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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 20 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
    (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES


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

(0)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
isPrefixOf [] _ = True;
isPrefixOf _ [] = False;
isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;

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

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

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

(2)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
isPrefixOf [] wu = True;
isPrefixOf wv [] = False;
isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;

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

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

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

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

(4)
Obligation:
mainModule Main 
module Maybe where {
import qualified List;
import qualified Main;
import qualified Prelude;
}
module List where {
import qualified Main;
import qualified Maybe;
import qualified Prelude;
isPrefixOf :: Eq a => [a]  ->  [a]  ->  Bool;
isPrefixOf [] wu = True;
isPrefixOf wv [] = False;
isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys;

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

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="List.isPrefixOf",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="List.isPrefixOf ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="List.isPrefixOf ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];520[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 520[label="",style="solid", color="burlywood", weight=9];
520 -> 5[label="",style="solid", color="burlywood", weight=3];
521[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 521[label="",style="solid", color="burlywood", weight=9];
521 -> 6[label="",style="solid", color="burlywood", weight=3];
5[label="List.isPrefixOf (ww30 : ww31) ww4",fontsize=16,color="burlywood",shape="box"];522[label="ww4/ww40 : ww41",fontsize=10,color="white",style="solid",shape="box"];5 -> 522[label="",style="solid", color="burlywood", weight=9];
522 -> 7[label="",style="solid", color="burlywood", weight=3];
523[label="ww4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 523[label="",style="solid", color="burlywood", weight=9];
523 -> 8[label="",style="solid", color="burlywood", weight=3];
6[label="List.isPrefixOf [] ww4",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3];
7[label="List.isPrefixOf (ww30 : ww31) (ww40 : ww41)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
8[label="List.isPrefixOf (ww30 : ww31) []",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9[label="True",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="red", weight=0];
10[label="ww30 == ww40 && List.isPrefixOf ww31 ww41",fontsize=16,color="magenta"];10 -> 13[label="",style="dashed", color="magenta", weight=3];
11[label="False",fontsize=16,color="green",shape="box"];13 -> 4[label="",style="dashed", color="red", weight=0];
13[label="List.isPrefixOf ww31 ww41",fontsize=16,color="magenta"];13 -> 14[label="",style="dashed", color="magenta", weight=3];
13 -> 15[label="",style="dashed", color="magenta", weight=3];
12[label="ww30 == ww40 && ww5",fontsize=16,color="black",shape="triangle"];12 -> 16[label="",style="solid", color="black", weight=3];
14[label="ww31",fontsize=16,color="green",shape="box"];15[label="ww41",fontsize=16,color="green",shape="box"];16[label="primEqFloat ww30 ww40 && ww5",fontsize=16,color="burlywood",shape="box"];524[label="ww30/Float ww300 ww301",fontsize=10,color="white",style="solid",shape="box"];16 -> 524[label="",style="solid", color="burlywood", weight=9];
524 -> 17[label="",style="solid", color="burlywood", weight=3];
17[label="primEqFloat (Float ww300 ww301) ww40 && ww5",fontsize=16,color="burlywood",shape="box"];525[label="ww40/Float ww400 ww401",fontsize=10,color="white",style="solid",shape="box"];17 -> 525[label="",style="solid", color="burlywood", weight=9];
525 -> 18[label="",style="solid", color="burlywood", weight=3];
18[label="primEqFloat (Float ww300 ww301) (Float ww400 ww401) && ww5",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
19[label="ww300 * ww401 == ww301 * ww400 && ww5",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
20[label="primEqInt (ww300 * ww401) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
21[label="primEqInt (primMulInt ww300 ww401) (ww301 * ww400) && ww5",fontsize=16,color="burlywood",shape="box"];526[label="ww300/Pos ww3000",fontsize=10,color="white",style="solid",shape="box"];21 -> 526[label="",style="solid", color="burlywood", weight=9];
526 -> 22[label="",style="solid", color="burlywood", weight=3];
527[label="ww300/Neg ww3000",fontsize=10,color="white",style="solid",shape="box"];21 -> 527[label="",style="solid", color="burlywood", weight=9];
527 -> 23[label="",style="solid", color="burlywood", weight=3];
22[label="primEqInt (primMulInt (Pos ww3000) ww401) (ww301 * ww400) && ww5",fontsize=16,color="burlywood",shape="box"];528[label="ww401/Pos ww4010",fontsize=10,color="white",style="solid",shape="box"];22 -> 528[label="",style="solid", color="burlywood", weight=9];
528 -> 24[label="",style="solid", color="burlywood", weight=3];
529[label="ww401/Neg ww4010",fontsize=10,color="white",style="solid",shape="box"];22 -> 529[label="",style="solid", color="burlywood", weight=9];
529 -> 25[label="",style="solid", color="burlywood", weight=3];
23[label="primEqInt (primMulInt (Neg ww3000) ww401) (ww301 * ww400) && ww5",fontsize=16,color="burlywood",shape="box"];530[label="ww401/Pos ww4010",fontsize=10,color="white",style="solid",shape="box"];23 -> 530[label="",style="solid", color="burlywood", weight=9];
530 -> 26[label="",style="solid", color="burlywood", weight=3];
531[label="ww401/Neg ww4010",fontsize=10,color="white",style="solid",shape="box"];23 -> 531[label="",style="solid", color="burlywood", weight=9];
531 -> 27[label="",style="solid", color="burlywood", weight=3];
24[label="primEqInt (primMulInt (Pos ww3000) (Pos ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="primEqInt (primMulInt (Pos ww3000) (Neg ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="primEqInt (primMulInt (Neg ww3000) (Pos ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
27[label="primEqInt (primMulInt (Neg ww3000) (Neg ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28 -> 283[label="",style="dashed", color="red", weight=0];
28[label="primEqInt (Pos (primMulNat ww3000 ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="magenta"];28 -> 284[label="",style="dashed", color="magenta", weight=3];
29 -> 359[label="",style="dashed", color="red", weight=0];
29[label="primEqInt (Neg (primMulNat ww3000 ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="magenta"];29 -> 360[label="",style="dashed", color="magenta", weight=3];
30 -> 359[label="",style="dashed", color="red", weight=0];
30[label="primEqInt (Neg (primMulNat ww3000 ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="magenta"];30 -> 361[label="",style="dashed", color="magenta", weight=3];
31 -> 283[label="",style="dashed", color="red", weight=0];
31[label="primEqInt (Pos (primMulNat ww3000 ww4010)) (ww301 * ww400) && ww5",fontsize=16,color="magenta"];31 -> 285[label="",style="dashed", color="magenta", weight=3];
284[label="primMulNat ww3000 ww4010",fontsize=16,color="burlywood",shape="triangle"];532[label="ww3000/Succ ww30000",fontsize=10,color="white",style="solid",shape="box"];284 -> 532[label="",style="solid", color="burlywood", weight=9];
532 -> 296[label="",style="solid", color="burlywood", weight=3];
533[label="ww3000/Zero",fontsize=10,color="white",style="solid",shape="box"];284 -> 533[label="",style="solid", color="burlywood", weight=9];
533 -> 297[label="",style="solid", color="burlywood", weight=3];
283[label="primEqInt (Pos ww11) (ww301 * ww400) && ww5",fontsize=16,color="burlywood",shape="triangle"];534[label="ww11/Succ ww110",fontsize=10,color="white",style="solid",shape="box"];283 -> 534[label="",style="solid", color="burlywood", weight=9];
534 -> 298[label="",style="solid", color="burlywood", weight=3];
535[label="ww11/Zero",fontsize=10,color="white",style="solid",shape="box"];283 -> 535[label="",style="solid", color="burlywood", weight=9];
535 -> 299[label="",style="solid", color="burlywood", weight=3];
360 -> 284[label="",style="dashed", color="red", weight=0];
360[label="primMulNat ww3000 ww4010",fontsize=16,color="magenta"];360 -> 372[label="",style="dashed", color="magenta", weight=3];
359[label="primEqInt (Neg ww16) (ww301 * ww400) && ww5",fontsize=16,color="burlywood",shape="triangle"];536[label="ww16/Succ ww160",fontsize=10,color="white",style="solid",shape="box"];359 -> 536[label="",style="solid", color="burlywood", weight=9];
536 -> 373[label="",style="solid", color="burlywood", weight=3];
537[label="ww16/Zero",fontsize=10,color="white",style="solid",shape="box"];359 -> 537[label="",style="solid", color="burlywood", weight=9];
537 -> 374[label="",style="solid", color="burlywood", weight=3];
361 -> 284[label="",style="dashed", color="red", weight=0];
361[label="primMulNat ww3000 ww4010",fontsize=16,color="magenta"];361 -> 375[label="",style="dashed", color="magenta", weight=3];
285 -> 284[label="",style="dashed", color="red", weight=0];
285[label="primMulNat ww3000 ww4010",fontsize=16,color="magenta"];285 -> 300[label="",style="dashed", color="magenta", weight=3];
285 -> 301[label="",style="dashed", color="magenta", weight=3];
296[label="primMulNat (Succ ww30000) ww4010",fontsize=16,color="burlywood",shape="box"];538[label="ww4010/Succ ww40100",fontsize=10,color="white",style="solid",shape="box"];296 -> 538[label="",style="solid", color="burlywood", weight=9];
538 -> 316[label="",style="solid", color="burlywood", weight=3];
539[label="ww4010/Zero",fontsize=10,color="white",style="solid",shape="box"];296 -> 539[label="",style="solid", color="burlywood", weight=9];
539 -> 317[label="",style="solid", color="burlywood", weight=3];
297[label="primMulNat Zero ww4010",fontsize=16,color="burlywood",shape="box"];540[label="ww4010/Succ ww40100",fontsize=10,color="white",style="solid",shape="box"];297 -> 540[label="",style="solid", color="burlywood", weight=9];
540 -> 318[label="",style="solid", color="burlywood", weight=3];
541[label="ww4010/Zero",fontsize=10,color="white",style="solid",shape="box"];297 -> 541[label="",style="solid", color="burlywood", weight=9];
541 -> 319[label="",style="solid", color="burlywood", weight=3];
298[label="primEqInt (Pos (Succ ww110)) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];298 -> 320[label="",style="solid", color="black", weight=3];
299[label="primEqInt (Pos Zero) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];299 -> 321[label="",style="solid", color="black", weight=3];
372[label="ww4010",fontsize=16,color="green",shape="box"];373[label="primEqInt (Neg (Succ ww160)) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];373 -> 386[label="",style="solid", color="black", weight=3];
374[label="primEqInt (Neg Zero) (ww301 * ww400) && ww5",fontsize=16,color="black",shape="box"];374 -> 387[label="",style="solid", color="black", weight=3];
375[label="ww3000",fontsize=16,color="green",shape="box"];300[label="ww4010",fontsize=16,color="green",shape="box"];301[label="ww3000",fontsize=16,color="green",shape="box"];316[label="primMulNat (Succ ww30000) (Succ ww40100)",fontsize=16,color="black",shape="box"];316 -> 332[label="",style="solid", color="black", weight=3];
317[label="primMulNat (Succ ww30000) Zero",fontsize=16,color="black",shape="box"];317 -> 333[label="",style="solid", color="black", weight=3];
318[label="primMulNat Zero (Succ ww40100)",fontsize=16,color="black",shape="box"];318 -> 334[label="",style="solid", color="black", weight=3];
319[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];319 -> 335[label="",style="solid", color="black", weight=3];
320[label="primEqInt (Pos (Succ ww110)) (primMulInt ww301 ww400) && ww5",fontsize=16,color="burlywood",shape="box"];542[label="ww301/Pos ww3010",fontsize=10,color="white",style="solid",shape="box"];320 -> 542[label="",style="solid", color="burlywood", weight=9];
542 -> 336[label="",style="solid", color="burlywood", weight=3];
543[label="ww301/Neg ww3010",fontsize=10,color="white",style="solid",shape="box"];320 -> 543[label="",style="solid", color="burlywood", weight=9];
543 -> 337[label="",style="solid", color="burlywood", weight=3];
321[label="primEqInt (Pos Zero) (primMulInt ww301 ww400) && ww5",fontsize=16,color="burlywood",shape="box"];544[label="ww301/Pos ww3010",fontsize=10,color="white",style="solid",shape="box"];321 -> 544[label="",style="solid", color="burlywood", weight=9];
544 -> 338[label="",style="solid", color="burlywood", weight=3];
545[label="ww301/Neg ww3010",fontsize=10,color="white",style="solid",shape="box"];321 -> 545[label="",style="solid", color="burlywood", weight=9];
545 -> 339[label="",style="solid", color="burlywood", weight=3];
386[label="primEqInt (Neg (Succ ww160)) (primMulInt ww301 ww400) && ww5",fontsize=16,color="burlywood",shape="box"];546[label="ww301/Pos ww3010",fontsize=10,color="white",style="solid",shape="box"];386 -> 546[label="",style="solid", color="burlywood", weight=9];
546 -> 391[label="",style="solid", color="burlywood", weight=3];
547[label="ww301/Neg ww3010",fontsize=10,color="white",style="solid",shape="box"];386 -> 547[label="",style="solid", color="burlywood", weight=9];
547 -> 392[label="",style="solid", color="burlywood", weight=3];
387[label="primEqInt (Neg Zero) (primMulInt ww301 ww400) && ww5",fontsize=16,color="burlywood",shape="box"];548[label="ww301/Pos ww3010",fontsize=10,color="white",style="solid",shape="box"];387 -> 548[label="",style="solid", color="burlywood", weight=9];
548 -> 393[label="",style="solid", color="burlywood", weight=3];
549[label="ww301/Neg ww3010",fontsize=10,color="white",style="solid",shape="box"];387 -> 549[label="",style="solid", color="burlywood", weight=9];
549 -> 394[label="",style="solid", color="burlywood", weight=3];
332 -> 345[label="",style="dashed", color="red", weight=0];
332[label="primPlusNat (primMulNat ww30000 (Succ ww40100)) (Succ ww40100)",fontsize=16,color="magenta"];332 -> 346[label="",style="dashed", color="magenta", weight=3];
333[label="Zero",fontsize=16,color="green",shape="box"];334[label="Zero",fontsize=16,color="green",shape="box"];335[label="Zero",fontsize=16,color="green",shape="box"];336[label="primEqInt (Pos (Succ ww110)) (primMulInt (Pos ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];550[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];336 -> 550[label="",style="solid", color="burlywood", weight=9];
550 -> 347[label="",style="solid", color="burlywood", weight=3];
551[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];336 -> 551[label="",style="solid", color="burlywood", weight=9];
551 -> 348[label="",style="solid", color="burlywood", weight=3];
337[label="primEqInt (Pos (Succ ww110)) (primMulInt (Neg ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];552[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];337 -> 552[label="",style="solid", color="burlywood", weight=9];
552 -> 349[label="",style="solid", color="burlywood", weight=3];
553[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];337 -> 553[label="",style="solid", color="burlywood", weight=9];
553 -> 350[label="",style="solid", color="burlywood", weight=3];
338[label="primEqInt (Pos Zero) (primMulInt (Pos ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];554[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];338 -> 554[label="",style="solid", color="burlywood", weight=9];
554 -> 351[label="",style="solid", color="burlywood", weight=3];
555[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];338 -> 555[label="",style="solid", color="burlywood", weight=9];
555 -> 352[label="",style="solid", color="burlywood", weight=3];
339[label="primEqInt (Pos Zero) (primMulInt (Neg ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];556[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];339 -> 556[label="",style="solid", color="burlywood", weight=9];
556 -> 353[label="",style="solid", color="burlywood", weight=3];
557[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];339 -> 557[label="",style="solid", color="burlywood", weight=9];
557 -> 354[label="",style="solid", color="burlywood", weight=3];
391[label="primEqInt (Neg (Succ ww160)) (primMulInt (Pos ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];558[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];391 -> 558[label="",style="solid", color="burlywood", weight=9];
558 -> 398[label="",style="solid", color="burlywood", weight=3];
559[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];391 -> 559[label="",style="solid", color="burlywood", weight=9];
559 -> 399[label="",style="solid", color="burlywood", weight=3];
392[label="primEqInt (Neg (Succ ww160)) (primMulInt (Neg ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];560[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];392 -> 560[label="",style="solid", color="burlywood", weight=9];
560 -> 400[label="",style="solid", color="burlywood", weight=3];
561[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];392 -> 561[label="",style="solid", color="burlywood", weight=9];
561 -> 401[label="",style="solid", color="burlywood", weight=3];
393[label="primEqInt (Neg Zero) (primMulInt (Pos ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];562[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];393 -> 562[label="",style="solid", color="burlywood", weight=9];
562 -> 402[label="",style="solid", color="burlywood", weight=3];
563[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];393 -> 563[label="",style="solid", color="burlywood", weight=9];
563 -> 403[label="",style="solid", color="burlywood", weight=3];
394[label="primEqInt (Neg Zero) (primMulInt (Neg ww3010) ww400) && ww5",fontsize=16,color="burlywood",shape="box"];564[label="ww400/Pos ww4000",fontsize=10,color="white",style="solid",shape="box"];394 -> 564[label="",style="solid", color="burlywood", weight=9];
564 -> 404[label="",style="solid", color="burlywood", weight=3];
565[label="ww400/Neg ww4000",fontsize=10,color="white",style="solid",shape="box"];394 -> 565[label="",style="solid", color="burlywood", weight=9];
565 -> 405[label="",style="solid", color="burlywood", weight=3];
346 -> 284[label="",style="dashed", color="red", weight=0];
346[label="primMulNat ww30000 (Succ ww40100)",fontsize=16,color="magenta"];346 -> 355[label="",style="dashed", color="magenta", weight=3];
346 -> 356[label="",style="dashed", color="magenta", weight=3];
345[label="primPlusNat ww15 (Succ ww40100)",fontsize=16,color="burlywood",shape="triangle"];566[label="ww15/Succ ww150",fontsize=10,color="white",style="solid",shape="box"];345 -> 566[label="",style="solid", color="burlywood", weight=9];
566 -> 357[label="",style="solid", color="burlywood", weight=3];
567[label="ww15/Zero",fontsize=10,color="white",style="solid",shape="box"];345 -> 567[label="",style="solid", color="burlywood", weight=9];
567 -> 358[label="",style="solid", color="burlywood", weight=3];
347[label="primEqInt (Pos (Succ ww110)) (primMulInt (Pos ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];347 -> 376[label="",style="solid", color="black", weight=3];
348[label="primEqInt (Pos (Succ ww110)) (primMulInt (Pos ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];348 -> 377[label="",style="solid", color="black", weight=3];
349[label="primEqInt (Pos (Succ ww110)) (primMulInt (Neg ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];349 -> 378[label="",style="solid", color="black", weight=3];
350[label="primEqInt (Pos (Succ ww110)) (primMulInt (Neg ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];350 -> 379[label="",style="solid", color="black", weight=3];
351[label="primEqInt (Pos Zero) (primMulInt (Pos ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];351 -> 380[label="",style="solid", color="black", weight=3];
352[label="primEqInt (Pos Zero) (primMulInt (Pos ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];352 -> 381[label="",style="solid", color="black", weight=3];
353[label="primEqInt (Pos Zero) (primMulInt (Neg ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];353 -> 382[label="",style="solid", color="black", weight=3];
354[label="primEqInt (Pos Zero) (primMulInt (Neg ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];354 -> 383[label="",style="solid", color="black", weight=3];
398[label="primEqInt (Neg (Succ ww160)) (primMulInt (Pos ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];398 -> 409[label="",style="solid", color="black", weight=3];
399[label="primEqInt (Neg (Succ ww160)) (primMulInt (Pos ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];399 -> 410[label="",style="solid", color="black", weight=3];
400[label="primEqInt (Neg (Succ ww160)) (primMulInt (Neg ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];400 -> 411[label="",style="solid", color="black", weight=3];
401[label="primEqInt (Neg (Succ ww160)) (primMulInt (Neg ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];401 -> 412[label="",style="solid", color="black", weight=3];
402[label="primEqInt (Neg Zero) (primMulInt (Pos ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];402 -> 413[label="",style="solid", color="black", weight=3];
403[label="primEqInt (Neg Zero) (primMulInt (Pos ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];403 -> 414[label="",style="solid", color="black", weight=3];
404[label="primEqInt (Neg Zero) (primMulInt (Neg ww3010) (Pos ww4000)) && ww5",fontsize=16,color="black",shape="box"];404 -> 415[label="",style="solid", color="black", weight=3];
405[label="primEqInt (Neg Zero) (primMulInt (Neg ww3010) (Neg ww4000)) && ww5",fontsize=16,color="black",shape="box"];405 -> 416[label="",style="solid", color="black", weight=3];
355[label="Succ ww40100",fontsize=16,color="green",shape="box"];356[label="ww30000",fontsize=16,color="green",shape="box"];357[label="primPlusNat (Succ ww150) (Succ ww40100)",fontsize=16,color="black",shape="box"];357 -> 384[label="",style="solid", color="black", weight=3];
358[label="primPlusNat Zero (Succ ww40100)",fontsize=16,color="black",shape="box"];358 -> 385[label="",style="solid", color="black", weight=3];
376 -> 388[label="",style="dashed", color="red", weight=0];
376[label="primEqInt (Pos (Succ ww110)) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];376 -> 389[label="",style="dashed", color="magenta", weight=3];
377 -> 395[label="",style="dashed", color="red", weight=0];
377[label="primEqInt (Pos (Succ ww110)) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];377 -> 396[label="",style="dashed", color="magenta", weight=3];
378 -> 395[label="",style="dashed", color="red", weight=0];
378[label="primEqInt (Pos (Succ ww110)) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];378 -> 397[label="",style="dashed", color="magenta", weight=3];
379 -> 388[label="",style="dashed", color="red", weight=0];
379[label="primEqInt (Pos (Succ ww110)) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];379 -> 390[label="",style="dashed", color="magenta", weight=3];
380 -> 406[label="",style="dashed", color="red", weight=0];
380[label="primEqInt (Pos Zero) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];380 -> 407[label="",style="dashed", color="magenta", weight=3];
381 -> 417[label="",style="dashed", color="red", weight=0];
381[label="primEqInt (Pos Zero) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];381 -> 418[label="",style="dashed", color="magenta", weight=3];
382 -> 417[label="",style="dashed", color="red", weight=0];
382[label="primEqInt (Pos Zero) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];382 -> 419[label="",style="dashed", color="magenta", weight=3];
383 -> 406[label="",style="dashed", color="red", weight=0];
383[label="primEqInt (Pos Zero) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];383 -> 408[label="",style="dashed", color="magenta", weight=3];
409 -> 420[label="",style="dashed", color="red", weight=0];
409[label="primEqInt (Neg (Succ ww160)) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];409 -> 421[label="",style="dashed", color="magenta", weight=3];
410 -> 423[label="",style="dashed", color="red", weight=0];
410[label="primEqInt (Neg (Succ ww160)) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];410 -> 424[label="",style="dashed", color="magenta", weight=3];
411 -> 423[label="",style="dashed", color="red", weight=0];
411[label="primEqInt (Neg (Succ ww160)) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];411 -> 425[label="",style="dashed", color="magenta", weight=3];
412 -> 420[label="",style="dashed", color="red", weight=0];
412[label="primEqInt (Neg (Succ ww160)) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];412 -> 422[label="",style="dashed", color="magenta", weight=3];
413 -> 426[label="",style="dashed", color="red", weight=0];
413[label="primEqInt (Neg Zero) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];413 -> 427[label="",style="dashed", color="magenta", weight=3];
414 -> 429[label="",style="dashed", color="red", weight=0];
414[label="primEqInt (Neg Zero) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];414 -> 430[label="",style="dashed", color="magenta", weight=3];
415 -> 429[label="",style="dashed", color="red", weight=0];
415[label="primEqInt (Neg Zero) (Neg (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];415 -> 431[label="",style="dashed", color="magenta", weight=3];
416 -> 426[label="",style="dashed", color="red", weight=0];
416[label="primEqInt (Neg Zero) (Pos (primMulNat ww3010 ww4000)) && ww5",fontsize=16,color="magenta"];416 -> 428[label="",style="dashed", color="magenta", weight=3];
384[label="Succ (Succ (primPlusNat ww150 ww40100))",fontsize=16,color="green",shape="box"];384 -> 432[label="",style="dashed", color="green", weight=3];
385[label="Succ ww40100",fontsize=16,color="green",shape="box"];389 -> 284[label="",style="dashed", color="red", weight=0];
389[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];389 -> 433[label="",style="dashed", color="magenta", weight=3];
389 -> 434[label="",style="dashed", color="magenta", weight=3];
388[label="primEqInt (Pos (Succ ww110)) (Pos ww17) && ww5",fontsize=16,color="burlywood",shape="triangle"];568[label="ww17/Succ ww170",fontsize=10,color="white",style="solid",shape="box"];388 -> 568[label="",style="solid", color="burlywood", weight=9];
568 -> 435[label="",style="solid", color="burlywood", weight=3];
569[label="ww17/Zero",fontsize=10,color="white",style="solid",shape="box"];388 -> 569[label="",style="solid", color="burlywood", weight=9];
569 -> 436[label="",style="solid", color="burlywood", weight=3];
396 -> 284[label="",style="dashed", color="red", weight=0];
396[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];396 -> 437[label="",style="dashed", color="magenta", weight=3];
396 -> 438[label="",style="dashed", color="magenta", weight=3];
395[label="primEqInt (Pos (Succ ww110)) (Neg ww18) && ww5",fontsize=16,color="black",shape="triangle"];395 -> 439[label="",style="solid", color="black", weight=3];
397 -> 284[label="",style="dashed", color="red", weight=0];
397[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];397 -> 440[label="",style="dashed", color="magenta", weight=3];
397 -> 441[label="",style="dashed", color="magenta", weight=3];
390 -> 284[label="",style="dashed", color="red", weight=0];
390[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];390 -> 442[label="",style="dashed", color="magenta", weight=3];
390 -> 443[label="",style="dashed", color="magenta", weight=3];
407 -> 284[label="",style="dashed", color="red", weight=0];
407[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];407 -> 444[label="",style="dashed", color="magenta", weight=3];
407 -> 445[label="",style="dashed", color="magenta", weight=3];
406[label="primEqInt (Pos Zero) (Pos ww19) && ww5",fontsize=16,color="burlywood",shape="triangle"];570[label="ww19/Succ ww190",fontsize=10,color="white",style="solid",shape="box"];406 -> 570[label="",style="solid", color="burlywood", weight=9];
570 -> 446[label="",style="solid", color="burlywood", weight=3];
571[label="ww19/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 571[label="",style="solid", color="burlywood", weight=9];
571 -> 447[label="",style="solid", color="burlywood", weight=3];
418 -> 284[label="",style="dashed", color="red", weight=0];
418[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];418 -> 448[label="",style="dashed", color="magenta", weight=3];
418 -> 449[label="",style="dashed", color="magenta", weight=3];
417[label="primEqInt (Pos Zero) (Neg ww20) && ww5",fontsize=16,color="burlywood",shape="triangle"];572[label="ww20/Succ ww200",fontsize=10,color="white",style="solid",shape="box"];417 -> 572[label="",style="solid", color="burlywood", weight=9];
572 -> 450[label="",style="solid", color="burlywood", weight=3];
573[label="ww20/Zero",fontsize=10,color="white",style="solid",shape="box"];417 -> 573[label="",style="solid", color="burlywood", weight=9];
573 -> 451[label="",style="solid", color="burlywood", weight=3];
419 -> 284[label="",style="dashed", color="red", weight=0];
419[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];419 -> 452[label="",style="dashed", color="magenta", weight=3];
419 -> 453[label="",style="dashed", color="magenta", weight=3];
408 -> 284[label="",style="dashed", color="red", weight=0];
408[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];408 -> 454[label="",style="dashed", color="magenta", weight=3];
408 -> 455[label="",style="dashed", color="magenta", weight=3];
421 -> 284[label="",style="dashed", color="red", weight=0];
421[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];421 -> 456[label="",style="dashed", color="magenta", weight=3];
421 -> 457[label="",style="dashed", color="magenta", weight=3];
420[label="primEqInt (Neg (Succ ww160)) (Pos ww21) && ww5",fontsize=16,color="black",shape="triangle"];420 -> 458[label="",style="solid", color="black", weight=3];
424 -> 284[label="",style="dashed", color="red", weight=0];
424[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];424 -> 459[label="",style="dashed", color="magenta", weight=3];
424 -> 460[label="",style="dashed", color="magenta", weight=3];
423[label="primEqInt (Neg (Succ ww160)) (Neg ww22) && ww5",fontsize=16,color="burlywood",shape="triangle"];574[label="ww22/Succ ww220",fontsize=10,color="white",style="solid",shape="box"];423 -> 574[label="",style="solid", color="burlywood", weight=9];
574 -> 461[label="",style="solid", color="burlywood", weight=3];
575[label="ww22/Zero",fontsize=10,color="white",style="solid",shape="box"];423 -> 575[label="",style="solid", color="burlywood", weight=9];
575 -> 462[label="",style="solid", color="burlywood", weight=3];
425 -> 284[label="",style="dashed", color="red", weight=0];
425[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];425 -> 463[label="",style="dashed", color="magenta", weight=3];
425 -> 464[label="",style="dashed", color="magenta", weight=3];
422 -> 284[label="",style="dashed", color="red", weight=0];
422[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];422 -> 465[label="",style="dashed", color="magenta", weight=3];
422 -> 466[label="",style="dashed", color="magenta", weight=3];
427 -> 284[label="",style="dashed", color="red", weight=0];
427[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];427 -> 467[label="",style="dashed", color="magenta", weight=3];
427 -> 468[label="",style="dashed", color="magenta", weight=3];
426[label="primEqInt (Neg Zero) (Pos ww23) && ww5",fontsize=16,color="burlywood",shape="triangle"];576[label="ww23/Succ ww230",fontsize=10,color="white",style="solid",shape="box"];426 -> 576[label="",style="solid", color="burlywood", weight=9];
576 -> 469[label="",style="solid", color="burlywood", weight=3];
577[label="ww23/Zero",fontsize=10,color="white",style="solid",shape="box"];426 -> 577[label="",style="solid", color="burlywood", weight=9];
577 -> 470[label="",style="solid", color="burlywood", weight=3];
430 -> 284[label="",style="dashed", color="red", weight=0];
430[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];430 -> 471[label="",style="dashed", color="magenta", weight=3];
430 -> 472[label="",style="dashed", color="magenta", weight=3];
429[label="primEqInt (Neg Zero) (Neg ww24) && ww5",fontsize=16,color="burlywood",shape="triangle"];578[label="ww24/Succ ww240",fontsize=10,color="white",style="solid",shape="box"];429 -> 578[label="",style="solid", color="burlywood", weight=9];
578 -> 473[label="",style="solid", color="burlywood", weight=3];
579[label="ww24/Zero",fontsize=10,color="white",style="solid",shape="box"];429 -> 579[label="",style="solid", color="burlywood", weight=9];
579 -> 474[label="",style="solid", color="burlywood", weight=3];
431 -> 284[label="",style="dashed", color="red", weight=0];
431[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];431 -> 475[label="",style="dashed", color="magenta", weight=3];
431 -> 476[label="",style="dashed", color="magenta", weight=3];
428 -> 284[label="",style="dashed", color="red", weight=0];
428[label="primMulNat ww3010 ww4000",fontsize=16,color="magenta"];428 -> 477[label="",style="dashed", color="magenta", weight=3];
428 -> 478[label="",style="dashed", color="magenta", weight=3];
432[label="primPlusNat ww150 ww40100",fontsize=16,color="burlywood",shape="triangle"];580[label="ww150/Succ ww1500",fontsize=10,color="white",style="solid",shape="box"];432 -> 580[label="",style="solid", color="burlywood", weight=9];
580 -> 479[label="",style="solid", color="burlywood", weight=3];
581[label="ww150/Zero",fontsize=10,color="white",style="solid",shape="box"];432 -> 581[label="",style="solid", color="burlywood", weight=9];
581 -> 480[label="",style="solid", color="burlywood", weight=3];
433[label="ww4000",fontsize=16,color="green",shape="box"];434[label="ww3010",fontsize=16,color="green",shape="box"];435[label="primEqInt (Pos (Succ ww110)) (Pos (Succ ww170)) && ww5",fontsize=16,color="black",shape="box"];435 -> 481[label="",style="solid", color="black", weight=3];
436[label="primEqInt (Pos (Succ ww110)) (Pos Zero) && ww5",fontsize=16,color="black",shape="box"];436 -> 482[label="",style="solid", color="black", weight=3];
437[label="ww4000",fontsize=16,color="green",shape="box"];438[label="ww3010",fontsize=16,color="green",shape="box"];439[label="False && ww5",fontsize=16,color="black",shape="triangle"];439 -> 483[label="",style="solid", color="black", weight=3];
440[label="ww4000",fontsize=16,color="green",shape="box"];441[label="ww3010",fontsize=16,color="green",shape="box"];442[label="ww4000",fontsize=16,color="green",shape="box"];443[label="ww3010",fontsize=16,color="green",shape="box"];444[label="ww4000",fontsize=16,color="green",shape="box"];445[label="ww3010",fontsize=16,color="green",shape="box"];446[label="primEqInt (Pos Zero) (Pos (Succ ww190)) && ww5",fontsize=16,color="black",shape="box"];446 -> 484[label="",style="solid", color="black", weight=3];
447[label="primEqInt (Pos Zero) (Pos Zero) && ww5",fontsize=16,color="black",shape="box"];447 -> 485[label="",style="solid", color="black", weight=3];
448[label="ww4000",fontsize=16,color="green",shape="box"];449[label="ww3010",fontsize=16,color="green",shape="box"];450[label="primEqInt (Pos Zero) (Neg (Succ ww200)) && ww5",fontsize=16,color="black",shape="box"];450 -> 486[label="",style="solid", color="black", weight=3];
451[label="primEqInt (Pos Zero) (Neg Zero) && ww5",fontsize=16,color="black",shape="box"];451 -> 487[label="",style="solid", color="black", weight=3];
452[label="ww4000",fontsize=16,color="green",shape="box"];453[label="ww3010",fontsize=16,color="green",shape="box"];454[label="ww4000",fontsize=16,color="green",shape="box"];455[label="ww3010",fontsize=16,color="green",shape="box"];456[label="ww4000",fontsize=16,color="green",shape="box"];457[label="ww3010",fontsize=16,color="green",shape="box"];458 -> 439[label="",style="dashed", color="red", weight=0];
458[label="False && ww5",fontsize=16,color="magenta"];459[label="ww4000",fontsize=16,color="green",shape="box"];460[label="ww3010",fontsize=16,color="green",shape="box"];461[label="primEqInt (Neg (Succ ww160)) (Neg (Succ ww220)) && ww5",fontsize=16,color="black",shape="box"];461 -> 488[label="",style="solid", color="black", weight=3];
462[label="primEqInt (Neg (Succ ww160)) (Neg Zero) && ww5",fontsize=16,color="black",shape="box"];462 -> 489[label="",style="solid", color="black", weight=3];
463[label="ww4000",fontsize=16,color="green",shape="box"];464[label="ww3010",fontsize=16,color="green",shape="box"];465[label="ww4000",fontsize=16,color="green",shape="box"];466[label="ww3010",fontsize=16,color="green",shape="box"];467[label="ww4000",fontsize=16,color="green",shape="box"];468[label="ww3010",fontsize=16,color="green",shape="box"];469[label="primEqInt (Neg Zero) (Pos (Succ ww230)) && ww5",fontsize=16,color="black",shape="box"];469 -> 490[label="",style="solid", color="black", weight=3];
470[label="primEqInt (Neg Zero) (Pos Zero) && ww5",fontsize=16,color="black",shape="box"];470 -> 491[label="",style="solid", color="black", weight=3];
471[label="ww4000",fontsize=16,color="green",shape="box"];472[label="ww3010",fontsize=16,color="green",shape="box"];473[label="primEqInt (Neg Zero) (Neg (Succ ww240)) && ww5",fontsize=16,color="black",shape="box"];473 -> 492[label="",style="solid", color="black", weight=3];
474[label="primEqInt (Neg Zero) (Neg Zero) && ww5",fontsize=16,color="black",shape="box"];474 -> 493[label="",style="solid", color="black", weight=3];
475[label="ww4000",fontsize=16,color="green",shape="box"];476[label="ww3010",fontsize=16,color="green",shape="box"];477[label="ww4000",fontsize=16,color="green",shape="box"];478[label="ww3010",fontsize=16,color="green",shape="box"];479[label="primPlusNat (Succ ww1500) ww40100",fontsize=16,color="burlywood",shape="box"];582[label="ww40100/Succ ww401000",fontsize=10,color="white",style="solid",shape="box"];479 -> 582[label="",style="solid", color="burlywood", weight=9];
582 -> 494[label="",style="solid", color="burlywood", weight=3];
583[label="ww40100/Zero",fontsize=10,color="white",style="solid",shape="box"];479 -> 583[label="",style="solid", color="burlywood", weight=9];
583 -> 495[label="",style="solid", color="burlywood", weight=3];
480[label="primPlusNat Zero ww40100",fontsize=16,color="burlywood",shape="box"];584[label="ww40100/Succ ww401000",fontsize=10,color="white",style="solid",shape="box"];480 -> 584[label="",style="solid", color="burlywood", weight=9];
584 -> 496[label="",style="solid", color="burlywood", weight=3];
585[label="ww40100/Zero",fontsize=10,color="white",style="solid",shape="box"];480 -> 585[label="",style="solid", color="burlywood", weight=9];
585 -> 497[label="",style="solid", color="burlywood", weight=3];
481[label="primEqNat ww110 ww170 && ww5",fontsize=16,color="burlywood",shape="triangle"];586[label="ww110/Succ ww1100",fontsize=10,color="white",style="solid",shape="box"];481 -> 586[label="",style="solid", color="burlywood", weight=9];
586 -> 498[label="",style="solid", color="burlywood", weight=3];
587[label="ww110/Zero",fontsize=10,color="white",style="solid",shape="box"];481 -> 587[label="",style="solid", color="burlywood", weight=9];
587 -> 499[label="",style="solid", color="burlywood", weight=3];
482 -> 439[label="",style="dashed", color="red", weight=0];
482[label="False && ww5",fontsize=16,color="magenta"];483[label="False",fontsize=16,color="green",shape="box"];484 -> 439[label="",style="dashed", color="red", weight=0];
484[label="False && ww5",fontsize=16,color="magenta"];485[label="True && ww5",fontsize=16,color="black",shape="triangle"];485 -> 500[label="",style="solid", color="black", weight=3];
486 -> 439[label="",style="dashed", color="red", weight=0];
486[label="False && ww5",fontsize=16,color="magenta"];487 -> 485[label="",style="dashed", color="red", weight=0];
487[label="True && ww5",fontsize=16,color="magenta"];488 -> 481[label="",style="dashed", color="red", weight=0];
488[label="primEqNat ww160 ww220 && ww5",fontsize=16,color="magenta"];488 -> 501[label="",style="dashed", color="magenta", weight=3];
488 -> 502[label="",style="dashed", color="magenta", weight=3];
489 -> 439[label="",style="dashed", color="red", weight=0];
489[label="False && ww5",fontsize=16,color="magenta"];490 -> 439[label="",style="dashed", color="red", weight=0];
490[label="False && ww5",fontsize=16,color="magenta"];491 -> 485[label="",style="dashed", color="red", weight=0];
491[label="True && ww5",fontsize=16,color="magenta"];492 -> 439[label="",style="dashed", color="red", weight=0];
492[label="False && ww5",fontsize=16,color="magenta"];493 -> 485[label="",style="dashed", color="red", weight=0];
493[label="True && ww5",fontsize=16,color="magenta"];494[label="primPlusNat (Succ ww1500) (Succ ww401000)",fontsize=16,color="black",shape="box"];494 -> 503[label="",style="solid", color="black", weight=3];
495[label="primPlusNat (Succ ww1500) Zero",fontsize=16,color="black",shape="box"];495 -> 504[label="",style="solid", color="black", weight=3];
496[label="primPlusNat Zero (Succ ww401000)",fontsize=16,color="black",shape="box"];496 -> 505[label="",style="solid", color="black", weight=3];
497[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];497 -> 506[label="",style="solid", color="black", weight=3];
498[label="primEqNat (Succ ww1100) ww170 && ww5",fontsize=16,color="burlywood",shape="box"];588[label="ww170/Succ ww1700",fontsize=10,color="white",style="solid",shape="box"];498 -> 588[label="",style="solid", color="burlywood", weight=9];
588 -> 507[label="",style="solid", color="burlywood", weight=3];
589[label="ww170/Zero",fontsize=10,color="white",style="solid",shape="box"];498 -> 589[label="",style="solid", color="burlywood", weight=9];
589 -> 508[label="",style="solid", color="burlywood", weight=3];
499[label="primEqNat Zero ww170 && ww5",fontsize=16,color="burlywood",shape="box"];590[label="ww170/Succ ww1700",fontsize=10,color="white",style="solid",shape="box"];499 -> 590[label="",style="solid", color="burlywood", weight=9];
590 -> 509[label="",style="solid", color="burlywood", weight=3];
591[label="ww170/Zero",fontsize=10,color="white",style="solid",shape="box"];499 -> 591[label="",style="solid", color="burlywood", weight=9];
591 -> 510[label="",style="solid", color="burlywood", weight=3];
500[label="ww5",fontsize=16,color="green",shape="box"];501[label="ww220",fontsize=16,color="green",shape="box"];502[label="ww160",fontsize=16,color="green",shape="box"];503[label="Succ (Succ (primPlusNat ww1500 ww401000))",fontsize=16,color="green",shape="box"];503 -> 511[label="",style="dashed", color="green", weight=3];
504[label="Succ ww1500",fontsize=16,color="green",shape="box"];505[label="Succ ww401000",fontsize=16,color="green",shape="box"];506[label="Zero",fontsize=16,color="green",shape="box"];507[label="primEqNat (Succ ww1100) (Succ ww1700) && ww5",fontsize=16,color="black",shape="box"];507 -> 512[label="",style="solid", color="black", weight=3];
508[label="primEqNat (Succ ww1100) Zero && ww5",fontsize=16,color="black",shape="box"];508 -> 513[label="",style="solid", color="black", weight=3];
509[label="primEqNat Zero (Succ ww1700) && ww5",fontsize=16,color="black",shape="box"];509 -> 514[label="",style="solid", color="black", weight=3];
510[label="primEqNat Zero Zero && ww5",fontsize=16,color="black",shape="box"];510 -> 515[label="",style="solid", color="black", weight=3];
511 -> 432[label="",style="dashed", color="red", weight=0];
511[label="primPlusNat ww1500 ww401000",fontsize=16,color="magenta"];511 -> 516[label="",style="dashed", color="magenta", weight=3];
511 -> 517[label="",style="dashed", color="magenta", weight=3];
512 -> 481[label="",style="dashed", color="red", weight=0];
512[label="primEqNat ww1100 ww1700 && ww5",fontsize=16,color="magenta"];512 -> 518[label="",style="dashed", color="magenta", weight=3];
512 -> 519[label="",style="dashed", color="magenta", weight=3];
513 -> 439[label="",style="dashed", color="red", weight=0];
513[label="False && ww5",fontsize=16,color="magenta"];514 -> 439[label="",style="dashed", color="red", weight=0];
514[label="False && ww5",fontsize=16,color="magenta"];515 -> 485[label="",style="dashed", color="red", weight=0];
515[label="True && ww5",fontsize=16,color="magenta"];516[label="ww1500",fontsize=16,color="green",shape="box"];517[label="ww401000",fontsize=16,color="green",shape="box"];518[label="ww1700",fontsize=16,color="green",shape="box"];519[label="ww1100",fontsize=16,color="green",shape="box"];}

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

(6)
Complex Obligation (AND)

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

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

   new_asAs(Succ(ww1100), Succ(ww1700), ww5) -> new_asAs(ww1100, ww1700, ww5)

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_asAs(Succ(ww1100), Succ(ww1700), ww5) -> new_asAs(ww1100, ww1700, ww5)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


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

(9)
YES

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

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

   new_primMulNat(Succ(ww30000), Succ(ww40100)) -> new_primMulNat(ww30000, Succ(ww40100))

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(ww30000), Succ(ww40100)) -> new_primMulNat(ww30000, Succ(ww40100))
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_isPrefixOf(:(ww30, ww31), :(ww40, ww41)) -> new_isPrefixOf(ww31, ww41)

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_isPrefixOf(:(ww30, ww31), :(ww40, ww41)) -> new_isPrefixOf(ww31, ww41)
The graph contains the following edges 1 > 1, 2 > 2


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

(15)
YES

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

(16)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat(Succ(ww1500), Succ(ww401000)) -> new_primPlusNat(ww1500, ww401000)

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

(17) 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(ww1500), Succ(ww401000)) -> new_primPlusNat(ww1500, ww401000)
The graph contains the following edges 1 > 1, 2 > 2


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

(18)
YES