/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) LR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) IFR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) BR [EQUIVALENT, 0 ms]
(6) HASKELL
(7) COR [EQUIVALENT, 0 ms]
(8) HASKELL
(9) LetRed [EQUIVALENT, 0 ms]
(10) HASKELL
(11) NumRed [SOUND, 0 ms]
(12) HASKELL
(13) Narrow [SOUND, 0 ms]
(14) AND
    (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) AND
            (18) QDP
                (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (20) YES
            (21) QDP
                (22) QDPOrderProof [EQUIVALENT, 41 ms]
                (23) QDP
                (24) DependencyGraphProof [EQUIVALENT, 0 ms]
                (25) QDP
                (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (27) YES
    (28) QDP
        (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (42) YES
    (43) QDP
        (44) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (45) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(1) LR (EQUIVALENT)
Lambda Reductions:
The following Lambda expression
"\(q,_)->q"
is transformed to
"q1 (q,_) = q;
"
The following Lambda expression
"\(_,r)->r"
is transformed to
"r0 (_,r) = r;
"
The following Lambda expression
"\(m,_)->m"
is transformed to
"m0 (m,_) = m;
"

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(3) IFR (EQUIVALENT)
If Reductions:
The following If expression
"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
is transformed to
"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
primDivNatS0 x y False = Zero;
"
The following If expression
"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
is transformed to
"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
primModNatS0 x y False = Succ x;
"

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

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

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

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

Binding Reductions:
The bind variable of the following binding Pattern
"frac@(Float vv vw)"
is replaced by the following term
"Float vv vw"
The bind variable of the following binding Pattern
"frac@(Double ww wx)"
is replaced by the following term
"Double ww wx"

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

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

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

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

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

(8)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(9) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"(fromIntegral q,r :% y) where {
q  = q1 vu30;
;
q1 (q,wy) = q;
;
r  = r0 vu30;
;
r0 (wz,r) = r;
;
vu30  = quotRem x y;
} 
"
are unpacked to the following functions on top level
"properFractionVu30 xw xx = quotRem xw xx;
"
"properFractionR xw xx = properFractionR0 xw xx (properFractionVu30 xw xx);
"
"properFractionQ1 xw xx (q,wy) = q;
"
"properFractionR0 xw xx (wz,r) = r;
"
"properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx);
"
The bindings of the following Let/Where expression
"m where {
m  = m0 vu6;
;
m0 (m,xv) = m;
;
vu6  = properFraction x;
} 
"
are unpacked to the following functions on top level
"truncateVu6 xy = properFraction xy;
"
"truncateM xy = truncateM0 xy (truncateVu6 xy);
"
"truncateM0 xy (m,xv) = m;
"

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

(10)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

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

(12)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
}

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

(13) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="pred xz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="primIntToFloat ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="Float ((subtract (Pos (Succ Zero))) . fromEnum) (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
8[label="(subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="subtract (Pos (Succ Zero)) (fromEnum xz3)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="flip (-) (Pos (Succ Zero)) (fromEnum xz3)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="(-) fromEnum xz3 Pos (Succ Zero)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="primMinusInt (fromEnum xz3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="primMinusInt (truncate xz3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="primMinusInt (truncateM xz3) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
15[label="primMinusInt (truncateM0 xz3 (truncateVu6 xz3)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
16[label="primMinusInt (truncateM0 xz3 (properFraction xz3)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
17[label="primMinusInt (truncateM0 xz3 (floatProperFractionFloat xz3)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2333[label="xz3/Float xz30 xz31",fontsize=10,color="white",style="solid",shape="box"];17 -> 2333[label="",style="solid", color="burlywood", weight=9];
2333 -> 18[label="",style="solid", color="burlywood", weight=3];
18[label="primMinusInt (truncateM0 (Float xz30 xz31) (floatProperFractionFloat (Float xz30 xz31))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
19[label="primMinusInt (truncateM0 (Float xz30 xz31) (fromInt (xz30 `quot` xz31),Float xz30 xz31 - fromInt (xz30 `quot` xz31))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
20[label="primMinusInt (fromInt (xz30 `quot` xz31)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
21[label="primMinusInt (xz30 `quot` xz31) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
22[label="primMinusInt (primQuotInt xz30 xz31) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2334[label="xz30/Pos xz300",fontsize=10,color="white",style="solid",shape="box"];22 -> 2334[label="",style="solid", color="burlywood", weight=9];
2334 -> 23[label="",style="solid", color="burlywood", weight=3];
2335[label="xz30/Neg xz300",fontsize=10,color="white",style="solid",shape="box"];22 -> 2335[label="",style="solid", color="burlywood", weight=9];
2335 -> 24[label="",style="solid", color="burlywood", weight=3];
23[label="primMinusInt (primQuotInt (Pos xz300) xz31) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2336[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];23 -> 2336[label="",style="solid", color="burlywood", weight=9];
2336 -> 25[label="",style="solid", color="burlywood", weight=3];
2337[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];23 -> 2337[label="",style="solid", color="burlywood", weight=9];
2337 -> 26[label="",style="solid", color="burlywood", weight=3];
24[label="primMinusInt (primQuotInt (Neg xz300) xz31) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2338[label="xz31/Pos xz310",fontsize=10,color="white",style="solid",shape="box"];24 -> 2338[label="",style="solid", color="burlywood", weight=9];
2338 -> 27[label="",style="solid", color="burlywood", weight=3];
2339[label="xz31/Neg xz310",fontsize=10,color="white",style="solid",shape="box"];24 -> 2339[label="",style="solid", color="burlywood", weight=9];
2339 -> 28[label="",style="solid", color="burlywood", weight=3];
25[label="primMinusInt (primQuotInt (Pos xz300) (Pos xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2340[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];25 -> 2340[label="",style="solid", color="burlywood", weight=9];
2340 -> 29[label="",style="solid", color="burlywood", weight=3];
2341[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 2341[label="",style="solid", color="burlywood", weight=9];
2341 -> 30[label="",style="solid", color="burlywood", weight=3];
26[label="primMinusInt (primQuotInt (Pos xz300) (Neg xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2342[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];26 -> 2342[label="",style="solid", color="burlywood", weight=9];
2342 -> 31[label="",style="solid", color="burlywood", weight=3];
2343[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];26 -> 2343[label="",style="solid", color="burlywood", weight=9];
2343 -> 32[label="",style="solid", color="burlywood", weight=3];
27[label="primMinusInt (primQuotInt (Neg xz300) (Pos xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2344[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];27 -> 2344[label="",style="solid", color="burlywood", weight=9];
2344 -> 33[label="",style="solid", color="burlywood", weight=3];
2345[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 2345[label="",style="solid", color="burlywood", weight=9];
2345 -> 34[label="",style="solid", color="burlywood", weight=3];
28[label="primMinusInt (primQuotInt (Neg xz300) (Neg xz310)) (Pos (Succ Zero))",fontsize=16,color="burlywood",shape="box"];2346[label="xz310/Succ xz3100",fontsize=10,color="white",style="solid",shape="box"];28 -> 2346[label="",style="solid", color="burlywood", weight=9];
2346 -> 35[label="",style="solid", color="burlywood", weight=3];
2347[label="xz310/Zero",fontsize=10,color="white",style="solid",shape="box"];28 -> 2347[label="",style="solid", color="burlywood", weight=9];
2347 -> 36[label="",style="solid", color="burlywood", weight=3];
29[label="primMinusInt (primQuotInt (Pos xz300) (Pos (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3];
30[label="primMinusInt (primQuotInt (Pos xz300) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3];
31[label="primMinusInt (primQuotInt (Pos xz300) (Neg (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3];
32[label="primMinusInt (primQuotInt (Pos xz300) (Neg Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3];
33[label="primMinusInt (primQuotInt (Neg xz300) (Pos (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];33 -> 41[label="",style="solid", color="black", weight=3];
34[label="primMinusInt (primQuotInt (Neg xz300) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3];
35[label="primMinusInt (primQuotInt (Neg xz300) (Neg (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
36[label="primMinusInt (primQuotInt (Neg xz300) (Neg Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
37[label="primMinusInt (Pos (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];37 -> 45[label="",style="solid", color="black", weight=3];
38[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];38 -> 46[label="",style="solid", color="black", weight=3];
39[label="primMinusInt (Neg (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];39 -> 47[label="",style="solid", color="black", weight=3];
40 -> 38[label="",style="dashed", color="red", weight=0];
40[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="magenta"];41 -> 39[label="",style="dashed", color="red", weight=0];
41[label="primMinusInt (Neg (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="magenta"];41 -> 48[label="",style="dashed", color="magenta", weight=3];
41 -> 49[label="",style="dashed", color="magenta", weight=3];
42 -> 38[label="",style="dashed", color="red", weight=0];
42[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="magenta"];43 -> 37[label="",style="dashed", color="red", weight=0];
43[label="primMinusInt (Pos (primDivNatS xz300 (Succ xz3100))) (Pos (Succ Zero))",fontsize=16,color="magenta"];43 -> 50[label="",style="dashed", color="magenta", weight=3];
43 -> 51[label="",style="dashed", color="magenta", weight=3];
44 -> 38[label="",style="dashed", color="red", weight=0];
44[label="primMinusInt (error []) (Pos (Succ Zero))",fontsize=16,color="magenta"];45[label="primMinusNat (primDivNatS xz300 (Succ xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2348[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];45 -> 2348[label="",style="solid", color="burlywood", weight=9];
2348 -> 52[label="",style="solid", color="burlywood", weight=3];
2349[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 2349[label="",style="solid", color="burlywood", weight=9];
2349 -> 53[label="",style="solid", color="burlywood", weight=3];
46[label="error []",fontsize=16,color="red",shape="box"];47[label="Neg (primPlusNat (primDivNatS xz300 (Succ xz3100)) (Succ Zero))",fontsize=16,color="green",shape="box"];47 -> 54[label="",style="dashed", color="green", weight=3];
48[label="xz300",fontsize=16,color="green",shape="box"];49[label="xz3100",fontsize=16,color="green",shape="box"];50[label="xz300",fontsize=16,color="green",shape="box"];51[label="xz3100",fontsize=16,color="green",shape="box"];52[label="primMinusNat (primDivNatS (Succ xz3000) (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3];
53[label="primMinusNat (primDivNatS Zero (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];53 -> 56[label="",style="solid", color="black", weight=3];
54[label="primPlusNat (primDivNatS xz300 (Succ xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2350[label="xz300/Succ xz3000",fontsize=10,color="white",style="solid",shape="box"];54 -> 2350[label="",style="solid", color="burlywood", weight=9];
2350 -> 57[label="",style="solid", color="burlywood", weight=3];
2351[label="xz300/Zero",fontsize=10,color="white",style="solid",shape="box"];54 -> 2351[label="",style="solid", color="burlywood", weight=9];
2351 -> 58[label="",style="solid", color="burlywood", weight=3];
55[label="primMinusNat (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2352[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];55 -> 2352[label="",style="solid", color="burlywood", weight=9];
2352 -> 59[label="",style="solid", color="burlywood", weight=3];
2353[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 2353[label="",style="solid", color="burlywood", weight=9];
2353 -> 60[label="",style="solid", color="burlywood", weight=3];
56[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="black",shape="triangle"];56 -> 61[label="",style="solid", color="black", weight=3];
57[label="primPlusNat (primDivNatS (Succ xz3000) (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3];
58[label="primPlusNat (primDivNatS Zero (Succ xz3100)) (Succ Zero)",fontsize=16,color="black",shape="box"];58 -> 63[label="",style="solid", color="black", weight=3];
59[label="primMinusNat (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2354[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];59 -> 2354[label="",style="solid", color="burlywood", weight=9];
2354 -> 64[label="",style="solid", color="burlywood", weight=3];
2355[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];59 -> 2355[label="",style="solid", color="burlywood", weight=9];
2355 -> 65[label="",style="solid", color="burlywood", weight=3];
60[label="primMinusNat (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2356[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];60 -> 2356[label="",style="solid", color="burlywood", weight=9];
2356 -> 66[label="",style="solid", color="burlywood", weight=3];
2357[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];60 -> 2357[label="",style="solid", color="burlywood", weight=9];
2357 -> 67[label="",style="solid", color="burlywood", weight=3];
61[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];62[label="primPlusNat (primDivNatS0 xz3000 xz3100 (primGEqNatS xz3000 xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2358[label="xz3000/Succ xz30000",fontsize=10,color="white",style="solid",shape="box"];62 -> 2358[label="",style="solid", color="burlywood", weight=9];
2358 -> 68[label="",style="solid", color="burlywood", weight=3];
2359[label="xz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];62 -> 2359[label="",style="solid", color="burlywood", weight=9];
2359 -> 69[label="",style="solid", color="burlywood", weight=3];
63[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="triangle"];63 -> 70[label="",style="solid", color="black", weight=3];
64[label="primMinusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];64 -> 71[label="",style="solid", color="black", weight=3];
65[label="primMinusNat (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];65 -> 72[label="",style="solid", color="black", weight=3];
66[label="primMinusNat (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];66 -> 73[label="",style="solid", color="black", weight=3];
67[label="primMinusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];67 -> 74[label="",style="solid", color="black", weight=3];
68[label="primPlusNat (primDivNatS0 (Succ xz30000) xz3100 (primGEqNatS (Succ xz30000) xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2360[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];68 -> 2360[label="",style="solid", color="burlywood", weight=9];
2360 -> 75[label="",style="solid", color="burlywood", weight=3];
2361[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];68 -> 2361[label="",style="solid", color="burlywood", weight=9];
2361 -> 76[label="",style="solid", color="burlywood", weight=3];
69[label="primPlusNat (primDivNatS0 Zero xz3100 (primGEqNatS Zero xz3100)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2362[label="xz3100/Succ xz31000",fontsize=10,color="white",style="solid",shape="box"];69 -> 2362[label="",style="solid", color="burlywood", weight=9];
2362 -> 77[label="",style="solid", color="burlywood", weight=3];
2363[label="xz3100/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 2363[label="",style="solid", color="burlywood", weight=9];
2363 -> 78[label="",style="solid", color="burlywood", weight=3];
70[label="Succ Zero",fontsize=16,color="green",shape="box"];71 -> 664[label="",style="dashed", color="red", weight=0];
71[label="primMinusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000)) (Succ Zero)",fontsize=16,color="magenta"];71 -> 665[label="",style="dashed", color="magenta", weight=3];
71 -> 666[label="",style="dashed", color="magenta", weight=3];
71 -> 667[label="",style="dashed", color="magenta", weight=3];
71 -> 668[label="",style="dashed", color="magenta", weight=3];
72[label="primMinusNat (primDivNatS0 (Succ xz30000) Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];72 -> 81[label="",style="solid", color="black", weight=3];
73[label="primMinusNat (primDivNatS0 Zero (Succ xz31000) False) (Succ Zero)",fontsize=16,color="black",shape="box"];73 -> 82[label="",style="solid", color="black", weight=3];
74[label="primMinusNat (primDivNatS0 Zero Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];74 -> 83[label="",style="solid", color="black", weight=3];
75[label="primPlusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS (Succ xz30000) (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];75 -> 84[label="",style="solid", color="black", weight=3];
76[label="primPlusNat (primDivNatS0 (Succ xz30000) Zero (primGEqNatS (Succ xz30000) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];76 -> 85[label="",style="solid", color="black", weight=3];
77[label="primPlusNat (primDivNatS0 Zero (Succ xz31000) (primGEqNatS Zero (Succ xz31000))) (Succ Zero)",fontsize=16,color="black",shape="box"];77 -> 86[label="",style="solid", color="black", weight=3];
78[label="primPlusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];78 -> 87[label="",style="solid", color="black", weight=3];
665[label="xz30000",fontsize=16,color="green",shape="box"];666[label="xz31000",fontsize=16,color="green",shape="box"];667[label="xz30000",fontsize=16,color="green",shape="box"];668[label="xz31000",fontsize=16,color="green",shape="box"];664[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS xz40 xz41)) (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];2364[label="xz40/Succ xz400",fontsize=10,color="white",style="solid",shape="box"];664 -> 2364[label="",style="solid", color="burlywood", weight=9];
2364 -> 705[label="",style="solid", color="burlywood", weight=3];
2365[label="xz40/Zero",fontsize=10,color="white",style="solid",shape="box"];664 -> 2365[label="",style="solid", color="burlywood", weight=9];
2365 -> 706[label="",style="solid", color="burlywood", weight=3];
81[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];81 -> 92[label="",style="solid", color="black", weight=3];
82 -> 56[label="",style="dashed", color="red", weight=0];
82[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="magenta"];83[label="primMinusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];83 -> 93[label="",style="solid", color="black", weight=3];
84 -> 737[label="",style="dashed", color="red", weight=0];
84[label="primPlusNat (primDivNatS0 (Succ xz30000) (Succ xz31000) (primGEqNatS xz30000 xz31000)) (Succ Zero)",fontsize=16,color="magenta"];84 -> 738[label="",style="dashed", color="magenta", weight=3];
84 -> 739[label="",style="dashed", color="magenta", weight=3];
84 -> 740[label="",style="dashed", color="magenta", weight=3];
84 -> 741[label="",style="dashed", color="magenta", weight=3];
85[label="primPlusNat (primDivNatS0 (Succ xz30000) Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];85 -> 96[label="",style="solid", color="black", weight=3];
86[label="primPlusNat (primDivNatS0 Zero (Succ xz31000) False) (Succ Zero)",fontsize=16,color="black",shape="box"];86 -> 97[label="",style="solid", color="black", weight=3];
87[label="primPlusNat (primDivNatS0 Zero Zero True) (Succ Zero)",fontsize=16,color="black",shape="box"];87 -> 98[label="",style="solid", color="black", weight=3];
705[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS (Succ xz400) xz41)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2366[label="xz41/Succ xz410",fontsize=10,color="white",style="solid",shape="box"];705 -> 2366[label="",style="solid", color="burlywood", weight=9];
2366 -> 711[label="",style="solid", color="burlywood", weight=3];
2367[label="xz41/Zero",fontsize=10,color="white",style="solid",shape="box"];705 -> 2367[label="",style="solid", color="burlywood", weight=9];
2367 -> 712[label="",style="solid", color="burlywood", weight=3];
706[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS Zero xz41)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2368[label="xz41/Succ xz410",fontsize=10,color="white",style="solid",shape="box"];706 -> 2368[label="",style="solid", color="burlywood", weight=9];
2368 -> 713[label="",style="solid", color="burlywood", weight=3];
2369[label="xz41/Zero",fontsize=10,color="white",style="solid",shape="box"];706 -> 2369[label="",style="solid", color="burlywood", weight=9];
2369 -> 714[label="",style="solid", color="burlywood", weight=3];
92 -> 1145[label="",style="dashed", color="red", weight=0];
92[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];92 -> 1146[label="",style="dashed", color="magenta", weight=3];
92 -> 1147[label="",style="dashed", color="magenta", weight=3];
92 -> 1148[label="",style="dashed", color="magenta", weight=3];
93 -> 1145[label="",style="dashed", color="red", weight=0];
93[label="primMinusNat (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];93 -> 1149[label="",style="dashed", color="magenta", weight=3];
93 -> 1150[label="",style="dashed", color="magenta", weight=3];
93 -> 1151[label="",style="dashed", color="magenta", weight=3];
738[label="xz31000",fontsize=16,color="green",shape="box"];739[label="xz30000",fontsize=16,color="green",shape="box"];740[label="xz31000",fontsize=16,color="green",shape="box"];741[label="xz30000",fontsize=16,color="green",shape="box"];737[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS xz53 xz54)) (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];2370[label="xz53/Succ xz530",fontsize=10,color="white",style="solid",shape="box"];737 -> 2370[label="",style="solid", color="burlywood", weight=9];
2370 -> 778[label="",style="solid", color="burlywood", weight=3];
2371[label="xz53/Zero",fontsize=10,color="white",style="solid",shape="box"];737 -> 2371[label="",style="solid", color="burlywood", weight=9];
2371 -> 779[label="",style="solid", color="burlywood", weight=3];
96[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];96 -> 109[label="",style="solid", color="black", weight=3];
97 -> 63[label="",style="dashed", color="red", weight=0];
97[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="magenta"];98[label="primPlusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) (Succ Zero)",fontsize=16,color="black",shape="box"];98 -> 110[label="",style="solid", color="black", weight=3];
711[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS (Succ xz400) (Succ xz410))) (Succ Zero)",fontsize=16,color="black",shape="box"];711 -> 718[label="",style="solid", color="black", weight=3];
712[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS (Succ xz400) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];712 -> 719[label="",style="solid", color="black", weight=3];
713[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS Zero (Succ xz410))) (Succ Zero)",fontsize=16,color="black",shape="box"];713 -> 720[label="",style="solid", color="black", weight=3];
714[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];714 -> 721[label="",style="solid", color="black", weight=3];
1146[label="Succ xz30000",fontsize=16,color="green",shape="box"];1147[label="Zero",fontsize=16,color="green",shape="box"];1148[label="Zero",fontsize=16,color="green",shape="box"];1145[label="primMinusNat (primDivNatS (primMinusNatS xz58 xz59) (Succ xz60)) Zero",fontsize=16,color="burlywood",shape="triangle"];2372[label="xz58/Succ xz580",fontsize=10,color="white",style="solid",shape="box"];1145 -> 2372[label="",style="solid", color="burlywood", weight=9];
2372 -> 1179[label="",style="solid", color="burlywood", weight=3];
2373[label="xz58/Zero",fontsize=10,color="white",style="solid",shape="box"];1145 -> 2373[label="",style="solid", color="burlywood", weight=9];
2373 -> 1180[label="",style="solid", color="burlywood", weight=3];
1149[label="Zero",fontsize=16,color="green",shape="box"];1150[label="Zero",fontsize=16,color="green",shape="box"];1151[label="Zero",fontsize=16,color="green",shape="box"];778[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS (Succ xz530) xz54)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2374[label="xz54/Succ xz540",fontsize=10,color="white",style="solid",shape="box"];778 -> 2374[label="",style="solid", color="burlywood", weight=9];
2374 -> 781[label="",style="solid", color="burlywood", weight=3];
2375[label="xz54/Zero",fontsize=10,color="white",style="solid",shape="box"];778 -> 2375[label="",style="solid", color="burlywood", weight=9];
2375 -> 782[label="",style="solid", color="burlywood", weight=3];
779[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS Zero xz54)) (Succ Zero)",fontsize=16,color="burlywood",shape="box"];2376[label="xz54/Succ xz540",fontsize=10,color="white",style="solid",shape="box"];779 -> 2376[label="",style="solid", color="burlywood", weight=9];
2376 -> 783[label="",style="solid", color="burlywood", weight=3];
2377[label="xz54/Zero",fontsize=10,color="white",style="solid",shape="box"];779 -> 2377[label="",style="solid", color="burlywood", weight=9];
2377 -> 784[label="",style="solid", color="burlywood", weight=3];
109[label="Succ (Succ (primPlusNat (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)) Zero))",fontsize=16,color="green",shape="box"];109 -> 122[label="",style="dashed", color="green", weight=3];
110[label="Succ (Succ (primPlusNat (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)) Zero))",fontsize=16,color="green",shape="box"];110 -> 123[label="",style="dashed", color="green", weight=3];
718 -> 664[label="",style="dashed", color="red", weight=0];
718[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) (primGEqNatS xz400 xz410)) (Succ Zero)",fontsize=16,color="magenta"];718 -> 724[label="",style="dashed", color="magenta", weight=3];
718 -> 725[label="",style="dashed", color="magenta", weight=3];
719[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) True) (Succ Zero)",fontsize=16,color="black",shape="triangle"];719 -> 726[label="",style="solid", color="black", weight=3];
720[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) False) (Succ Zero)",fontsize=16,color="black",shape="box"];720 -> 727[label="",style="solid", color="black", weight=3];
721 -> 719[label="",style="dashed", color="red", weight=0];
721[label="primMinusNat (primDivNatS0 (Succ xz38) (Succ xz39) True) (Succ Zero)",fontsize=16,color="magenta"];1179[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz580) xz59) (Succ xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2378[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1179 -> 2378[label="",style="solid", color="burlywood", weight=9];
2378 -> 1194[label="",style="solid", color="burlywood", weight=3];
2379[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1179 -> 2379[label="",style="solid", color="burlywood", weight=9];
2379 -> 1195[label="",style="solid", color="burlywood", weight=3];
1180[label="primMinusNat (primDivNatS (primMinusNatS Zero xz59) (Succ xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2380[label="xz59/Succ xz590",fontsize=10,color="white",style="solid",shape="box"];1180 -> 2380[label="",style="solid", color="burlywood", weight=9];
2380 -> 1196[label="",style="solid", color="burlywood", weight=3];
2381[label="xz59/Zero",fontsize=10,color="white",style="solid",shape="box"];1180 -> 2381[label="",style="solid", color="burlywood", weight=9];
2381 -> 1197[label="",style="solid", color="burlywood", weight=3];
781[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS (Succ xz530) (Succ xz540))) (Succ Zero)",fontsize=16,color="black",shape="box"];781 -> 786[label="",style="solid", color="black", weight=3];
782[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS (Succ xz530) Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];782 -> 787[label="",style="solid", color="black", weight=3];
783[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS Zero (Succ xz540))) (Succ Zero)",fontsize=16,color="black",shape="box"];783 -> 788[label="",style="solid", color="black", weight=3];
784[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS Zero Zero)) (Succ Zero)",fontsize=16,color="black",shape="box"];784 -> 789[label="",style="solid", color="black", weight=3];
122 -> 1257[label="",style="dashed", color="red", weight=0];
122[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz30000) Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];122 -> 1258[label="",style="dashed", color="magenta", weight=3];
122 -> 1259[label="",style="dashed", color="magenta", weight=3];
122 -> 1260[label="",style="dashed", color="magenta", weight=3];
123 -> 1257[label="",style="dashed", color="red", weight=0];
123[label="primPlusNat (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)) Zero",fontsize=16,color="magenta"];123 -> 1261[label="",style="dashed", color="magenta", weight=3];
123 -> 1262[label="",style="dashed", color="magenta", weight=3];
123 -> 1263[label="",style="dashed", color="magenta", weight=3];
724[label="xz400",fontsize=16,color="green",shape="box"];725[label="xz410",fontsize=16,color="green",shape="box"];726[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz38) (Succ xz39)) (Succ (Succ xz39)))) (Succ Zero)",fontsize=16,color="black",shape="box"];726 -> 780[label="",style="solid", color="black", weight=3];
727 -> 56[label="",style="dashed", color="red", weight=0];
727[label="primMinusNat Zero (Succ Zero)",fontsize=16,color="magenta"];1194[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz580) (Succ xz590)) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1194 -> 1213[label="",style="solid", color="black", weight=3];
1195[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz580) Zero) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1195 -> 1214[label="",style="solid", color="black", weight=3];
1196[label="primMinusNat (primDivNatS (primMinusNatS Zero (Succ xz590)) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1196 -> 1215[label="",style="solid", color="black", weight=3];
1197[label="primMinusNat (primDivNatS (primMinusNatS Zero Zero) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1197 -> 1216[label="",style="solid", color="black", weight=3];
786 -> 737[label="",style="dashed", color="red", weight=0];
786[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) (primGEqNatS xz530 xz540)) (Succ Zero)",fontsize=16,color="magenta"];786 -> 792[label="",style="dashed", color="magenta", weight=3];
786 -> 793[label="",style="dashed", color="magenta", weight=3];
787[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) True) (Succ Zero)",fontsize=16,color="black",shape="triangle"];787 -> 794[label="",style="solid", color="black", weight=3];
788[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) False) (Succ Zero)",fontsize=16,color="black",shape="box"];788 -> 795[label="",style="solid", color="black", weight=3];
789 -> 787[label="",style="dashed", color="red", weight=0];
789[label="primPlusNat (primDivNatS0 (Succ xz51) (Succ xz52) True) (Succ Zero)",fontsize=16,color="magenta"];1258[label="Succ xz30000",fontsize=16,color="green",shape="box"];1259[label="Zero",fontsize=16,color="green",shape="box"];1260[label="Zero",fontsize=16,color="green",shape="box"];1257[label="primPlusNat (primDivNatS (primMinusNatS xz64 xz65) (Succ xz66)) Zero",fontsize=16,color="burlywood",shape="triangle"];2382[label="xz64/Succ xz640",fontsize=10,color="white",style="solid",shape="box"];1257 -> 2382[label="",style="solid", color="burlywood", weight=9];
2382 -> 1291[label="",style="solid", color="burlywood", weight=3];
2383[label="xz64/Zero",fontsize=10,color="white",style="solid",shape="box"];1257 -> 2383[label="",style="solid", color="burlywood", weight=9];
2383 -> 1292[label="",style="solid", color="burlywood", weight=3];
1261[label="Zero",fontsize=16,color="green",shape="box"];1262[label="Zero",fontsize=16,color="green",shape="box"];1263[label="Zero",fontsize=16,color="green",shape="box"];780 -> 1145[label="",style="dashed", color="red", weight=0];
780[label="primMinusNat (primDivNatS (primMinusNatS (Succ xz38) (Succ xz39)) (Succ (Succ xz39))) Zero",fontsize=16,color="magenta"];780 -> 1152[label="",style="dashed", color="magenta", weight=3];
780 -> 1153[label="",style="dashed", color="magenta", weight=3];
780 -> 1154[label="",style="dashed", color="magenta", weight=3];
1213 -> 1145[label="",style="dashed", color="red", weight=0];
1213[label="primMinusNat (primDivNatS (primMinusNatS xz580 xz590) (Succ xz60)) Zero",fontsize=16,color="magenta"];1213 -> 1232[label="",style="dashed", color="magenta", weight=3];
1213 -> 1233[label="",style="dashed", color="magenta", weight=3];
1214[label="primMinusNat (primDivNatS (Succ xz580) (Succ xz60)) Zero",fontsize=16,color="black",shape="box"];1214 -> 1234[label="",style="solid", color="black", weight=3];
1215[label="primMinusNat (primDivNatS Zero (Succ xz60)) Zero",fontsize=16,color="black",shape="triangle"];1215 -> 1235[label="",style="solid", color="black", weight=3];
1216 -> 1215[label="",style="dashed", color="red", weight=0];
1216[label="primMinusNat (primDivNatS Zero (Succ xz60)) Zero",fontsize=16,color="magenta"];792[label="xz540",fontsize=16,color="green",shape="box"];793[label="xz530",fontsize=16,color="green",shape="box"];794[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz51) (Succ xz52)) (Succ (Succ xz52)))) (Succ Zero)",fontsize=16,color="black",shape="box"];794 -> 800[label="",style="solid", color="black", weight=3];
795 -> 63[label="",style="dashed", color="red", weight=0];
795[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="magenta"];1291[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz640) xz65) (Succ xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2384[label="xz65/Succ xz650",fontsize=10,color="white",style="solid",shape="box"];1291 -> 2384[label="",style="solid", color="burlywood", weight=9];
2384 -> 1297[label="",style="solid", color="burlywood", weight=3];
2385[label="xz65/Zero",fontsize=10,color="white",style="solid",shape="box"];1291 -> 2385[label="",style="solid", color="burlywood", weight=9];
2385 -> 1298[label="",style="solid", color="burlywood", weight=3];
1292[label="primPlusNat (primDivNatS (primMinusNatS Zero xz65) (Succ xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2386[label="xz65/Succ xz650",fontsize=10,color="white",style="solid",shape="box"];1292 -> 2386[label="",style="solid", color="burlywood", weight=9];
2386 -> 1299[label="",style="solid", color="burlywood", weight=3];
2387[label="xz65/Zero",fontsize=10,color="white",style="solid",shape="box"];1292 -> 2387[label="",style="solid", color="burlywood", weight=9];
2387 -> 1300[label="",style="solid", color="burlywood", weight=3];
1152[label="Succ xz38",fontsize=16,color="green",shape="box"];1153[label="Succ xz39",fontsize=16,color="green",shape="box"];1154[label="Succ xz39",fontsize=16,color="green",shape="box"];1232[label="xz580",fontsize=16,color="green",shape="box"];1233[label="xz590",fontsize=16,color="green",shape="box"];1234[label="primMinusNat (primDivNatS0 xz580 xz60 (primGEqNatS xz580 xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2388[label="xz580/Succ xz5800",fontsize=10,color="white",style="solid",shape="box"];1234 -> 2388[label="",style="solid", color="burlywood", weight=9];
2388 -> 1249[label="",style="solid", color="burlywood", weight=3];
2389[label="xz580/Zero",fontsize=10,color="white",style="solid",shape="box"];1234 -> 2389[label="",style="solid", color="burlywood", weight=9];
2389 -> 1250[label="",style="solid", color="burlywood", weight=3];
1235[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1235 -> 1251[label="",style="solid", color="black", weight=3];
800[label="Succ (Succ (primPlusNat (primDivNatS (primMinusNatS (Succ xz51) (Succ xz52)) (Succ (Succ xz52))) Zero))",fontsize=16,color="green",shape="box"];800 -> 805[label="",style="dashed", color="green", weight=3];
1297[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz640) (Succ xz650)) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1297 -> 1305[label="",style="solid", color="black", weight=3];
1298[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz640) Zero) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1298 -> 1306[label="",style="solid", color="black", weight=3];
1299[label="primPlusNat (primDivNatS (primMinusNatS Zero (Succ xz650)) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1299 -> 1307[label="",style="solid", color="black", weight=3];
1300[label="primPlusNat (primDivNatS (primMinusNatS Zero Zero) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1300 -> 1308[label="",style="solid", color="black", weight=3];
1249[label="primMinusNat (primDivNatS0 (Succ xz5800) xz60 (primGEqNatS (Succ xz5800) xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2390[label="xz60/Succ xz600",fontsize=10,color="white",style="solid",shape="box"];1249 -> 2390[label="",style="solid", color="burlywood", weight=9];
2390 -> 1293[label="",style="solid", color="burlywood", weight=3];
2391[label="xz60/Zero",fontsize=10,color="white",style="solid",shape="box"];1249 -> 2391[label="",style="solid", color="burlywood", weight=9];
2391 -> 1294[label="",style="solid", color="burlywood", weight=3];
1250[label="primMinusNat (primDivNatS0 Zero xz60 (primGEqNatS Zero xz60)) Zero",fontsize=16,color="burlywood",shape="box"];2392[label="xz60/Succ xz600",fontsize=10,color="white",style="solid",shape="box"];1250 -> 2392[label="",style="solid", color="burlywood", weight=9];
2392 -> 1295[label="",style="solid", color="burlywood", weight=3];
2393[label="xz60/Zero",fontsize=10,color="white",style="solid",shape="box"];1250 -> 2393[label="",style="solid", color="burlywood", weight=9];
2393 -> 1296[label="",style="solid", color="burlywood", weight=3];
1251[label="Pos Zero",fontsize=16,color="green",shape="box"];805 -> 1257[label="",style="dashed", color="red", weight=0];
805[label="primPlusNat (primDivNatS (primMinusNatS (Succ xz51) (Succ xz52)) (Succ (Succ xz52))) Zero",fontsize=16,color="magenta"];805 -> 1264[label="",style="dashed", color="magenta", weight=3];
805 -> 1265[label="",style="dashed", color="magenta", weight=3];
805 -> 1266[label="",style="dashed", color="magenta", weight=3];
1305 -> 1257[label="",style="dashed", color="red", weight=0];
1305[label="primPlusNat (primDivNatS (primMinusNatS xz640 xz650) (Succ xz66)) Zero",fontsize=16,color="magenta"];1305 -> 1314[label="",style="dashed", color="magenta", weight=3];
1305 -> 1315[label="",style="dashed", color="magenta", weight=3];
1306[label="primPlusNat (primDivNatS (Succ xz640) (Succ xz66)) Zero",fontsize=16,color="black",shape="box"];1306 -> 1316[label="",style="solid", color="black", weight=3];
1307[label="primPlusNat (primDivNatS Zero (Succ xz66)) Zero",fontsize=16,color="black",shape="triangle"];1307 -> 1317[label="",style="solid", color="black", weight=3];
1308 -> 1307[label="",style="dashed", color="red", weight=0];
1308[label="primPlusNat (primDivNatS Zero (Succ xz66)) Zero",fontsize=16,color="magenta"];1293[label="primMinusNat (primDivNatS0 (Succ xz5800) (Succ xz600) (primGEqNatS (Succ xz5800) (Succ xz600))) Zero",fontsize=16,color="black",shape="box"];1293 -> 1301[label="",style="solid", color="black", weight=3];
1294[label="primMinusNat (primDivNatS0 (Succ xz5800) Zero (primGEqNatS (Succ xz5800) Zero)) Zero",fontsize=16,color="black",shape="box"];1294 -> 1302[label="",style="solid", color="black", weight=3];
1295[label="primMinusNat (primDivNatS0 Zero (Succ xz600) (primGEqNatS Zero (Succ xz600))) Zero",fontsize=16,color="black",shape="box"];1295 -> 1303[label="",style="solid", color="black", weight=3];
1296[label="primMinusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];1296 -> 1304[label="",style="solid", color="black", weight=3];
1264[label="Succ xz51",fontsize=16,color="green",shape="box"];1265[label="Succ xz52",fontsize=16,color="green",shape="box"];1266[label="Succ xz52",fontsize=16,color="green",shape="box"];1314[label="xz640",fontsize=16,color="green",shape="box"];1315[label="xz650",fontsize=16,color="green",shape="box"];1316[label="primPlusNat (primDivNatS0 xz640 xz66 (primGEqNatS xz640 xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2394[label="xz640/Succ xz6400",fontsize=10,color="white",style="solid",shape="box"];1316 -> 2394[label="",style="solid", color="burlywood", weight=9];
2394 -> 1324[label="",style="solid", color="burlywood", weight=3];
2395[label="xz640/Zero",fontsize=10,color="white",style="solid",shape="box"];1316 -> 2395[label="",style="solid", color="burlywood", weight=9];
2395 -> 1325[label="",style="solid", color="burlywood", weight=3];
1317[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="triangle"];1317 -> 1326[label="",style="solid", color="black", weight=3];
1301 -> 1820[label="",style="dashed", color="red", weight=0];
1301[label="primMinusNat (primDivNatS0 (Succ xz5800) (Succ xz600) (primGEqNatS xz5800 xz600)) Zero",fontsize=16,color="magenta"];1301 -> 1821[label="",style="dashed", color="magenta", weight=3];
1301 -> 1822[label="",style="dashed", color="magenta", weight=3];
1301 -> 1823[label="",style="dashed", color="magenta", weight=3];
1301 -> 1824[label="",style="dashed", color="magenta", weight=3];
1302[label="primMinusNat (primDivNatS0 (Succ xz5800) Zero True) Zero",fontsize=16,color="black",shape="box"];1302 -> 1311[label="",style="solid", color="black", weight=3];
1303[label="primMinusNat (primDivNatS0 Zero (Succ xz600) False) Zero",fontsize=16,color="black",shape="box"];1303 -> 1312[label="",style="solid", color="black", weight=3];
1304[label="primMinusNat (primDivNatS0 Zero Zero True) Zero",fontsize=16,color="black",shape="box"];1304 -> 1313[label="",style="solid", color="black", weight=3];
1324[label="primPlusNat (primDivNatS0 (Succ xz6400) xz66 (primGEqNatS (Succ xz6400) xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2396[label="xz66/Succ xz660",fontsize=10,color="white",style="solid",shape="box"];1324 -> 2396[label="",style="solid", color="burlywood", weight=9];
2396 -> 1333[label="",style="solid", color="burlywood", weight=3];
2397[label="xz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1324 -> 2397[label="",style="solid", color="burlywood", weight=9];
2397 -> 1334[label="",style="solid", color="burlywood", weight=3];
1325[label="primPlusNat (primDivNatS0 Zero xz66 (primGEqNatS Zero xz66)) Zero",fontsize=16,color="burlywood",shape="box"];2398[label="xz66/Succ xz660",fontsize=10,color="white",style="solid",shape="box"];1325 -> 2398[label="",style="solid", color="burlywood", weight=9];
2398 -> 1335[label="",style="solid", color="burlywood", weight=3];
2399[label="xz66/Zero",fontsize=10,color="white",style="solid",shape="box"];1325 -> 2399[label="",style="solid", color="burlywood", weight=9];
2399 -> 1336[label="",style="solid", color="burlywood", weight=3];
1326[label="Zero",fontsize=16,color="green",shape="box"];1821[label="xz600",fontsize=16,color="green",shape="box"];1822[label="xz5800",fontsize=16,color="green",shape="box"];1823[label="xz5800",fontsize=16,color="green",shape="box"];1824[label="xz600",fontsize=16,color="green",shape="box"];1820[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS xz97 xz98)) Zero",fontsize=16,color="burlywood",shape="triangle"];2400[label="xz97/Succ xz970",fontsize=10,color="white",style="solid",shape="box"];1820 -> 2400[label="",style="solid", color="burlywood", weight=9];
2400 -> 1861[label="",style="solid", color="burlywood", weight=3];
2401[label="xz97/Zero",fontsize=10,color="white",style="solid",shape="box"];1820 -> 2401[label="",style="solid", color="burlywood", weight=9];
2401 -> 1862[label="",style="solid", color="burlywood", weight=3];
1311 -> 1666[label="",style="dashed", color="red", weight=0];
1311[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz5800) Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1311 -> 1667[label="",style="dashed", color="magenta", weight=3];
1312 -> 1235[label="",style="dashed", color="red", weight=0];
1312[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];1313 -> 1666[label="",style="dashed", color="red", weight=0];
1313[label="primMinusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1313 -> 1668[label="",style="dashed", color="magenta", weight=3];
1333[label="primPlusNat (primDivNatS0 (Succ xz6400) (Succ xz660) (primGEqNatS (Succ xz6400) (Succ xz660))) Zero",fontsize=16,color="black",shape="box"];1333 -> 1344[label="",style="solid", color="black", weight=3];
1334[label="primPlusNat (primDivNatS0 (Succ xz6400) Zero (primGEqNatS (Succ xz6400) Zero)) Zero",fontsize=16,color="black",shape="box"];1334 -> 1345[label="",style="solid", color="black", weight=3];
1335[label="primPlusNat (primDivNatS0 Zero (Succ xz660) (primGEqNatS Zero (Succ xz660))) Zero",fontsize=16,color="black",shape="box"];1335 -> 1346[label="",style="solid", color="black", weight=3];
1336[label="primPlusNat (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];1336 -> 1347[label="",style="solid", color="black", weight=3];
1861[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS (Succ xz970) xz98)) Zero",fontsize=16,color="burlywood",shape="box"];2402[label="xz98/Succ xz980",fontsize=10,color="white",style="solid",shape="box"];1861 -> 2402[label="",style="solid", color="burlywood", weight=9];
2402 -> 1876[label="",style="solid", color="burlywood", weight=3];
2403[label="xz98/Zero",fontsize=10,color="white",style="solid",shape="box"];1861 -> 2403[label="",style="solid", color="burlywood", weight=9];
2403 -> 1877[label="",style="solid", color="burlywood", weight=3];
1862[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS Zero xz98)) Zero",fontsize=16,color="burlywood",shape="box"];2404[label="xz98/Succ xz980",fontsize=10,color="white",style="solid",shape="box"];1862 -> 2404[label="",style="solid", color="burlywood", weight=9];
2404 -> 1878[label="",style="solid", color="burlywood", weight=3];
2405[label="xz98/Zero",fontsize=10,color="white",style="solid",shape="box"];1862 -> 2405[label="",style="solid", color="burlywood", weight=9];
2405 -> 1879[label="",style="solid", color="burlywood", weight=3];
1667 -> 2048[label="",style="dashed", color="red", weight=0];
1667[label="primDivNatS (primMinusNatS (Succ xz5800) Zero) (Succ Zero)",fontsize=16,color="magenta"];1667 -> 2049[label="",style="dashed", color="magenta", weight=3];
1667 -> 2050[label="",style="dashed", color="magenta", weight=3];
1667 -> 2051[label="",style="dashed", color="magenta", weight=3];
1666[label="primMinusNat (Succ xz79) Zero",fontsize=16,color="black",shape="triangle"];1666 -> 1682[label="",style="solid", color="black", weight=3];
1668 -> 2048[label="",style="dashed", color="red", weight=0];
1668[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1668 -> 2052[label="",style="dashed", color="magenta", weight=3];
1668 -> 2053[label="",style="dashed", color="magenta", weight=3];
1668 -> 2054[label="",style="dashed", color="magenta", weight=3];
1344 -> 1953[label="",style="dashed", color="red", weight=0];
1344[label="primPlusNat (primDivNatS0 (Succ xz6400) (Succ xz660) (primGEqNatS xz6400 xz660)) Zero",fontsize=16,color="magenta"];1344 -> 1954[label="",style="dashed", color="magenta", weight=3];
1344 -> 1955[label="",style="dashed", color="magenta", weight=3];
1344 -> 1956[label="",style="dashed", color="magenta", weight=3];
1344 -> 1957[label="",style="dashed", color="magenta", weight=3];
1345[label="primPlusNat (primDivNatS0 (Succ xz6400) Zero True) Zero",fontsize=16,color="black",shape="box"];1345 -> 1358[label="",style="solid", color="black", weight=3];
1346[label="primPlusNat (primDivNatS0 Zero (Succ xz660) False) Zero",fontsize=16,color="black",shape="box"];1346 -> 1359[label="",style="solid", color="black", weight=3];
1347[label="primPlusNat (primDivNatS0 Zero Zero True) Zero",fontsize=16,color="black",shape="box"];1347 -> 1360[label="",style="solid", color="black", weight=3];
1876[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS (Succ xz970) (Succ xz980))) Zero",fontsize=16,color="black",shape="box"];1876 -> 1894[label="",style="solid", color="black", weight=3];
1877[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS (Succ xz970) Zero)) Zero",fontsize=16,color="black",shape="box"];1877 -> 1895[label="",style="solid", color="black", weight=3];
1878[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS Zero (Succ xz980))) Zero",fontsize=16,color="black",shape="box"];1878 -> 1896[label="",style="solid", color="black", weight=3];
1879[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];1879 -> 1897[label="",style="solid", color="black", weight=3];
2049[label="Succ xz5800",fontsize=16,color="green",shape="box"];2050[label="Zero",fontsize=16,color="green",shape="box"];2051[label="Zero",fontsize=16,color="green",shape="box"];2048[label="primDivNatS (primMinusNatS xz116 xz117) (Succ xz118)",fontsize=16,color="burlywood",shape="triangle"];2406[label="xz116/Succ xz1160",fontsize=10,color="white",style="solid",shape="box"];2048 -> 2406[label="",style="solid", color="burlywood", weight=9];
2406 -> 2100[label="",style="solid", color="burlywood", weight=3];
2407[label="xz116/Zero",fontsize=10,color="white",style="solid",shape="box"];2048 -> 2407[label="",style="solid", color="burlywood", weight=9];
2407 -> 2101[label="",style="solid", color="burlywood", weight=3];
1682[label="Pos (Succ xz79)",fontsize=16,color="green",shape="box"];2052[label="Zero",fontsize=16,color="green",shape="box"];2053[label="Zero",fontsize=16,color="green",shape="box"];2054[label="Zero",fontsize=16,color="green",shape="box"];1954[label="xz660",fontsize=16,color="green",shape="box"];1955[label="xz6400",fontsize=16,color="green",shape="box"];1956[label="xz660",fontsize=16,color="green",shape="box"];1957[label="xz6400",fontsize=16,color="green",shape="box"];1953[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS xz113 xz114)) Zero",fontsize=16,color="burlywood",shape="triangle"];2408[label="xz113/Succ xz1130",fontsize=10,color="white",style="solid",shape="box"];1953 -> 2408[label="",style="solid", color="burlywood", weight=9];
2408 -> 1994[label="",style="solid", color="burlywood", weight=3];
2409[label="xz113/Zero",fontsize=10,color="white",style="solid",shape="box"];1953 -> 2409[label="",style="solid", color="burlywood", weight=9];
2409 -> 1995[label="",style="solid", color="burlywood", weight=3];
1358 -> 1373[label="",style="dashed", color="red", weight=0];
1358[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz6400) Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1358 -> 1374[label="",style="dashed", color="magenta", weight=3];
1359 -> 1317[label="",style="dashed", color="red", weight=0];
1359[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];1360 -> 1373[label="",style="dashed", color="red", weight=0];
1360[label="primPlusNat (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) Zero",fontsize=16,color="magenta"];1360 -> 1375[label="",style="dashed", color="magenta", weight=3];
1894 -> 1820[label="",style="dashed", color="red", weight=0];
1894[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) (primGEqNatS xz970 xz980)) Zero",fontsize=16,color="magenta"];1894 -> 1913[label="",style="dashed", color="magenta", weight=3];
1894 -> 1914[label="",style="dashed", color="magenta", weight=3];
1895[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) True) Zero",fontsize=16,color="black",shape="triangle"];1895 -> 1915[label="",style="solid", color="black", weight=3];
1896[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) False) Zero",fontsize=16,color="black",shape="box"];1896 -> 1916[label="",style="solid", color="black", weight=3];
1897 -> 1895[label="",style="dashed", color="red", weight=0];
1897[label="primMinusNat (primDivNatS0 (Succ xz95) (Succ xz96) True) Zero",fontsize=16,color="magenta"];2100[label="primDivNatS (primMinusNatS (Succ xz1160) xz117) (Succ xz118)",fontsize=16,color="burlywood",shape="box"];2410[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2100 -> 2410[label="",style="solid", color="burlywood", weight=9];
2410 -> 2102[label="",style="solid", color="burlywood", weight=3];
2411[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2100 -> 2411[label="",style="solid", color="burlywood", weight=9];
2411 -> 2103[label="",style="solid", color="burlywood", weight=3];
2101[label="primDivNatS (primMinusNatS Zero xz117) (Succ xz118)",fontsize=16,color="burlywood",shape="box"];2412[label="xz117/Succ xz1170",fontsize=10,color="white",style="solid",shape="box"];2101 -> 2412[label="",style="solid", color="burlywood", weight=9];
2412 -> 2104[label="",style="solid", color="burlywood", weight=3];
2413[label="xz117/Zero",fontsize=10,color="white",style="solid",shape="box"];2101 -> 2413[label="",style="solid", color="burlywood", weight=9];
2413 -> 2105[label="",style="solid", color="burlywood", weight=3];
1994[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS (Succ xz1130) xz114)) Zero",fontsize=16,color="burlywood",shape="box"];2414[label="xz114/Succ xz1140",fontsize=10,color="white",style="solid",shape="box"];1994 -> 2414[label="",style="solid", color="burlywood", weight=9];
2414 -> 2002[label="",style="solid", color="burlywood", weight=3];
2415[label="xz114/Zero",fontsize=10,color="white",style="solid",shape="box"];1994 -> 2415[label="",style="solid", color="burlywood", weight=9];
2415 -> 2003[label="",style="solid", color="burlywood", weight=3];
1995[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS Zero xz114)) Zero",fontsize=16,color="burlywood",shape="box"];2416[label="xz114/Succ xz1140",fontsize=10,color="white",style="solid",shape="box"];1995 -> 2416[label="",style="solid", color="burlywood", weight=9];
2416 -> 2004[label="",style="solid", color="burlywood", weight=3];
2417[label="xz114/Zero",fontsize=10,color="white",style="solid",shape="box"];1995 -> 2417[label="",style="solid", color="burlywood", weight=9];
2417 -> 2005[label="",style="solid", color="burlywood", weight=3];
1374 -> 2048[label="",style="dashed", color="red", weight=0];
1374[label="primDivNatS (primMinusNatS (Succ xz6400) Zero) (Succ Zero)",fontsize=16,color="magenta"];1374 -> 2061[label="",style="dashed", color="magenta", weight=3];
1374 -> 2062[label="",style="dashed", color="magenta", weight=3];
1374 -> 2063[label="",style="dashed", color="magenta", weight=3];
1373[label="primPlusNat (Succ xz67) Zero",fontsize=16,color="black",shape="triangle"];1373 -> 1381[label="",style="solid", color="black", weight=3];
1375 -> 2048[label="",style="dashed", color="red", weight=0];
1375[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1375 -> 2064[label="",style="dashed", color="magenta", weight=3];
1375 -> 2065[label="",style="dashed", color="magenta", weight=3];
1375 -> 2066[label="",style="dashed", color="magenta", weight=3];
1913[label="xz980",fontsize=16,color="green",shape="box"];1914[label="xz970",fontsize=16,color="green",shape="box"];1915 -> 1666[label="",style="dashed", color="red", weight=0];
1915[label="primMinusNat (Succ (primDivNatS (primMinusNatS (Succ xz95) (Succ xz96)) (Succ (Succ xz96)))) Zero",fontsize=16,color="magenta"];1915 -> 1928[label="",style="dashed", color="magenta", weight=3];
1916 -> 1235[label="",style="dashed", color="red", weight=0];
1916[label="primMinusNat Zero Zero",fontsize=16,color="magenta"];2102[label="primDivNatS (primMinusNatS (Succ xz1160) (Succ xz1170)) (Succ xz118)",fontsize=16,color="black",shape="box"];2102 -> 2106[label="",style="solid", color="black", weight=3];
2103[label="primDivNatS (primMinusNatS (Succ xz1160) Zero) (Succ xz118)",fontsize=16,color="black",shape="box"];2103 -> 2107[label="",style="solid", color="black", weight=3];
2104[label="primDivNatS (primMinusNatS Zero (Succ xz1170)) (Succ xz118)",fontsize=16,color="black",shape="box"];2104 -> 2108[label="",style="solid", color="black", weight=3];
2105[label="primDivNatS (primMinusNatS Zero Zero) (Succ xz118)",fontsize=16,color="black",shape="box"];2105 -> 2109[label="",style="solid", color="black", weight=3];
2002[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS (Succ xz1130) (Succ xz1140))) Zero",fontsize=16,color="black",shape="box"];2002 -> 2016[label="",style="solid", color="black", weight=3];
2003[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS (Succ xz1130) Zero)) Zero",fontsize=16,color="black",shape="box"];2003 -> 2017[label="",style="solid", color="black", weight=3];
2004[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS Zero (Succ xz1140))) Zero",fontsize=16,color="black",shape="box"];2004 -> 2018[label="",style="solid", color="black", weight=3];
2005[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS Zero Zero)) Zero",fontsize=16,color="black",shape="box"];2005 -> 2019[label="",style="solid", color="black", weight=3];
2061[label="Succ xz6400",fontsize=16,color="green",shape="box"];2062[label="Zero",fontsize=16,color="green",shape="box"];2063[label="Zero",fontsize=16,color="green",shape="box"];1381[label="Succ xz67",fontsize=16,color="green",shape="box"];2064[label="Zero",fontsize=16,color="green",shape="box"];2065[label="Zero",fontsize=16,color="green",shape="box"];2066[label="Zero",fontsize=16,color="green",shape="box"];1928 -> 2048[label="",style="dashed", color="red", weight=0];
1928[label="primDivNatS (primMinusNatS (Succ xz95) (Succ xz96)) (Succ (Succ xz96))",fontsize=16,color="magenta"];1928 -> 2070[label="",style="dashed", color="magenta", weight=3];
1928 -> 2071[label="",style="dashed", color="magenta", weight=3];
1928 -> 2072[label="",style="dashed", color="magenta", weight=3];
2106 -> 2048[label="",style="dashed", color="red", weight=0];
2106[label="primDivNatS (primMinusNatS xz1160 xz1170) (Succ xz118)",fontsize=16,color="magenta"];2106 -> 2110[label="",style="dashed", color="magenta", weight=3];
2106 -> 2111[label="",style="dashed", color="magenta", weight=3];
2107[label="primDivNatS (Succ xz1160) (Succ xz118)",fontsize=16,color="black",shape="box"];2107 -> 2112[label="",style="solid", color="black", weight=3];
2108[label="primDivNatS Zero (Succ xz118)",fontsize=16,color="black",shape="triangle"];2108 -> 2113[label="",style="solid", color="black", weight=3];
2109 -> 2108[label="",style="dashed", color="red", weight=0];
2109[label="primDivNatS Zero (Succ xz118)",fontsize=16,color="magenta"];2016 -> 1953[label="",style="dashed", color="red", weight=0];
2016[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) (primGEqNatS xz1130 xz1140)) Zero",fontsize=16,color="magenta"];2016 -> 2028[label="",style="dashed", color="magenta", weight=3];
2016 -> 2029[label="",style="dashed", color="magenta", weight=3];
2017[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) True) Zero",fontsize=16,color="black",shape="triangle"];2017 -> 2030[label="",style="solid", color="black", weight=3];
2018[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) False) Zero",fontsize=16,color="black",shape="box"];2018 -> 2031[label="",style="solid", color="black", weight=3];
2019 -> 2017[label="",style="dashed", color="red", weight=0];
2019[label="primPlusNat (primDivNatS0 (Succ xz111) (Succ xz112) True) Zero",fontsize=16,color="magenta"];2070[label="Succ xz95",fontsize=16,color="green",shape="box"];2071[label="Succ xz96",fontsize=16,color="green",shape="box"];2072[label="Succ xz96",fontsize=16,color="green",shape="box"];2110[label="xz1160",fontsize=16,color="green",shape="box"];2111[label="xz1170",fontsize=16,color="green",shape="box"];2112[label="primDivNatS0 xz1160 xz118 (primGEqNatS xz1160 xz118)",fontsize=16,color="burlywood",shape="box"];2418[label="xz1160/Succ xz11600",fontsize=10,color="white",style="solid",shape="box"];2112 -> 2418[label="",style="solid", color="burlywood", weight=9];
2418 -> 2114[label="",style="solid", color="burlywood", weight=3];
2419[label="xz1160/Zero",fontsize=10,color="white",style="solid",shape="box"];2112 -> 2419[label="",style="solid", color="burlywood", weight=9];
2419 -> 2115[label="",style="solid", color="burlywood", weight=3];
2113[label="Zero",fontsize=16,color="green",shape="box"];2028[label="xz1140",fontsize=16,color="green",shape="box"];2029[label="xz1130",fontsize=16,color="green",shape="box"];2030 -> 1373[label="",style="dashed", color="red", weight=0];
2030[label="primPlusNat (Succ (primDivNatS (primMinusNatS (Succ xz111) (Succ xz112)) (Succ (Succ xz112)))) Zero",fontsize=16,color="magenta"];2030 -> 2041[label="",style="dashed", color="magenta", weight=3];
2031 -> 1317[label="",style="dashed", color="red", weight=0];
2031[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];2114[label="primDivNatS0 (Succ xz11600) xz118 (primGEqNatS (Succ xz11600) xz118)",fontsize=16,color="burlywood",shape="box"];2420[label="xz118/Succ xz1180",fontsize=10,color="white",style="solid",shape="box"];2114 -> 2420[label="",style="solid", color="burlywood", weight=9];
2420 -> 2116[label="",style="solid", color="burlywood", weight=3];
2421[label="xz118/Zero",fontsize=10,color="white",style="solid",shape="box"];2114 -> 2421[label="",style="solid", color="burlywood", weight=9];
2421 -> 2117[label="",style="solid", color="burlywood", weight=3];
2115[label="primDivNatS0 Zero xz118 (primGEqNatS Zero xz118)",fontsize=16,color="burlywood",shape="box"];2422[label="xz118/Succ xz1180",fontsize=10,color="white",style="solid",shape="box"];2115 -> 2422[label="",style="solid", color="burlywood", weight=9];
2422 -> 2118[label="",style="solid", color="burlywood", weight=3];
2423[label="xz118/Zero",fontsize=10,color="white",style="solid",shape="box"];2115 -> 2423[label="",style="solid", color="burlywood", weight=9];
2423 -> 2119[label="",style="solid", color="burlywood", weight=3];
2041 -> 2048[label="",style="dashed", color="red", weight=0];
2041[label="primDivNatS (primMinusNatS (Succ xz111) (Succ xz112)) (Succ (Succ xz112))",fontsize=16,color="magenta"];2041 -> 2076[label="",style="dashed", color="magenta", weight=3];
2041 -> 2077[label="",style="dashed", color="magenta", weight=3];
2041 -> 2078[label="",style="dashed", color="magenta", weight=3];
2116[label="primDivNatS0 (Succ xz11600) (Succ xz1180) (primGEqNatS (Succ xz11600) (Succ xz1180))",fontsize=16,color="black",shape="box"];2116 -> 2120[label="",style="solid", color="black", weight=3];
2117[label="primDivNatS0 (Succ xz11600) Zero (primGEqNatS (Succ xz11600) Zero)",fontsize=16,color="black",shape="box"];2117 -> 2121[label="",style="solid", color="black", weight=3];
2118[label="primDivNatS0 Zero (Succ xz1180) (primGEqNatS Zero (Succ xz1180))",fontsize=16,color="black",shape="box"];2118 -> 2122[label="",style="solid", color="black", weight=3];
2119[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2119 -> 2123[label="",style="solid", color="black", weight=3];
2076[label="Succ xz111",fontsize=16,color="green",shape="box"];2077[label="Succ xz112",fontsize=16,color="green",shape="box"];2078[label="Succ xz112",fontsize=16,color="green",shape="box"];2120 -> 2282[label="",style="dashed", color="red", weight=0];
2120[label="primDivNatS0 (Succ xz11600) (Succ xz1180) (primGEqNatS xz11600 xz1180)",fontsize=16,color="magenta"];2120 -> 2283[label="",style="dashed", color="magenta", weight=3];
2120 -> 2284[label="",style="dashed", color="magenta", weight=3];
2120 -> 2285[label="",style="dashed", color="magenta", weight=3];
2120 -> 2286[label="",style="dashed", color="magenta", weight=3];
2121[label="primDivNatS0 (Succ xz11600) Zero True",fontsize=16,color="black",shape="box"];2121 -> 2126[label="",style="solid", color="black", weight=3];
2122[label="primDivNatS0 Zero (Succ xz1180) False",fontsize=16,color="black",shape="box"];2122 -> 2127[label="",style="solid", color="black", weight=3];
2123[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2123 -> 2128[label="",style="solid", color="black", weight=3];
2283[label="xz11600",fontsize=16,color="green",shape="box"];2284[label="xz11600",fontsize=16,color="green",shape="box"];2285[label="xz1180",fontsize=16,color="green",shape="box"];2286[label="xz1180",fontsize=16,color="green",shape="box"];2282[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS xz137 xz138)",fontsize=16,color="burlywood",shape="triangle"];2424[label="xz137/Succ xz1370",fontsize=10,color="white",style="solid",shape="box"];2282 -> 2424[label="",style="solid", color="burlywood", weight=9];
2424 -> 2315[label="",style="solid", color="burlywood", weight=3];
2425[label="xz137/Zero",fontsize=10,color="white",style="solid",shape="box"];2282 -> 2425[label="",style="solid", color="burlywood", weight=9];
2425 -> 2316[label="",style="solid", color="burlywood", weight=3];
2126[label="Succ (primDivNatS (primMinusNatS (Succ xz11600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2126 -> 2133[label="",style="dashed", color="green", weight=3];
2127[label="Zero",fontsize=16,color="green",shape="box"];2128[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2128 -> 2134[label="",style="dashed", color="green", weight=3];
2315[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS (Succ xz1370) xz138)",fontsize=16,color="burlywood",shape="box"];2426[label="xz138/Succ xz1380",fontsize=10,color="white",style="solid",shape="box"];2315 -> 2426[label="",style="solid", color="burlywood", weight=9];
2426 -> 2317[label="",style="solid", color="burlywood", weight=3];
2427[label="xz138/Zero",fontsize=10,color="white",style="solid",shape="box"];2315 -> 2427[label="",style="solid", color="burlywood", weight=9];
2427 -> 2318[label="",style="solid", color="burlywood", weight=3];
2316[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS Zero xz138)",fontsize=16,color="burlywood",shape="box"];2428[label="xz138/Succ xz1380",fontsize=10,color="white",style="solid",shape="box"];2316 -> 2428[label="",style="solid", color="burlywood", weight=9];
2428 -> 2319[label="",style="solid", color="burlywood", weight=3];
2429[label="xz138/Zero",fontsize=10,color="white",style="solid",shape="box"];2316 -> 2429[label="",style="solid", color="burlywood", weight=9];
2429 -> 2320[label="",style="solid", color="burlywood", weight=3];
2133 -> 2048[label="",style="dashed", color="red", weight=0];
2133[label="primDivNatS (primMinusNatS (Succ xz11600) Zero) (Succ Zero)",fontsize=16,color="magenta"];2133 -> 2139[label="",style="dashed", color="magenta", weight=3];
2133 -> 2140[label="",style="dashed", color="magenta", weight=3];
2133 -> 2141[label="",style="dashed", color="magenta", weight=3];
2134 -> 2048[label="",style="dashed", color="red", weight=0];
2134[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2134 -> 2142[label="",style="dashed", color="magenta", weight=3];
2134 -> 2143[label="",style="dashed", color="magenta", weight=3];
2134 -> 2144[label="",style="dashed", color="magenta", weight=3];
2317[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS (Succ xz1370) (Succ xz1380))",fontsize=16,color="black",shape="box"];2317 -> 2321[label="",style="solid", color="black", weight=3];
2318[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS (Succ xz1370) Zero)",fontsize=16,color="black",shape="box"];2318 -> 2322[label="",style="solid", color="black", weight=3];
2319[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS Zero (Succ xz1380))",fontsize=16,color="black",shape="box"];2319 -> 2323[label="",style="solid", color="black", weight=3];
2320[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2320 -> 2324[label="",style="solid", color="black", weight=3];
2139[label="Succ xz11600",fontsize=16,color="green",shape="box"];2140[label="Zero",fontsize=16,color="green",shape="box"];2141[label="Zero",fontsize=16,color="green",shape="box"];2142[label="Zero",fontsize=16,color="green",shape="box"];2143[label="Zero",fontsize=16,color="green",shape="box"];2144[label="Zero",fontsize=16,color="green",shape="box"];2321 -> 2282[label="",style="dashed", color="red", weight=0];
2321[label="primDivNatS0 (Succ xz135) (Succ xz136) (primGEqNatS xz1370 xz1380)",fontsize=16,color="magenta"];2321 -> 2325[label="",style="dashed", color="magenta", weight=3];
2321 -> 2326[label="",style="dashed", color="magenta", weight=3];
2322[label="primDivNatS0 (Succ xz135) (Succ xz136) True",fontsize=16,color="black",shape="triangle"];2322 -> 2327[label="",style="solid", color="black", weight=3];
2323[label="primDivNatS0 (Succ xz135) (Succ xz136) False",fontsize=16,color="black",shape="box"];2323 -> 2328[label="",style="solid", color="black", weight=3];
2324 -> 2322[label="",style="dashed", color="red", weight=0];
2324[label="primDivNatS0 (Succ xz135) (Succ xz136) True",fontsize=16,color="magenta"];2325[label="xz1370",fontsize=16,color="green",shape="box"];2326[label="xz1380",fontsize=16,color="green",shape="box"];2327[label="Succ (primDivNatS (primMinusNatS (Succ xz135) (Succ xz136)) (Succ (Succ xz136)))",fontsize=16,color="green",shape="box"];2327 -> 2329[label="",style="dashed", color="green", weight=3];
2328[label="Zero",fontsize=16,color="green",shape="box"];2329 -> 2048[label="",style="dashed", color="red", weight=0];
2329[label="primDivNatS (primMinusNatS (Succ xz135) (Succ xz136)) (Succ (Succ xz136))",fontsize=16,color="magenta"];2329 -> 2330[label="",style="dashed", color="magenta", weight=3];
2329 -> 2331[label="",style="dashed", color="magenta", weight=3];
2329 -> 2332[label="",style="dashed", color="magenta", weight=3];
2330[label="Succ xz135",fontsize=16,color="green",shape="box"];2331[label="Succ xz136",fontsize=16,color="green",shape="box"];2332[label="Succ xz136",fontsize=16,color="green",shape="box"];}

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

(14)
Complex Obligation (AND)

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

(15)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primDivNatS0(xz135, xz136, Zero, Zero) -> new_primDivNatS00(xz135, xz136)
   new_primDivNatS(Succ(Zero), Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero)
   new_primDivNatS00(xz135, xz136) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136))
   new_primDivNatS(Succ(xz1160), Succ(xz1170), xz118) -> new_primDivNatS(xz1160, xz1170, xz118)
   new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380)
   new_primDivNatS(Succ(Succ(xz11600)), Zero, Succ(xz1180)) -> new_primDivNatS0(xz11600, xz1180, xz11600, xz1180)
   new_primDivNatS0(xz135, xz136, Succ(xz1370), Zero) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136))
   new_primDivNatS(Succ(Succ(xz11600)), Zero, Zero) -> new_primDivNatS(Succ(xz11600), Zero, Zero)

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

(16) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
----------------------------------------

(17)
Complex Obligation (AND)

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

(18)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primDivNatS(Succ(Succ(xz11600)), Zero, Zero) -> new_primDivNatS(Succ(xz11600), Zero, Zero)

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

(19) 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_primDivNatS(Succ(Succ(xz11600)), Zero, Zero) -> new_primDivNatS(Succ(xz11600), Zero, Zero)
The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 2, 2 >= 3, 3 >= 3


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

(20)
YES

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

(21)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primDivNatS00(xz135, xz136) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136))
   new_primDivNatS(Succ(xz1160), Succ(xz1170), xz118) -> new_primDivNatS(xz1160, xz1170, xz118)
   new_primDivNatS(Succ(Succ(xz11600)), Zero, Succ(xz1180)) -> new_primDivNatS0(xz11600, xz1180, xz11600, xz1180)
   new_primDivNatS0(xz135, xz136, Zero, Zero) -> new_primDivNatS00(xz135, xz136)
   new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380)
   new_primDivNatS0(xz135, xz136, Succ(xz1370), Zero) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136))

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

(22) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   new_primDivNatS(Succ(xz1160), Succ(xz1170), xz118) -> new_primDivNatS(xz1160, xz1170, xz118)
   new_primDivNatS(Succ(Succ(xz11600)), Zero, Succ(xz1180)) -> new_primDivNatS0(xz11600, xz1180, xz11600, xz1180)
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

   POL(Succ(x_1)) = 1 + x_1
   POL(Zero) = 1
   POL(new_primDivNatS(x_1, x_2, x_3)) = x_1
   POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
   POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none


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

(23)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primDivNatS00(xz135, xz136) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136))
   new_primDivNatS0(xz135, xz136, Zero, Zero) -> new_primDivNatS00(xz135, xz136)
   new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380)
   new_primDivNatS0(xz135, xz136, Succ(xz1370), Zero) -> new_primDivNatS(Succ(xz135), Succ(xz136), Succ(xz136))

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

(24) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
----------------------------------------

(25)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380)

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

(26) 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_primDivNatS0(xz135, xz136, Succ(xz1370), Succ(xz1380)) -> new_primDivNatS0(xz135, xz136, xz1370, xz1380)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4


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

(27)
YES

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

(28)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMinusNat0(Succ(xz580), Succ(xz590), xz60) -> new_primMinusNat0(xz580, xz590, xz60)

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

(29) 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_primMinusNat0(Succ(xz580), Succ(xz590), xz60) -> new_primMinusNat0(xz580, xz590, xz60)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


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

(30)
YES

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

(31)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat0(Succ(xz640), Succ(xz650), xz66) -> new_primPlusNat0(xz640, xz650, xz66)

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

(32) 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_primPlusNat0(Succ(xz640), Succ(xz650), xz66) -> new_primPlusNat0(xz640, xz650, xz66)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


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

(33)
YES

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

(34)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat1(xz51, xz52, Succ(xz530), Succ(xz540)) -> new_primPlusNat1(xz51, xz52, xz530, xz540)

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

(35) 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_primPlusNat1(xz51, xz52, Succ(xz530), Succ(xz540)) -> new_primPlusNat1(xz51, xz52, xz530, xz540)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4


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

(36)
YES

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

(37)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMinusNat(xz95, xz96, Succ(xz970), Succ(xz980)) -> new_primMinusNat(xz95, xz96, xz970, xz980)

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

(38) 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_primMinusNat(xz95, xz96, Succ(xz970), Succ(xz980)) -> new_primMinusNat(xz95, xz96, xz970, xz980)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4


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(39)
YES

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(40)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primPlusNat(xz111, xz112, Succ(xz1130), Succ(xz1140)) -> new_primPlusNat(xz111, xz112, xz1130, xz1140)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(41) 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(xz111, xz112, Succ(xz1130), Succ(xz1140)) -> new_primPlusNat(xz111, xz112, xz1130, xz1140)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4


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(42)
YES

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(43)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMinusNat1(xz38, xz39, Succ(xz400), Succ(xz410)) -> new_primMinusNat1(xz38, xz39, xz400, xz410)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(44) 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_primMinusNat1(xz38, xz39, Succ(xz400), Succ(xz410)) -> new_primMinusNat1(xz38, xz39, xz400, xz410)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4


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(45)
YES