/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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


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

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

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

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

data Ratio a = CnPc a a ;

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

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

esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);

fsEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
fsEsRatio x y = not (esEsRatio x y);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

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;

}

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

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

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data MyBool = MyTrue  | MyFalse ;

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

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

data Ratio a = CnPc a a ;

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

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

esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);

fsEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
fsEsRatio x y = not (esEsRatio x y);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

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;

}

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

(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 MyBool = MyTrue  | MyFalse ;

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

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

data Ratio a = CnPc a a ;

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

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

esEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
esEsRatio (CnPc x0 x1) (CnPc y0 y1) = asAs (esEsMyInt x0 y0) (esEsMyInt x1 y1);

fsEsRatio :: Ratio MyInt  ->  Ratio MyInt  ->  MyBool;
fsEsRatio x y = not (esEsRatio x y);

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

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;

}

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="fsEsRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fsEsRatio vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="fsEsRatio vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="not (esEsRatio vz3 vz4)",fontsize=16,color="burlywood",shape="box"];123[label="vz3/CnPc vz30 vz31",fontsize=10,color="white",style="solid",shape="box"];5 -> 123[label="",style="solid", color="burlywood", weight=9];
123 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="not (esEsRatio (CnPc vz30 vz31) vz4)",fontsize=16,color="burlywood",shape="box"];124[label="vz4/CnPc vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];6 -> 124[label="",style="solid", color="burlywood", weight=9];
124 -> 7[label="",style="solid", color="burlywood", weight=3];
7[label="not (esEsRatio (CnPc vz30 vz31) (CnPc vz40 vz41))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="not (asAs (esEsMyInt vz30 vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="not (asAs (primEqInt vz30 vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];125[label="vz30/Pos vz300",fontsize=10,color="white",style="solid",shape="box"];9 -> 125[label="",style="solid", color="burlywood", weight=9];
125 -> 10[label="",style="solid", color="burlywood", weight=3];
126[label="vz30/Neg vz300",fontsize=10,color="white",style="solid",shape="box"];9 -> 126[label="",style="solid", color="burlywood", weight=9];
126 -> 11[label="",style="solid", color="burlywood", weight=3];
10[label="not (asAs (primEqInt (Pos vz300) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];127[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];10 -> 127[label="",style="solid", color="burlywood", weight=9];
127 -> 12[label="",style="solid", color="burlywood", weight=3];
128[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];10 -> 128[label="",style="solid", color="burlywood", weight=9];
128 -> 13[label="",style="solid", color="burlywood", weight=3];
11[label="not (asAs (primEqInt (Neg vz300) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];129[label="vz300/Succ vz3000",fontsize=10,color="white",style="solid",shape="box"];11 -> 129[label="",style="solid", color="burlywood", weight=9];
129 -> 14[label="",style="solid", color="burlywood", weight=3];
130[label="vz300/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 130[label="",style="solid", color="burlywood", weight=9];
130 -> 15[label="",style="solid", color="burlywood", weight=3];
12[label="not (asAs (primEqInt (Pos (Succ vz3000)) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];131[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 131[label="",style="solid", color="burlywood", weight=9];
131 -> 16[label="",style="solid", color="burlywood", weight=3];
132[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];12 -> 132[label="",style="solid", color="burlywood", weight=9];
132 -> 17[label="",style="solid", color="burlywood", weight=3];
13[label="not (asAs (primEqInt (Pos Zero) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];133[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 133[label="",style="solid", color="burlywood", weight=9];
133 -> 18[label="",style="solid", color="burlywood", weight=3];
134[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];13 -> 134[label="",style="solid", color="burlywood", weight=9];
134 -> 19[label="",style="solid", color="burlywood", weight=3];
14[label="not (asAs (primEqInt (Neg (Succ vz3000)) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];135[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 135[label="",style="solid", color="burlywood", weight=9];
135 -> 20[label="",style="solid", color="burlywood", weight=3];
136[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];14 -> 136[label="",style="solid", color="burlywood", weight=9];
136 -> 21[label="",style="solid", color="burlywood", weight=3];
15[label="not (asAs (primEqInt (Neg Zero) vz40) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];137[label="vz40/Pos vz400",fontsize=10,color="white",style="solid",shape="box"];15 -> 137[label="",style="solid", color="burlywood", weight=9];
137 -> 22[label="",style="solid", color="burlywood", weight=3];
138[label="vz40/Neg vz400",fontsize=10,color="white",style="solid",shape="box"];15 -> 138[label="",style="solid", color="burlywood", weight=9];
138 -> 23[label="",style="solid", color="burlywood", weight=3];
16[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];139[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];16 -> 139[label="",style="solid", color="burlywood", weight=9];
139 -> 24[label="",style="solid", color="burlywood", weight=3];
140[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];16 -> 140[label="",style="solid", color="burlywood", weight=9];
140 -> 25[label="",style="solid", color="burlywood", weight=3];
17[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
18[label="not (asAs (primEqInt (Pos Zero) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];141[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];18 -> 141[label="",style="solid", color="burlywood", weight=9];
141 -> 27[label="",style="solid", color="burlywood", weight=3];
142[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];18 -> 142[label="",style="solid", color="burlywood", weight=9];
142 -> 28[label="",style="solid", color="burlywood", weight=3];
19[label="not (asAs (primEqInt (Pos Zero) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];143[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];19 -> 143[label="",style="solid", color="burlywood", weight=9];
143 -> 29[label="",style="solid", color="burlywood", weight=3];
144[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];19 -> 144[label="",style="solid", color="burlywood", weight=9];
144 -> 30[label="",style="solid", color="burlywood", weight=3];
20[label="not (asAs (primEqInt (Neg (Succ vz3000)) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];20 -> 31[label="",style="solid", color="black", weight=3];
21[label="not (asAs (primEqInt (Neg (Succ vz3000)) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];145[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];21 -> 145[label="",style="solid", color="burlywood", weight=9];
145 -> 32[label="",style="solid", color="burlywood", weight=3];
146[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 146[label="",style="solid", color="burlywood", weight=9];
146 -> 33[label="",style="solid", color="burlywood", weight=3];
22[label="not (asAs (primEqInt (Neg Zero) (Pos vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];147[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];22 -> 147[label="",style="solid", color="burlywood", weight=9];
147 -> 34[label="",style="solid", color="burlywood", weight=3];
148[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 148[label="",style="solid", color="burlywood", weight=9];
148 -> 35[label="",style="solid", color="burlywood", weight=3];
23[label="not (asAs (primEqInt (Neg Zero) (Neg vz400)) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];149[label="vz400/Succ vz4000",fontsize=10,color="white",style="solid",shape="box"];23 -> 149[label="",style="solid", color="burlywood", weight=9];
149 -> 36[label="",style="solid", color="burlywood", weight=3];
150[label="vz400/Zero",fontsize=10,color="white",style="solid",shape="box"];23 -> 150[label="",style="solid", color="burlywood", weight=9];
150 -> 37[label="",style="solid", color="burlywood", weight=3];
24[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Pos (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];24 -> 38[label="",style="solid", color="black", weight=3];
25[label="not (asAs (primEqInt (Pos (Succ vz3000)) (Pos Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];25 -> 39[label="",style="solid", color="black", weight=3];
26[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="triangle"];26 -> 40[label="",style="solid", color="black", weight=3];
27[label="not (asAs (primEqInt (Pos Zero) (Pos (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];27 -> 41[label="",style="solid", color="black", weight=3];
28[label="not (asAs (primEqInt (Pos Zero) (Pos Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];28 -> 42[label="",style="solid", color="black", weight=3];
29[label="not (asAs (primEqInt (Pos Zero) (Neg (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];29 -> 43[label="",style="solid", color="black", weight=3];
30[label="not (asAs (primEqInt (Pos Zero) (Neg Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];30 -> 44[label="",style="solid", color="black", weight=3];
31 -> 26[label="",style="dashed", color="red", weight=0];
31[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];32[label="not (asAs (primEqInt (Neg (Succ vz3000)) (Neg (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];32 -> 45[label="",style="solid", color="black", weight=3];
33[label="not (asAs (primEqInt (Neg (Succ vz3000)) (Neg Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];33 -> 46[label="",style="solid", color="black", weight=3];
34[label="not (asAs (primEqInt (Neg Zero) (Pos (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];34 -> 47[label="",style="solid", color="black", weight=3];
35[label="not (asAs (primEqInt (Neg Zero) (Pos Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];35 -> 48[label="",style="solid", color="black", weight=3];
36[label="not (asAs (primEqInt (Neg Zero) (Neg (Succ vz4000))) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];36 -> 49[label="",style="solid", color="black", weight=3];
37[label="not (asAs (primEqInt (Neg Zero) (Neg Zero)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];37 -> 50[label="",style="solid", color="black", weight=3];
38[label="not (asAs (primEqNat vz3000 vz4000) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="triangle"];151[label="vz3000/Succ vz30000",fontsize=10,color="white",style="solid",shape="box"];38 -> 151[label="",style="solid", color="burlywood", weight=9];
151 -> 51[label="",style="solid", color="burlywood", weight=3];
152[label="vz3000/Zero",fontsize=10,color="white",style="solid",shape="box"];38 -> 152[label="",style="solid", color="burlywood", weight=9];
152 -> 52[label="",style="solid", color="burlywood", weight=3];
39 -> 26[label="",style="dashed", color="red", weight=0];
39[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];40[label="not MyFalse",fontsize=16,color="black",shape="triangle"];40 -> 53[label="",style="solid", color="black", weight=3];
41 -> 26[label="",style="dashed", color="red", weight=0];
41[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];42[label="not (asAs MyTrue (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="triangle"];42 -> 54[label="",style="solid", color="black", weight=3];
43 -> 26[label="",style="dashed", color="red", weight=0];
43[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];44 -> 42[label="",style="dashed", color="red", weight=0];
44[label="not (asAs MyTrue (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];45 -> 38[label="",style="dashed", color="red", weight=0];
45[label="not (asAs (primEqNat vz3000 vz4000) (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];45 -> 55[label="",style="dashed", color="magenta", weight=3];
45 -> 56[label="",style="dashed", color="magenta", weight=3];
46 -> 26[label="",style="dashed", color="red", weight=0];
46[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];47 -> 26[label="",style="dashed", color="red", weight=0];
47[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];48 -> 42[label="",style="dashed", color="red", weight=0];
48[label="not (asAs MyTrue (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];49 -> 26[label="",style="dashed", color="red", weight=0];
49[label="not (asAs MyFalse (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];50 -> 42[label="",style="dashed", color="red", weight=0];
50[label="not (asAs MyTrue (esEsMyInt vz31 vz41))",fontsize=16,color="magenta"];51[label="not (asAs (primEqNat (Succ vz30000) vz4000) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];153[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];51 -> 153[label="",style="solid", color="burlywood", weight=9];
153 -> 57[label="",style="solid", color="burlywood", weight=3];
154[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 154[label="",style="solid", color="burlywood", weight=9];
154 -> 58[label="",style="solid", color="burlywood", weight=3];
52[label="not (asAs (primEqNat Zero vz4000) (esEsMyInt vz31 vz41))",fontsize=16,color="burlywood",shape="box"];155[label="vz4000/Succ vz40000",fontsize=10,color="white",style="solid",shape="box"];52 -> 155[label="",style="solid", color="burlywood", weight=9];
155 -> 59[label="",style="solid", color="burlywood", weight=3];
156[label="vz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];52 -> 156[label="",style="solid", color="burlywood", weight=9];
156 -> 60[label="",style="solid", color="burlywood", weight=3];
53[label="MyTrue",fontsize=16,color="green",shape="box"];54[label="not (esEsMyInt vz31 vz41)",fontsize=16,color="black",shape="box"];54 -> 61[label="",style="solid", color="black", weight=3];
55[label="vz3000",fontsize=16,color="green",shape="box"];56[label="vz4000",fontsize=16,color="green",shape="box"];57[label="not (asAs (primEqNat (Succ vz30000) (Succ vz40000)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];57 -> 62[label="",style="solid", color="black", weight=3];
58[label="not (asAs (primEqNat (Succ vz30000) Zero) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];58 -> 63[label="",style="solid", color="black", weight=3];
59[label="not (asAs (primEqNat Zero (Succ vz40000)) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];59 -> 64[label="",style="solid", color="black", weight=3];
60[label="not (asAs (primEqNat Zero Zero) (esEsMyInt vz31 vz41))",fontsize=16,color="black",shape="box"];60 -> 65[label="",style="solid", color="black", weight=3];
61[label="not (primEqInt vz31 vz41)",fontsize=16,color="burlywood",shape="box"];157[label="vz31/Pos vz310",fontsize=10,color="white",style="solid",shape="box"];61 -> 157[label="",style="solid", color="burlywood", weight=9];
157 -> 66[label="",style="solid", color="burlywood", weight=3];
158[label="vz31/Neg vz310",fontsize=10,color="white",style="solid",shape="box"];61 -> 158[label="",style="solid", color="burlywood", weight=9];
158 -> 67[label="",style="solid", color="burlywood", weight=3];
62 -> 38[label="",style="dashed", color="red", weight=0];
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62 -> 69[label="",style="dashed", color="magenta", weight=3];
63 -> 26[label="",style="dashed", color="red", weight=0];
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159 -> 70[label="",style="solid", color="burlywood", weight=3];
160[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];66 -> 160[label="",style="solid", color="burlywood", weight=9];
160 -> 71[label="",style="solid", color="burlywood", weight=3];
67[label="not (primEqInt (Neg vz310) vz41)",fontsize=16,color="burlywood",shape="box"];161[label="vz310/Succ vz3100",fontsize=10,color="white",style="solid",shape="box"];67 -> 161[label="",style="solid", color="burlywood", weight=9];
161 -> 72[label="",style="solid", color="burlywood", weight=3];
162[label="vz310/Zero",fontsize=10,color="white",style="solid",shape="box"];67 -> 162[label="",style="solid", color="burlywood", weight=9];
162 -> 73[label="",style="solid", color="burlywood", weight=3];
68[label="vz30000",fontsize=16,color="green",shape="box"];69[label="vz40000",fontsize=16,color="green",shape="box"];70[label="not (primEqInt (Pos (Succ vz3100)) vz41)",fontsize=16,color="burlywood",shape="box"];163[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];70 -> 163[label="",style="solid", color="burlywood", weight=9];
163 -> 74[label="",style="solid", color="burlywood", weight=3];
164[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];70 -> 164[label="",style="solid", color="burlywood", weight=9];
164 -> 75[label="",style="solid", color="burlywood", weight=3];
71[label="not (primEqInt (Pos Zero) vz41)",fontsize=16,color="burlywood",shape="box"];165[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];71 -> 165[label="",style="solid", color="burlywood", weight=9];
165 -> 76[label="",style="solid", color="burlywood", weight=3];
166[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];71 -> 166[label="",style="solid", color="burlywood", weight=9];
166 -> 77[label="",style="solid", color="burlywood", weight=3];
72[label="not (primEqInt (Neg (Succ vz3100)) vz41)",fontsize=16,color="burlywood",shape="box"];167[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];72 -> 167[label="",style="solid", color="burlywood", weight=9];
167 -> 78[label="",style="solid", color="burlywood", weight=3];
168[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];72 -> 168[label="",style="solid", color="burlywood", weight=9];
168 -> 79[label="",style="solid", color="burlywood", weight=3];
73[label="not (primEqInt (Neg Zero) vz41)",fontsize=16,color="burlywood",shape="box"];169[label="vz41/Pos vz410",fontsize=10,color="white",style="solid",shape="box"];73 -> 169[label="",style="solid", color="burlywood", weight=9];
169 -> 80[label="",style="solid", color="burlywood", weight=3];
170[label="vz41/Neg vz410",fontsize=10,color="white",style="solid",shape="box"];73 -> 170[label="",style="solid", color="burlywood", weight=9];
170 -> 81[label="",style="solid", color="burlywood", weight=3];
74[label="not (primEqInt (Pos (Succ vz3100)) (Pos vz410))",fontsize=16,color="burlywood",shape="box"];171[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];74 -> 171[label="",style="solid", color="burlywood", weight=9];
171 -> 82[label="",style="solid", color="burlywood", weight=3];
172[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];74 -> 172[label="",style="solid", color="burlywood", weight=9];
172 -> 83[label="",style="solid", color="burlywood", weight=3];
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76[label="not (primEqInt (Pos Zero) (Pos vz410))",fontsize=16,color="burlywood",shape="box"];173[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];76 -> 173[label="",style="solid", color="burlywood", weight=9];
173 -> 85[label="",style="solid", color="burlywood", weight=3];
174[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];76 -> 174[label="",style="solid", color="burlywood", weight=9];
174 -> 86[label="",style="solid", color="burlywood", weight=3];
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175 -> 87[label="",style="solid", color="burlywood", weight=3];
176[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];77 -> 176[label="",style="solid", color="burlywood", weight=9];
176 -> 88[label="",style="solid", color="burlywood", weight=3];
78[label="not (primEqInt (Neg (Succ vz3100)) (Pos vz410))",fontsize=16,color="black",shape="box"];78 -> 89[label="",style="solid", color="black", weight=3];
79[label="not (primEqInt (Neg (Succ vz3100)) (Neg vz410))",fontsize=16,color="burlywood",shape="box"];177[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];79 -> 177[label="",style="solid", color="burlywood", weight=9];
177 -> 90[label="",style="solid", color="burlywood", weight=3];
178[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 178[label="",style="solid", color="burlywood", weight=9];
178 -> 91[label="",style="solid", color="burlywood", weight=3];
80[label="not (primEqInt (Neg Zero) (Pos vz410))",fontsize=16,color="burlywood",shape="box"];179[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];80 -> 179[label="",style="solid", color="burlywood", weight=9];
179 -> 92[label="",style="solid", color="burlywood", weight=3];
180[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];80 -> 180[label="",style="solid", color="burlywood", weight=9];
180 -> 93[label="",style="solid", color="burlywood", weight=3];
81[label="not (primEqInt (Neg Zero) (Neg vz410))",fontsize=16,color="burlywood",shape="box"];181[label="vz410/Succ vz4100",fontsize=10,color="white",style="solid",shape="box"];81 -> 181[label="",style="solid", color="burlywood", weight=9];
181 -> 94[label="",style="solid", color="burlywood", weight=3];
182[label="vz410/Zero",fontsize=10,color="white",style="solid",shape="box"];81 -> 182[label="",style="solid", color="burlywood", weight=9];
182 -> 95[label="",style="solid", color="burlywood", weight=3];
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84 -> 40[label="",style="dashed", color="red", weight=0];
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95[label="not (primEqInt (Neg Zero) (Neg Zero))",fontsize=16,color="black",shape="box"];95 -> 107[label="",style="solid", color="black", weight=3];
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183 -> 108[label="",style="solid", color="burlywood", weight=3];
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184 -> 109[label="",style="solid", color="burlywood", weight=3];
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101[label="not MyTrue",fontsize=16,color="magenta"];102 -> 96[label="",style="dashed", color="red", weight=0];
102[label="not (primEqNat vz3100 vz4100)",fontsize=16,color="magenta"];102 -> 111[label="",style="dashed", color="magenta", weight=3];
102 -> 112[label="",style="dashed", color="magenta", weight=3];
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103[label="not MyFalse",fontsize=16,color="magenta"];104 -> 40[label="",style="dashed", color="red", weight=0];
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106[label="not MyFalse",fontsize=16,color="magenta"];107 -> 99[label="",style="dashed", color="red", weight=0];
107[label="not MyTrue",fontsize=16,color="magenta"];108[label="not (primEqNat (Succ vz31000) vz4100)",fontsize=16,color="burlywood",shape="box"];185[label="vz4100/Succ vz41000",fontsize=10,color="white",style="solid",shape="box"];108 -> 185[label="",style="solid", color="burlywood", weight=9];
185 -> 113[label="",style="solid", color="burlywood", weight=3];
186[label="vz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];108 -> 186[label="",style="solid", color="burlywood", weight=9];
186 -> 114[label="",style="solid", color="burlywood", weight=3];
109[label="not (primEqNat Zero vz4100)",fontsize=16,color="burlywood",shape="box"];187[label="vz4100/Succ vz41000",fontsize=10,color="white",style="solid",shape="box"];109 -> 187[label="",style="solid", color="burlywood", weight=9];
187 -> 115[label="",style="solid", color="burlywood", weight=3];
188[label="vz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];109 -> 188[label="",style="solid", color="burlywood", weight=9];
188 -> 116[label="",style="solid", color="burlywood", weight=3];
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114[label="not (primEqNat (Succ vz31000) Zero)",fontsize=16,color="black",shape="box"];114 -> 118[label="",style="solid", color="black", weight=3];
115[label="not (primEqNat Zero (Succ vz41000))",fontsize=16,color="black",shape="box"];115 -> 119[label="",style="solid", color="black", weight=3];
116[label="not (primEqNat Zero Zero)",fontsize=16,color="black",shape="box"];116 -> 120[label="",style="solid", color="black", weight=3];
117 -> 96[label="",style="dashed", color="red", weight=0];
117[label="not (primEqNat vz31000 vz41000)",fontsize=16,color="magenta"];117 -> 121[label="",style="dashed", color="magenta", weight=3];
117 -> 122[label="",style="dashed", color="magenta", weight=3];
118 -> 40[label="",style="dashed", color="red", weight=0];
118[label="not MyFalse",fontsize=16,color="magenta"];119 -> 40[label="",style="dashed", color="red", weight=0];
119[label="not MyFalse",fontsize=16,color="magenta"];120 -> 99[label="",style="dashed", color="red", weight=0];
120[label="not MyTrue",fontsize=16,color="magenta"];121[label="vz31000",fontsize=16,color="green",shape="box"];122[label="vz41000",fontsize=16,color="green",shape="box"];}

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

(6)
Complex Obligation (AND)

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

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

   new_not0(Main.Succ(vz30000), Main.Succ(vz40000), vz31, vz41) -> new_not0(vz30000, vz40000, vz31, 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_not0(Main.Succ(vz30000), Main.Succ(vz40000), vz31, vz41) -> new_not0(vz30000, vz40000, vz31, vz41)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3, 4 >= 4


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

(9)
YES

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

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

   new_not(Main.Succ(vz31000), Main.Succ(vz41000)) -> new_not(vz31000, vz41000)

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_not(Main.Succ(vz31000), Main.Succ(vz41000)) -> new_not(vz31000, vz41000)
The graph contains the following edges 1 > 1, 2 > 2


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

(12)
YES