/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) LetRed [EQUIVALENT, 0 ms]
(6) HASKELL
(7) Narrow [SOUND, 0 ms]
(8) AND
    (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES


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

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

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

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

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

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

(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;
}

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

(5) LetRed (EQUIVALENT)
Let/Where Reductions:
The bindings of the following Let/Where expression
"fromEnum c <= i && i <= fromEnum c' where {
i  = fromEnum ci;
} 
"
are unpacked to the following functions on top level
"inRangeI vx = fromEnum vx;
"

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

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

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

(7) Narrow (SOUND)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="inRange",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="inRange vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
4[label="inRange vy3 vy4",fontsize=16,color="burlywood",shape="triangle"];157[label="vy3/(vy30,vy31)",fontsize=10,color="white",style="solid",shape="box"];4 -> 157[label="",style="solid", color="burlywood", weight=9];
157 -> 5[label="",style="solid", color="burlywood", weight=3];
5[label="inRange (vy30,vy31) vy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="fromEnum vy30 <= inRangeI vy4 && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="compare (fromEnum vy30) (inRangeI vy4) /= GT && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="not (compare (fromEnum vy30) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="not (primCmpInt (fromEnum vy30) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="not (primCmpInt (primCharToInt vy30) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];158[label="vy30/Char vy300",fontsize=10,color="white",style="solid",shape="box"];10 -> 158[label="",style="solid", color="burlywood", weight=9];
158 -> 11[label="",style="solid", color="burlywood", weight=3];
11[label="not (primCmpInt (primCharToInt (Char vy300)) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12[label="not (primCmpInt (Pos vy300) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];159[label="vy300/Succ vy3000",fontsize=10,color="white",style="solid",shape="box"];12 -> 159[label="",style="solid", color="burlywood", weight=9];
159 -> 13[label="",style="solid", color="burlywood", weight=3];
160[label="vy300/Zero",fontsize=10,color="white",style="solid",shape="box"];12 -> 160[label="",style="solid", color="burlywood", weight=9];
160 -> 14[label="",style="solid", color="burlywood", weight=3];
13[label="not (primCmpInt (Pos (Succ vy3000)) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
14[label="not (primCmpInt (Pos Zero) (inRangeI vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
15[label="not (primCmpInt (Pos (Succ vy3000)) (fromEnum vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
16[label="not (primCmpInt (Pos Zero) (fromEnum vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
17[label="not (primCmpInt (Pos (Succ vy3000)) (primCharToInt vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];161[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];17 -> 161[label="",style="solid", color="burlywood", weight=9];
161 -> 19[label="",style="solid", color="burlywood", weight=3];
18[label="not (primCmpInt (Pos Zero) (primCharToInt vy4) == GT) && inRangeI vy4 <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];162[label="vy4/Char vy40",fontsize=10,color="white",style="solid",shape="box"];18 -> 162[label="",style="solid", color="burlywood", weight=9];
162 -> 20[label="",style="solid", color="burlywood", weight=3];
19[label="not (primCmpInt (Pos (Succ vy3000)) (primCharToInt (Char vy40)) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
20[label="not (primCmpInt (Pos Zero) (primCharToInt (Char vy40)) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
21[label="not (primCmpInt (Pos (Succ vy3000)) (Pos vy40) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
22[label="not (primCmpInt (Pos Zero) (Pos vy40) == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="burlywood",shape="box"];163[label="vy40/Succ vy400",fontsize=10,color="white",style="solid",shape="box"];22 -> 163[label="",style="solid", color="burlywood", weight=9];
163 -> 24[label="",style="solid", color="burlywood", weight=3];
164[label="vy40/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 164[label="",style="solid", color="burlywood", weight=9];
164 -> 25[label="",style="solid", color="burlywood", weight=3];
23 -> 79[label="",style="dashed", color="red", weight=0];
23[label="not (primCmpNat (Succ vy3000) vy40 == GT) && inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="magenta"];23 -> 80[label="",style="dashed", color="magenta", weight=3];
23 -> 81[label="",style="dashed", color="magenta", weight=3];
23 -> 82[label="",style="dashed", color="magenta", weight=3];
24[label="not (primCmpInt (Pos Zero) (Pos (Succ vy400)) == GT) && inRangeI (Char (Succ vy400)) <= fromEnum vy31",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
25[label="not (primCmpInt (Pos Zero) (Pos Zero) == GT) && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
80[label="inRangeI (Char vy40) <= fromEnum vy31",fontsize=16,color="black",shape="triangle"];80 -> 93[label="",style="solid", color="black", weight=3];
81[label="Succ vy3000",fontsize=16,color="green",shape="box"];82[label="vy40",fontsize=16,color="green",shape="box"];79[label="not (primCmpNat vy300000 vy40000 == GT) && vy6",fontsize=16,color="burlywood",shape="triangle"];165[label="vy300000/Succ vy3000000",fontsize=10,color="white",style="solid",shape="box"];79 -> 165[label="",style="solid", color="burlywood", weight=9];
165 -> 94[label="",style="solid", color="burlywood", weight=3];
166[label="vy300000/Zero",fontsize=10,color="white",style="solid",shape="box"];79 -> 166[label="",style="solid", color="burlywood", weight=9];
166 -> 95[label="",style="solid", color="burlywood", weight=3];
28 -> 79[label="",style="dashed", color="red", weight=0];
28[label="not (primCmpNat Zero (Succ vy400) == GT) && inRangeI (Char (Succ vy400)) <= fromEnum vy31",fontsize=16,color="magenta"];28 -> 83[label="",style="dashed", color="magenta", weight=3];
28 -> 84[label="",style="dashed", color="magenta", weight=3];
28 -> 85[label="",style="dashed", color="magenta", weight=3];
29[label="not (EQ == GT) && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
93[label="compare (inRangeI (Char vy40)) (fromEnum vy31) /= GT",fontsize=16,color="black",shape="box"];93 -> 98[label="",style="solid", color="black", weight=3];
94[label="not (primCmpNat (Succ vy3000000) vy40000 == GT) && vy6",fontsize=16,color="burlywood",shape="box"];167[label="vy40000/Succ vy400000",fontsize=10,color="white",style="solid",shape="box"];94 -> 167[label="",style="solid", color="burlywood", weight=9];
167 -> 99[label="",style="solid", color="burlywood", weight=3];
168[label="vy40000/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 168[label="",style="solid", color="burlywood", weight=9];
168 -> 100[label="",style="solid", color="burlywood", weight=3];
95[label="not (primCmpNat Zero vy40000 == GT) && vy6",fontsize=16,color="burlywood",shape="box"];169[label="vy40000/Succ vy400000",fontsize=10,color="white",style="solid",shape="box"];95 -> 169[label="",style="solid", color="burlywood", weight=9];
169 -> 101[label="",style="solid", color="burlywood", weight=3];
170[label="vy40000/Zero",fontsize=10,color="white",style="solid",shape="box"];95 -> 170[label="",style="solid", color="burlywood", weight=9];
170 -> 102[label="",style="solid", color="burlywood", weight=3];
83 -> 80[label="",style="dashed", color="red", weight=0];
83[label="inRangeI (Char (Succ vy400)) <= fromEnum vy31",fontsize=16,color="magenta"];83 -> 96[label="",style="dashed", color="magenta", weight=3];
84[label="Zero",fontsize=16,color="green",shape="box"];85[label="Succ vy400",fontsize=16,color="green",shape="box"];33[label="not False && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];33 -> 38[label="",style="solid", color="black", weight=3];
98[label="not (compare (inRangeI (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];98 -> 104[label="",style="solid", color="black", weight=3];
99[label="not (primCmpNat (Succ vy3000000) (Succ vy400000) == GT) && vy6",fontsize=16,color="black",shape="box"];99 -> 105[label="",style="solid", color="black", weight=3];
100[label="not (primCmpNat (Succ vy3000000) Zero == GT) && vy6",fontsize=16,color="black",shape="box"];100 -> 106[label="",style="solid", color="black", weight=3];
101[label="not (primCmpNat Zero (Succ vy400000) == GT) && vy6",fontsize=16,color="black",shape="box"];101 -> 107[label="",style="solid", color="black", weight=3];
102[label="not (primCmpNat Zero Zero == GT) && vy6",fontsize=16,color="black",shape="box"];102 -> 108[label="",style="solid", color="black", weight=3];
96[label="Succ vy400",fontsize=16,color="green",shape="box"];38[label="True && inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="box"];38 -> 45[label="",style="solid", color="black", weight=3];
104[label="not (primCmpInt (inRangeI (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];104 -> 110[label="",style="solid", color="black", weight=3];
105 -> 79[label="",style="dashed", color="red", weight=0];
105[label="not (primCmpNat vy3000000 vy400000 == GT) && vy6",fontsize=16,color="magenta"];105 -> 111[label="",style="dashed", color="magenta", weight=3];
105 -> 112[label="",style="dashed", color="magenta", weight=3];
106[label="not (GT == GT) && vy6",fontsize=16,color="black",shape="box"];106 -> 113[label="",style="solid", color="black", weight=3];
107[label="not (LT == GT) && vy6",fontsize=16,color="black",shape="box"];107 -> 114[label="",style="solid", color="black", weight=3];
108[label="not (EQ == GT) && vy6",fontsize=16,color="black",shape="box"];108 -> 115[label="",style="solid", color="black", weight=3];
45[label="inRangeI (Char Zero) <= fromEnum vy31",fontsize=16,color="black",shape="triangle"];45 -> 52[label="",style="solid", color="black", weight=3];
110[label="not (primCmpInt (fromEnum (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];110 -> 117[label="",style="solid", color="black", weight=3];
111[label="vy3000000",fontsize=16,color="green",shape="box"];112[label="vy400000",fontsize=16,color="green",shape="box"];113[label="not True && vy6",fontsize=16,color="black",shape="box"];113 -> 118[label="",style="solid", color="black", weight=3];
114[label="not False && vy6",fontsize=16,color="black",shape="triangle"];114 -> 119[label="",style="solid", color="black", weight=3];
115 -> 114[label="",style="dashed", color="red", weight=0];
115[label="not False && vy6",fontsize=16,color="magenta"];52[label="compare (inRangeI (Char Zero)) (fromEnum vy31) /= GT",fontsize=16,color="black",shape="box"];52 -> 59[label="",style="solid", color="black", weight=3];
117[label="not (primCmpInt (primCharToInt (Char vy40)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];117 -> 121[label="",style="solid", color="black", weight=3];
118[label="False && vy6",fontsize=16,color="black",shape="box"];118 -> 122[label="",style="solid", color="black", weight=3];
119[label="True && vy6",fontsize=16,color="black",shape="box"];119 -> 123[label="",style="solid", color="black", weight=3];
59[label="not (compare (inRangeI (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];59 -> 70[label="",style="solid", color="black", weight=3];
121[label="not (primCmpInt (Pos vy40) (fromEnum vy31) == GT)",fontsize=16,color="burlywood",shape="box"];171[label="vy40/Succ vy400",fontsize=10,color="white",style="solid",shape="box"];121 -> 171[label="",style="solid", color="burlywood", weight=9];
171 -> 126[label="",style="solid", color="burlywood", weight=3];
172[label="vy40/Zero",fontsize=10,color="white",style="solid",shape="box"];121 -> 172[label="",style="solid", color="burlywood", weight=9];
172 -> 127[label="",style="solid", color="burlywood", weight=3];
122[label="False",fontsize=16,color="green",shape="box"];123[label="vy6",fontsize=16,color="green",shape="box"];70[label="not (primCmpInt (inRangeI (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];70 -> 78[label="",style="solid", color="black", weight=3];
126[label="not (primCmpInt (Pos (Succ vy400)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3];
127[label="not (primCmpInt (Pos Zero) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];127 -> 131[label="",style="solid", color="black", weight=3];
78[label="not (primCmpInt (fromEnum (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];78 -> 97[label="",style="solid", color="black", weight=3];
130[label="not (primCmpInt (Pos (Succ vy400)) (primCharToInt vy31) == GT)",fontsize=16,color="burlywood",shape="box"];173[label="vy31/Char vy310",fontsize=10,color="white",style="solid",shape="box"];130 -> 173[label="",style="solid", color="burlywood", weight=9];
173 -> 134[label="",style="solid", color="burlywood", weight=3];
131 -> 109[label="",style="dashed", color="red", weight=0];
131[label="not (primCmpInt (Pos Zero) (primCharToInt vy31) == GT)",fontsize=16,color="magenta"];97[label="not (primCmpInt (primCharToInt (Char Zero)) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];97 -> 103[label="",style="solid", color="black", weight=3];
134[label="not (primCmpInt (Pos (Succ vy400)) (primCharToInt (Char vy310)) == GT)",fontsize=16,color="black",shape="box"];134 -> 137[label="",style="solid", color="black", weight=3];
109[label="not (primCmpInt (Pos Zero) (primCharToInt vy31) == GT)",fontsize=16,color="burlywood",shape="triangle"];174[label="vy31/Char vy310",fontsize=10,color="white",style="solid",shape="box"];109 -> 174[label="",style="solid", color="burlywood", weight=9];
174 -> 116[label="",style="solid", color="burlywood", weight=3];
103[label="not (primCmpInt (Pos Zero) (fromEnum vy31) == GT)",fontsize=16,color="black",shape="box"];103 -> 109[label="",style="solid", color="black", weight=3];
137[label="not (primCmpInt (Pos (Succ vy400)) (Pos vy310) == GT)",fontsize=16,color="black",shape="box"];137 -> 138[label="",style="solid", color="black", weight=3];
116[label="not (primCmpInt (Pos Zero) (primCharToInt (Char vy310)) == GT)",fontsize=16,color="black",shape="box"];116 -> 120[label="",style="solid", color="black", weight=3];
138[label="not (primCmpNat (Succ vy400) vy310 == GT)",fontsize=16,color="burlywood",shape="box"];175[label="vy310/Succ vy3100",fontsize=10,color="white",style="solid",shape="box"];138 -> 175[label="",style="solid", color="burlywood", weight=9];
175 -> 139[label="",style="solid", color="burlywood", weight=3];
176[label="vy310/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 176[label="",style="solid", color="burlywood", weight=9];
176 -> 140[label="",style="solid", color="burlywood", weight=3];
120[label="not (primCmpInt (Pos Zero) (Pos vy310) == GT)",fontsize=16,color="burlywood",shape="box"];177[label="vy310/Succ vy3100",fontsize=10,color="white",style="solid",shape="box"];120 -> 177[label="",style="solid", color="burlywood", weight=9];
177 -> 124[label="",style="solid", color="burlywood", weight=3];
178[label="vy310/Zero",fontsize=10,color="white",style="solid",shape="box"];120 -> 178[label="",style="solid", color="burlywood", weight=9];
178 -> 125[label="",style="solid", color="burlywood", weight=3];
139[label="not (primCmpNat (Succ vy400) (Succ vy3100) == GT)",fontsize=16,color="black",shape="box"];139 -> 141[label="",style="solid", color="black", weight=3];
140[label="not (primCmpNat (Succ vy400) Zero == GT)",fontsize=16,color="black",shape="box"];140 -> 142[label="",style="solid", color="black", weight=3];
124[label="not (primCmpInt (Pos Zero) (Pos (Succ vy3100)) == GT)",fontsize=16,color="black",shape="box"];124 -> 128[label="",style="solid", color="black", weight=3];
125[label="not (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3];
141[label="not (primCmpNat vy400 vy3100 == GT)",fontsize=16,color="burlywood",shape="triangle"];179[label="vy400/Succ vy4000",fontsize=10,color="white",style="solid",shape="box"];141 -> 179[label="",style="solid", color="burlywood", weight=9];
179 -> 143[label="",style="solid", color="burlywood", weight=3];
180[label="vy400/Zero",fontsize=10,color="white",style="solid",shape="box"];141 -> 180[label="",style="solid", color="burlywood", weight=9];
180 -> 144[label="",style="solid", color="burlywood", weight=3];
142[label="not (GT == GT)",fontsize=16,color="black",shape="triangle"];142 -> 145[label="",style="solid", color="black", weight=3];
128[label="not (primCmpNat Zero (Succ vy3100) == GT)",fontsize=16,color="black",shape="box"];128 -> 132[label="",style="solid", color="black", weight=3];
129[label="not (EQ == GT)",fontsize=16,color="black",shape="triangle"];129 -> 133[label="",style="solid", color="black", weight=3];
143[label="not (primCmpNat (Succ vy4000) vy3100 == GT)",fontsize=16,color="burlywood",shape="box"];181[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];143 -> 181[label="",style="solid", color="burlywood", weight=9];
181 -> 146[label="",style="solid", color="burlywood", weight=3];
182[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];143 -> 182[label="",style="solid", color="burlywood", weight=9];
182 -> 147[label="",style="solid", color="burlywood", weight=3];
144[label="not (primCmpNat Zero vy3100 == GT)",fontsize=16,color="burlywood",shape="box"];183[label="vy3100/Succ vy31000",fontsize=10,color="white",style="solid",shape="box"];144 -> 183[label="",style="solid", color="burlywood", weight=9];
183 -> 148[label="",style="solid", color="burlywood", weight=3];
184[label="vy3100/Zero",fontsize=10,color="white",style="solid",shape="box"];144 -> 184[label="",style="solid", color="burlywood", weight=9];
184 -> 149[label="",style="solid", color="burlywood", weight=3];
145[label="not True",fontsize=16,color="black",shape="box"];145 -> 150[label="",style="solid", color="black", weight=3];
132[label="not (LT == GT)",fontsize=16,color="black",shape="triangle"];132 -> 135[label="",style="solid", color="black", weight=3];
133[label="not False",fontsize=16,color="black",shape="triangle"];133 -> 136[label="",style="solid", color="black", weight=3];
146[label="not (primCmpNat (Succ vy4000) (Succ vy31000) == GT)",fontsize=16,color="black",shape="box"];146 -> 151[label="",style="solid", color="black", weight=3];
147[label="not (primCmpNat (Succ vy4000) Zero == GT)",fontsize=16,color="black",shape="box"];147 -> 152[label="",style="solid", color="black", weight=3];
148[label="not (primCmpNat Zero (Succ vy31000) == GT)",fontsize=16,color="black",shape="box"];148 -> 153[label="",style="solid", color="black", weight=3];
149[label="not (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];149 -> 154[label="",style="solid", color="black", weight=3];
150[label="False",fontsize=16,color="green",shape="box"];135 -> 133[label="",style="dashed", color="red", weight=0];
135[label="not False",fontsize=16,color="magenta"];136[label="True",fontsize=16,color="green",shape="box"];151 -> 141[label="",style="dashed", color="red", weight=0];
151[label="not (primCmpNat vy4000 vy31000 == GT)",fontsize=16,color="magenta"];151 -> 155[label="",style="dashed", color="magenta", weight=3];
151 -> 156[label="",style="dashed", color="magenta", weight=3];
152 -> 142[label="",style="dashed", color="red", weight=0];
152[label="not (GT == GT)",fontsize=16,color="magenta"];153 -> 132[label="",style="dashed", color="red", weight=0];
153[label="not (LT == GT)",fontsize=16,color="magenta"];154 -> 129[label="",style="dashed", color="red", weight=0];
154[label="not (EQ == GT)",fontsize=16,color="magenta"];155[label="vy4000",fontsize=16,color="green",shape="box"];156[label="vy31000",fontsize=16,color="green",shape="box"];}

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   new_not(Succ(vy4000), Succ(vy31000)) -> new_not(vy4000, vy31000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(10) 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(Succ(vy4000), Succ(vy31000)) -> new_not(vy4000, vy31000)
The graph contains the following edges 1 > 1, 2 > 2


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(11)
YES

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(12)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(13) 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(Succ(vy3000000), Succ(vy400000), vy6) -> new_asAs(vy3000000, vy400000, vy6)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3


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(14)
YES