[label="primCmpInt (Neg Zero) (Pos (primMulNat vx400 vx310)) == LT",fontsize=16,color="magenta"];400 -> 412[label="",style="dashed", color="magenta", weight=3];
368[label="Succ (Succ (primPlusNat vx140 vx4100))",fontsize=16,color="green",shape="box"];368 -> 416[label="",style="dashed", color="green", weight=3];
369[label="Succ vx4100",fontsize=16,color="green",shape="box"];373 -> 268[label="",style="dashed", color="red", weight=0];
373[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];373 -> 417[label="",style="dashed", color="magenta", weight=3];
373 -> 418[label="",style="dashed", color="magenta", weight=3];
372[label="primCmpInt (Pos (Succ vx100)) (Pos vx16) == LT",fontsize=16,color="black",shape="triangle"];372 -> 419[label="",style="solid", color="black", weight=3];
380 -> 268[label="",style="dashed", color="red", weight=0];
380[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];380 -> 420[label="",style="dashed", color="magenta", weight=3];
380 -> 421[label="",style="dashed", color="magenta", weight=3];
379[label="primCmpInt (Pos (Succ vx100)) (Neg vx17) == LT",fontsize=16,color="black",shape="triangle"];379 -> 422[label="",style="solid", color="black", weight=3];
381 -> 268[label="",style="dashed", color="red", weight=0];
381[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];381 -> 423[label="",style="dashed", color="magenta", weight=3];
381 -> 424[label="",style="dashed", color="magenta", weight=3];
374 -> 268[label="",style="dashed", color="red", weight=0];
374[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];374 -> 425[label="",style="dashed", color="magenta", weight=3];
374 -> 426[label="",style="dashed", color="magenta", weight=3];
391 -> 268[label="",style="dashed", color="red", weight=0];
391[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];391 -> 427[label="",style="dashed", color="magenta", weight=3];
391 -> 428[label="",style="dashed", color="magenta", weight=3];
390[label="primCmpInt (Pos Zero) (Pos vx18) == LT",fontsize=16,color="burlywood",shape="triangle"];555[label="vx18/Succ vx180",fontsize=10,color="white",style="solid",shape="box"];390 -> 555[label="",style="solid", color="burlywood", weight=9];
555 -> 429[label="",style="solid", color="burlywood", weight=3];
556[label="vx18/Zero",fontsize=10,color="white",style="solid",shape="box"];390 -> 556[label="",style="solid", color="burlywood", weight=9];
556 -> 430[label="",style="solid", color="burlywood", weight=3];
402 -> 268[label="",style="dashed", color="red", weight=0];
402[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];402 -> 431[label="",style="dashed", color="magenta", weight=3];
402 -> 432[label="",style="dashed", color="magenta", weight=3];
401[label="primCmpInt (Pos Zero) (Neg vx19) == LT",fontsize=16,color="burlywood",shape="triangle"];557[label="vx19/Succ vx190",fontsize=10,color="white",style="solid",shape="box"];401 -> 557[label="",style="solid", color="burlywood", weight=9];
557 -> 433[label="",style="solid", color="burlywood", weight=3];
558[label="vx19/Zero",fontsize=10,color="white",style="solid",shape="box"];401 -> 558[label="",style="solid", color="burlywood", weight=9];
558 -> 434[label="",style="solid", color="burlywood", weight=3];
403 -> 268[label="",style="dashed", color="red", weight=0];
403[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];403 -> 435[label="",style="dashed", color="magenta", weight=3];
403 -> 436[label="",style="dashed", color="magenta", weight=3];
392 -> 268[label="",style="dashed", color="red", weight=0];
392[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];392 -> 437[label="",style="dashed", color="magenta", weight=3];
392 -> 438[label="",style="dashed", color="magenta", weight=3];
405 -> 268[label="",style="dashed", color="red", weight=0];
405[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];405 -> 439[label="",style="dashed", color="magenta", weight=3];
405 -> 440[label="",style="dashed", color="magenta", weight=3];
404[label="primCmpInt (Neg (Succ vx150)) (Pos vx20) == LT",fontsize=16,color="black",shape="triangle"];404 -> 441[label="",style="solid", color="black", weight=3];
408 -> 268[label="",style="dashed", color="red", weight=0];
408[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];408 -> 442[label="",style="dashed", color="magenta", weight=3];
408 -> 443[label="",style="dashed", color="magenta", weight=3];
407[label="primCmpInt (Neg (Succ vx150)) (Neg vx21) == LT",fontsize=16,color="black",shape="triangle"];407 -> 444[label="",style="solid", color="black", weight=3];
409 -> 268[label="",style="dashed", color="red", weight=0];
409[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];409 -> 445[label="",style="dashed", color="magenta", weight=3];
409 -> 446[label="",style="dashed", color="magenta", weight=3];
406 -> 268[label="",style="dashed", color="red", weight=0];
406[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];406 -> 447[label="",style="dashed", color="magenta", weight=3];
406 -> 448[label="",style="dashed", color="magenta", weight=3];
411 -> 268[label="",style="dashed", color="red", weight=0];
411[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];411 -> 449[label="",style="dashed", color="magenta", weight=3];
411 -> 450[label="",style="dashed", color="magenta", weight=3];
410[label="primCmpInt (Neg Zero) (Pos vx22) == LT",fontsize=16,color="burlywood",shape="triangle"];559[label="vx22/Succ vx220",fontsize=10,color="white",style="solid",shape="box"];410 -> 559[label="",style="solid", color="burlywood", weight=9];
559 -> 451[label="",style="solid", color="burlywood", weight=3];
560[label="vx22/Zero",fontsize=10,color="white",style="solid",shape="box"];410 -> 560[label="",style="solid", color="burlywood", weight=9];
560 -> 452[label="",style="solid", color="burlywood", weight=3];
414 -> 268[label="",style="dashed", color="red", weight=0];
414[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];414 -> 453[label="",style="dashed", color="magenta", weight=3];
414 -> 454[label="",style="dashed", color="magenta", weight=3];
413[label="primCmpInt (Neg Zero) (Neg vx23) == LT",fontsize=16,color="burlywood",shape="triangle"];561[label="vx23/Succ vx230",fontsize=10,color="white",style="solid",shape="box"];413 -> 561[label="",style="solid", color="burlywood", weight=9];
561 -> 455[label="",style="solid", color="burlywood", weight=3];
562[label="vx23/Zero",fontsize=10,color="white",style="solid",shape="box"];413 -> 562[label="",style="solid", color="burlywood", weight=9];
562 -> 456[label="",style="solid", color="burlywood", weight=3];
415 -> 268[label="",style="dashed", color="red", weight=0];
415[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];415 -> 457[label="",style="dashed", color="magenta", weight=3];
415 -> 458[label="",style="dashed", color="magenta", weight=3];
412 -> 268[label="",style="dashed", color="red", weight=0];
412[label="primMulNat vx400 vx310",fontsize=16,color="magenta"];412 -> 459[label="",style="dashed", color="magenta", weight=3];
412 -> 460[label="",style="dashed", color="magenta", weight=3];
416[label="primPlusNat vx140 vx4100",fontsize=16,color="burlywood",shape="triangle"];563[label="vx140/Succ vx1400",fontsize=10,color="white",style="solid",shape="box"];416 -> 563[label="",style="solid", color="burlywood", weight=9];
563 -> 461[label="",style="solid", color="burlywood", weight=3];
564[label="vx140/Zero",fontsize=10,color="white",style="solid",shape="box"];416 -> 564[label="",style="solid", color="burlywood", weight=9];
564 -> 462[label="",style="solid", color="burlywood", weight=3];
417[label="vx400",fontsize=16,color="green",shape="box"];418[label="vx310",fontsize=16,color="green",shape="box"];419[label="primCmpNat (Succ vx100) vx16 == LT",fontsize=16,color="burlywood",shape="triangle"];565[label="vx16/Succ vx160",fontsize=10,color="white",style="solid",shape="box"];419 -> 565[label="",style="solid", color="burlywood", weight=9];
565 -> 463[label="",style="solid", color="burlywood", weight=3];
566[label="vx16/Zero",fontsize=10,color="white",style="solid",shape="box"];419 -> 566[label="",style="solid", color="burlywood", weight=9];
566 -> 464[label="",style="solid", color="burlywood", weight=3];
420[label="vx400",fontsize=16,color="green",shape="box"];421[label="vx310",fontsize=16,color="green",shape="box"];422[label="GT == LT",fontsize=16,color="black",shape="triangle"];422 -> 465[label="",style="solid", color="black", weight=3];
423[label="vx400",fontsize=16,color="green",shape="box"];424[label="vx310",fontsize=16,color="green",shape="box"];425[label="vx400",fontsize=16,color="green",shape="box"];426[label="vx310",fontsize=16,color="green",shape="box"];427[label="vx400",fontsize=16,color="green",shape="box"];428[label="vx310",fontsize=16,color="green",shape="box"];429[label="primCmpInt (Pos Zero) (Pos (Succ vx180)) == LT",fontsize=16,color="black",shape="box"];429 -> 466[label="",style="solid", color="black", weight=3];
430[label="primCmpInt (Pos Zero) (Pos Zero) == LT",fontsize=16,color="black",shape="box"];430 -> 467[label="",style="solid", color="black", weight=3];
431[label="vx400",fontsize=16,color="green",shape="box"];432[label="vx310",fontsize=16,color="green",shape="box"];433[label="primCmpInt (Pos Zero) (Neg (Succ vx190)) == LT",fontsize=16,color="black",shape="box"];433 -> 468[label="",style="solid", color="black", weight=3];
434[label="primCmpInt (Pos Zero) (Neg Zero) == LT",fontsize=16,color="black",shape="box"];434 -> 469[label="",style="solid", color="black", weight=3];
435[label="vx400",fontsize=16,color="green",shape="box"];436[label="vx310",fontsize=16,color="green",shape="box"];437[label="vx400",fontsize=16,color="green",shape="box"];438[label="vx310",fontsize=16,color="green",shape="box"];439[label="vx400",fontsize=16,color="green",shape="box"];440[label="vx310",fontsize=16,color="green",shape="box"];441[label="LT == LT",fontsize=16,color="black",shape="triangle"];441 -> 470[label="",style="solid", color="black", weight=3];
442[label="vx400",fontsize=16,color="green",shape="box"];443[label="vx310",fontsize=16,color="green",shape="box"];444[label="primCmpNat vx21 (Succ vx150) == LT",fontsize=16,color="burlywood",shape="triangle"];567[label="vx21/Succ vx210",fontsize=10,color="white",style="solid",shape="box"];444 -> 567[label="",style="solid", color="burlywood", weight=9];
567 -> 471[label="",style="solid", color="burlywood", weight=3];
568[label="vx21/Zero",fontsize=10,color="white",style="solid",shape="box"];444 -> 568[label="",style="solid", color="burlywood", weight=9];
568 -> 472[label="",style="solid", color="burlywood", weight=3];
445[label="vx400",fontsize=16,color="green",shape="box"];446[label="vx310",fontsize=16,color="green",shape="box"];447[label="vx400",fontsize=16,color="green",shape="box"];448[label="vx310",fontsize=16,color="green",shape="box"];449[label="vx400",fontsize=16,color="green",shape="box"];450[label="vx310",fontsize=16,color="green",shape="box"];451[label="primCmpInt (Neg Zero) (Pos (Succ vx220)) == LT",fontsize=16,color="black",shape="box"];451 -> 473[label="",style="solid", color="black", weight=3];
452[label="primCmpInt (Neg Zero) (Pos Zero) == LT",fontsize=16,color="black",shape="box"];452 -> 474[label="",style="solid", color="black", weight=3];
453[label="vx400",fontsize=16,color="green",shape="box"];454[label="vx310",fontsize=16,color="green",shape="box"];455[label="primCmpInt (Neg Zero) (Neg (Succ vx230)) == LT",fontsize=16,color="black",shape="box"];455 -> 475[label="",style="solid", color="black", weight=3];
456[label="primCmpInt (Neg Zero) (Neg Zero) == LT",fontsize=16,color="black",shape="box"];456 -> 476[label="",style="solid", color="black", weight=3];
457[label="vx400",fontsize=16,color="green",shape="box"];458[label="vx310",fontsize=16,color="green",shape="box"];459[label="vx400",fontsize=16,color="green",shape="box"];460[label="vx310",fontsize=16,color="green",shape="box"];461[label="primPlusNat (Succ vx1400) vx4100",fontsize=16,color="burlywood",shape="box"];569[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];461 -> 569[label="",style="solid", color="burlywood", weight=9];
569 -> 477[label="",style="solid", color="burlywood", weight=3];
570[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];461 -> 570[label="",style="solid", color="burlywood", weight=9];
570 -> 478[label="",style="solid", color="burlywood", weight=3];
462[label="primPlusNat Zero vx4100",fontsize=16,color="burlywood",shape="box"];571[label="vx4100/Succ vx41000",fontsize=10,color="white",style="solid",shape="box"];462 -> 571[label="",style="solid", color="burlywood", weight=9];
571 -> 479[label="",style="solid", color="burlywood", weight=3];
572[label="vx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];462 -> 572[label="",style="solid", color="burlywood", weight=9];
572 -> 480[label="",style="solid", color="burlywood", weight=3];
463[label="primCmpNat (Succ vx100) (Succ vx160) == LT",fontsize=16,color="black",shape="box"];463 -> 481[label="",style="solid", color="black", weight=3];
464[label="primCmpNat (Succ vx100) Zero == LT",fontsize=16,color="black",shape="box"];464 -> 482[label="",style="solid", color="black", weight=3];
465[label="False",fontsize=16,color="green",shape="box"];466 -> 444[label="",style="dashed", color="red", weight=0];
466[label="primCmpNat Zero (Succ vx180) == LT",fontsize=16,color="magenta"];466 -> 483[label="",style="dashed", color="magenta", weight=3];
466 -> 484[label="",style="dashed", color="magenta", weight=3];
467[label="EQ == LT",fontsize=16,color="black",shape="triangle"];467 -> 485[label="",style="solid", color="black", weight=3];
468 -> 422[label="",style="dashed", color="red", weight=0];
468[label="GT == LT",fontsize=16,color="magenta"];469 -> 467[label="",style="dashed", color="red", weight=0];
469[label="EQ == LT",fontsize=16,color="magenta"];470[label="True",fontsize=16,color="green",shape="box"];471[label="primCmpNat (Succ vx210) (Succ vx150) == LT",fontsize=16,color="black",shape="box"];471 -> 486[label="",style="solid", color="black", weight=3];
472[label="primCmpNat Zero (Succ vx150) == LT",fontsize=16,color="black",shape="box"];472 -> 487[label="",style="solid", color="black", weight=3];
473 -> 441[label="",style="dashed", color="red", weight=0];
473[label="LT == LT",fontsize=16,color="magenta"];474 -> 467[label="",style="dashed", color="red", weight=0];
474[label="EQ == LT",fontsize=16,color="magenta"];475 -> 419[label="",style="dashed", color="red", weight=0];
475[label="primCmpNat (Succ vx230) Zero == LT",fontsize=16,color="magenta"];475 -> 488[label="",style="dashed", color="magenta", weight=3];
475 -> 489[label="",style="dashed", color="magenta", weight=3];
476 -> 467[label="",style="dashed", color="red", weight=0];
476[label="EQ == LT",fontsize=16,color="magenta"];477[label="primPlusNat (Succ vx1400) (Succ vx41000)",fontsize=16,color="black",shape="box"];477 -> 490[label="",style="solid", color="black", weight=3];
478[label="primPlusNat (Succ vx1400) Zero",fontsize=16,color="black",shape="box"];478 -> 491[label="",style="solid", color="black", weight=3];
479[label="primPlusNat Zero (Succ vx41000)",fontsize=16,color="black",shape="box"];479 -> 492[label="",style="solid", color="black", weight=3];
480[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];480 -> 493[label="",style="solid", color="black", weight=3];
481[label="primCmpNat vx100 vx160 == LT",fontsize=16,color="burlywood",shape="triangle"];573[label="vx100/Succ vx1000",fontsize=10,color="white",style="solid",shape="box"];481 -> 573[label="",style="solid", color="burlywood", weight=9];
573 -> 494[label="",style="solid", color="burlywood", weight=3];
574[label="vx100/Zero",fontsize=10,color="white",style="solid",shape="box"];481 -> 574[label="",style="solid", color="burlywood", weight=9];
574 -> 495[label="",style="solid", color="burlywood", weight=3];
482 -> 422[label="",style="dashed", color="red", weight=0];
482[label="GT == LT",fontsize=16,color="magenta"];483[label="vx180",fontsize=16,color="green",shape="box"];484[label="Zero",fontsize=16,color="green",shape="box"];485[label="False",fontsize=16,color="green",shape="box"];486 -> 481[label="",style="dashed", color="red", weight=0];
486[label="primCmpNat vx210 vx150 == LT",fontsize=16,color="magenta"];486 -> 496[label="",style="dashed", color="magenta", weight=3];
486 -> 497[label="",style="dashed", color="magenta", weight=3];
487 -> 441[label="",style="dashed", color="red", weight=0];
487[label="LT == LT",fontsize=16,color="magenta"];488[label="Zero",fontsize=16,color="green",shape="box"];489[label="vx230",fontsize=16,color="green",shape="box"];490[label="Succ (Succ (primPlusNat vx1400 vx41000))",fontsize=16,color="green",shape="box"];490 -> 498[label="",style="dashed", color="green", weight=3];
491[label="Succ vx1400",fontsize=16,color="green",shape="box"];492[label="Succ vx41000",fontsize=16,color="green",shape="box"];493[label="Zero",fontsize=16,color="green",shape="box"];494[label="primCmpNat (Succ vx1000) vx160 == LT",fontsize=16,color="burlywood",shape="box"];575[label="vx160/Succ vx1600",fontsize=10,color="white",style="solid",shape="box"];494 -> 575[label="",style="solid", color="burlywood", weight=9];
575 -> 499[label="",style="solid", color="burlywood", weight=3];
576[label="vx160/Zero",fontsize=10,color="white",style="solid",shape="box"];494 -> 576[label="",style="solid", color="burlywood", weight=9];
576 -> 500[label="",style="solid", color="burlywood", weight=3];
495[label="primCmpNat Zero vx160 == LT",fontsize=16,color="burlywood",shape="box"];577[label="vx160/Succ vx1600",fontsize=10,color="white",style="solid",shape="box"];495 -> 577[label="",style="solid", color="burlywood", weight=9];
577 -> 501[label="",style="solid", color="burlywood", weight=3];
578[label="vx160/Zero",fontsize=10,color="white",style="solid",shape="box"];495 -> 578[label="",style="solid", color="burlywood", weight=9];
578 -> 502[label="",style="solid", color="burlywood", weight=3];
496[label="vx150",fontsize=16,color="green",shape="box"];497[label="vx210",fontsize=16,color="green",shape="box"];498 -> 416[label="",style="dashed", color="red", weight=0];
498[label="primPlusNat vx1400 vx41000",fontsize=16,color="magenta"];498 -> 503[label="",style="dashed", color="magenta", weight=3];
498 -> 504[label="",style="dashed", color="magenta", weight=3];
499[label="primCmpNat (Succ vx1000) (Succ vx1600) == LT",fontsize=16,color="black",shape="box"];499 -> 505[label="",style="solid", color="black", weight=3];
500[label="primCmpNat (Succ vx1000) Zero == LT",fontsize=16,color="black",shape="box"];500 -> 506[label="",style="solid", color="black", weight=3];
501[label="primCmpNat Zero (Succ vx1600) == LT",fontsize=16,color="black",shape="box"];501 -> 507[label="",style="solid", color="black", weight=3];
502[label="primCmpNat Zero Zero == LT",fontsize=16,color="black",shape="box"];502 -> 508[label="",style="solid", color="black", weight=3];
503[label="vx1400",fontsize=16,color="green",shape="box"];504[label="vx41000",fontsize=16,color="green",shape="box"];505 -> 481[label="",style="dashed", color="red", weight=0];
505[label="primCmpNat vx1000 vx1600 == LT",fontsize=16,color="magenta"];505 -> 509[label="",style="dashed", color="magenta", weight=3];
505 -> 510[label="",style="dashed", color="magenta", weight=3];
506 -> 422[label="",style="dashed", color="red", weight=0];
506[label="GT == LT",fontsize=16,color="magenta"];507 -> 441[label="",style="dashed", color="red", weight=0];
507[label="LT == LT",fontsize=16,color="magenta"];508 -> 467[label="",style="dashed", color="red", weight=0];
508[label="EQ == LT",fontsize=16,color="magenta"];509[label="vx1600",fontsize=16,color="green",shape="box"];510[label="vx1000",fontsize=16,color="green",shape="box"];}

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(6)
Complex Obligation (AND)

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(7)
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.
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(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_primMulNat(Succ(vx3000), Succ(vx4100)) -> new_primMulNat(vx3000, Succ(vx4100))
The graph contains the following edges 1 > 1, 2 >= 2


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(9)
YES

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

   new_esEs(Succ(vx1000), Succ(vx1600)) -> new_esEs(vx1000, vx1600)

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_esEs(Succ(vx1000), Succ(vx1600)) -> new_esEs(vx1000, vx1600)
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(vx1400), Succ(vx41000)) -> new_primPlusNat(vx1400, 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(vx1400), Succ(vx41000)) -> new_primPlusNat(vx1400, vx41000)
The graph contains the following edges 1 > 1, 2 > 2


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(15)
YES