/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QDP
(7) QDPSizeChangeProof [EQUIVALENT, 0 ms]
(8) YES


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

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

data MyBool = MyTrue  | MyFalse ;

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

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

data Ordering = LT  | EQ  | GT ;

absFloat :: Float  ->  Float;
absFloat = absReal;

absReal x = absReal2 x;

absReal0 x MyTrue = negateFloat x;

absReal1 x MyTrue = x;
absReal1 x MyFalse = absReal0 x otherwise;

absReal2 x = absReal1 x (gtEsFloat x (fromIntFloat (Main.Pos Main.Zero)));

compareFloat :: Float  ->  Float  ->  Ordering;
compareFloat = primCmpFloat;

compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
compareMyInt = primCmpInt;

fromIntFloat :: MyInt  ->  Float;
fromIntFloat = primIntToFloat;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering LT LT = MyFalse;
fsEsOrdering EQ EQ = MyFalse;
fsEsOrdering GT GT = MyFalse;
fsEsOrdering _ _ = MyTrue;

gtEsFloat :: Float  ->  Float  ->  MyBool;
gtEsFloat x y = fsEsOrdering (compareFloat x y) LT;

negateFloat :: Float  ->  Float;
negateFloat = primNegFloat;

negateMyInt :: MyInt  ->  MyInt;
negateMyInt = primNegInt;

otherwise :: MyBool;
otherwise = MyTrue;

primCmpFloat :: Float  ->  Float  ->  Ordering;
primCmpFloat (Float x1 x2) (Float y1 y2) = compareMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
primCmpInt (Main.Pos x) (Main.Neg y) = GT;
primCmpInt (Main.Neg x) (Main.Pos y) = LT;
primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;

primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
primCmpNat Main.Zero Main.Zero = EQ;
primCmpNat Main.Zero (Main.Succ y) = LT;
primCmpNat (Main.Succ x) Main.Zero = GT;
primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

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);

primNegFloat :: Float  ->  Float;
primNegFloat (Float x1 x2) = Float (negateMyInt x1) x2;

primNegInt :: MyInt  ->  MyInt;
primNegInt (Main.Pos x) = Main.Neg x;
primNegInt (Main.Neg x) = Main.Pos x;

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));

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 MyBool = MyTrue  | MyFalse ;

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

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

data Ordering = LT  | EQ  | GT ;

absFloat :: Float  ->  Float;
absFloat = absReal;

absReal x = absReal2 x;

absReal0 x MyTrue = negateFloat x;

absReal1 x MyTrue = x;
absReal1 x MyFalse = absReal0 x otherwise;

absReal2 x = absReal1 x (gtEsFloat x (fromIntFloat (Main.Pos Main.Zero)));

compareFloat :: Float  ->  Float  ->  Ordering;
compareFloat = primCmpFloat;

compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
compareMyInt = primCmpInt;

fromIntFloat :: MyInt  ->  Float;
fromIntFloat = primIntToFloat;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering LT LT = MyFalse;
fsEsOrdering EQ EQ = MyFalse;
fsEsOrdering GT GT = MyFalse;
fsEsOrdering vx vy = MyTrue;

gtEsFloat :: Float  ->  Float  ->  MyBool;
gtEsFloat x y = fsEsOrdering (compareFloat x y) LT;

negateFloat :: Float  ->  Float;
negateFloat = primNegFloat;

negateMyInt :: MyInt  ->  MyInt;
negateMyInt = primNegInt;

otherwise :: MyBool;
otherwise = MyTrue;

primCmpFloat :: Float  ->  Float  ->  Ordering;
primCmpFloat (Float x1 x2) (Float y1 y2) = compareMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
primCmpInt (Main.Pos x) (Main.Neg y) = GT;
primCmpInt (Main.Neg x) (Main.Pos y) = LT;
primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;

primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
primCmpNat Main.Zero Main.Zero = EQ;
primCmpNat Main.Zero (Main.Succ y) = LT;
primCmpNat (Main.Succ x) Main.Zero = GT;
primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

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);

primNegFloat :: Float  ->  Float;
primNegFloat (Float x1 x2) = Float (negateMyInt x1) x2;

primNegInt :: MyInt  ->  MyInt;
primNegInt (Main.Pos x) = Main.Neg x;
primNegInt (Main.Neg x) = Main.Pos x;

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));

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 MyBool = MyTrue  | MyFalse ;

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

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

data Ordering = LT  | EQ  | GT ;

absFloat :: Float  ->  Float;
absFloat = absReal;

absReal x = absReal2 x;

absReal0 x MyTrue = negateFloat x;

absReal1 x MyTrue = x;
absReal1 x MyFalse = absReal0 x otherwise;

absReal2 x = absReal1 x (gtEsFloat x (fromIntFloat (Main.Pos Main.Zero)));

compareFloat :: Float  ->  Float  ->  Ordering;
compareFloat = primCmpFloat;

compareMyInt :: MyInt  ->  MyInt  ->  Ordering;
compareMyInt = primCmpInt;

fromIntFloat :: MyInt  ->  Float;
fromIntFloat = primIntToFloat;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering LT LT = MyFalse;
fsEsOrdering EQ EQ = MyFalse;
fsEsOrdering GT GT = MyFalse;
fsEsOrdering vx vy = MyTrue;

gtEsFloat :: Float  ->  Float  ->  MyBool;
gtEsFloat x y = fsEsOrdering (compareFloat x y) LT;

negateFloat :: Float  ->  Float;
negateFloat = primNegFloat;

negateMyInt :: MyInt  ->  MyInt;
negateMyInt = primNegInt;

otherwise :: MyBool;
otherwise = MyTrue;

primCmpFloat :: Float  ->  Float  ->  Ordering;
primCmpFloat (Float x1 x2) (Float y1 y2) = compareMyInt (srMyInt x1 y1) (srMyInt x2 y2);

primCmpInt :: MyInt  ->  MyInt  ->  Ordering;
primCmpInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = EQ;
primCmpInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = EQ;
primCmpInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = EQ;
primCmpInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = EQ;
primCmpInt (Main.Pos x) (Main.Pos y) = primCmpNat x y;
primCmpInt (Main.Pos x) (Main.Neg y) = GT;
primCmpInt (Main.Neg x) (Main.Pos y) = LT;
primCmpInt (Main.Neg x) (Main.Neg y) = primCmpNat y x;

primCmpNat :: Main.Nat  ->  Main.Nat  ->  Ordering;
primCmpNat Main.Zero Main.Zero = EQ;
primCmpNat Main.Zero (Main.Succ y) = LT;
primCmpNat (Main.Succ x) Main.Zero = GT;
primCmpNat (Main.Succ x) (Main.Succ y) = primCmpNat x y;

primIntToFloat :: MyInt  ->  Float;
primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));

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);

primNegFloat :: Float  ->  Float;
primNegFloat (Float x1 x2) = Float (negateMyInt x1) x2;

primNegInt :: MyInt  ->  MyInt;
primNegInt (Main.Pos x) = Main.Neg x;
primNegInt (Main.Neg x) = Main.Pos x;

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));

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

}

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="absFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="absFloat vz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="absReal vz3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="absReal2 vz3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="absReal1 vz3 (gtEsFloat vz3 (fromIntFloat (Pos Zero)))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="absReal1 vz3 (fsEsOrdering (compareFloat vz3 (fromIntFloat (Pos Zero))) LT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="absReal1 vz3 (fsEsOrdering (primCmpFloat vz3 (fromIntFloat (Pos Zero))) LT)",fontsize=16,color="burlywood",shape="box"];1113[label="vz3/Float vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];8 -> 1113[label="",style="solid", color="burlywood", weight=9];
1113 -> 9[label="",style="solid", color="burlywood", weight=3];
9[label="absReal1 (Float vz30 vz31) (fsEsOrdering (primCmpFloat (Float vz30 vz31) (fromIntFloat (Pos Zero))) LT)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="absReal1 (Float vz30 vz31) (fsEsOrdering (primCmpFloat (Float vz30 vz31) (primIntToFloat (Pos Zero))) LT)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="absReal1 (Float vz30 vz31) (fsEsOrdering (primCmpFloat (Float vz30 vz31) (Float (Pos Zero) (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="absReal1 (Float vz30 vz31) (fsEsOrdering (compareMyInt (srMyInt vz30 (Pos Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13[label="absReal1 (Float vz30 vz31) (fsEsOrdering (primCmpInt (srMyInt vz30 (Pos Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
14[label="absReal1 (Float vz30 vz31) (fsEsOrdering (primCmpInt (primMulInt vz30 (Pos Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1114[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];14 -> 1114[label="",style="solid", color="burlywood", weight=9];
1114 -> 15[label="",style="solid", color="burlywood", weight=3];
1115[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];14 -> 1115[label="",style="solid", color="burlywood", weight=9];
1115 -> 16[label="",style="solid", color="burlywood", weight=3];
15[label="absReal1 (Float (Pos vz300) vz31) (fsEsOrdering (primCmpInt (primMulInt (Pos vz300) (Pos Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="absReal1 (Float (Neg vz300) vz31) (fsEsOrdering (primCmpInt (primMulInt (Neg vz300) (Pos Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="absReal1 (Float (Pos vz300) vz31) (fsEsOrdering (primCmpInt (Pos (primMulNat vz300 Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1116[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];17 -> 1116[label="",style="solid", color="burlywood", weight=9];
1116 -> 19[label="",style="solid", color="burlywood", weight=3];
1117[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];17 -> 1117[label="",style="solid", color="burlywood", weight=9];
1117 -> 20[label="",style="solid", color="burlywood", weight=3];
18[label="absReal1 (Float (Neg vz300) vz31) (fsEsOrdering (primCmpInt (Neg (primMulNat vz300 Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1118[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];18 -> 1118[label="",style="solid", color="burlywood", weight=9];
1118 -> 21[label="",style="solid", color="burlywood", weight=3];
1119[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 1119[label="",style="solid", color="burlywood", weight=9];
1119 -> 22[label="",style="solid", color="burlywood", weight=3];
19[label="absReal1 (Float (Pos (Succ vz3000)) vz31) (fsEsOrdering (primCmpInt (Pos (primMulNat (Succ vz3000) Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="absReal1 (Float (Pos Zero) vz31) (fsEsOrdering (primCmpInt (Pos (primMulNat Zero Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="absReal1 (Float (Neg (Succ vz3000)) vz31) (fsEsOrdering (primCmpInt (Neg (primMulNat (Succ vz3000) Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="absReal1 (Float (Neg Zero) vz31) (fsEsOrdering (primCmpInt (Neg (primMulNat Zero Zero)) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="absReal1 (Float (Pos (Succ vz3000)) vz31) (fsEsOrdering (primCmpInt (Pos Zero) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
24[label="absReal1 (Float (Pos Zero) vz31) (fsEsOrdering (primCmpInt (Pos Zero) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="absReal1 (Float (Neg (Succ vz3000)) vz31) (fsEsOrdering (primCmpInt (Neg Zero) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
26[label="absReal1 (Float (Neg Zero) vz31) (fsEsOrdering (primCmpInt (Neg Zero) (srMyInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
27[label="absReal1 (Float (Pos (Succ vz3000)) vz31) (fsEsOrdering (primCmpInt (Pos Zero) (primMulInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1120[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];27 -> 1120[label="",style="solid", color="burlywood", weight=9];
1120 -> 31[label="",style="solid", color="burlywood", weight=3];
1121[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];27 -> 1121[label="",style="solid", color="burlywood", weight=9];
1121 -> 32[label="",style="solid", color="burlywood", weight=3];
28[label="absReal1 (Float (Pos Zero) vz31) (fsEsOrdering (primCmpInt (Pos Zero) (primMulInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1122[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];28 -> 1122[label="",style="solid", color="burlywood", weight=9];
1122 -> 33[label="",style="solid", color="burlywood", weight=3];
1123[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];28 -> 1123[label="",style="solid", color="burlywood", weight=9];
1123 -> 34[label="",style="solid", color="burlywood", weight=3];
29[label="absReal1 (Float (Neg (Succ vz3000)) vz31) (fsEsOrdering (primCmpInt (Neg Zero) (primMulInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1124[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];29 -> 1124[label="",style="solid", color="burlywood", weight=9];
1124 -> 35[label="",style="solid", color="burlywood", weight=3];
1125[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];29 -> 1125[label="",style="solid", color="burlywood", weight=9];
1125 -> 36[label="",style="solid", color="burlywood", weight=3];
30[label="absReal1 (Float (Neg Zero) vz31) (fsEsOrdering (primCmpInt (Neg Zero) (primMulInt vz31 (Pos (Succ Zero)))) LT)",fontsize=16,color="burlywood",shape="box"];1126[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];30 -> 1126[label="",style="solid", color="burlywood", weight=9];
1126 -> 37[label="",style="solid", color="burlywood", weight=3];
1127[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];30 -> 1127[label="",style="solid", color="burlywood", weight=9];
1127 -> 38[label="",style="solid", color="burlywood", weight=3];
31[label="absReal1 (Float (Pos (Succ vz3000)) (Pos vz310)) (fsEsOrdering (primCmpInt (Pos Zero) (primMulInt (Pos vz310) (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3];
32[label="absReal1 (Float (Pos (Succ vz3000)) (Neg vz310)) (fsEsOrdering (primCmpInt (Pos Zero) (primMulInt (Neg vz310) (Pos (Succ Zero)))) LT)",fontsize=16,color="black",shape="box"];32 -> 40[label="",style="solid", color="black", weight=3];
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960[label="vz3100",fontsize=16,color="green",shape="box"];961 -> 650[label="",style="dashed", color="red", weight=0];
961[label="primPlusNat (primMulNat vz3100 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];961 -> 1005[label="",style="dashed", color="magenta", weight=3];
959[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) (fsEsOrdering (primCmpInt (Neg Zero) (Pos vz63)) LT)",fontsize=16,color="burlywood",shape="triangle"];1156[label="vz63/Succ vz630",fontsize=10,color="white",style="solid",shape="box"];959 -> 1156[label="",style="solid", color="burlywood", weight=9];
1156 -> 1006[label="",style="solid", color="burlywood", weight=3];
1157[label="vz63/Zero",fontsize=10,color="white",style="solid",shape="box"];959 -> 1157[label="",style="solid", color="burlywood", weight=9];
1157 -> 1007[label="",style="solid", color="burlywood", weight=3];
99[label="absReal1 (Float (Neg Zero) (Pos Zero)) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];99 -> 123[label="",style="solid", color="black", weight=3];
1019[label="vz3100",fontsize=16,color="green",shape="box"];1020 -> 650[label="",style="dashed", color="red", weight=0];
1020[label="primPlusNat (primMulNat vz3100 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];1020 -> 1064[label="",style="dashed", color="magenta", weight=3];
1018[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) (fsEsOrdering (primCmpInt (Neg Zero) (Neg vz68)) LT)",fontsize=16,color="burlywood",shape="triangle"];1158[label="vz68/Succ vz680",fontsize=10,color="white",style="solid",shape="box"];1018 -> 1158[label="",style="solid", color="burlywood", weight=9];
1158 -> 1065[label="",style="solid", color="burlywood", weight=3];
1159[label="vz68/Zero",fontsize=10,color="white",style="solid",shape="box"];1018 -> 1159[label="",style="solid", color="burlywood", weight=9];
1159 -> 1066[label="",style="solid", color="burlywood", weight=3];
102[label="absReal1 (Float (Neg Zero) (Neg Zero)) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];102 -> 126[label="",style="solid", color="black", weight=3];
678 -> 524[label="",style="dashed", color="red", weight=0];
678[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];678 -> 700[label="",style="dashed", color="magenta", weight=3];
650[label="primPlusNat vz44 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];1160[label="vz44/Succ vz440",fontsize=10,color="white",style="solid",shape="box"];650 -> 1160[label="",style="solid", color="burlywood", weight=9];
1160 -> 701[label="",style="solid", color="burlywood", weight=3];
1161[label="vz44/Zero",fontsize=10,color="white",style="solid",shape="box"];650 -> 1161[label="",style="solid", color="burlywood", weight=9];
1161 -> 702[label="",style="solid", color="burlywood", weight=3];
679[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) (fsEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vz450))) LT)",fontsize=16,color="black",shape="box"];679 -> 703[label="",style="solid", color="black", weight=3];
680[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) (fsEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) LT)",fontsize=16,color="black",shape="box"];680 -> 704[label="",style="solid", color="black", weight=3];
105[label="absReal1 (Float (Pos (Succ vz3000)) (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];105 -> 130[label="",style="solid", color="black", weight=3];
697 -> 524[label="",style="dashed", color="red", weight=0];
697[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];697 -> 720[label="",style="dashed", color="magenta", weight=3];
698[label="absReal1 (Float (Pos (Succ vz10)) (Neg (Succ vz11))) (fsEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vz460))) LT)",fontsize=16,color="black",shape="box"];698 -> 721[label="",style="solid", color="black", weight=3];
699[label="absReal1 (Float (Pos (Succ vz10)) (Neg (Succ vz11))) (fsEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) LT)",fontsize=16,color="black",shape="box"];699 -> 722[label="",style="solid", color="black", weight=3];
108[label="absReal1 (Float (Pos (Succ vz3000)) (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];108 -> 134[label="",style="solid", color="black", weight=3];
717 -> 524[label="",style="dashed", color="red", weight=0];
717[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];717 -> 784[label="",style="dashed", color="magenta", weight=3];
718[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) (fsEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vz470))) LT)",fontsize=16,color="black",shape="box"];718 -> 785[label="",style="solid", color="black", weight=3];
719[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) (fsEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) LT)",fontsize=16,color="black",shape="box"];719 -> 786[label="",style="solid", color="black", weight=3];
111[label="absReal1 (Float (Pos Zero) (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];111 -> 138[label="",style="solid", color="black", weight=3];
781 -> 524[label="",style="dashed", color="red", weight=0];
781[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];781 -> 865[label="",style="dashed", color="magenta", weight=3];
782[label="absReal1 (Float (Pos Zero) (Neg (Succ vz18))) (fsEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vz480))) LT)",fontsize=16,color="black",shape="box"];782 -> 866[label="",style="solid", color="black", weight=3];
783[label="absReal1 (Float (Pos Zero) (Neg (Succ vz18))) (fsEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) LT)",fontsize=16,color="black",shape="box"];783 -> 867[label="",style="solid", color="black", weight=3];
114[label="absReal1 (Float (Pos Zero) (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];114 -> 142[label="",style="solid", color="black", weight=3];
862 -> 524[label="",style="dashed", color="red", weight=0];
862[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];862 -> 947[label="",style="dashed", color="magenta", weight=3];
863[label="absReal1 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) (fsEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vz530))) LT)",fontsize=16,color="black",shape="box"];863 -> 948[label="",style="solid", color="black", weight=3];
864[label="absReal1 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) (fsEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) LT)",fontsize=16,color="black",shape="box"];864 -> 949[label="",style="solid", color="black", weight=3];
117[label="absReal1 (Float (Neg (Succ vz3000)) (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];117 -> 146[label="",style="solid", color="black", weight=3];
944 -> 524[label="",style="dashed", color="red", weight=0];
944[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];944 -> 1008[label="",style="dashed", color="magenta", weight=3];
945[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) (fsEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vz580))) LT)",fontsize=16,color="black",shape="box"];945 -> 1009[label="",style="solid", color="black", weight=3];
946[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) (fsEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) LT)",fontsize=16,color="black",shape="box"];946 -> 1010[label="",style="solid", color="black", weight=3];
120[label="absReal1 (Float (Neg (Succ vz3000)) (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];120 -> 150[label="",style="solid", color="black", weight=3];
1005 -> 524[label="",style="dashed", color="red", weight=0];
1005[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];1005 -> 1067[label="",style="dashed", color="magenta", weight=3];
1006[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) (fsEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vz630))) LT)",fontsize=16,color="black",shape="box"];1006 -> 1068[label="",style="solid", color="black", weight=3];
1007[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) (fsEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) LT)",fontsize=16,color="black",shape="box"];1007 -> 1069[label="",style="solid", color="black", weight=3];
123[label="absReal1 (Float (Neg Zero) (Pos Zero)) MyTrue",fontsize=16,color="black",shape="box"];123 -> 154[label="",style="solid", color="black", weight=3];
1064 -> 524[label="",style="dashed", color="red", weight=0];
1064[label="primMulNat vz3100 (Succ Zero)",fontsize=16,color="magenta"];1064 -> 1076[label="",style="dashed", color="magenta", weight=3];
1065[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) (fsEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vz680))) LT)",fontsize=16,color="black",shape="box"];1065 -> 1077[label="",style="solid", color="black", weight=3];
1066[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) (fsEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) LT)",fontsize=16,color="black",shape="box"];1066 -> 1078[label="",style="solid", color="black", weight=3];
126[label="absReal1 (Float (Neg Zero) (Neg Zero)) MyTrue",fontsize=16,color="black",shape="box"];126 -> 158[label="",style="solid", color="black", weight=3];
700[label="vz3100",fontsize=16,color="green",shape="box"];524[label="primMulNat vz31000 (Succ Zero)",fontsize=16,color="burlywood",shape="triangle"];1162[label="vz31000/Succ vz310000",fontsize=10,color="white",style="solid",shape="box"];524 -> 1162[label="",style="solid", color="burlywood", weight=9];
1162 -> 562[label="",style="solid", color="burlywood", weight=3];
1163[label="vz31000/Zero",fontsize=10,color="white",style="solid",shape="box"];524 -> 1163[label="",style="solid", color="burlywood", weight=9];
1163 -> 563[label="",style="solid", color="burlywood", weight=3];
701[label="primPlusNat (Succ vz440) (Succ Zero)",fontsize=16,color="black",shape="box"];701 -> 723[label="",style="solid", color="black", weight=3];
702[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];702 -> 724[label="",style="solid", color="black", weight=3];
703[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) (fsEsOrdering (primCmpNat Zero (Succ vz450)) LT)",fontsize=16,color="black",shape="box"];703 -> 725[label="",style="solid", color="black", weight=3];
704[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];704 -> 726[label="",style="solid", color="black", weight=3];
130[label="Float (Pos (Succ vz3000)) (Pos Zero)",fontsize=16,color="green",shape="box"];720[label="vz3100",fontsize=16,color="green",shape="box"];721[label="absReal1 (Float (Pos (Succ vz10)) (Neg (Succ vz11))) (fsEsOrdering GT LT)",fontsize=16,color="black",shape="box"];721 -> 787[label="",style="solid", color="black", weight=3];
722[label="absReal1 (Float (Pos (Succ vz10)) (Neg (Succ vz11))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];722 -> 788[label="",style="solid", color="black", weight=3];
134[label="Float (Pos (Succ vz3000)) (Neg Zero)",fontsize=16,color="green",shape="box"];784[label="vz3100",fontsize=16,color="green",shape="box"];785[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) (fsEsOrdering (primCmpNat Zero (Succ vz470)) LT)",fontsize=16,color="black",shape="box"];785 -> 868[label="",style="solid", color="black", weight=3];
786[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];786 -> 869[label="",style="solid", color="black", weight=3];
138[label="Float (Pos Zero) (Pos Zero)",fontsize=16,color="green",shape="box"];865[label="vz3100",fontsize=16,color="green",shape="box"];866[label="absReal1 (Float (Pos Zero) (Neg (Succ vz18))) (fsEsOrdering GT LT)",fontsize=16,color="black",shape="box"];866 -> 950[label="",style="solid", color="black", weight=3];
867[label="absReal1 (Float (Pos Zero) (Neg (Succ vz18))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];867 -> 951[label="",style="solid", color="black", weight=3];
142[label="Float (Pos Zero) (Neg Zero)",fontsize=16,color="green",shape="box"];947[label="vz3100",fontsize=16,color="green",shape="box"];948[label="absReal1 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) (fsEsOrdering LT LT)",fontsize=16,color="black",shape="box"];948 -> 1011[label="",style="solid", color="black", weight=3];
949[label="absReal1 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];949 -> 1012[label="",style="solid", color="black", weight=3];
146[label="Float (Neg (Succ vz3000)) (Pos Zero)",fontsize=16,color="green",shape="box"];1008[label="vz3100",fontsize=16,color="green",shape="box"];1009[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) (fsEsOrdering (primCmpNat (Succ vz580) Zero) LT)",fontsize=16,color="black",shape="box"];1009 -> 1070[label="",style="solid", color="black", weight=3];
1010[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];1010 -> 1071[label="",style="solid", color="black", weight=3];
150[label="Float (Neg (Succ vz3000)) (Neg Zero)",fontsize=16,color="green",shape="box"];1067[label="vz3100",fontsize=16,color="green",shape="box"];1068[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) (fsEsOrdering LT LT)",fontsize=16,color="black",shape="box"];1068 -> 1079[label="",style="solid", color="black", weight=3];
1069[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];1069 -> 1080[label="",style="solid", color="black", weight=3];
154[label="Float (Neg Zero) (Pos Zero)",fontsize=16,color="green",shape="box"];1076[label="vz3100",fontsize=16,color="green",shape="box"];1077[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) (fsEsOrdering (primCmpNat (Succ vz680) Zero) LT)",fontsize=16,color="black",shape="box"];1077 -> 1086[label="",style="solid", color="black", weight=3];
1078[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) (fsEsOrdering EQ LT)",fontsize=16,color="black",shape="box"];1078 -> 1087[label="",style="solid", color="black", weight=3];
158[label="Float (Neg Zero) (Neg Zero)",fontsize=16,color="green",shape="box"];562[label="primMulNat (Succ vz310000) (Succ Zero)",fontsize=16,color="black",shape="box"];562 -> 612[label="",style="solid", color="black", weight=3];
563[label="primMulNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];563 -> 613[label="",style="solid", color="black", weight=3];
723[label="Succ (Succ (primPlusNat vz440 Zero))",fontsize=16,color="green",shape="box"];723 -> 789[label="",style="dashed", color="green", weight=3];
724[label="Succ Zero",fontsize=16,color="green",shape="box"];725[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) (fsEsOrdering LT LT)",fontsize=16,color="black",shape="box"];725 -> 790[label="",style="solid", color="black", weight=3];
726[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) MyTrue",fontsize=16,color="black",shape="box"];726 -> 791[label="",style="solid", color="black", weight=3];
787[label="absReal1 (Float (Pos (Succ vz10)) (Neg (Succ vz11))) MyTrue",fontsize=16,color="black",shape="triangle"];787 -> 870[label="",style="solid", color="black", weight=3];
788 -> 787[label="",style="dashed", color="red", weight=0];
788[label="absReal1 (Float (Pos (Succ vz10)) (Neg (Succ vz11))) MyTrue",fontsize=16,color="magenta"];868[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) (fsEsOrdering LT LT)",fontsize=16,color="black",shape="box"];868 -> 952[label="",style="solid", color="black", weight=3];
869[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) MyTrue",fontsize=16,color="black",shape="box"];869 -> 953[label="",style="solid", color="black", weight=3];
950[label="absReal1 (Float (Pos Zero) (Neg (Succ vz18))) MyTrue",fontsize=16,color="black",shape="triangle"];950 -> 1013[label="",style="solid", color="black", weight=3];
951 -> 950[label="",style="dashed", color="red", weight=0];
951[label="absReal1 (Float (Pos Zero) (Neg (Succ vz18))) MyTrue",fontsize=16,color="magenta"];1011[label="absReal1 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) MyFalse",fontsize=16,color="black",shape="box"];1011 -> 1072[label="",style="solid", color="black", weight=3];
1012[label="absReal1 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) MyTrue",fontsize=16,color="black",shape="box"];1012 -> 1073[label="",style="solid", color="black", weight=3];
1070[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) (fsEsOrdering GT LT)",fontsize=16,color="black",shape="box"];1070 -> 1081[label="",style="solid", color="black", weight=3];
1071[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) MyTrue",fontsize=16,color="black",shape="triangle"];1071 -> 1082[label="",style="solid", color="black", weight=3];
1079[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) MyFalse",fontsize=16,color="black",shape="box"];1079 -> 1088[label="",style="solid", color="black", weight=3];
1080[label="absReal1 (Float (Neg Zero) (Pos (Succ vz34))) MyTrue",fontsize=16,color="black",shape="box"];1080 -> 1089[label="",style="solid", color="black", weight=3];
1086[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) (fsEsOrdering GT LT)",fontsize=16,color="black",shape="box"];1086 -> 1093[label="",style="solid", color="black", weight=3];
1087[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) MyTrue",fontsize=16,color="black",shape="triangle"];1087 -> 1094[label="",style="solid", color="black", weight=3];
612 -> 650[label="",style="dashed", color="red", weight=0];
612[label="primPlusNat (primMulNat vz310000 (Succ Zero)) (Succ Zero)",fontsize=16,color="magenta"];612 -> 651[label="",style="dashed", color="magenta", weight=3];
613[label="Zero",fontsize=16,color="green",shape="box"];789[label="primPlusNat vz440 Zero",fontsize=16,color="burlywood",shape="box"];1164[label="vz440/Succ vz4400",fontsize=10,color="white",style="solid",shape="box"];789 -> 1164[label="",style="solid", color="burlywood", weight=9];
1164 -> 871[label="",style="solid", color="burlywood", weight=3];
1165[label="vz440/Zero",fontsize=10,color="white",style="solid",shape="box"];789 -> 1165[label="",style="solid", color="burlywood", weight=9];
1165 -> 872[label="",style="solid", color="burlywood", weight=3];
790[label="absReal1 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) MyFalse",fontsize=16,color="black",shape="box"];790 -> 873[label="",style="solid", color="black", weight=3];
791[label="Float (Pos (Succ vz7)) (Pos (Succ vz8))",fontsize=16,color="green",shape="box"];870[label="Float (Pos (Succ vz10)) (Neg (Succ vz11))",fontsize=16,color="green",shape="box"];952[label="absReal1 (Float (Pos Zero) (Pos (Succ vz16))) MyFalse",fontsize=16,color="black",shape="box"];952 -> 1014[label="",style="solid", color="black", weight=3];
953[label="Float (Pos Zero) (Pos (Succ vz16))",fontsize=16,color="green",shape="box"];1013[label="Float (Pos Zero) (Neg (Succ vz18))",fontsize=16,color="green",shape="box"];1072[label="absReal0 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) otherwise",fontsize=16,color="black",shape="box"];1072 -> 1083[label="",style="solid", color="black", weight=3];
1073[label="Float (Neg (Succ vz22)) (Pos (Succ vz23))",fontsize=16,color="green",shape="box"];1081 -> 1071[label="",style="dashed", color="red", weight=0];
1081[label="absReal1 (Float (Neg (Succ vz28)) (Neg (Succ vz29))) MyTrue",fontsize=16,color="magenta"];1082[label="Float (Neg (Succ vz28)) (Neg (Succ vz29))",fontsize=16,color="green",shape="box"];1088[label="absReal0 (Float (Neg Zero) (Pos (Succ vz34))) otherwise",fontsize=16,color="black",shape="box"];1088 -> 1095[label="",style="solid", color="black", weight=3];
1089[label="Float (Neg Zero) (Pos (Succ vz34))",fontsize=16,color="green",shape="box"];1093 -> 1087[label="",style="dashed", color="red", weight=0];
1093[label="absReal1 (Float (Neg Zero) (Neg (Succ vz38))) MyTrue",fontsize=16,color="magenta"];1094[label="Float (Neg Zero) (Neg (Succ vz38))",fontsize=16,color="green",shape="box"];651 -> 524[label="",style="dashed", color="red", weight=0];
651[label="primMulNat vz310000 (Succ Zero)",fontsize=16,color="magenta"];651 -> 727[label="",style="dashed", color="magenta", weight=3];
871[label="primPlusNat (Succ vz4400) Zero",fontsize=16,color="black",shape="box"];871 -> 954[label="",style="solid", color="black", weight=3];
872[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];872 -> 955[label="",style="solid", color="black", weight=3];
873[label="absReal0 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) otherwise",fontsize=16,color="black",shape="box"];873 -> 956[label="",style="solid", color="black", weight=3];
1014[label="absReal0 (Float (Pos Zero) (Pos (Succ vz16))) otherwise",fontsize=16,color="black",shape="box"];1014 -> 1074[label="",style="solid", color="black", weight=3];
1083[label="absReal0 (Float (Neg (Succ vz22)) (Pos (Succ vz23))) MyTrue",fontsize=16,color="black",shape="box"];1083 -> 1090[label="",style="solid", color="black", weight=3];
1095[label="absReal0 (Float (Neg Zero) (Pos (Succ vz34))) MyTrue",fontsize=16,color="black",shape="box"];1095 -> 1099[label="",style="solid", color="black", weight=3];
727[label="vz310000",fontsize=16,color="green",shape="box"];954[label="Succ vz4400",fontsize=16,color="green",shape="box"];955[label="Zero",fontsize=16,color="green",shape="box"];956[label="absReal0 (Float (Pos (Succ vz7)) (Pos (Succ vz8))) MyTrue",fontsize=16,color="black",shape="box"];956 -> 1015[label="",style="solid", color="black", weight=3];
1074[label="absReal0 (Float (Pos Zero) (Pos (Succ vz16))) MyTrue",fontsize=16,color="black",shape="box"];1074 -> 1084[label="",style="solid", color="black", weight=3];
1090[label="negateFloat (Float (Neg (Succ vz22)) (Pos (Succ vz23)))",fontsize=16,color="black",shape="box"];1090 -> 1096[label="",style="solid", color="black", weight=3];
1099[label="negateFloat (Float (Neg Zero) (Pos (Succ vz34)))",fontsize=16,color="black",shape="box"];1099 -> 1103[label="",style="solid", color="black", weight=3];
1015[label="negateFloat (Float (Pos (Succ vz7)) (Pos (Succ vz8)))",fontsize=16,color="black",shape="box"];1015 -> 1075[label="",style="solid", color="black", weight=3];
1084[label="negateFloat (Float (Pos Zero) (Pos (Succ vz16)))",fontsize=16,color="black",shape="box"];1084 -> 1091[label="",style="solid", color="black", weight=3];
1096[label="primNegFloat (Float (Neg (Succ vz22)) (Pos (Succ vz23)))",fontsize=16,color="black",shape="box"];1096 -> 1100[label="",style="solid", color="black", weight=3];
1103[label="primNegFloat (Float (Neg Zero) (Pos (Succ vz34)))",fontsize=16,color="black",shape="box"];1103 -> 1106[label="",style="solid", color="black", weight=3];
1075[label="primNegFloat (Float (Pos (Succ vz7)) (Pos (Succ vz8)))",fontsize=16,color="black",shape="box"];1075 -> 1085[label="",style="solid", color="black", weight=3];
1091[label="primNegFloat (Float (Pos Zero) (Pos (Succ vz16)))",fontsize=16,color="black",shape="box"];1091 -> 1097[label="",style="solid", color="black", weight=3];
1100[label="Float (negateMyInt (Neg (Succ vz22))) (Pos (Succ vz23))",fontsize=16,color="green",shape="box"];1100 -> 1104[label="",style="dashed", color="green", weight=3];
1106[label="Float (negateMyInt (Neg Zero)) (Pos (Succ vz34))",fontsize=16,color="green",shape="box"];1106 -> 1109[label="",style="dashed", color="green", weight=3];
1085[label="Float (negateMyInt (Pos (Succ vz7))) (Pos (Succ vz8))",fontsize=16,color="green",shape="box"];1085 -> 1092[label="",style="dashed", color="green", weight=3];
1097[label="Float (negateMyInt (Pos Zero)) (Pos (Succ vz16))",fontsize=16,color="green",shape="box"];1097 -> 1101[label="",style="dashed", color="green", weight=3];
1104[label="negateMyInt (Neg (Succ vz22))",fontsize=16,color="black",shape="box"];1104 -> 1107[label="",style="solid", color="black", weight=3];
1109[label="negateMyInt (Neg Zero)",fontsize=16,color="black",shape="box"];1109 -> 1111[label="",style="solid", color="black", weight=3];
1092[label="negateMyInt (Pos (Succ vz7))",fontsize=16,color="black",shape="box"];1092 -> 1098[label="",style="solid", color="black", weight=3];
1101[label="negateMyInt (Pos Zero)",fontsize=16,color="black",shape="box"];1101 -> 1105[label="",style="solid", color="black", weight=3];
1107[label="primNegInt (Neg (Succ vz22))",fontsize=16,color="black",shape="box"];1107 -> 1110[label="",style="solid", color="black", weight=3];
1111[label="primNegInt (Neg Zero)",fontsize=16,color="black",shape="box"];1111 -> 1112[label="",style="solid", color="black", weight=3];
1098[label="primNegInt (Pos (Succ vz7))",fontsize=16,color="black",shape="box"];1098 -> 1102[label="",style="solid", color="black", weight=3];
1105[label="primNegInt (Pos Zero)",fontsize=16,color="black",shape="box"];1105 -> 1108[label="",style="solid", color="black", weight=3];
1110[label="Pos (Succ vz22)",fontsize=16,color="green",shape="box"];1112[label="Pos Zero",fontsize=16,color="green",shape="box"];1102[label="Neg (Succ vz7)",fontsize=16,color="green",shape="box"];1108[label="Neg Zero",fontsize=16,color="green",shape="box"];}

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

(6)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_primMulNat(Main.Succ(vz310000)) -> new_primMulNat(vz310000)

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

(7) 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(vz310000)) -> new_primMulNat(vz310000)
The graph contains the following edges 1 > 1


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

(8)
YES