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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) NumRed [SOUND, 5 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) QDP
(9) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(10) 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
"absReal x|x >= 0x|otherwise`negate` x;
"
is transformed to
"absReal x = absReal2 x;
"
"absReal0 x True = `negate` x;
"
"absReal1 x True = x;
absReal1 x False = absReal0 x otherwise;
"
"absReal2 x = absReal1 x (x >= 0);
"
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

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

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

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

(5) NumRed (SOUND)
Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
----------------------------------------

(6)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="abs",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="abs vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="absReal vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="absReal2 vx3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="absReal1 vx3 (vx3 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="absReal1 vx3 (compare vx3 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="absReal1 vx3 (not (compare vx3 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="absReal1 vx3 (not (primCmpFloat vx3 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];767[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];9 -> 767[label="",style="solid", color="burlywood", weight=9];
767 -> 10[label="",style="solid", color="burlywood", weight=3];
10[label="absReal1 (Float vx30 vx31) (not (primCmpFloat (Float vx30 vx31) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];768[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];10 -> 768[label="",style="solid", color="burlywood", weight=9];
768 -> 11[label="",style="solid", color="burlywood", weight=3];
769[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];10 -> 769[label="",style="solid", color="burlywood", weight=9];
769 -> 12[label="",style="solid", color="burlywood", weight=3];
11[label="absReal1 (Float vx30 (Pos vx310)) (not (primCmpFloat (Float vx30 (Pos vx310)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="absReal1 (Float vx30 (Neg vx310)) (not (primCmpFloat (Float vx30 (Neg vx310)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="absReal1 (Float vx30 (Pos vx310)) (not (primCmpFloat (Float vx30 (Pos vx310)) (primIntToFloat (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14[label="absReal1 (Float vx30 (Neg vx310)) (not (primCmpFloat (Float vx30 (Neg vx310)) (primIntToFloat (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="absReal1 (Float vx30 (Pos vx310)) (not (primCmpFloat (Float vx30 (Pos vx310)) (Float (Pos Zero) (Pos (Succ Zero))) == LT))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="absReal1 (Float vx30 (Neg vx310)) (not (primCmpFloat (Float vx30 (Neg vx310)) (Float (Pos Zero) (Pos (Succ Zero))) == LT))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="absReal1 (Float vx30 (Pos vx310)) (not (compare (vx30 * Pos (Succ Zero)) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
18[label="absReal1 (Float vx30 (Neg vx310)) (not (compare (vx30 * Neg (Succ Zero)) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
19[label="absReal1 (Float vx30 (Pos vx310)) (not (primCmpInt (vx30 * Pos (Succ Zero)) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
20[label="absReal1 (Float vx30 (Neg vx310)) (not (primCmpInt (vx30 * Neg (Succ Zero)) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
21[label="absReal1 (Float vx30 (Pos vx310)) (not (primCmpInt (primMulInt vx30 (Pos (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="box"];770[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];21 -> 770[label="",style="solid", color="burlywood", weight=9];
770 -> 23[label="",style="solid", color="burlywood", weight=3];
771[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];21 -> 771[label="",style="solid", color="burlywood", weight=9];
771 -> 24[label="",style="solid", color="burlywood", weight=3];
22[label="absReal1 (Float vx30 (Neg vx310)) (not (primCmpInt (primMulInt vx30 (Neg (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="box"];772[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 772[label="",style="solid", color="burlywood", weight=9];
772 -> 25[label="",style="solid", color="burlywood", weight=3];
773[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 773[label="",style="solid", color="burlywood", weight=9];
773 -> 26[label="",style="solid", color="burlywood", weight=3];
23[label="absReal1 (Float (Pos vx300) (Pos vx310)) (not (primCmpInt (primMulInt (Pos vx300) (Pos (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="absReal1 (Float (Neg vx300) (Pos vx310)) (not (primCmpInt (primMulInt (Neg vx300) (Pos (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="absReal1 (Float (Pos vx300) (Neg vx310)) (not (primCmpInt (primMulInt (Pos vx300) (Neg (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="absReal1 (Float (Neg vx300) (Neg vx310)) (not (primCmpInt (primMulInt (Neg vx300) (Neg (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
27[label="absReal1 (Float (Pos vx300) (Pos vx310)) (not (primCmpInt (Pos (primMulNat vx300 (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="box"];774[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];27 -> 774[label="",style="solid", color="burlywood", weight=9];
774 -> 31[label="",style="solid", color="burlywood", weight=3];
775[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 775[label="",style="solid", color="burlywood", weight=9];
775 -> 32[label="",style="solid", color="burlywood", weight=3];
28[label="absReal1 (Float (Neg vx300) (Pos vx310)) (not (primCmpInt (Neg (primMulNat vx300 (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="box"];776[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];28 -> 776[label="",style="solid", color="burlywood", weight=9];
776 -> 33[label="",style="solid", color="burlywood", weight=3];
777[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 777[label="",style="solid", color="burlywood", weight=9];
777 -> 34[label="",style="solid", color="burlywood", weight=3];
29[label="absReal1 (Float (Pos vx300) (Neg vx310)) (not (primCmpInt (Neg (primMulNat vx300 (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="box"];778[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];29 -> 778[label="",style="solid", color="burlywood", weight=9];
778 -> 35[label="",style="solid", color="burlywood", weight=3];
779[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];29 -> 779[label="",style="solid", color="burlywood", weight=9];
779 -> 36[label="",style="solid", color="burlywood", weight=3];
30[label="absReal1 (Float (Neg vx300) (Neg vx310)) (not (primCmpInt (Pos (primMulNat vx300 (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="box"];780[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];30 -> 780[label="",style="solid", color="burlywood", weight=9];
780 -> 37[label="",style="solid", color="burlywood", weight=3];
781[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];30 -> 781[label="",style="solid", color="burlywood", weight=9];
781 -> 38[label="",style="solid", color="burlywood", weight=3];
31[label="absReal1 (Float (Pos (Succ vx3000)) (Pos vx310)) (not (primCmpInt (Pos (primMulNat (Succ vx3000) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3];
32[label="absReal1 (Float (Pos Zero) (Pos vx310)) (not (primCmpInt (Pos (primMulNat Zero (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3];
33[label="absReal1 (Float (Neg (Succ vx3000)) (Pos vx310)) (not (primCmpInt (Neg (primMulNat (Succ vx3000) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3];
34[label="absReal1 (Float (Neg Zero) (Pos vx310)) (not (primCmpInt (Neg (primMulNat Zero (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3];
35[label="absReal1 (Float (Pos (Succ vx3000)) (Neg vx310)) (not (primCmpInt (Neg (primMulNat (Succ vx3000) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
36[label="absReal1 (Float (Pos Zero) (Neg vx310)) (not (primCmpInt (Neg (primMulNat Zero (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
37[label="absReal1 (Float (Neg (Succ vx3000)) (Neg vx310)) (not (primCmpInt (Pos (primMulNat (Succ vx3000) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];37 -> 45[label="",style="solid", color="black", weight=3];
38[label="absReal1 (Float (Neg Zero) (Neg vx310)) (not (primCmpInt (Pos (primMulNat Zero (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];38 -> 46[label="",style="solid", color="black", weight=3];
39 -> 595[label="",style="dashed", color="red", weight=0];
39[label="absReal1 (Float (Pos (Succ vx3000)) (Pos vx310)) (not (primCmpInt (Pos (primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="magenta"];39 -> 596[label="",style="dashed", color="magenta", weight=3];
39 -> 597[label="",style="dashed", color="magenta", weight=3];
39 -> 598[label="",style="dashed", color="magenta", weight=3];
40[label="absReal1 (Float (Pos Zero) (Pos vx310)) (not (primCmpInt (Pos Zero) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
41 -> 503[label="",style="dashed", color="red", weight=0];
41[label="absReal1 (Float (Neg (Succ vx3000)) (Pos vx310)) (not (primCmpInt (Neg (primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="magenta"];41 -> 504[label="",style="dashed", color="magenta", weight=3];
41 -> 505[label="",style="dashed", color="magenta", weight=3];
41 -> 506[label="",style="dashed", color="magenta", weight=3];
42[label="absReal1 (Float (Neg Zero) (Pos vx310)) (not (primCmpInt (Neg Zero) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];42 -> 52[label="",style="solid", color="black", weight=3];
43 -> 522[label="",style="dashed", color="red", weight=0];
43[label="absReal1 (Float (Pos (Succ vx3000)) (Neg vx310)) (not (primCmpInt (Neg (primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="magenta"];43 -> 523[label="",style="dashed", color="magenta", weight=3];
43 -> 524[label="",style="dashed", color="magenta", weight=3];
43 -> 525[label="",style="dashed", color="magenta", weight=3];
44[label="absReal1 (Float (Pos Zero) (Neg vx310)) (not (primCmpInt (Neg Zero) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];44 -> 55[label="",style="solid", color="black", weight=3];
45 -> 546[label="",style="dashed", color="red", weight=0];
45[label="absReal1 (Float (Neg (Succ vx3000)) (Neg vx310)) (not (primCmpInt (Pos (primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero))) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="magenta"];45 -> 547[label="",style="dashed", color="magenta", weight=3];
45 -> 548[label="",style="dashed", color="magenta", weight=3];
45 -> 549[label="",style="dashed", color="magenta", weight=3];
46[label="absReal1 (Float (Neg Zero) (Neg vx310)) (not (primCmpInt (Pos Zero) (Pos vx310 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];46 -> 58[label="",style="solid", color="black", weight=3];
596[label="vx310",fontsize=16,color="green",shape="box"];597 -> 495[label="",style="dashed", color="red", weight=0];
597[label="primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];597 -> 668[label="",style="dashed", color="magenta", weight=3];
598[label="vx3000",fontsize=16,color="green",shape="box"];595[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos vx28) (Pos vx6 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="triangle"];782[label="vx28/Succ vx280",fontsize=10,color="white",style="solid",shape="box"];595 -> 782[label="",style="solid", color="burlywood", weight=9];
782 -> 669[label="",style="solid", color="burlywood", weight=3];
783[label="vx28/Zero",fontsize=10,color="white",style="solid",shape="box"];595 -> 783[label="",style="solid", color="burlywood", weight=9];
783 -> 670[label="",style="solid", color="burlywood", weight=3];
49[label="absReal1 (Float (Pos Zero) (Pos vx310)) (not (primCmpInt (Pos Zero) (primMulInt (Pos vx310) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];49 -> 61[label="",style="solid", color="black", weight=3];
504[label="vx310",fontsize=16,color="green",shape="box"];505 -> 495[label="",style="dashed", color="red", weight=0];
505[label="primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];505 -> 519[label="",style="dashed", color="magenta", weight=3];
506[label="vx3000",fontsize=16,color="green",shape="box"];503[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg vx25) (Pos vx13 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="triangle"];784[label="vx25/Succ vx250",fontsize=10,color="white",style="solid",shape="box"];503 -> 784[label="",style="solid", color="burlywood", weight=9];
784 -> 520[label="",style="solid", color="burlywood", weight=3];
785[label="vx25/Zero",fontsize=10,color="white",style="solid",shape="box"];503 -> 785[label="",style="solid", color="burlywood", weight=9];
785 -> 521[label="",style="solid", color="burlywood", weight=3];
52[label="absReal1 (Float (Neg Zero) (Pos vx310)) (not (primCmpInt (Neg Zero) (primMulInt (Pos vx310) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];52 -> 64[label="",style="solid", color="black", weight=3];
523[label="vx3000",fontsize=16,color="green",shape="box"];524[label="vx310",fontsize=16,color="green",shape="box"];525 -> 495[label="",style="dashed", color="red", weight=0];
525[label="primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];525 -> 538[label="",style="dashed", color="magenta", weight=3];
522[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg vx26) (Pos vx16 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="triangle"];786[label="vx26/Succ vx260",fontsize=10,color="white",style="solid",shape="box"];522 -> 786[label="",style="solid", color="burlywood", weight=9];
786 -> 539[label="",style="solid", color="burlywood", weight=3];
787[label="vx26/Zero",fontsize=10,color="white",style="solid",shape="box"];522 -> 787[label="",style="solid", color="burlywood", weight=9];
787 -> 540[label="",style="solid", color="burlywood", weight=3];
55[label="absReal1 (Float (Pos Zero) (Neg vx310)) (not (primCmpInt (Neg Zero) (primMulInt (Pos vx310) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];55 -> 67[label="",style="solid", color="black", weight=3];
547 -> 495[label="",style="dashed", color="red", weight=0];
547[label="primPlusNat (primMulNat vx3000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];547 -> 562[label="",style="dashed", color="magenta", weight=3];
548[label="vx3000",fontsize=16,color="green",shape="box"];549[label="vx310",fontsize=16,color="green",shape="box"];546[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos vx27) (Pos vx19 * Pos Zero) == LT))",fontsize=16,color="burlywood",shape="triangle"];788[label="vx27/Succ vx270",fontsize=10,color="white",style="solid",shape="box"];546 -> 788[label="",style="solid", color="burlywood", weight=9];
788 -> 563[label="",style="solid", color="burlywood", weight=3];
789[label="vx27/Zero",fontsize=10,color="white",style="solid",shape="box"];546 -> 789[label="",style="solid", color="burlywood", weight=9];
789 -> 564[label="",style="solid", color="burlywood", weight=3];
58[label="absReal1 (Float (Neg Zero) (Neg vx310)) (not (primCmpInt (Pos Zero) (primMulInt (Pos vx310) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];58 -> 70[label="",style="solid", color="black", weight=3];
668 -> 343[label="",style="dashed", color="red", weight=0];
668[label="primMulNat vx3000 (Succ Zero)",fontsize=16,color="magenta"];668 -> 681[label="",style="dashed", color="magenta", weight=3];
495[label="primPlusNat vx24 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];790[label="vx24/Succ vx240",fontsize=10,color="white",style="solid",shape="box"];495 -> 790[label="",style="solid", color="burlywood", weight=9];
790 -> 542[label="",style="solid", color="burlywood", weight=3];
791[label="vx24/Zero",fontsize=10,color="white",style="solid",shape="box"];495 -> 791[label="",style="solid", color="burlywood", weight=9];
791 -> 543[label="",style="solid", color="burlywood", weight=3];
669[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos (Succ vx280)) (Pos vx6 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];669 -> 682[label="",style="solid", color="black", weight=3];
670[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos Zero) (Pos vx6 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];670 -> 683[label="",style="solid", color="black", weight=3];
61[label="absReal1 (Float (Pos Zero) (Pos vx310)) (not (primCmpInt (Pos Zero) (Pos (primMulNat vx310 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];792[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];61 -> 792[label="",style="solid", color="burlywood", weight=9];
792 -> 74[label="",style="solid", color="burlywood", weight=3];
793[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];61 -> 793[label="",style="solid", color="burlywood", weight=9];
793 -> 75[label="",style="solid", color="burlywood", weight=3];
519 -> 343[label="",style="dashed", color="red", weight=0];
519[label="primMulNat vx3000 (Succ Zero)",fontsize=16,color="magenta"];519 -> 541[label="",style="dashed", color="magenta", weight=3];
520[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg (Succ vx250)) (Pos vx13 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];520 -> 544[label="",style="solid", color="black", weight=3];
521[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg Zero) (Pos vx13 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];521 -> 545[label="",style="solid", color="black", weight=3];
64[label="absReal1 (Float (Neg Zero) (Pos vx310)) (not (primCmpInt (Neg Zero) (Pos (primMulNat vx310 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];794[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];64 -> 794[label="",style="solid", color="burlywood", weight=9];
794 -> 79[label="",style="solid", color="burlywood", weight=3];
795[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 795[label="",style="solid", color="burlywood", weight=9];
795 -> 80[label="",style="solid", color="burlywood", weight=3];
538 -> 343[label="",style="dashed", color="red", weight=0];
538[label="primMulNat vx3000 (Succ Zero)",fontsize=16,color="magenta"];538 -> 565[label="",style="dashed", color="magenta", weight=3];
539[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg (Succ vx260)) (Pos vx16 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];539 -> 566[label="",style="solid", color="black", weight=3];
540[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg Zero) (Pos vx16 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];540 -> 567[label="",style="solid", color="black", weight=3];
67[label="absReal1 (Float (Pos Zero) (Neg vx310)) (not (primCmpInt (Neg Zero) (Pos (primMulNat vx310 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];796[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];67 -> 796[label="",style="solid", color="burlywood", weight=9];
796 -> 84[label="",style="solid", color="burlywood", weight=3];
797[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];67 -> 797[label="",style="solid", color="burlywood", weight=9];
797 -> 85[label="",style="solid", color="burlywood", weight=3];
562 -> 343[label="",style="dashed", color="red", weight=0];
562[label="primMulNat vx3000 (Succ Zero)",fontsize=16,color="magenta"];562 -> 585[label="",style="dashed", color="magenta", weight=3];
563[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos (Succ vx270)) (Pos vx19 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];563 -> 586[label="",style="solid", color="black", weight=3];
564[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos Zero) (Pos vx19 * Pos Zero) == LT))",fontsize=16,color="black",shape="box"];564 -> 587[label="",style="solid", color="black", weight=3];
70[label="absReal1 (Float (Neg Zero) (Neg vx310)) (not (primCmpInt (Pos Zero) (Pos (primMulNat vx310 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];798[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];70 -> 798[label="",style="solid", color="burlywood", weight=9];
798 -> 89[label="",style="solid", color="burlywood", weight=3];
799[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 799[label="",style="solid", color="burlywood", weight=9];
799 -> 90[label="",style="solid", color="burlywood", weight=3];
681[label="vx3000",fontsize=16,color="green",shape="box"];343[label="primMulNat vx30000 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];800[label="vx30000/Succ vx300000",fontsize=10,color="white",style="solid",shape="box"];343 -> 800[label="",style="solid", color="burlywood", weight=9];
800 -> 386[label="",style="solid", color="burlywood", weight=3];
801[label="vx30000/Zero",fontsize=10,color="white",style="solid",shape="box"];343 -> 801[label="",style="solid", color="burlywood", weight=9];
801 -> 387[label="",style="solid", color="burlywood", weight=3];
542[label="primPlusNat (Succ vx240) (Succ Zero)",fontsize=16,color="black",shape="box"];542 -> 568[label="",style="solid", color="black", weight=3];
543[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];543 -> 569[label="",style="solid", color="black", weight=3];
682[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos (Succ vx280)) (primMulInt (Pos vx6) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];682 -> 695[label="",style="solid", color="black", weight=3];
683[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos Zero) (primMulInt (Pos vx6) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];683 -> 696[label="",style="solid", color="black", weight=3];
74[label="absReal1 (Float (Pos Zero) (Pos (Succ vx3100))) (not (primCmpInt (Pos Zero) (Pos (primMulNat (Succ vx3100) Zero)) == LT))",fontsize=16,color="black",shape="box"];74 -> 94[label="",style="solid", color="black", weight=3];
75[label="absReal1 (Float (Pos Zero) (Pos Zero)) (not (primCmpInt (Pos Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];75 -> 95[label="",style="solid", color="black", weight=3];
541[label="vx3000",fontsize=16,color="green",shape="box"];544[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg (Succ vx250)) (primMulInt (Pos vx13) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];544 -> 570[label="",style="solid", color="black", weight=3];
545[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg Zero) (primMulInt (Pos vx13) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];545 -> 571[label="",style="solid", color="black", weight=3];
79[label="absReal1 (Float (Neg Zero) (Pos (Succ vx3100))) (not (primCmpInt (Neg Zero) (Pos (primMulNat (Succ vx3100) Zero)) == LT))",fontsize=16,color="black",shape="box"];79 -> 99[label="",style="solid", color="black", weight=3];
80[label="absReal1 (Float (Neg Zero) (Pos Zero)) (not (primCmpInt (Neg Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];80 -> 100[label="",style="solid", color="black", weight=3];
565[label="vx3000",fontsize=16,color="green",shape="box"];566[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg (Succ vx260)) (primMulInt (Pos vx16) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];566 -> 588[label="",style="solid", color="black", weight=3];
567[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg Zero) (primMulInt (Pos vx16) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];567 -> 589[label="",style="solid", color="black", weight=3];
84[label="absReal1 (Float (Pos Zero) (Neg (Succ vx3100))) (not (primCmpInt (Neg Zero) (Pos (primMulNat (Succ vx3100) Zero)) == LT))",fontsize=16,color="black",shape="box"];84 -> 104[label="",style="solid", color="black", weight=3];
85[label="absReal1 (Float (Pos Zero) (Neg Zero)) (not (primCmpInt (Neg Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];85 -> 105[label="",style="solid", color="black", weight=3];
585[label="vx3000",fontsize=16,color="green",shape="box"];586[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos (Succ vx270)) (primMulInt (Pos vx19) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];586 -> 671[label="",style="solid", color="black", weight=3];
587[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos Zero) (primMulInt (Pos vx19) (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];587 -> 672[label="",style="solid", color="black", weight=3];
89[label="absReal1 (Float (Neg Zero) (Neg (Succ vx3100))) (not (primCmpInt (Pos Zero) (Pos (primMulNat (Succ vx3100) Zero)) == LT))",fontsize=16,color="black",shape="box"];89 -> 109[label="",style="solid", color="black", weight=3];
90[label="absReal1 (Float (Neg Zero) (Neg Zero)) (not (primCmpInt (Pos Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];90 -> 110[label="",style="solid", color="black", weight=3];
386[label="primMulNat (Succ vx300000) (Succ Zero)",fontsize=16,color="black",shape="box"];386 -> 440[label="",style="solid", color="black", weight=3];
387[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];387 -> 441[label="",style="solid", color="black", weight=3];
568[label="Succ (Succ (primPlusNat vx240 Zero))",fontsize=16,color="green",shape="box"];568 -> 590[label="",style="dashed", color="green", weight=3];
569[label="Succ Zero",fontsize=16,color="green",shape="box"];695[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos (Succ vx280)) (Pos (primMulNat vx6 Zero)) == LT))",fontsize=16,color="black",shape="box"];695 -> 707[label="",style="solid", color="black", weight=3];
696[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpInt (Pos Zero) (Pos (primMulNat vx6 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];802[label="vx6/Succ vx60",fontsize=10,color="white",style="solid",shape="box"];696 -> 802[label="",style="solid", color="burlywood", weight=9];
802 -> 708[label="",style="solid", color="burlywood", weight=3];
803[label="vx6/Zero",fontsize=10,color="white",style="solid",shape="box"];696 -> 803[label="",style="solid", color="burlywood", weight=9];
803 -> 709[label="",style="solid", color="burlywood", weight=3];
94[label="absReal1 (Float (Pos Zero) (Pos (Succ vx3100))) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];94 -> 115[label="",style="solid", color="black", weight=3];
95[label="absReal1 (Float (Pos Zero) (Pos Zero)) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];95 -> 116[label="",style="solid", color="black", weight=3];
570[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg (Succ vx250)) (Pos (primMulNat vx13 Zero)) == LT))",fontsize=16,color="black",shape="box"];570 -> 591[label="",style="solid", color="black", weight=3];
571[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (primCmpInt (Neg Zero) (Pos (primMulNat vx13 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];804[label="vx13/Succ vx130",fontsize=10,color="white",style="solid",shape="box"];571 -> 804[label="",style="solid", color="burlywood", weight=9];
804 -> 592[label="",style="solid", color="burlywood", weight=3];
805[label="vx13/Zero",fontsize=10,color="white",style="solid",shape="box"];571 -> 805[label="",style="solid", color="burlywood", weight=9];
805 -> 593[label="",style="solid", color="burlywood", weight=3];
99[label="absReal1 (Float (Neg Zero) (Pos (Succ vx3100))) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];99 -> 121[label="",style="solid", color="black", weight=3];
100[label="absReal1 (Float (Neg Zero) (Pos Zero)) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];100 -> 122[label="",style="solid", color="black", weight=3];
588[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg (Succ vx260)) (Pos (primMulNat vx16 Zero)) == LT))",fontsize=16,color="black",shape="box"];588 -> 673[label="",style="solid", color="black", weight=3];
589[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (primCmpInt (Neg Zero) (Pos (primMulNat vx16 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];806[label="vx16/Succ vx160",fontsize=10,color="white",style="solid",shape="box"];589 -> 806[label="",style="solid", color="burlywood", weight=9];
806 -> 674[label="",style="solid", color="burlywood", weight=3];
807[label="vx16/Zero",fontsize=10,color="white",style="solid",shape="box"];589 -> 807[label="",style="solid", color="burlywood", weight=9];
807 -> 675[label="",style="solid", color="burlywood", weight=3];
104[label="absReal1 (Float (Pos Zero) (Neg (Succ vx3100))) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];104 -> 127[label="",style="solid", color="black", weight=3];
105[label="absReal1 (Float (Pos Zero) (Neg Zero)) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];105 -> 128[label="",style="solid", color="black", weight=3];
671[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos (Succ vx270)) (Pos (primMulNat vx19 Zero)) == LT))",fontsize=16,color="black",shape="box"];671 -> 684[label="",style="solid", color="black", weight=3];
672[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpInt (Pos Zero) (Pos (primMulNat vx19 Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];808[label="vx19/Succ vx190",fontsize=10,color="white",style="solid",shape="box"];672 -> 808[label="",style="solid", color="burlywood", weight=9];
808 -> 685[label="",style="solid", color="burlywood", weight=3];
809[label="vx19/Zero",fontsize=10,color="white",style="solid",shape="box"];672 -> 809[label="",style="solid", color="burlywood", weight=9];
809 -> 686[label="",style="solid", color="burlywood", weight=3];
109[label="absReal1 (Float (Neg Zero) (Neg (Succ vx3100))) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];109 -> 133[label="",style="solid", color="black", weight=3];
110[label="absReal1 (Float (Neg Zero) (Neg Zero)) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];110 -> 134[label="",style="solid", color="black", weight=3];
440 -> 495[label="",style="dashed", color="red", weight=0];
440[label="primPlusNat (primMulNat vx300000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];440 -> 496[label="",style="dashed", color="magenta", weight=3];
441[label="Zero",fontsize=16,color="green",shape="box"];590[label="primPlusNat vx240 Zero",fontsize=16,color="burlywood",shape="box"];810[label="vx240/Succ vx2400",fontsize=10,color="white",style="solid",shape="box"];590 -> 810[label="",style="solid", color="burlywood", weight=9];
810 -> 676[label="",style="solid", color="burlywood", weight=3];
811[label="vx240/Zero",fontsize=10,color="white",style="solid",shape="box"];590 -> 811[label="",style="solid", color="burlywood", weight=9];
811 -> 677[label="",style="solid", color="burlywood", weight=3];
707[label="absReal1 (Float (Pos (Succ vx5)) (Pos vx6)) (not (primCmpNat (Succ vx280) (primMulNat vx6 Zero) == LT))",fontsize=16,color="burlywood",shape="box"];812[label="vx6/Succ vx60",fontsize=10,color="white",style="solid",shape="box"];707 -> 812[label="",style="solid", color="burlywood", weight=9];
812 -> 720[label="",style="solid", color="burlywood", weight=3];
813[label="vx6/Zero",fontsize=10,color="white",style="solid",shape="box"];707 -> 813[label="",style="solid", color="burlywood", weight=9];
813 -> 721[label="",style="solid", color="burlywood", weight=3];
708[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not (primCmpInt (Pos Zero) (Pos (primMulNat (Succ vx60) Zero)) == LT))",fontsize=16,color="black",shape="box"];708 -> 722[label="",style="solid", color="black", weight=3];
709[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not (primCmpInt (Pos Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];709 -> 723[label="",style="solid", color="black", weight=3];
115[label="absReal1 (Float (Pos Zero) (Pos (Succ vx3100))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];115 -> 139[label="",style="solid", color="black", weight=3];
116[label="absReal1 (Float (Pos Zero) (Pos Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];116 -> 140[label="",style="solid", color="black", weight=3];
591[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not (LT == LT))",fontsize=16,color="black",shape="box"];591 -> 678[label="",style="solid", color="black", weight=3];
592[label="absReal1 (Float (Neg (Succ vx12)) (Pos (Succ vx130))) (not (primCmpInt (Neg Zero) (Pos (primMulNat (Succ vx130) Zero)) == LT))",fontsize=16,color="black",shape="box"];592 -> 679[label="",style="solid", color="black", weight=3];
593[label="absReal1 (Float (Neg (Succ vx12)) (Pos Zero)) (not (primCmpInt (Neg Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];593 -> 680[label="",style="solid", color="black", weight=3];
121[label="absReal1 (Float (Neg Zero) (Pos (Succ vx3100))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];121 -> 145[label="",style="solid", color="black", weight=3];
122[label="absReal1 (Float (Neg Zero) (Pos Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];122 -> 146[label="",style="solid", color="black", weight=3];
673[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not (LT == LT))",fontsize=16,color="black",shape="box"];673 -> 687[label="",style="solid", color="black", weight=3];
674[label="absReal1 (Float (Pos (Succ vx15)) (Neg (Succ vx160))) (not (primCmpInt (Neg Zero) (Pos (primMulNat (Succ vx160) Zero)) == LT))",fontsize=16,color="black",shape="box"];674 -> 688[label="",style="solid", color="black", weight=3];
675[label="absReal1 (Float (Pos (Succ vx15)) (Neg Zero)) (not (primCmpInt (Neg Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];675 -> 689[label="",style="solid", color="black", weight=3];
127[label="absReal1 (Float (Pos Zero) (Neg (Succ vx3100))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];127 -> 151[label="",style="solid", color="black", weight=3];
128[label="absReal1 (Float (Pos Zero) (Neg Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];128 -> 152[label="",style="solid", color="black", weight=3];
684[label="absReal1 (Float (Neg (Succ vx18)) (Neg vx19)) (not (primCmpNat (Succ vx270) (primMulNat vx19 Zero) == LT))",fontsize=16,color="burlywood",shape="box"];814[label="vx19/Succ vx190",fontsize=10,color="white",style="solid",shape="box"];684 -> 814[label="",style="solid", color="burlywood", weight=9];
814 -> 697[label="",style="solid", color="burlywood", weight=3];
815[label="vx19/Zero",fontsize=10,color="white",style="solid",shape="box"];684 -> 815[label="",style="solid", color="burlywood", weight=9];
815 -> 698[label="",style="solid", color="burlywood", weight=3];
685[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not (primCmpInt (Pos Zero) (Pos (primMulNat (Succ vx190) Zero)) == LT))",fontsize=16,color="black",shape="box"];685 -> 699[label="",style="solid", color="black", weight=3];
686[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not (primCmpInt (Pos Zero) (Pos (primMulNat Zero Zero)) == LT))",fontsize=16,color="black",shape="box"];686 -> 700[label="",style="solid", color="black", weight=3];
133[label="absReal1 (Float (Neg Zero) (Neg (Succ vx3100))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];133 -> 157[label="",style="solid", color="black", weight=3];
134[label="absReal1 (Float (Neg Zero) (Neg Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];134 -> 158[label="",style="solid", color="black", weight=3];
496 -> 343[label="",style="dashed", color="red", weight=0];
496[label="primMulNat vx300000 (Succ Zero)",fontsize=16,color="magenta"];496 -> 572[label="",style="dashed", color="magenta", weight=3];
676[label="primPlusNat (Succ vx2400) Zero",fontsize=16,color="black",shape="box"];676 -> 690[label="",style="solid", color="black", weight=3];
677[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];677 -> 691[label="",style="solid", color="black", weight=3];
720[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not (primCmpNat (Succ vx280) (primMulNat (Succ vx60) Zero) == LT))",fontsize=16,color="black",shape="box"];720 -> 734[label="",style="solid", color="black", weight=3];
721[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not (primCmpNat (Succ vx280) (primMulNat Zero Zero) == LT))",fontsize=16,color="black",shape="box"];721 -> 735[label="",style="solid", color="black", weight=3];
722[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];722 -> 736[label="",style="solid", color="black", weight=3];
723[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];723 -> 737[label="",style="solid", color="black", weight=3];
139[label="absReal1 (Float (Pos Zero) (Pos (Succ vx3100))) (not False)",fontsize=16,color="black",shape="box"];139 -> 165[label="",style="solid", color="black", weight=3];
140[label="absReal1 (Float (Pos Zero) (Pos Zero)) (not False)",fontsize=16,color="black",shape="box"];140 -> 166[label="",style="solid", color="black", weight=3];
678[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) (not True)",fontsize=16,color="black",shape="box"];678 -> 692[label="",style="solid", color="black", weight=3];
679[label="absReal1 (Float (Neg (Succ vx12)) (Pos (Succ vx130))) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];679 -> 693[label="",style="solid", color="black", weight=3];
680[label="absReal1 (Float (Neg (Succ vx12)) (Pos Zero)) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];680 -> 694[label="",style="solid", color="black", weight=3];
145[label="absReal1 (Float (Neg Zero) (Pos (Succ vx3100))) (not False)",fontsize=16,color="black",shape="box"];145 -> 172[label="",style="solid", color="black", weight=3];
146[label="absReal1 (Float (Neg Zero) (Pos Zero)) (not False)",fontsize=16,color="black",shape="box"];146 -> 173[label="",style="solid", color="black", weight=3];
687[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) (not True)",fontsize=16,color="black",shape="box"];687 -> 701[label="",style="solid", color="black", weight=3];
688[label="absReal1 (Float (Pos (Succ vx15)) (Neg (Succ vx160))) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];688 -> 702[label="",style="solid", color="black", weight=3];
689[label="absReal1 (Float (Pos (Succ vx15)) (Neg Zero)) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];689 -> 703[label="",style="solid", color="black", weight=3];
151[label="absReal1 (Float (Pos Zero) (Neg (Succ vx3100))) (not False)",fontsize=16,color="black",shape="box"];151 -> 179[label="",style="solid", color="black", weight=3];
152[label="absReal1 (Float (Pos Zero) (Neg Zero)) (not False)",fontsize=16,color="black",shape="box"];152 -> 180[label="",style="solid", color="black", weight=3];
697[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not (primCmpNat (Succ vx270) (primMulNat (Succ vx190) Zero) == LT))",fontsize=16,color="black",shape="box"];697 -> 710[label="",style="solid", color="black", weight=3];
698[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not (primCmpNat (Succ vx270) (primMulNat Zero Zero) == LT))",fontsize=16,color="black",shape="box"];698 -> 711[label="",style="solid", color="black", weight=3];
699[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];699 -> 712[label="",style="solid", color="black", weight=3];
700[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];700 -> 713[label="",style="solid", color="black", weight=3];
157[label="absReal1 (Float (Neg Zero) (Neg (Succ vx3100))) (not False)",fontsize=16,color="black",shape="box"];157 -> 187[label="",style="solid", color="black", weight=3];
158[label="absReal1 (Float (Neg Zero) (Neg Zero)) (not False)",fontsize=16,color="black",shape="box"];158 -> 188[label="",style="solid", color="black", weight=3];
572[label="vx300000",fontsize=16,color="green",shape="box"];690[label="Succ vx2400",fontsize=16,color="green",shape="box"];691[label="Zero",fontsize=16,color="green",shape="box"];734[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not (primCmpNat (Succ vx280) Zero == LT))",fontsize=16,color="black",shape="box"];734 -> 746[label="",style="solid", color="black", weight=3];
735[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not (primCmpNat (Succ vx280) Zero == LT))",fontsize=16,color="black",shape="box"];735 -> 747[label="",style="solid", color="black", weight=3];
736[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];736 -> 748[label="",style="solid", color="black", weight=3];
737[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];737 -> 749[label="",style="solid", color="black", weight=3];
165[label="absReal1 (Float (Pos Zero) (Pos (Succ vx3100))) True",fontsize=16,color="black",shape="box"];165 -> 195[label="",style="solid", color="black", weight=3];
166[label="absReal1 (Float (Pos Zero) (Pos Zero)) True",fontsize=16,color="black",shape="box"];166 -> 196[label="",style="solid", color="black", weight=3];
692[label="absReal1 (Float (Neg (Succ vx12)) (Pos vx13)) False",fontsize=16,color="black",shape="box"];692 -> 704[label="",style="solid", color="black", weight=3];
693[label="absReal1 (Float (Neg (Succ vx12)) (Pos (Succ vx130))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];693 -> 705[label="",style="solid", color="black", weight=3];
694[label="absReal1 (Float (Neg (Succ vx12)) (Pos Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];694 -> 706[label="",style="solid", color="black", weight=3];
172[label="absReal1 (Float (Neg Zero) (Pos (Succ vx3100))) True",fontsize=16,color="black",shape="box"];172 -> 202[label="",style="solid", color="black", weight=3];
173[label="absReal1 (Float (Neg Zero) (Pos Zero)) True",fontsize=16,color="black",shape="box"];173 -> 203[label="",style="solid", color="black", weight=3];
701[label="absReal1 (Float (Pos (Succ vx15)) (Neg vx16)) False",fontsize=16,color="black",shape="box"];701 -> 714[label="",style="solid", color="black", weight=3];
702[label="absReal1 (Float (Pos (Succ vx15)) (Neg (Succ vx160))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];702 -> 715[label="",style="solid", color="black", weight=3];
703[label="absReal1 (Float (Pos (Succ vx15)) (Neg Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];703 -> 716[label="",style="solid", color="black", weight=3];
179[label="absReal1 (Float (Pos Zero) (Neg (Succ vx3100))) True",fontsize=16,color="black",shape="box"];179 -> 209[label="",style="solid", color="black", weight=3];
180[label="absReal1 (Float (Pos Zero) (Neg Zero)) True",fontsize=16,color="black",shape="box"];180 -> 210[label="",style="solid", color="black", weight=3];
710[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not (primCmpNat (Succ vx270) Zero == LT))",fontsize=16,color="black",shape="box"];710 -> 724[label="",style="solid", color="black", weight=3];
711[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not (primCmpNat (Succ vx270) Zero == LT))",fontsize=16,color="black",shape="box"];711 -> 725[label="",style="solid", color="black", weight=3];
712[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not (EQ == LT))",fontsize=16,color="black",shape="box"];712 -> 726[label="",style="solid", color="black", weight=3];
713[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not (EQ == LT))",fontsize=16,color="black",shape="box"];713 -> 727[label="",style="solid", color="black", weight=3];
187[label="absReal1 (Float (Neg Zero) (Neg (Succ vx3100))) True",fontsize=16,color="black",shape="box"];187 -> 217[label="",style="solid", color="black", weight=3];
188[label="absReal1 (Float (Neg Zero) (Neg Zero)) True",fontsize=16,color="black",shape="box"];188 -> 218[label="",style="solid", color="black", weight=3];
746[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not (GT == LT))",fontsize=16,color="black",shape="box"];746 -> 754[label="",style="solid", color="black", weight=3];
747[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not (GT == LT))",fontsize=16,color="black",shape="box"];747 -> 755[label="",style="solid", color="black", weight=3];
748[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not False)",fontsize=16,color="black",shape="triangle"];748 -> 756[label="",style="solid", color="black", weight=3];
749[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not False)",fontsize=16,color="black",shape="triangle"];749 -> 757[label="",style="solid", color="black", weight=3];
195[label="Float (Pos Zero) (Pos (Succ vx3100))",fontsize=16,color="green",shape="box"];196[label="Float (Pos Zero) (Pos Zero)",fontsize=16,color="green",shape="box"];704[label="absReal0 (Float (Neg (Succ vx12)) (Pos vx13)) otherwise",fontsize=16,color="black",shape="box"];704 -> 717[label="",style="solid", color="black", weight=3];
705[label="absReal1 (Float (Neg (Succ vx12)) (Pos (Succ vx130))) (not False)",fontsize=16,color="black",shape="box"];705 -> 718[label="",style="solid", color="black", weight=3];
706[label="absReal1 (Float (Neg (Succ vx12)) (Pos Zero)) (not False)",fontsize=16,color="black",shape="box"];706 -> 719[label="",style="solid", color="black", weight=3];
202[label="Float (Neg Zero) (Pos (Succ vx3100))",fontsize=16,color="green",shape="box"];203[label="Float (Neg Zero) (Pos Zero)",fontsize=16,color="green",shape="box"];714[label="absReal0 (Float (Pos (Succ vx15)) (Neg vx16)) otherwise",fontsize=16,color="black",shape="box"];714 -> 728[label="",style="solid", color="black", weight=3];
715[label="absReal1 (Float (Pos (Succ vx15)) (Neg (Succ vx160))) (not False)",fontsize=16,color="black",shape="box"];715 -> 729[label="",style="solid", color="black", weight=3];
716[label="absReal1 (Float (Pos (Succ vx15)) (Neg Zero)) (not False)",fontsize=16,color="black",shape="box"];716 -> 730[label="",style="solid", color="black", weight=3];
209[label="Float (Pos Zero) (Neg (Succ vx3100))",fontsize=16,color="green",shape="box"];210[label="Float (Pos Zero) (Neg Zero)",fontsize=16,color="green",shape="box"];724[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not (GT == LT))",fontsize=16,color="black",shape="box"];724 -> 738[label="",style="solid", color="black", weight=3];
725[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not (GT == LT))",fontsize=16,color="black",shape="box"];725 -> 739[label="",style="solid", color="black", weight=3];
726[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not False)",fontsize=16,color="black",shape="triangle"];726 -> 740[label="",style="solid", color="black", weight=3];
727[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not False)",fontsize=16,color="black",shape="triangle"];727 -> 741[label="",style="solid", color="black", weight=3];
217[label="Float (Neg Zero) (Neg (Succ vx3100))",fontsize=16,color="green",shape="box"];218[label="Float (Neg Zero) (Neg Zero)",fontsize=16,color="green",shape="box"];754 -> 748[label="",style="dashed", color="red", weight=0];
754[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) (not False)",fontsize=16,color="magenta"];755 -> 749[label="",style="dashed", color="red", weight=0];
755[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) (not False)",fontsize=16,color="magenta"];756[label="absReal1 (Float (Pos (Succ vx5)) (Pos (Succ vx60))) True",fontsize=16,color="black",shape="box"];756 -> 760[label="",style="solid", color="black", weight=3];
757[label="absReal1 (Float (Pos (Succ vx5)) (Pos Zero)) True",fontsize=16,color="black",shape="box"];757 -> 761[label="",style="solid", color="black", weight=3];
717[label="absReal0 (Float (Neg (Succ vx12)) (Pos vx13)) True",fontsize=16,color="black",shape="box"];717 -> 731[label="",style="solid", color="black", weight=3];
718[label="absReal1 (Float (Neg (Succ vx12)) (Pos (Succ vx130))) True",fontsize=16,color="black",shape="box"];718 -> 732[label="",style="solid", color="black", weight=3];
719[label="absReal1 (Float (Neg (Succ vx12)) (Pos Zero)) True",fontsize=16,color="black",shape="box"];719 -> 733[label="",style="solid", color="black", weight=3];
728[label="absReal0 (Float (Pos (Succ vx15)) (Neg vx16)) True",fontsize=16,color="black",shape="box"];728 -> 742[label="",style="solid", color="black", weight=3];
729[label="absReal1 (Float (Pos (Succ vx15)) (Neg (Succ vx160))) True",fontsize=16,color="black",shape="box"];729 -> 743[label="",style="solid", color="black", weight=3];
730[label="absReal1 (Float (Pos (Succ vx15)) (Neg Zero)) True",fontsize=16,color="black",shape="box"];730 -> 744[label="",style="solid", color="black", weight=3];
738 -> 726[label="",style="dashed", color="red", weight=0];
738[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) (not False)",fontsize=16,color="magenta"];739 -> 727[label="",style="dashed", color="red", weight=0];
739[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) (not False)",fontsize=16,color="magenta"];740[label="absReal1 (Float (Neg (Succ vx18)) (Neg (Succ vx190))) True",fontsize=16,color="black",shape="box"];740 -> 750[label="",style="solid", color="black", weight=3];
741[label="absReal1 (Float (Neg (Succ vx18)) (Neg Zero)) True",fontsize=16,color="black",shape="box"];741 -> 751[label="",style="solid", color="black", weight=3];
760[label="Float (Pos (Succ vx5)) (Pos (Succ vx60))",fontsize=16,color="green",shape="box"];761[label="Float (Pos (Succ vx5)) (Pos Zero)",fontsize=16,color="green",shape="box"];731[label="`negate` Float (Neg (Succ vx12)) (Pos vx13)",fontsize=16,color="black",shape="box"];731 -> 745[label="",style="solid", color="black", weight=3];
732[label="Float (Neg (Succ vx12)) (Pos (Succ vx130))",fontsize=16,color="green",shape="box"];733[label="Float (Neg (Succ vx12)) (Pos Zero)",fontsize=16,color="green",shape="box"];742[label="`negate` Float (Pos (Succ vx15)) (Neg vx16)",fontsize=16,color="black",shape="box"];742 -> 752[label="",style="solid", color="black", weight=3];
743[label="Float (Pos (Succ vx15)) (Neg (Succ vx160))",fontsize=16,color="green",shape="box"];744[label="Float (Pos (Succ vx15)) (Neg Zero)",fontsize=16,color="green",shape="box"];750[label="Float (Neg (Succ vx18)) (Neg (Succ vx190))",fontsize=16,color="green",shape="box"];751[label="Float (Neg (Succ vx18)) (Neg Zero)",fontsize=16,color="green",shape="box"];745[label="primNegFloat (Float (Neg (Succ vx12)) (Pos vx13))",fontsize=16,color="black",shape="box"];745 -> 753[label="",style="solid", color="black", weight=3];
752[label="primNegFloat (Float (Pos (Succ vx15)) (Neg vx16))",fontsize=16,color="black",shape="box"];752 -> 758[label="",style="solid", color="black", weight=3];
753[label="Float (`negate` Neg (Succ vx12)) (Pos vx13)",fontsize=16,color="green",shape="box"];753 -> 759[label="",style="dashed", color="green", weight=3];
758[label="Float (`negate` Pos (Succ vx15)) (Neg vx16)",fontsize=16,color="green",shape="box"];758 -> 762[label="",style="dashed", color="green", weight=3];
759[label="`negate` Neg (Succ vx12)",fontsize=16,color="black",shape="box"];759 -> 763[label="",style="solid", color="black", weight=3];
762[label="`negate` Pos (Succ vx15)",fontsize=16,color="black",shape="box"];762 -> 764[label="",style="solid", color="black", weight=3];
763[label="primNegInt (Neg (Succ vx12))",fontsize=16,color="black",shape="box"];763 -> 765[label="",style="solid", color="black", weight=3];
764[label="primNegInt (Pos (Succ vx15))",fontsize=16,color="black",shape="box"];764 -> 766[label="",style="solid", color="black", weight=3];
765[label="Pos (Succ vx12)",fontsize=16,color="green",shape="box"];766[label="Neg (Succ vx15)",fontsize=16,color="green",shape="box"];}

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

(8)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMulNat(Succ(vx300000)) -> new_primMulNat(vx300000)

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

(9) 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(vx300000)) -> new_primMulNat(vx300000)
The graph contains the following edges 1 > 1


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

(10)
YES