/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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 Main.Char = Char 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 ;

data Tup2 b a = Tup2 b a ;

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

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

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

fromEnumChar :: Main.Char  ->  MyInt;
fromEnumChar = primCharToInt;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

inRangeChar :: Tup2 Main.Char Main.Char  ->  Main.Char  ->  MyBool;
inRangeChar (Tup2 c c') ci = asAs (ltEsMyInt (fromEnumChar c) (inRangeI ci)) (ltEsMyInt (inRangeI ci) (fromEnumChar c'));

inRangeI vv = fromEnumChar vv;

ltEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
ltEsMyInt x y = fsEsOrdering (compareMyInt x y) GT;

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

primCharToInt :: Main.Char  ->  MyInt;
primCharToInt (Main.Char x) = x;

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;

}

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

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

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

data Tup2 b a = Tup2 b a ;

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

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

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

fromEnumChar :: Main.Char  ->  MyInt;
fromEnumChar = primCharToInt;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

inRangeChar :: Tup2 Main.Char Main.Char  ->  Main.Char  ->  MyBool;
inRangeChar (Tup2 c c') ci = asAs (ltEsMyInt (fromEnumChar c) (inRangeI ci)) (ltEsMyInt (inRangeI ci) (fromEnumChar c'));

inRangeI vv = fromEnumChar vv;

ltEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
ltEsMyInt x y = fsEsOrdering (compareMyInt x y) GT;

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

primCharToInt :: Main.Char  ->  MyInt;
primCharToInt (Main.Char x) = x;

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;

}

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

(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 Main.Char = Char 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 ;

data Tup2 a b = Tup2 a b ;

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

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

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

fromEnumChar :: Main.Char  ->  MyInt;
fromEnumChar = primCharToInt;

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool;
fsEsOrdering x y = not (esEsOrdering x y);

inRangeChar :: Tup2 Main.Char Main.Char  ->  Main.Char  ->  MyBool;
inRangeChar (Tup2 c c') ci = asAs (ltEsMyInt (fromEnumChar c) (inRangeI ci)) (ltEsMyInt (inRangeI ci) (fromEnumChar c'));

inRangeI vv = fromEnumChar vv;

ltEsMyInt :: MyInt  ->  MyInt  ->  MyBool;
ltEsMyInt x y = fsEsOrdering (compareMyInt x y) GT;

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

primCharToInt :: Main.Char  ->  MyInt;
primCharToInt (Main.Char x) = x;

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;

}

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

(5) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="inRangeChar",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="inRangeChar vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="inRangeChar vy3 vy4",fontsize=16,color="burlywood",shape="triangle"];247[label="vy3/Tup2 vy30 vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 247[label="",style="solid", color="burlywood", weight=9];
247 -> 5[label="",style="solid", color="burlywood", weight=3];
5[label="inRangeChar (Tup2 vy30 vy31) vy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="asAs (ltEsMyInt (fromEnumChar vy30) (inRangeI vy4)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="asAs (fsEsOrdering (compareMyInt (fromEnumChar vy30) (inRangeI vy4)) GT) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="asAs (not (esEsOrdering (compareMyInt (fromEnumChar vy30) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="asAs (not (esEsOrdering (primCmpInt (fromEnumChar vy30) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="asAs (not (esEsOrdering (primCmpInt (primCharToInt vy30) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];248[label="vy30/Char vy300",fontsize=10,color="white",style="solid",shape="box"];10 -> 248[label="",style="solid", color="burlywood", weight=9];
248 -> 11[label="",style="solid", color="burlywood", weight=3];
11[label="asAs (not (esEsOrdering (primCmpInt (primCharToInt (Char vy300)) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="asAs (not (esEsOrdering (primCmpInt vy300 (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];249[label="vy300/Pos vy3000",fontsize=10,color="white",style="solid",shape="box"];12 -> 249[label="",style="solid", color="burlywood", weight=9];
249 -> 13[label="",style="solid", color="burlywood", weight=3];
250[label="vy300/Neg vy3000",fontsize=10,color="white",style="solid",shape="box"];12 -> 250[label="",style="solid", color="burlywood", weight=9];
250 -> 14[label="",style="solid", color="burlywood", weight=3];
13[label="asAs (not (esEsOrdering (primCmpInt (Pos vy3000) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];251[label="vy3000/Succ vy30000",fontsize=10,color="white",style="solid",shape="box"];13 -> 251[label="",style="solid", color="burlywood", weight=9];
251 -> 15[label="",style="solid", color="burlywood", weight=3];
252[label="vy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];13 -> 252[label="",style="solid", color="burlywood", weight=9];
252 -> 16[label="",style="solid", color="burlywood", weight=3];
14[label="asAs (not (esEsOrdering (primCmpInt (Neg vy3000) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];253[label="vy3000/Succ vy30000",fontsize=10,color="white",style="solid",shape="box"];14 -> 253[label="",style="solid", color="burlywood", weight=9];
253 -> 17[label="",style="solid", color="burlywood", weight=3];
254[label="vy3000/Zero",fontsize=10,color="white",style="solid",shape="box"];14 -> 254[label="",style="solid", color="burlywood", weight=9];
254 -> 18[label="",style="solid", color="burlywood", weight=3];
15[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
17[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
18[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) (inRangeI vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
19[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) (fromEnumChar vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
20[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (fromEnumChar vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
21[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) (fromEnumChar vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
22[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) (fromEnumChar vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
23[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) (primCharToInt vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];255[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];23 -> 255[label="",style="solid", color="burlywood", weight=9];
255 -> 27[label="",style="solid", color="burlywood", weight=3];
24[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (primCharToInt vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];256[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];24 -> 256[label="",style="solid", color="burlywood", weight=9];
256 -> 28[label="",style="solid", color="burlywood", weight=3];
25[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) (primCharToInt vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];257[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];25 -> 257[label="",style="solid", color="burlywood", weight=9];
257 -> 29[label="",style="solid", color="burlywood", weight=3];
26[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) (primCharToInt vy4)) GT)) (ltEsMyInt (inRangeI vy4) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];258[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];26 -> 258[label="",style="solid", color="burlywood", weight=9];
258 -> 30[label="",style="solid", color="burlywood", weight=3];
27[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) (primCharToInt (Char vy40))) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
28[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (primCharToInt (Char vy40))) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
29[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) (primCharToInt (Char vy40))) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
30[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) (primCharToInt (Char vy40))) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
31[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) vy40) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];259[label="vy40/Pos vy400",fontsize=10,color="white",style="solid",shape="box"];31 -> 259[label="",style="solid", color="burlywood", weight=9];
259 -> 35[label="",style="solid", color="burlywood", weight=3];
260[label="vy40/Neg vy400",fontsize=10,color="white",style="solid",shape="box"];31 -> 260[label="",style="solid", color="burlywood", weight=9];
260 -> 36[label="",style="solid", color="burlywood", weight=3];
32[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) vy40) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];261[label="vy40/Pos vy400",fontsize=10,color="white",style="solid",shape="box"];32 -> 261[label="",style="solid", color="burlywood", weight=9];
261 -> 37[label="",style="solid", color="burlywood", weight=3];
262[label="vy40/Neg vy400",fontsize=10,color="white",style="solid",shape="box"];32 -> 262[label="",style="solid", color="burlywood", weight=9];
262 -> 38[label="",style="solid", color="burlywood", weight=3];
33[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) vy40) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];263[label="vy40/Pos vy400",fontsize=10,color="white",style="solid",shape="box"];33 -> 263[label="",style="solid", color="burlywood", weight=9];
263 -> 39[label="",style="solid", color="burlywood", weight=3];
264[label="vy40/Neg vy400",fontsize=10,color="white",style="solid",shape="box"];33 -> 264[label="",style="solid", color="burlywood", weight=9];
264 -> 40[label="",style="solid", color="burlywood", weight=3];
34[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) vy40) GT)) (ltEsMyInt (inRangeI (Char vy40)) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];265[label="vy40/Pos vy400",fontsize=10,color="white",style="solid",shape="box"];34 -> 265[label="",style="solid", color="burlywood", weight=9];
265 -> 41[label="",style="solid", color="burlywood", weight=3];
266[label="vy40/Neg vy400",fontsize=10,color="white",style="solid",shape="box"];34 -> 266[label="",style="solid", color="burlywood", weight=9];
266 -> 42[label="",style="solid", color="burlywood", weight=3];
35[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) (Pos vy400)) GT)) (ltEsMyInt (inRangeI (Char (Pos vy400))) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
36[label="asAs (not (esEsOrdering (primCmpInt (Pos (Succ vy30000)) (Neg vy400)) GT)) (ltEsMyInt (inRangeI (Char (Neg vy400))) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
37[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (Pos vy400)) GT)) (ltEsMyInt (inRangeI (Char (Pos vy400))) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];267[label="vy400/Succ vy4000",fontsize=10,color="white",style="solid",shape="box"];37 -> 267[label="",style="solid", color="burlywood", weight=9];
267 -> 45[label="",style="solid", color="burlywood", weight=3];
268[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];37 -> 268[label="",style="solid", color="burlywood", weight=9];
268 -> 46[label="",style="solid", color="burlywood", weight=3];
38[label="asAs (not (esEsOrdering (primCmpInt (Pos Zero) (Neg vy400)) GT)) (ltEsMyInt (inRangeI (Char (Neg vy400))) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];269[label="vy400/Succ vy4000",fontsize=10,color="white",style="solid",shape="box"];38 -> 269[label="",style="solid", color="burlywood", weight=9];
269 -> 47[label="",style="solid", color="burlywood", weight=3];
270[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];38 -> 270[label="",style="solid", color="burlywood", weight=9];
270 -> 48[label="",style="solid", color="burlywood", weight=3];
39[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) (Pos vy400)) GT)) (ltEsMyInt (inRangeI (Char (Pos vy400))) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];39 -> 49[label="",style="solid", color="black", weight=3];
40[label="asAs (not (esEsOrdering (primCmpInt (Neg (Succ vy30000)) (Neg vy400)) GT)) (ltEsMyInt (inRangeI (Char (Neg vy400))) (fromEnumChar vy31))",fontsize=16,color="black",shape="box"];40 -> 50[label="",style="solid", color="black", weight=3];
41[label="asAs (not (esEsOrdering (primCmpInt (Neg Zero) (Pos vy400)) GT)) (ltEsMyInt (inRangeI (Char (Pos vy400))) (fromEnumChar vy31))",fontsize=16,color="burlywood",shape="box"];271[label="vy400/Succ vy4000",fontsize=10,color="white",style="solid",shape="box"];41 -> 271[label="",style="solid", color="burlywood", weight=9];
271 -> 51[label="",style="solid", color="burlywood", weight=3];
272[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 272[label="",style="solid", color="burlywood", weight=9];
272 -> 52[label="",style="solid", color="burlywood", weight=3];
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280[label="vy40000/Zero",fontsize=10,color="white",style="solid",shape="box"];143 -> 280[label="",style="solid", color="burlywood", weight=9];
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109[label="ltEsMyInt (inRangeI (Char (Neg vy400))) (fromEnumChar vy31)",fontsize=16,color="black",shape="triangle"];109 -> 111[label="",style="solid", color="black", weight=3];
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153[label="not (esEsOrdering (primCmpInt (fromEnumChar (Char (Pos vy400))) (fromEnumChar vy31)) GT)",fontsize=16,color="black",shape="box"];153 -> 159[label="",style="solid", color="black", weight=3];
167 -> 108[label="",style="dashed", color="red", weight=0];
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159[label="not (esEsOrdering (primCmpInt (primCharToInt (Char (Pos vy400))) (fromEnumChar vy31)) GT)",fontsize=16,color="black",shape="box"];159 -> 166[label="",style="solid", color="black", weight=3];
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281 -> 170[label="",style="solid", color="burlywood", weight=3];
282[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];166 -> 282[label="",style="solid", color="burlywood", weight=9];
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283 -> 174[label="",style="solid", color="burlywood", weight=3];
284[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];169 -> 284[label="",style="solid", color="burlywood", weight=9];
284 -> 175[label="",style="solid", color="burlywood", weight=3];
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171[label="not (esEsOrdering (primCmpInt (Pos Zero) (fromEnumChar vy31)) GT)",fontsize=16,color="black",shape="box"];171 -> 177[label="",style="solid", color="black", weight=3];
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175[label="not (esEsOrdering (primCmpInt (Neg Zero) (fromEnumChar vy31)) GT)",fontsize=16,color="black",shape="box"];175 -> 179[label="",style="solid", color="black", weight=3];
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182[label="not (esEsOrdering (primCmpInt (Neg (Succ vy4000)) (primCharToInt (Char vy310))) GT)",fontsize=16,color="black",shape="box"];182 -> 186[label="",style="solid", color="black", weight=3];
183[label="not (esEsOrdering (primCmpInt (Neg Zero) (primCharToInt (Char vy310))) GT)",fontsize=16,color="black",shape="box"];183 -> 187[label="",style="solid", color="black", weight=3];
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293 -> 192[label="",style="solid", color="burlywood", weight=3];
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294 -> 193[label="",style="solid", color="burlywood", weight=3];
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295 -> 194[label="",style="solid", color="burlywood", weight=3];
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296 -> 195[label="",style="solid", color="burlywood", weight=3];
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190[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos vy3100)) GT)",fontsize=16,color="burlywood",shape="box"];297[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];190 -> 297[label="",style="solid", color="burlywood", weight=9];
297 -> 198[label="",style="solid", color="burlywood", weight=3];
298[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];190 -> 298[label="",style="solid", color="burlywood", weight=9];
298 -> 199[label="",style="solid", color="burlywood", weight=3];
191[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg vy3100)) GT)",fontsize=16,color="burlywood",shape="box"];299[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];191 -> 299[label="",style="solid", color="burlywood", weight=9];
299 -> 200[label="",style="solid", color="burlywood", weight=3];
300[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];191 -> 300[label="",style="solid", color="burlywood", weight=9];
300 -> 201[label="",style="solid", color="burlywood", weight=3];
192[label="not (esEsOrdering (primCmpInt (Neg (Succ vy4000)) (Pos vy3100)) GT)",fontsize=16,color="black",shape="box"];192 -> 202[label="",style="solid", color="black", weight=3];
193[label="not (esEsOrdering (primCmpInt (Neg (Succ vy4000)) (Neg vy3100)) GT)",fontsize=16,color="black",shape="box"];193 -> 203[label="",style="solid", color="black", weight=3];
194[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos vy3100)) GT)",fontsize=16,color="burlywood",shape="box"];301[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];194 -> 301[label="",style="solid", color="burlywood", weight=9];
301 -> 204[label="",style="solid", color="burlywood", weight=3];
302[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];194 -> 302[label="",style="solid", color="burlywood", weight=9];
302 -> 205[label="",style="solid", color="burlywood", weight=3];
195[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg vy3100)) GT)",fontsize=16,color="burlywood",shape="box"];303[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];195 -> 303[label="",style="solid", color="burlywood", weight=9];
303 -> 206[label="",style="solid", color="burlywood", weight=3];
304[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];195 -> 304[label="",style="solid", color="burlywood", weight=9];
304 -> 207[label="",style="solid", color="burlywood", weight=3];
196[label="not (esEsOrdering (primCmpNat (Succ vy4000) vy3100) GT)",fontsize=16,color="burlywood",shape="triangle"];305[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];196 -> 305[label="",style="solid", color="burlywood", weight=9];
305 -> 208[label="",style="solid", color="burlywood", weight=3];
306[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];196 -> 306[label="",style="solid", color="burlywood", weight=9];
306 -> 209[label="",style="solid", color="burlywood", weight=3];
197[label="not (esEsOrdering GT GT)",fontsize=16,color="black",shape="triangle"];197 -> 210[label="",style="solid", color="black", weight=3];
198[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos (Succ vy31000))) GT)",fontsize=16,color="black",shape="box"];198 -> 211[label="",style="solid", color="black", weight=3];
199[label="not (esEsOrdering (primCmpInt (Pos Zero) (Pos Zero)) GT)",fontsize=16,color="black",shape="box"];199 -> 212[label="",style="solid", color="black", weight=3];
200[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg (Succ vy31000))) GT)",fontsize=16,color="black",shape="box"];200 -> 213[label="",style="solid", color="black", weight=3];
201[label="not (esEsOrdering (primCmpInt (Pos Zero) (Neg Zero)) GT)",fontsize=16,color="black",shape="box"];201 -> 214[label="",style="solid", color="black", weight=3];
202[label="not (esEsOrdering LT GT)",fontsize=16,color="black",shape="triangle"];202 -> 215[label="",style="solid", color="black", weight=3];
203[label="not (esEsOrdering (primCmpNat vy3100 (Succ vy4000)) GT)",fontsize=16,color="burlywood",shape="triangle"];307[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];203 -> 307[label="",style="solid", color="burlywood", weight=9];
307 -> 216[label="",style="solid", color="burlywood", weight=3];
308[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];203 -> 308[label="",style="solid", color="burlywood", weight=9];
308 -> 217[label="",style="solid", color="burlywood", weight=3];
204[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos (Succ vy31000))) GT)",fontsize=16,color="black",shape="box"];204 -> 218[label="",style="solid", color="black", weight=3];
205[label="not (esEsOrdering (primCmpInt (Neg Zero) (Pos Zero)) GT)",fontsize=16,color="black",shape="box"];205 -> 219[label="",style="solid", color="black", weight=3];
206[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg (Succ vy31000))) GT)",fontsize=16,color="black",shape="box"];206 -> 220[label="",style="solid", color="black", weight=3];
207[label="not (esEsOrdering (primCmpInt (Neg Zero) (Neg Zero)) GT)",fontsize=16,color="black",shape="box"];207 -> 221[label="",style="solid", color="black", weight=3];
208[label="not (esEsOrdering (primCmpNat (Succ vy4000) (Succ vy31000)) GT)",fontsize=16,color="black",shape="box"];208 -> 222[label="",style="solid", color="black", weight=3];
209[label="not (esEsOrdering (primCmpNat (Succ vy4000) Zero) GT)",fontsize=16,color="black",shape="box"];209 -> 223[label="",style="solid", color="black", weight=3];
210[label="not MyTrue",fontsize=16,color="black",shape="box"];210 -> 224[label="",style="solid", color="black", weight=3];
211 -> 203[label="",style="dashed", color="red", weight=0];
211[label="not (esEsOrdering (primCmpNat Zero (Succ vy31000)) GT)",fontsize=16,color="magenta"];211 -> 225[label="",style="dashed", color="magenta", weight=3];
211 -> 226[label="",style="dashed", color="magenta", weight=3];
212[label="not (esEsOrdering EQ GT)",fontsize=16,color="black",shape="triangle"];212 -> 227[label="",style="solid", color="black", weight=3];
213 -> 197[label="",style="dashed", color="red", weight=0];
213[label="not (esEsOrdering GT GT)",fontsize=16,color="magenta"];214 -> 212[label="",style="dashed", color="red", weight=0];
214[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];215[label="not MyFalse",fontsize=16,color="black",shape="triangle"];215 -> 228[label="",style="solid", color="black", weight=3];
216[label="not (esEsOrdering (primCmpNat (Succ vy31000) (Succ vy4000)) GT)",fontsize=16,color="black",shape="box"];216 -> 229[label="",style="solid", color="black", weight=3];
217[label="not (esEsOrdering (primCmpNat Zero (Succ vy4000)) GT)",fontsize=16,color="black",shape="box"];217 -> 230[label="",style="solid", color="black", weight=3];
218 -> 202[label="",style="dashed", color="red", weight=0];
218[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];219 -> 212[label="",style="dashed", color="red", weight=0];
219[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];220 -> 196[label="",style="dashed", color="red", weight=0];
220[label="not (esEsOrdering (primCmpNat (Succ vy31000) Zero) GT)",fontsize=16,color="magenta"];220 -> 231[label="",style="dashed", color="magenta", weight=3];
220 -> 232[label="",style="dashed", color="magenta", weight=3];
221 -> 212[label="",style="dashed", color="red", weight=0];
221[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];222[label="not (esEsOrdering (primCmpNat vy4000 vy31000) GT)",fontsize=16,color="burlywood",shape="triangle"];309[label="vy4000/Succ vy40000",fontsize=10,color="white",style="solid",shape="box"];222 -> 309[label="",style="solid", color="burlywood", weight=9];
309 -> 233[label="",style="solid", color="burlywood", weight=3];
310[label="vy4000/Zero",fontsize=10,color="white",style="solid",shape="box"];222 -> 310[label="",style="solid", color="burlywood", weight=9];
310 -> 234[label="",style="solid", color="burlywood", weight=3];
223 -> 197[label="",style="dashed", color="red", weight=0];
223[label="not (esEsOrdering GT GT)",fontsize=16,color="magenta"];224[label="MyFalse",fontsize=16,color="green",shape="box"];225[label="Zero",fontsize=16,color="green",shape="box"];226[label="vy31000",fontsize=16,color="green",shape="box"];227 -> 215[label="",style="dashed", color="red", weight=0];
227[label="not MyFalse",fontsize=16,color="magenta"];228[label="MyTrue",fontsize=16,color="green",shape="box"];229 -> 222[label="",style="dashed", color="red", weight=0];
229[label="not (esEsOrdering (primCmpNat vy31000 vy4000) GT)",fontsize=16,color="magenta"];229 -> 235[label="",style="dashed", color="magenta", weight=3];
229 -> 236[label="",style="dashed", color="magenta", weight=3];
230 -> 202[label="",style="dashed", color="red", weight=0];
230[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];231[label="vy31000",fontsize=16,color="green",shape="box"];232[label="Zero",fontsize=16,color="green",shape="box"];233[label="not (esEsOrdering (primCmpNat (Succ vy40000) vy31000) GT)",fontsize=16,color="burlywood",shape="box"];311[label="vy31000/Succ vy310000",fontsize=10,color="white",style="solid",shape="box"];233 -> 311[label="",style="solid", color="burlywood", weight=9];
311 -> 237[label="",style="solid", color="burlywood", weight=3];
312[label="vy31000/Zero",fontsize=10,color="white",style="solid",shape="box"];233 -> 312[label="",style="solid", color="burlywood", weight=9];
312 -> 238[label="",style="solid", color="burlywood", weight=3];
234[label="not (esEsOrdering (primCmpNat Zero vy31000) GT)",fontsize=16,color="burlywood",shape="box"];313[label="vy31000/Succ vy310000",fontsize=10,color="white",style="solid",shape="box"];234 -> 313[label="",style="solid", color="burlywood", weight=9];
313 -> 239[label="",style="solid", color="burlywood", weight=3];
314[label="vy31000/Zero",fontsize=10,color="white",style="solid",shape="box"];234 -> 314[label="",style="solid", color="burlywood", weight=9];
314 -> 240[label="",style="solid", color="burlywood", weight=3];
235[label="vy31000",fontsize=16,color="green",shape="box"];236[label="vy4000",fontsize=16,color="green",shape="box"];237[label="not (esEsOrdering (primCmpNat (Succ vy40000) (Succ vy310000)) GT)",fontsize=16,color="black",shape="box"];237 -> 241[label="",style="solid", color="black", weight=3];
238[label="not (esEsOrdering (primCmpNat (Succ vy40000) Zero) GT)",fontsize=16,color="black",shape="box"];238 -> 242[label="",style="solid", color="black", weight=3];
239[label="not (esEsOrdering (primCmpNat Zero (Succ vy310000)) GT)",fontsize=16,color="black",shape="box"];239 -> 243[label="",style="solid", color="black", weight=3];
240[label="not (esEsOrdering (primCmpNat Zero Zero) GT)",fontsize=16,color="black",shape="box"];240 -> 244[label="",style="solid", color="black", weight=3];
241 -> 222[label="",style="dashed", color="red", weight=0];
241[label="not (esEsOrdering (primCmpNat vy40000 vy310000) GT)",fontsize=16,color="magenta"];241 -> 245[label="",style="dashed", color="magenta", weight=3];
241 -> 246[label="",style="dashed", color="magenta", weight=3];
242 -> 197[label="",style="dashed", color="red", weight=0];
242[label="not (esEsOrdering GT GT)",fontsize=16,color="magenta"];243 -> 202[label="",style="dashed", color="red", weight=0];
243[label="not (esEsOrdering LT GT)",fontsize=16,color="magenta"];244 -> 212[label="",style="dashed", color="red", weight=0];
244[label="not (esEsOrdering EQ GT)",fontsize=16,color="magenta"];245[label="vy40000",fontsize=16,color="green",shape="box"];246[label="vy310000",fontsize=16,color="green",shape="box"];}

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

(6)
Complex Obligation (AND)

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

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

   new_asAs(Main.Succ(vy3000000), Main.Succ(vy400000), vy6) -> new_asAs(vy3000000, vy400000, vy6)

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_asAs(Main.Succ(vy3000000), Main.Succ(vy400000), vy6) -> new_asAs(vy3000000, vy400000, vy6)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


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

(9)
YES

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

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

   new_not(Main.Succ(vy40000), Main.Succ(vy310000)) -> new_not(vy40000, vy310000)

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(vy40000), Main.Succ(vy310000)) -> new_not(vy40000, vy310000)
The graph contains the following edges 1 > 1, 2 > 2


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

(12)
YES