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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [SOUND, 0 ms]
(6) AND
    (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (12) YES
    (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Float = Float MyInt MyInt ;

data List a = Cons a (List a)  | Nil ;

data MyBool = MyTrue  | MyFalse ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

any :: (a  ->  MyBool)  ->  List a  ->  MyBool;
any p = pt or (map p);

elemFloat :: Float  ->  List Float  ->  MyBool;
elemFloat = pt any esEsFloat;

esEsFloat :: Float  ->  Float  ->  MyBool;
esEsFloat = primEqFloat;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

foldr :: (b  ->  a  ->  a)  ->  a  ->  List b  ->  a;
foldr f z Nil = z;
foldr f z (Cons x xs) = f x (foldr f z xs);

map :: (b  ->  a)  ->  List b  ->  List a;
map f Nil = Nil;
map f (Cons x xs) = Cons (f x) (map f xs);

or :: List MyBool  ->  MyBool;
or = foldr pePe MyFalse;

pePe :: MyBool  ->  MyBool  ->  MyBool;
pePe MyFalse x = x;
pePe MyTrue x = MyTrue;

primEqFloat :: Float  ->  Float  ->  MyBool;
primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
primEqNat Main.Zero Main.Zero = MyTrue;
primEqNat Main.Zero (Main.Succ y) = MyFalse;
primEqNat (Main.Succ x) Main.Zero = MyFalse;
primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);

primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primMulNat Main.Zero Main.Zero = Main.Zero;
primMulNat Main.Zero (Main.Succ y) = Main.Zero;
primMulNat (Main.Succ x) Main.Zero = Main.Zero;
primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);

primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primPlusNat Main.Zero Main.Zero = Main.Zero;
primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));

pt :: (b  ->  c)  ->  (a  ->  b)  ->  a  ->  c;
pt f g x = f (g x);

srMyInt :: MyInt  ->  MyInt  ->  MyInt;
srMyInt = primMulInt;

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Float = Float MyInt MyInt ;

data List a = Cons a (List a)  | Nil ;

data MyBool = MyTrue  | MyFalse ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

any :: (a  ->  MyBool)  ->  List a  ->  MyBool;
any p = pt or (map p);

elemFloat :: Float  ->  List Float  ->  MyBool;
elemFloat = pt any esEsFloat;

esEsFloat :: Float  ->  Float  ->  MyBool;
esEsFloat = primEqFloat;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

foldr :: (a  ->  b  ->  b)  ->  b  ->  List a  ->  b;
foldr f z Nil = z;
foldr f z (Cons x xs) = f x (foldr f z xs);

map :: (b  ->  a)  ->  List b  ->  List a;
map f Nil = Nil;
map f (Cons x xs) = Cons (f x) (map f xs);

or :: List MyBool  ->  MyBool;
or = foldr pePe MyFalse;

pePe :: MyBool  ->  MyBool  ->  MyBool;
pePe MyFalse x = x;
pePe MyTrue x = MyTrue;

primEqFloat :: Float  ->  Float  ->  MyBool;
primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
primEqNat Main.Zero Main.Zero = MyTrue;
primEqNat Main.Zero (Main.Succ y) = MyFalse;
primEqNat (Main.Succ x) Main.Zero = MyFalse;
primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);

primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primMulNat Main.Zero Main.Zero = Main.Zero;
primMulNat Main.Zero (Main.Succ y) = Main.Zero;
primMulNat (Main.Succ x) Main.Zero = Main.Zero;
primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);

primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primPlusNat Main.Zero Main.Zero = Main.Zero;
primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));

pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
pt f g x = f (g x);

srMyInt :: MyInt  ->  MyInt  ->  MyInt;
srMyInt = primMulInt;

}

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

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

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

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Float = Float MyInt MyInt ;

data List a = Cons a (List a)  | Nil ;

data MyBool = MyTrue  | MyFalse ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

any :: (a  ->  MyBool)  ->  List a  ->  MyBool;
any p = pt or (map p);

elemFloat :: Float  ->  List Float  ->  MyBool;
elemFloat = pt any esEsFloat;

esEsFloat :: Float  ->  Float  ->  MyBool;
esEsFloat = primEqFloat;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
esEsMyInt = primEqInt;

foldr :: (b  ->  a  ->  a)  ->  a  ->  List b  ->  a;
foldr f z Nil = z;
foldr f z (Cons x xs) = f x (foldr f z xs);

map :: (b  ->  a)  ->  List b  ->  List a;
map f Nil = Nil;
map f (Cons x xs) = Cons (f x) (map f xs);

or :: List MyBool  ->  MyBool;
or = foldr pePe MyFalse;

pePe :: MyBool  ->  MyBool  ->  MyBool;
pePe MyFalse x = x;
pePe MyTrue x = MyTrue;

primEqFloat :: Float  ->  Float  ->  MyBool;
primEqFloat (Float x1 x2) (Float y1 y2) = esEsMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primEqInt :: MyInt  ->  MyInt  ->  MyBool;
primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y;
primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue;
primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue;
primEqInt vv vw = MyFalse;

primEqNat :: Main.Nat  ->  Main.Nat  ->  MyBool;
primEqNat Main.Zero Main.Zero = MyTrue;
primEqNat Main.Zero (Main.Succ y) = MyFalse;
primEqNat (Main.Succ x) Main.Zero = MyFalse;
primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y;

primMulInt :: MyInt  ->  MyInt  ->  MyInt;
primMulInt (Main.Pos x) (Main.Pos y) = Main.Pos (primMulNat x y);
primMulInt (Main.Pos x) (Main.Neg y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Pos y) = Main.Neg (primMulNat x y);
primMulInt (Main.Neg x) (Main.Neg y) = Main.Pos (primMulNat x y);

primMulNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primMulNat Main.Zero Main.Zero = Main.Zero;
primMulNat Main.Zero (Main.Succ y) = Main.Zero;
primMulNat (Main.Succ x) Main.Zero = Main.Zero;
primMulNat (Main.Succ x) (Main.Succ y) = primPlusNat (primMulNat x (Main.Succ y)) (Main.Succ y);

primPlusNat :: Main.Nat  ->  Main.Nat  ->  Main.Nat;
primPlusNat Main.Zero Main.Zero = Main.Zero;
primPlusNat Main.Zero (Main.Succ y) = Main.Succ y;
primPlusNat (Main.Succ x) Main.Zero = Main.Succ x;
primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y));

pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
pt f g x = f (g x);

srMyInt :: MyInt  ->  MyInt  ->  MyInt;
srMyInt = primMulInt;

}

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="elemFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="elemFloat vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="elemFloat vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="pt any esEsFloat vz3 vz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="any (esEsFloat vz3) vz4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="pt or (map (esEsFloat vz3)) vz4",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="or (map (esEsFloat vz3) vz4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="foldr pePe MyFalse (map (esEsFloat vz3) vz4)",fontsize=16,color="burlywood",shape="triangle"];523[label="vz4/Cons vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];9 -> 523[label="",style="solid", color="burlywood", weight=9];
523 -> 10[label="",style="solid", color="burlywood", weight=3];
524[label="vz4/Nil",fontsize=10,color="white",style="solid",shape="box"];9 -> 524[label="",style="solid", color="burlywood", weight=9];
524 -> 11[label="",style="solid", color="burlywood", weight=3];
10[label="foldr pePe MyFalse (map (esEsFloat vz3) (Cons vz40 vz41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
11[label="foldr pePe MyFalse (map (esEsFloat vz3) Nil)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12[label="foldr pePe MyFalse (Cons (esEsFloat vz3 vz40) (map (esEsFloat vz3) vz41))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13[label="foldr pePe MyFalse Nil",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14 -> 16[label="",style="dashed", color="red", weight=0];
14[label="pePe (esEsFloat vz3 vz40) (foldr pePe MyFalse (map (esEsFloat vz3) vz41))",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3];
15[label="MyFalse",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0];
17[label="foldr pePe MyFalse (map (esEsFloat vz3) vz41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3];
16[label="pePe (esEsFloat vz3 vz40) vz5",fontsize=16,color="black",shape="triangle"];16 -> 19[label="",style="solid", color="black", weight=3];
18[label="vz41",fontsize=16,color="green",shape="box"];19[label="pePe (primEqFloat vz3 vz40) vz5",fontsize=16,color="burlywood",shape="box"];525[label="vz3/Float vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];19 -> 525[label="",style="solid", color="burlywood", weight=9];
525 -> 20[label="",style="solid", color="burlywood", weight=3];
20[label="pePe (primEqFloat (Float vz30 vz31) vz40) vz5",fontsize=16,color="burlywood",shape="box"];526[label="vz40/Float vz400 vz401",fontsize=10,color="white",style="solid",shape="box"];20 -> 526[label="",style="solid", color="burlywood", weight=9];
526 -> 21[label="",style="solid", color="burlywood", weight=3];
21[label="pePe (primEqFloat (Float vz30 vz31) (Float vz400 vz401)) vz5",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
22[label="pePe (esEsMyInt (srMyInt vz30 vz400) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
23[label="pePe (primEqInt (srMyInt vz30 vz400) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
24[label="pePe (primEqInt (primMulInt vz30 vz400) (srMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];527[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];24 -> 527[label="",style="solid", color="burlywood", weight=9];
527 -> 25[label="",style="solid", color="burlywood", weight=3];
528[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];24 -> 528[label="",style="solid", color="burlywood", weight=9];
528 -> 26[label="",style="solid", color="burlywood", weight=3];
25[label="pePe (primEqInt (primMulInt (Pos vz300) vz400) (srMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];529[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 529[label="",style="solid", color="burlywood", weight=9];
529 -> 27[label="",style="solid", color="burlywood", weight=3];
530[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];25 -> 530[label="",style="solid", color="burlywood", weight=9];
530 -> 28[label="",style="solid", color="burlywood", weight=3];
26[label="pePe (primEqInt (primMulInt (Neg vz300) vz400) (srMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];531[label="vz400/Pos vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 531[label="",style="solid", color="burlywood", weight=9];
531 -> 29[label="",style="solid", color="burlywood", weight=3];
532[label="vz400/Neg vz4000",fontsize=10,color="white",style="solid",shape="box"];26 -> 532[label="",style="solid", color="burlywood", weight=9];
532 -> 30[label="",style="solid", color="burlywood", weight=3];
27[label="pePe (primEqInt (primMulInt (Pos vz300) (Pos vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28[label="pePe (primEqInt (primMulInt (Pos vz300) (Neg vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
29[label="pePe (primEqInt (primMulInt (Neg vz300) (Pos vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
30[label="pePe (primEqInt (primMulInt (Neg vz300) (Neg vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
31 -> 286[label="",style="dashed", color="red", weight=0];
31[label="pePe (primEqInt (Pos (primMulNat vz300 vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];31 -> 287[label="",style="dashed", color="magenta", weight=3];
32 -> 362[label="",style="dashed", color="red", weight=0];
32[label="pePe (primEqInt (Neg (primMulNat vz300 vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];32 -> 363[label="",style="dashed", color="magenta", weight=3];
33 -> 362[label="",style="dashed", color="red", weight=0];
33[label="pePe (primEqInt (Neg (primMulNat vz300 vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];33 -> 364[label="",style="dashed", color="magenta", weight=3];
34 -> 286[label="",style="dashed", color="red", weight=0];
34[label="pePe (primEqInt (Pos (primMulNat vz300 vz4000)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="magenta"];34 -> 288[label="",style="dashed", color="magenta", weight=3];
287[label="primMulNat vz300 vz4000",fontsize=16,color="burlywood",shape="triangle"];533[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];287 -> 533[label="",style="solid", color="burlywood", weight=9];
533 -> 299[label="",style="solid", color="burlywood", weight=3];
534[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];287 -> 534[label="",style="solid", color="burlywood", weight=9];
534 -> 300[label="",style="solid", color="burlywood", weight=3];
286[label="pePe (primEqInt (Pos vz11) (srMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="triangle"];535[label="vz11/Succ vz110",fontsize=10,color="white",style="solid",shape="box"];286 -> 535[label="",style="solid", color="burlywood", weight=9];
535 -> 301[label="",style="solid", color="burlywood", weight=3];
536[label="vz11/Zero",fontsize=10,color="white",style="solid",shape="box"];286 -> 536[label="",style="solid", color="burlywood", weight=9];
536 -> 302[label="",style="solid", color="burlywood", weight=3];
363 -> 287[label="",style="dashed", color="red", weight=0];
363[label="primMulNat vz300 vz4000",fontsize=16,color="magenta"];363 -> 375[label="",style="dashed", color="magenta", weight=3];
362[label="pePe (primEqInt (Neg vz16) (srMyInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="triangle"];537[label="vz16/Succ vz160",fontsize=10,color="white",style="solid",shape="box"];362 -> 537[label="",style="solid", color="burlywood", weight=9];
537 -> 376[label="",style="solid", color="burlywood", weight=3];
538[label="vz16/Zero",fontsize=10,color="white",style="solid",shape="box"];362 -> 538[label="",style="solid", color="burlywood", weight=9];
538 -> 377[label="",style="solid", color="burlywood", weight=3];
364 -> 287[label="",style="dashed", color="red", weight=0];
364[label="primMulNat vz300 vz4000",fontsize=16,color="magenta"];364 -> 378[label="",style="dashed", color="magenta", weight=3];
288 -> 287[label="",style="dashed", color="red", weight=0];
288[label="primMulNat vz300 vz4000",fontsize=16,color="magenta"];288 -> 303[label="",style="dashed", color="magenta", weight=3];
288 -> 304[label="",style="dashed", color="magenta", weight=3];
299[label="primMulNat (Succ vz3000) vz4000",fontsize=16,color="burlywood",shape="box"];539[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];299 -> 539[label="",style="solid", color="burlywood", weight=9];
539 -> 319[label="",style="solid", color="burlywood", weight=3];
540[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];299 -> 540[label="",style="solid", color="burlywood", weight=9];
540 -> 320[label="",style="solid", color="burlywood", weight=3];
300[label="primMulNat Zero vz4000",fontsize=16,color="burlywood",shape="box"];541[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];300 -> 541[label="",style="solid", color="burlywood", weight=9];
541 -> 321[label="",style="solid", color="burlywood", weight=3];
542[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];300 -> 542[label="",style="solid", color="burlywood", weight=9];
542 -> 322[label="",style="solid", color="burlywood", weight=3];
301[label="pePe (primEqInt (Pos (Succ vz110)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];301 -> 323[label="",style="solid", color="black", weight=3];
302[label="pePe (primEqInt (Pos Zero) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];302 -> 324[label="",style="solid", color="black", weight=3];
375[label="vz4000",fontsize=16,color="green",shape="box"];376[label="pePe (primEqInt (Neg (Succ vz160)) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];376 -> 389[label="",style="solid", color="black", weight=3];
377[label="pePe (primEqInt (Neg Zero) (srMyInt vz31 vz401)) vz5",fontsize=16,color="black",shape="box"];377 -> 390[label="",style="solid", color="black", weight=3];
378[label="vz300",fontsize=16,color="green",shape="box"];303[label="vz300",fontsize=16,color="green",shape="box"];304[label="vz4000",fontsize=16,color="green",shape="box"];319[label="primMulNat (Succ vz3000) (Succ vz40000)",fontsize=16,color="black",shape="box"];319 -> 335[label="",style="solid", color="black", weight=3];
320[label="primMulNat (Succ vz3000) Zero",fontsize=16,color="black",shape="box"];320 -> 336[label="",style="solid", color="black", weight=3];
321[label="primMulNat Zero (Succ vz40000)",fontsize=16,color="black",shape="box"];321 -> 337[label="",style="solid", color="black", weight=3];
322[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];322 -> 338[label="",style="solid", color="black", weight=3];
323[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];543[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];323 -> 543[label="",style="solid", color="burlywood", weight=9];
543 -> 339[label="",style="solid", color="burlywood", weight=3];
544[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];323 -> 544[label="",style="solid", color="burlywood", weight=9];
544 -> 340[label="",style="solid", color="burlywood", weight=3];
324[label="pePe (primEqInt (Pos Zero) (primMulInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];545[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];324 -> 545[label="",style="solid", color="burlywood", weight=9];
545 -> 341[label="",style="solid", color="burlywood", weight=3];
546[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];324 -> 546[label="",style="solid", color="burlywood", weight=9];
546 -> 342[label="",style="solid", color="burlywood", weight=3];
389[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];547[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];389 -> 547[label="",style="solid", color="burlywood", weight=9];
547 -> 394[label="",style="solid", color="burlywood", weight=3];
548[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];389 -> 548[label="",style="solid", color="burlywood", weight=9];
548 -> 395[label="",style="solid", color="burlywood", weight=3];
390[label="pePe (primEqInt (Neg Zero) (primMulInt vz31 vz401)) vz5",fontsize=16,color="burlywood",shape="box"];549[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];390 -> 549[label="",style="solid", color="burlywood", weight=9];
549 -> 396[label="",style="solid", color="burlywood", weight=3];
550[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];390 -> 550[label="",style="solid", color="burlywood", weight=9];
550 -> 397[label="",style="solid", color="burlywood", weight=3];
335 -> 348[label="",style="dashed", color="red", weight=0];
335[label="primPlusNat (primMulNat vz3000 (Succ vz40000)) (Succ vz40000)",fontsize=16,color="magenta"];335 -> 349[label="",style="dashed", color="magenta", weight=3];
336[label="Zero",fontsize=16,color="green",shape="box"];337[label="Zero",fontsize=16,color="green",shape="box"];338[label="Zero",fontsize=16,color="green",shape="box"];339[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt (Pos vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];551[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];339 -> 551[label="",style="solid", color="burlywood", weight=9];
551 -> 350[label="",style="solid", color="burlywood", weight=3];
552[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];339 -> 552[label="",style="solid", color="burlywood", weight=9];
552 -> 351[label="",style="solid", color="burlywood", weight=3];
340[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt (Neg vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];553[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];340 -> 553[label="",style="solid", color="burlywood", weight=9];
553 -> 352[label="",style="solid", color="burlywood", weight=3];
554[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];340 -> 554[label="",style="solid", color="burlywood", weight=9];
554 -> 353[label="",style="solid", color="burlywood", weight=3];
341[label="pePe (primEqInt (Pos Zero) (primMulInt (Pos vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];555[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];341 -> 555[label="",style="solid", color="burlywood", weight=9];
555 -> 354[label="",style="solid", color="burlywood", weight=3];
556[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];341 -> 556[label="",style="solid", color="burlywood", weight=9];
556 -> 355[label="",style="solid", color="burlywood", weight=3];
342[label="pePe (primEqInt (Pos Zero) (primMulInt (Neg vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];557[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];342 -> 557[label="",style="solid", color="burlywood", weight=9];
557 -> 356[label="",style="solid", color="burlywood", weight=3];
558[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];342 -> 558[label="",style="solid", color="burlywood", weight=9];
558 -> 357[label="",style="solid", color="burlywood", weight=3];
394[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt (Pos vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];559[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];394 -> 559[label="",style="solid", color="burlywood", weight=9];
559 -> 401[label="",style="solid", color="burlywood", weight=3];
560[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];394 -> 560[label="",style="solid", color="burlywood", weight=9];
560 -> 402[label="",style="solid", color="burlywood", weight=3];
395[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt (Neg vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];561[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];395 -> 561[label="",style="solid", color="burlywood", weight=9];
561 -> 403[label="",style="solid", color="burlywood", weight=3];
562[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];395 -> 562[label="",style="solid", color="burlywood", weight=9];
562 -> 404[label="",style="solid", color="burlywood", weight=3];
396[label="pePe (primEqInt (Neg Zero) (primMulInt (Pos vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];563[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];396 -> 563[label="",style="solid", color="burlywood", weight=9];
563 -> 405[label="",style="solid", color="burlywood", weight=3];
564[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];396 -> 564[label="",style="solid", color="burlywood", weight=9];
564 -> 406[label="",style="solid", color="burlywood", weight=3];
397[label="pePe (primEqInt (Neg Zero) (primMulInt (Neg vz310) vz401)) vz5",fontsize=16,color="burlywood",shape="box"];565[label="vz401/Pos vz4010",fontsize=10,color="white",style="solid",shape="box"];397 -> 565[label="",style="solid", color="burlywood", weight=9];
565 -> 407[label="",style="solid", color="burlywood", weight=3];
566[label="vz401/Neg vz4010",fontsize=10,color="white",style="solid",shape="box"];397 -> 566[label="",style="solid", color="burlywood", weight=9];
566 -> 408[label="",style="solid", color="burlywood", weight=3];
349 -> 287[label="",style="dashed", color="red", weight=0];
349[label="primMulNat vz3000 (Succ vz40000)",fontsize=16,color="magenta"];349 -> 358[label="",style="dashed", color="magenta", weight=3];
349 -> 359[label="",style="dashed", color="magenta", weight=3];
348[label="primPlusNat vz15 (Succ vz40000)",fontsize=16,color="burlywood",shape="triangle"];567[label="vz15/Succ vz150",fontsize=10,color="white",style="solid",shape="box"];348 -> 567[label="",style="solid", color="burlywood", weight=9];
567 -> 360[label="",style="solid", color="burlywood", weight=3];
568[label="vz15/Zero",fontsize=10,color="white",style="solid",shape="box"];348 -> 568[label="",style="solid", color="burlywood", weight=9];
568 -> 361[label="",style="solid", color="burlywood", weight=3];
350[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt (Pos vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];350 -> 379[label="",style="solid", color="black", weight=3];
351[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt (Pos vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];351 -> 380[label="",style="solid", color="black", weight=3];
352[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt (Neg vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];352 -> 381[label="",style="solid", color="black", weight=3];
353[label="pePe (primEqInt (Pos (Succ vz110)) (primMulInt (Neg vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];353 -> 382[label="",style="solid", color="black", weight=3];
354[label="pePe (primEqInt (Pos Zero) (primMulInt (Pos vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];354 -> 383[label="",style="solid", color="black", weight=3];
355[label="pePe (primEqInt (Pos Zero) (primMulInt (Pos vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];355 -> 384[label="",style="solid", color="black", weight=3];
356[label="pePe (primEqInt (Pos Zero) (primMulInt (Neg vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];356 -> 385[label="",style="solid", color="black", weight=3];
357[label="pePe (primEqInt (Pos Zero) (primMulInt (Neg vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];357 -> 386[label="",style="solid", color="black", weight=3];
401[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt (Pos vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];401 -> 412[label="",style="solid", color="black", weight=3];
402[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt (Pos vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];402 -> 413[label="",style="solid", color="black", weight=3];
403[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt (Neg vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];403 -> 414[label="",style="solid", color="black", weight=3];
404[label="pePe (primEqInt (Neg (Succ vz160)) (primMulInt (Neg vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];404 -> 415[label="",style="solid", color="black", weight=3];
405[label="pePe (primEqInt (Neg Zero) (primMulInt (Pos vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];405 -> 416[label="",style="solid", color="black", weight=3];
406[label="pePe (primEqInt (Neg Zero) (primMulInt (Pos vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];406 -> 417[label="",style="solid", color="black", weight=3];
407[label="pePe (primEqInt (Neg Zero) (primMulInt (Neg vz310) (Pos vz4010))) vz5",fontsize=16,color="black",shape="box"];407 -> 418[label="",style="solid", color="black", weight=3];
408[label="pePe (primEqInt (Neg Zero) (primMulInt (Neg vz310) (Neg vz4010))) vz5",fontsize=16,color="black",shape="box"];408 -> 419[label="",style="solid", color="black", weight=3];
358[label="vz3000",fontsize=16,color="green",shape="box"];359[label="Succ vz40000",fontsize=16,color="green",shape="box"];360[label="primPlusNat (Succ vz150) (Succ vz40000)",fontsize=16,color="black",shape="box"];360 -> 387[label="",style="solid", color="black", weight=3];
361[label="primPlusNat Zero (Succ vz40000)",fontsize=16,color="black",shape="box"];361 -> 388[label="",style="solid", color="black", weight=3];
379 -> 391[label="",style="dashed", color="red", weight=0];
379[label="pePe (primEqInt (Pos (Succ vz110)) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];379 -> 392[label="",style="dashed", color="magenta", weight=3];
380 -> 398[label="",style="dashed", color="red", weight=0];
380[label="pePe (primEqInt (Pos (Succ vz110)) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];380 -> 399[label="",style="dashed", color="magenta", weight=3];
381 -> 398[label="",style="dashed", color="red", weight=0];
381[label="pePe (primEqInt (Pos (Succ vz110)) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];381 -> 400[label="",style="dashed", color="magenta", weight=3];
382 -> 391[label="",style="dashed", color="red", weight=0];
382[label="pePe (primEqInt (Pos (Succ vz110)) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];382 -> 393[label="",style="dashed", color="magenta", weight=3];
383 -> 409[label="",style="dashed", color="red", weight=0];
383[label="pePe (primEqInt (Pos Zero) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];383 -> 410[label="",style="dashed", color="magenta", weight=3];
384 -> 420[label="",style="dashed", color="red", weight=0];
384[label="pePe (primEqInt (Pos Zero) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];384 -> 421[label="",style="dashed", color="magenta", weight=3];
385 -> 420[label="",style="dashed", color="red", weight=0];
385[label="pePe (primEqInt (Pos Zero) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];385 -> 422[label="",style="dashed", color="magenta", weight=3];
386 -> 409[label="",style="dashed", color="red", weight=0];
386[label="pePe (primEqInt (Pos Zero) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];386 -> 411[label="",style="dashed", color="magenta", weight=3];
412 -> 423[label="",style="dashed", color="red", weight=0];
412[label="pePe (primEqInt (Neg (Succ vz160)) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];412 -> 424[label="",style="dashed", color="magenta", weight=3];
413 -> 426[label="",style="dashed", color="red", weight=0];
413[label="pePe (primEqInt (Neg (Succ vz160)) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];413 -> 427[label="",style="dashed", color="magenta", weight=3];
414 -> 426[label="",style="dashed", color="red", weight=0];
414[label="pePe (primEqInt (Neg (Succ vz160)) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];414 -> 428[label="",style="dashed", color="magenta", weight=3];
415 -> 423[label="",style="dashed", color="red", weight=0];
415[label="pePe (primEqInt (Neg (Succ vz160)) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];415 -> 425[label="",style="dashed", color="magenta", weight=3];
416 -> 429[label="",style="dashed", color="red", weight=0];
416[label="pePe (primEqInt (Neg Zero) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];416 -> 430[label="",style="dashed", color="magenta", weight=3];
417 -> 432[label="",style="dashed", color="red", weight=0];
417[label="pePe (primEqInt (Neg Zero) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];417 -> 433[label="",style="dashed", color="magenta", weight=3];
418 -> 432[label="",style="dashed", color="red", weight=0];
418[label="pePe (primEqInt (Neg Zero) (Neg (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];418 -> 434[label="",style="dashed", color="magenta", weight=3];
419 -> 429[label="",style="dashed", color="red", weight=0];
419[label="pePe (primEqInt (Neg Zero) (Pos (primMulNat vz310 vz4010))) vz5",fontsize=16,color="magenta"];419 -> 431[label="",style="dashed", color="magenta", weight=3];
387[label="Succ (Succ (primPlusNat vz150 vz40000))",fontsize=16,color="green",shape="box"];387 -> 435[label="",style="dashed", color="green", weight=3];
388[label="Succ vz40000",fontsize=16,color="green",shape="box"];392 -> 287[label="",style="dashed", color="red", weight=0];
392[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];392 -> 436[label="",style="dashed", color="magenta", weight=3];
392 -> 437[label="",style="dashed", color="magenta", weight=3];
391[label="pePe (primEqInt (Pos (Succ vz110)) (Pos vz17)) vz5",fontsize=16,color="burlywood",shape="triangle"];569[label="vz17/Succ vz170",fontsize=10,color="white",style="solid",shape="box"];391 -> 569[label="",style="solid", color="burlywood", weight=9];
569 -> 438[label="",style="solid", color="burlywood", weight=3];
570[label="vz17/Zero",fontsize=10,color="white",style="solid",shape="box"];391 -> 570[label="",style="solid", color="burlywood", weight=9];
570 -> 439[label="",style="solid", color="burlywood", weight=3];
399 -> 287[label="",style="dashed", color="red", weight=0];
399[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];399 -> 440[label="",style="dashed", color="magenta", weight=3];
399 -> 441[label="",style="dashed", color="magenta", weight=3];
398[label="pePe (primEqInt (Pos (Succ vz110)) (Neg vz18)) vz5",fontsize=16,color="black",shape="triangle"];398 -> 442[label="",style="solid", color="black", weight=3];
400 -> 287[label="",style="dashed", color="red", weight=0];
400[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];400 -> 443[label="",style="dashed", color="magenta", weight=3];
400 -> 444[label="",style="dashed", color="magenta", weight=3];
393 -> 287[label="",style="dashed", color="red", weight=0];
393[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];393 -> 445[label="",style="dashed", color="magenta", weight=3];
393 -> 446[label="",style="dashed", color="magenta", weight=3];
410 -> 287[label="",style="dashed", color="red", weight=0];
410[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];410 -> 447[label="",style="dashed", color="magenta", weight=3];
410 -> 448[label="",style="dashed", color="magenta", weight=3];
409[label="pePe (primEqInt (Pos Zero) (Pos vz19)) vz5",fontsize=16,color="burlywood",shape="triangle"];571[label="vz19/Succ vz190",fontsize=10,color="white",style="solid",shape="box"];409 -> 571[label="",style="solid", color="burlywood", weight=9];
571 -> 449[label="",style="solid", color="burlywood", weight=3];
572[label="vz19/Zero",fontsize=10,color="white",style="solid",shape="box"];409 -> 572[label="",style="solid", color="burlywood", weight=9];
572 -> 450[label="",style="solid", color="burlywood", weight=3];
421 -> 287[label="",style="dashed", color="red", weight=0];
421[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];421 -> 451[label="",style="dashed", color="magenta", weight=3];
421 -> 452[label="",style="dashed", color="magenta", weight=3];
420[label="pePe (primEqInt (Pos Zero) (Neg vz20)) vz5",fontsize=16,color="burlywood",shape="triangle"];573[label="vz20/Succ vz200",fontsize=10,color="white",style="solid",shape="box"];420 -> 573[label="",style="solid", color="burlywood", weight=9];
573 -> 453[label="",style="solid", color="burlywood", weight=3];
574[label="vz20/Zero",fontsize=10,color="white",style="solid",shape="box"];420 -> 574[label="",style="solid", color="burlywood", weight=9];
574 -> 454[label="",style="solid", color="burlywood", weight=3];
422 -> 287[label="",style="dashed", color="red", weight=0];
422[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];422 -> 455[label="",style="dashed", color="magenta", weight=3];
422 -> 456[label="",style="dashed", color="magenta", weight=3];
411 -> 287[label="",style="dashed", color="red", weight=0];
411[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];411 -> 457[label="",style="dashed", color="magenta", weight=3];
411 -> 458[label="",style="dashed", color="magenta", weight=3];
424 -> 287[label="",style="dashed", color="red", weight=0];
424[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];424 -> 459[label="",style="dashed", color="magenta", weight=3];
424 -> 460[label="",style="dashed", color="magenta", weight=3];
423[label="pePe (primEqInt (Neg (Succ vz160)) (Pos vz21)) vz5",fontsize=16,color="black",shape="triangle"];423 -> 461[label="",style="solid", color="black", weight=3];
427 -> 287[label="",style="dashed", color="red", weight=0];
427[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];427 -> 462[label="",style="dashed", color="magenta", weight=3];
427 -> 463[label="",style="dashed", color="magenta", weight=3];
426[label="pePe (primEqInt (Neg (Succ vz160)) (Neg vz22)) vz5",fontsize=16,color="burlywood",shape="triangle"];575[label="vz22/Succ vz220",fontsize=10,color="white",style="solid",shape="box"];426 -> 575[label="",style="solid", color="burlywood", weight=9];
575 -> 464[label="",style="solid", color="burlywood", weight=3];
576[label="vz22/Zero",fontsize=10,color="white",style="solid",shape="box"];426 -> 576[label="",style="solid", color="burlywood", weight=9];
576 -> 465[label="",style="solid", color="burlywood", weight=3];
428 -> 287[label="",style="dashed", color="red", weight=0];
428[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];428 -> 466[label="",style="dashed", color="magenta", weight=3];
428 -> 467[label="",style="dashed", color="magenta", weight=3];
425 -> 287[label="",style="dashed", color="red", weight=0];
425[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];425 -> 468[label="",style="dashed", color="magenta", weight=3];
425 -> 469[label="",style="dashed", color="magenta", weight=3];
430 -> 287[label="",style="dashed", color="red", weight=0];
430[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];430 -> 470[label="",style="dashed", color="magenta", weight=3];
430 -> 471[label="",style="dashed", color="magenta", weight=3];
429[label="pePe (primEqInt (Neg Zero) (Pos vz23)) vz5",fontsize=16,color="burlywood",shape="triangle"];577[label="vz23/Succ vz230",fontsize=10,color="white",style="solid",shape="box"];429 -> 577[label="",style="solid", color="burlywood", weight=9];
577 -> 472[label="",style="solid", color="burlywood", weight=3];
578[label="vz23/Zero",fontsize=10,color="white",style="solid",shape="box"];429 -> 578[label="",style="solid", color="burlywood", weight=9];
578 -> 473[label="",style="solid", color="burlywood", weight=3];
433 -> 287[label="",style="dashed", color="red", weight=0];
433[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];433 -> 474[label="",style="dashed", color="magenta", weight=3];
433 -> 475[label="",style="dashed", color="magenta", weight=3];
432[label="pePe (primEqInt (Neg Zero) (Neg vz24)) vz5",fontsize=16,color="burlywood",shape="triangle"];579[label="vz24/Succ vz240",fontsize=10,color="white",style="solid",shape="box"];432 -> 579[label="",style="solid", color="burlywood", weight=9];
579 -> 476[label="",style="solid", color="burlywood", weight=3];
580[label="vz24/Zero",fontsize=10,color="white",style="solid",shape="box"];432 -> 580[label="",style="solid", color="burlywood", weight=9];
580 -> 477[label="",style="solid", color="burlywood", weight=3];
434 -> 287[label="",style="dashed", color="red", weight=0];
434[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];434 -> 478[label="",style="dashed", color="magenta", weight=3];
434 -> 479[label="",style="dashed", color="magenta", weight=3];
431 -> 287[label="",style="dashed", color="red", weight=0];
431[label="primMulNat vz310 vz4010",fontsize=16,color="magenta"];431 -> 480[label="",style="dashed", color="magenta", weight=3];
431 -> 481[label="",style="dashed", color="magenta", weight=3];
435[label="primPlusNat vz150 vz40000",fontsize=16,color="burlywood",shape="triangle"];581[label="vz150/Succ vz1500",fontsize=10,color="white",style="solid",shape="box"];435 -> 581[label="",style="solid", color="burlywood", weight=9];
581 -> 482[label="",style="solid", color="burlywood", weight=3];
582[label="vz150/Zero",fontsize=10,color="white",style="solid",shape="box"];435 -> 582[label="",style="solid", color="burlywood", weight=9];
582 -> 483[label="",style="solid", color="burlywood", weight=3];
436[label="vz310",fontsize=16,color="green",shape="box"];437[label="vz4010",fontsize=16,color="green",shape="box"];438[label="pePe (primEqInt (Pos (Succ vz110)) (Pos (Succ vz170))) vz5",fontsize=16,color="black",shape="box"];438 -> 484[label="",style="solid", color="black", weight=3];
439[label="pePe (primEqInt (Pos (Succ vz110)) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];439 -> 485[label="",style="solid", color="black", weight=3];
440[label="vz310",fontsize=16,color="green",shape="box"];441[label="vz4010",fontsize=16,color="green",shape="box"];442[label="pePe MyFalse vz5",fontsize=16,color="black",shape="triangle"];442 -> 486[label="",style="solid", color="black", weight=3];
443[label="vz310",fontsize=16,color="green",shape="box"];444[label="vz4010",fontsize=16,color="green",shape="box"];445[label="vz310",fontsize=16,color="green",shape="box"];446[label="vz4010",fontsize=16,color="green",shape="box"];447[label="vz310",fontsize=16,color="green",shape="box"];448[label="vz4010",fontsize=16,color="green",shape="box"];449[label="pePe (primEqInt (Pos Zero) (Pos (Succ vz190))) vz5",fontsize=16,color="black",shape="box"];449 -> 487[label="",style="solid", color="black", weight=3];
450[label="pePe (primEqInt (Pos Zero) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];450 -> 488[label="",style="solid", color="black", weight=3];
451[label="vz310",fontsize=16,color="green",shape="box"];452[label="vz4010",fontsize=16,color="green",shape="box"];453[label="pePe (primEqInt (Pos Zero) (Neg (Succ vz200))) vz5",fontsize=16,color="black",shape="box"];453 -> 489[label="",style="solid", color="black", weight=3];
454[label="pePe (primEqInt (Pos Zero) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];454 -> 490[label="",style="solid", color="black", weight=3];
455[label="vz310",fontsize=16,color="green",shape="box"];456[label="vz4010",fontsize=16,color="green",shape="box"];457[label="vz310",fontsize=16,color="green",shape="box"];458[label="vz4010",fontsize=16,color="green",shape="box"];459[label="vz310",fontsize=16,color="green",shape="box"];460[label="vz4010",fontsize=16,color="green",shape="box"];461 -> 442[label="",style="dashed", color="red", weight=0];
461[label="pePe MyFalse vz5",fontsize=16,color="magenta"];462[label="vz310",fontsize=16,color="green",shape="box"];463[label="vz4010",fontsize=16,color="green",shape="box"];464[label="pePe (primEqInt (Neg (Succ vz160)) (Neg (Succ vz220))) vz5",fontsize=16,color="black",shape="box"];464 -> 491[label="",style="solid", color="black", weight=3];
465[label="pePe (primEqInt (Neg (Succ vz160)) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];465 -> 492[label="",style="solid", color="black", weight=3];
466[label="vz310",fontsize=16,color="green",shape="box"];467[label="vz4010",fontsize=16,color="green",shape="box"];468[label="vz310",fontsize=16,color="green",shape="box"];469[label="vz4010",fontsize=16,color="green",shape="box"];470[label="vz310",fontsize=16,color="green",shape="box"];471[label="vz4010",fontsize=16,color="green",shape="box"];472[label="pePe (primEqInt (Neg Zero) (Pos (Succ vz230))) vz5",fontsize=16,color="black",shape="box"];472 -> 493[label="",style="solid", color="black", weight=3];
473[label="pePe (primEqInt (Neg Zero) (Pos Zero)) vz5",fontsize=16,color="black",shape="box"];473 -> 494[label="",style="solid", color="black", weight=3];
474[label="vz310",fontsize=16,color="green",shape="box"];475[label="vz4010",fontsize=16,color="green",shape="box"];476[label="pePe (primEqInt (Neg Zero) (Neg (Succ vz240))) vz5",fontsize=16,color="black",shape="box"];476 -> 495[label="",style="solid", color="black", weight=3];
477[label="pePe (primEqInt (Neg Zero) (Neg Zero)) vz5",fontsize=16,color="black",shape="box"];477 -> 496[label="",style="solid", color="black", weight=3];
478[label="vz310",fontsize=16,color="green",shape="box"];479[label="vz4010",fontsize=16,color="green",shape="box"];480[label="vz310",fontsize=16,color="green",shape="box"];481[label="vz4010",fontsize=16,color="green",shape="box"];482[label="primPlusNat (Succ vz1500) vz40000",fontsize=16,color="burlywood",shape="box"];583[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];482 -> 583[label="",style="solid", color="burlywood", weight=9];
583 -> 497[label="",style="solid", color="burlywood", weight=3];
584[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];482 -> 584[label="",style="solid", color="burlywood", weight=9];
584 -> 498[label="",style="solid", color="burlywood", weight=3];
483[label="primPlusNat Zero vz40000",fontsize=16,color="burlywood",shape="box"];585[label="vz40000/Succ vz400000",fontsize=10,color="white",style="solid",shape="box"];483 -> 585[label="",style="solid", color="burlywood", weight=9];
585 -> 499[label="",style="solid", color="burlywood", weight=3];
586[label="vz40000/Zero",fontsize=10,color="white",style="solid",shape="box"];483 -> 586[label="",style="solid", color="burlywood", weight=9];
586 -> 500[label="",style="solid", color="burlywood", weight=3];
484[label="pePe (primEqNat vz110 vz170) vz5",fontsize=16,color="burlywood",shape="triangle"];587[label="vz110/Succ vz1100",fontsize=10,color="white",style="solid",shape="box"];484 -> 587[label="",style="solid", color="burlywood", weight=9];
587 -> 501[label="",style="solid", color="burlywood", weight=3];
588[label="vz110/Zero",fontsize=10,color="white",style="solid",shape="box"];484 -> 588[label="",style="solid", color="burlywood", weight=9];
588 -> 502[label="",style="solid", color="burlywood", weight=3];
485 -> 442[label="",style="dashed", color="red", weight=0];
485[label="pePe MyFalse vz5",fontsize=16,color="magenta"];486[label="vz5",fontsize=16,color="green",shape="box"];487 -> 442[label="",style="dashed", color="red", weight=0];
487[label="pePe MyFalse vz5",fontsize=16,color="magenta"];488[label="pePe MyTrue vz5",fontsize=16,color="black",shape="triangle"];488 -> 503[label="",style="solid", color="black", weight=3];
489 -> 442[label="",style="dashed", color="red", weight=0];
489[label="pePe MyFalse vz5",fontsize=16,color="magenta"];490 -> 488[label="",style="dashed", color="red", weight=0];
490[label="pePe MyTrue vz5",fontsize=16,color="magenta"];491 -> 484[label="",style="dashed", color="red", weight=0];
491[label="pePe (primEqNat vz160 vz220) vz5",fontsize=16,color="magenta"];491 -> 504[label="",style="dashed", color="magenta", weight=3];
491 -> 505[label="",style="dashed", color="magenta", weight=3];
492 -> 442[label="",style="dashed", color="red", weight=0];
492[label="pePe MyFalse vz5",fontsize=16,color="magenta"];493 -> 442[label="",style="dashed", color="red", weight=0];
493[label="pePe MyFalse vz5",fontsize=16,color="magenta"];494 -> 488[label="",style="dashed", color="red", weight=0];
494[label="pePe MyTrue vz5",fontsize=16,color="magenta"];495 -> 442[label="",style="dashed", color="red", weight=0];
495[label="pePe MyFalse vz5",fontsize=16,color="magenta"];496 -> 488[label="",style="dashed", color="red", weight=0];
496[label="pePe MyTrue vz5",fontsize=16,color="magenta"];497[label="primPlusNat (Succ vz1500) (Succ vz400000)",fontsize=16,color="black",shape="box"];497 -> 506[label="",style="solid", color="black", weight=3];
498[label="primPlusNat (Succ vz1500) Zero",fontsize=16,color="black",shape="box"];498 -> 507[label="",style="solid", color="black", weight=3];
499[label="primPlusNat Zero (Succ vz400000)",fontsize=16,color="black",shape="box"];499 -> 508[label="",style="solid", color="black", weight=3];
500[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];500 -> 509[label="",style="solid", color="black", weight=3];
501[label="pePe (primEqNat (Succ vz1100) vz170) vz5",fontsize=16,color="burlywood",shape="box"];589[label="vz170/Succ vz1700",fontsize=10,color="white",style="solid",shape="box"];501 -> 589[label="",style="solid", color="burlywood", weight=9];
589 -> 510[label="",style="solid", color="burlywood", weight=3];
590[label="vz170/Zero",fontsize=10,color="white",style="solid",shape="box"];501 -> 590[label="",style="solid", color="burlywood", weight=9];
590 -> 511[label="",style="solid", color="burlywood", weight=3];
502[label="pePe (primEqNat Zero vz170) vz5",fontsize=16,color="burlywood",shape="box"];591[label="vz170/Succ vz1700",fontsize=10,color="white",style="solid",shape="box"];502 -> 591[label="",style="solid", color="burlywood", weight=9];
591 -> 512[label="",style="solid", color="burlywood", weight=3];
592[label="vz170/Zero",fontsize=10,color="white",style="solid",shape="box"];502 -> 592[label="",style="solid", color="burlywood", weight=9];
592 -> 513[label="",style="solid", color="burlywood", weight=3];
503[label="MyTrue",fontsize=16,color="green",shape="box"];504[label="vz220",fontsize=16,color="green",shape="box"];505[label="vz160",fontsize=16,color="green",shape="box"];506[label="Succ (Succ (primPlusNat vz1500 vz400000))",fontsize=16,color="green",shape="box"];506 -> 514[label="",style="dashed", color="green", weight=3];
507[label="Succ vz1500",fontsize=16,color="green",shape="box"];508[label="Succ vz400000",fontsize=16,color="green",shape="box"];509[label="Zero",fontsize=16,color="green",shape="box"];510[label="pePe (primEqNat (Succ vz1100) (Succ vz1700)) vz5",fontsize=16,color="black",shape="box"];510 -> 515[label="",style="solid", color="black", weight=3];
511[label="pePe (primEqNat (Succ vz1100) Zero) vz5",fontsize=16,color="black",shape="box"];511 -> 516[label="",style="solid", color="black", weight=3];
512[label="pePe (primEqNat Zero (Succ vz1700)) vz5",fontsize=16,color="black",shape="box"];512 -> 517[label="",style="solid", color="black", weight=3];
513[label="pePe (primEqNat Zero Zero) vz5",fontsize=16,color="black",shape="box"];513 -> 518[label="",style="solid", color="black", weight=3];
514 -> 435[label="",style="dashed", color="red", weight=0];
514[label="primPlusNat vz1500 vz400000",fontsize=16,color="magenta"];514 -> 519[label="",style="dashed", color="magenta", weight=3];
514 -> 520[label="",style="dashed", color="magenta", weight=3];
515 -> 484[label="",style="dashed", color="red", weight=0];
515[label="pePe (primEqNat vz1100 vz1700) vz5",fontsize=16,color="magenta"];515 -> 521[label="",style="dashed", color="magenta", weight=3];
515 -> 522[label="",style="dashed", color="magenta", weight=3];
516 -> 442[label="",style="dashed", color="red", weight=0];
516[label="pePe MyFalse vz5",fontsize=16,color="magenta"];517 -> 442[label="",style="dashed", color="red", weight=0];
517[label="pePe MyFalse vz5",fontsize=16,color="magenta"];518 -> 488[label="",style="dashed", color="red", weight=0];
518[label="pePe MyTrue vz5",fontsize=16,color="magenta"];519[label="vz400000",fontsize=16,color="green",shape="box"];520[label="vz1500",fontsize=16,color="green",shape="box"];521[label="vz1700",fontsize=16,color="green",shape="box"];522[label="vz1100",fontsize=16,color="green",shape="box"];}

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

(6)
Complex Obligation (AND)

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

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

   new_foldr(vz3, Cons(vz40, vz41)) -> new_foldr(vz3, vz41)

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

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

From the DPs we obtained the following set of size-change graphs:
*new_foldr(vz3, Cons(vz40, vz41)) -> new_foldr(vz3, vz41)
The graph contains the following edges 1 >= 1, 2 > 2


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

(9)
YES

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

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

   new_primMulNat(Main.Succ(vz3000), Main.Succ(vz40000)) -> new_primMulNat(vz3000, Main.Succ(vz40000))

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

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

From the DPs we obtained the following set of size-change graphs:
*new_primMulNat(Main.Succ(vz3000), Main.Succ(vz40000)) -> new_primMulNat(vz3000, Main.Succ(vz40000))
The graph contains the following edges 1 > 1, 2 >= 2


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

(12)
YES

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

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

   new_primPlusNat(Main.Succ(vz1500), Main.Succ(vz400000)) -> new_primPlusNat(vz1500, vz400000)

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

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

From the DPs we obtained the following set of size-change graphs:
*new_primPlusNat(Main.Succ(vz1500), Main.Succ(vz400000)) -> new_primPlusNat(vz1500, vz400000)
The graph contains the following edges 1 > 1, 2 > 2


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

(15)
YES

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

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

   new_pePe(Main.Succ(vz1100), Main.Succ(vz1700), vz5) -> new_pePe(vz1100, vz1700, vz5)

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

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

From the DPs we obtained the following set of size-change graphs:
*new_pePe(Main.Succ(vz1100), Main.Succ(vz1700), vz5) -> new_pePe(vz1100, vz1700, vz5)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


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

(18)
YES