LTS Termination Proof

Input

Integer Transition System

Initial Location: l5, l7, l11, l1, l13, l2, l9, l14, l4, l10, l6, l8, l0, l12

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _i11HAT0 ∧ x2 = _i13HAT0 ∧ x3 = _i7HAT0 ∧ x4 = _i9HAT0 ∧ x5 = _iHAT0 ∧ x6 = _tmpHAT0 ∧ x7 = _tmp___0HAT0 ∧ x1 = _i11HATpost ∧ x2 = _i13HATpost ∧ x3 = _i7HATpost ∧ x4 = _i9HATpost ∧ x5 = _iHATpost ∧ x6 = _tmpHATpost ∧ x7 = _tmp___0HATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _i9HAT0 = _i9HATpost ∧ _i7HAT0 = _i7HATpost ∧ _i13HAT0 = _i13HATpost ∧ _i11HAT0 = _i11HATpost ∧ _iHAT0 = _iHATpost
l2	2	l3:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x1 = _x7 ∧ x2 = _x8 ∧ x3 = _x9 ∧ x4 = _x10 ∧ x5 = _x11 ∧ x6 = _x12 ∧ x7 = _x13 ∧ _x6 = _x13 ∧ _x5 = _x12 ∧ _x3 = _x10 ∧ _x2 = _x9 ∧ _x1 = _x8 ∧ _x = _x7 ∧ _x4 = _x11 ∧ 50 ≤ _x4
l2	3	l4:	x1 = _x14 ∧ x2 = _x15 ∧ x3 = _x16 ∧ x4 = _x17 ∧ x5 = _x18 ∧ x6 = _x19 ∧ x7 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ x4 = _x24 ∧ x5 = _x25 ∧ x6 = _x26 ∧ x7 = _x27 ∧ _x20 = _x27 ∧ _x19 = _x26 ∧ _x17 = _x24 ∧ _x16 = _x23 ∧ _x15 = _x22 ∧ _x14 = _x21 ∧ _x25 = 1 + _x18 ∧ 1 + _x18 ≤ 50
l5	4	l6:	x1 = _x28 ∧ x2 = _x29 ∧ x3 = _x30 ∧ x4 = _x31 ∧ x5 = _x32 ∧ x6 = _x33 ∧ x7 = _x34 ∧ x1 = _x35 ∧ x2 = _x36 ∧ x3 = _x37 ∧ x4 = _x38 ∧ x5 = _x39 ∧ x6 = _x40 ∧ x7 = _x41 ∧ _x34 = _x41 ∧ _x33 = _x40 ∧ _x31 = _x38 ∧ _x30 = _x37 ∧ _x29 = _x36 ∧ _x28 = _x35 ∧ _x32 = _x39
l7	5	l4:	x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x4 = _x45 ∧ x5 = _x46 ∧ x6 = _x47 ∧ x7 = _x48 ∧ x1 = _x49 ∧ x2 = _x50 ∧ x3 = _x51 ∧ x4 = _x52 ∧ x5 = _x53 ∧ x6 = _x54 ∧ x7 = _x55 ∧ _x48 = _x55 ∧ _x47 = _x54 ∧ _x45 = _x52 ∧ _x44 = _x51 ∧ _x43 = _x50 ∧ _x42 = _x49 ∧ _x53 = 0 ∧ 50 ≤ _x43
l7	6	l8:	x1 = _x56 ∧ x2 = _x57 ∧ x3 = _x58 ∧ x4 = _x59 ∧ x5 = _x60 ∧ x6 = _x61 ∧ x7 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ x4 = _x66 ∧ x5 = _x67 ∧ x6 = _x68 ∧ x7 = _x69 ∧ _x62 = _x69 ∧ _x61 = _x68 ∧ _x59 = _x66 ∧ _x58 = _x65 ∧ _x56 = _x63 ∧ _x60 = _x67 ∧ _x64 = 1 + _x57 ∧ 1 + _x57 ≤ 50
l9	7	l10:	x1 = _x70 ∧ x2 = _x71 ∧ x3 = _x72 ∧ x4 = _x73 ∧ x5 = _x74 ∧ x6 = _x75 ∧ x7 = _x76 ∧ x1 = _x77 ∧ x2 = _x78 ∧ x3 = _x79 ∧ x4 = _x80 ∧ x5 = _x81 ∧ x6 = _x82 ∧ x7 = _x83 ∧ _x76 = _x83 ∧ _x75 = _x82 ∧ _x73 = _x80 ∧ _x72 = _x79 ∧ _x71 = _x78 ∧ _x70 = _x77 ∧ _x74 = _x81
l11	8	l8:	x1 = _x84 ∧ x2 = _x85 ∧ x3 = _x86 ∧ x4 = _x87 ∧ x5 = _x88 ∧ x6 = _x89 ∧ x7 = _x90 ∧ x1 = _x91 ∧ x2 = _x92 ∧ x3 = _x93 ∧ x4 = _x94 ∧ x5 = _x95 ∧ x6 = _x96 ∧ x7 = _x97 ∧ 50 ≤ _x84 ∧ _x98 = 0 ∧ _x92 = 0 ∧ _x88 = _x95 ∧ _x84 = _x91 ∧ _x86 = _x93 ∧ _x87 = _x94 ∧ _x89 = _x96 ∧ _x90 = _x97
l11	9	l12:	x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ x4 = _x102 ∧ x5 = _x103 ∧ x6 = _x104 ∧ x7 = _x105 ∧ x1 = _x106 ∧ x2 = _x107 ∧ x3 = _x108 ∧ x4 = _x109 ∧ x5 = _x110 ∧ x6 = _x111 ∧ x7 = _x112 ∧ _x105 = _x112 ∧ _x104 = _x111 ∧ _x102 = _x109 ∧ _x101 = _x108 ∧ _x100 = _x107 ∧ _x103 = _x110 ∧ _x106 = 1 + _x99 ∧ 1 + _x99 ≤ 50
l12	10	l11:	x1 = _x113 ∧ x2 = _x114 ∧ x3 = _x115 ∧ x4 = _x116 ∧ x5 = _x117 ∧ x6 = _x118 ∧ x7 = _x119 ∧ x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x4 = _x123 ∧ x5 = _x124 ∧ x6 = _x125 ∧ x7 = _x126 ∧ _x119 = _x126 ∧ _x118 = _x125 ∧ _x116 = _x123 ∧ _x115 = _x122 ∧ _x114 = _x121 ∧ _x113 = _x120 ∧ _x117 = _x124
l10	11	l12:	x1 = _x127 ∧ x2 = _x128 ∧ x3 = _x129 ∧ x4 = _x130 ∧ x5 = _x131 ∧ x6 = _x132 ∧ x7 = _x133 ∧ x1 = _x134 ∧ x2 = _x135 ∧ x3 = _x136 ∧ x4 = _x137 ∧ x5 = _x138 ∧ x6 = _x139 ∧ x7 = _x140 ∧ 50 ≤ _x131 ∧ _x141 = 0 ∧ _x134 = 0 ∧ _x131 = _x138 ∧ _x128 = _x135 ∧ _x129 = _x136 ∧ _x130 = _x137 ∧ _x132 = _x139 ∧ _x133 = _x140
l10	12	l9:	x1 = _x142 ∧ x2 = _x143 ∧ x3 = _x144 ∧ x4 = _x145 ∧ x5 = _x146 ∧ x6 = _x147 ∧ x7 = _x148 ∧ x1 = _x149 ∧ x2 = _x150 ∧ x3 = _x151 ∧ x4 = _x152 ∧ x5 = _x153 ∧ x6 = _x154 ∧ x7 = _x155 ∧ _x148 = _x155 ∧ _x147 = _x154 ∧ _x145 = _x152 ∧ _x144 = _x151 ∧ _x143 = _x150 ∧ _x142 = _x149 ∧ _x153 = 1 + _x146 ∧ 1 + _x146 ≤ 50
l8	13	l7:	x1 = _x156 ∧ x2 = _x157 ∧ x3 = _x158 ∧ x4 = _x159 ∧ x5 = _x160 ∧ x6 = _x161 ∧ x7 = _x162 ∧ x1 = _x163 ∧ x2 = _x164 ∧ x3 = _x165 ∧ x4 = _x166 ∧ x5 = _x167 ∧ x6 = _x168 ∧ x7 = _x169 ∧ _x162 = _x169 ∧ _x161 = _x168 ∧ _x159 = _x166 ∧ _x158 = _x165 ∧ _x157 = _x164 ∧ _x156 = _x163 ∧ _x160 = _x167
l6	14	l9:	x1 = _x170 ∧ x2 = _x171 ∧ x3 = _x172 ∧ x4 = _x173 ∧ x5 = _x174 ∧ x6 = _x175 ∧ x7 = _x176 ∧ x1 = _x177 ∧ x2 = _x178 ∧ x3 = _x179 ∧ x4 = _x180 ∧ x5 = _x181 ∧ x6 = _x182 ∧ x7 = _x183 ∧ _x176 = _x183 ∧ _x175 = _x182 ∧ _x173 = _x180 ∧ _x172 = _x179 ∧ _x171 = _x178 ∧ _x170 = _x177 ∧ _x181 = 0 ∧ 50 ≤ _x173
l6	15	l5:	x1 = _x184 ∧ x2 = _x185 ∧ x3 = _x186 ∧ x4 = _x187 ∧ x5 = _x188 ∧ x6 = _x189 ∧ x7 = _x190 ∧ x1 = _x191 ∧ x2 = _x192 ∧ x3 = _x193 ∧ x4 = _x194 ∧ x5 = _x195 ∧ x6 = _x196 ∧ x7 = _x197 ∧ _x190 = _x197 ∧ _x189 = _x196 ∧ _x186 = _x193 ∧ _x185 = _x192 ∧ _x184 = _x191 ∧ _x188 = _x195 ∧ _x194 = 1 + _x187 ∧ 1 + _x187 ≤ 50
l4	16	l2:	x1 = _x198 ∧ x2 = _x199 ∧ x3 = _x200 ∧ x4 = _x201 ∧ x5 = _x202 ∧ x6 = _x203 ∧ x7 = _x204 ∧ x1 = _x205 ∧ x2 = _x206 ∧ x3 = _x207 ∧ x4 = _x208 ∧ x5 = _x209 ∧ x6 = _x210 ∧ x7 = _x211 ∧ _x204 = _x211 ∧ _x203 = _x210 ∧ _x201 = _x208 ∧ _x200 = _x207 ∧ _x199 = _x206 ∧ _x198 = _x205 ∧ _x202 = _x209
l1	17	l5:	x1 = _x212 ∧ x2 = _x213 ∧ x3 = _x214 ∧ x4 = _x215 ∧ x5 = _x216 ∧ x6 = _x217 ∧ x7 = _x218 ∧ x1 = _x219 ∧ x2 = _x220 ∧ x3 = _x221 ∧ x4 = _x222 ∧ x5 = _x223 ∧ x6 = _x224 ∧ x7 = _x225 ∧ 50 ≤ _x214 ∧ _x226 = 0 ∧ _x222 = 0 ∧ _x216 = _x223 ∧ _x212 = _x219 ∧ _x213 = _x220 ∧ _x214 = _x221 ∧ _x217 = _x224 ∧ _x218 = _x225
l1	18	l0:	x1 = _x227 ∧ x2 = _x228 ∧ x3 = _x229 ∧ x4 = _x230 ∧ x5 = _x231 ∧ x6 = _x232 ∧ x7 = _x233 ∧ x1 = _x234 ∧ x2 = _x235 ∧ x3 = _x236 ∧ x4 = _x237 ∧ x5 = _x238 ∧ x6 = _x239 ∧ x7 = _x240 ∧ _x233 = _x240 ∧ _x232 = _x239 ∧ _x230 = _x237 ∧ _x228 = _x235 ∧ _x227 = _x234 ∧ _x231 = _x238 ∧ _x236 = 1 + _x229 ∧ 1 + _x229 ≤ 50
l13	19	l0:	x1 = _x241 ∧ x2 = _x242 ∧ x3 = _x243 ∧ x4 = _x244 ∧ x5 = _x245 ∧ x6 = _x246 ∧ x7 = _x247 ∧ x1 = _x248 ∧ x2 = _x249 ∧ x3 = _x250 ∧ x4 = _x251 ∧ x5 = _x252 ∧ x6 = _x253 ∧ x7 = _x254 ∧ _x252 = 0 ∧ _x253 = _x253 ∧ _x254 = _x254 ∧ _x255 = 0 ∧ _x250 = 0 ∧ _x241 = _x248 ∧ _x242 = _x249 ∧ _x244 = _x251
l14	20	l13:	x1 = _x256 ∧ x2 = _x257 ∧ x3 = _x258 ∧ x4 = _x259 ∧ x5 = _x260 ∧ x6 = _x261 ∧ x7 = _x262 ∧ x1 = _x263 ∧ x2 = _x264 ∧ x3 = _x265 ∧ x4 = _x266 ∧ x5 = _x267 ∧ x6 = _x268 ∧ x7 = _x269 ∧ _x262 = _x269 ∧ _x261 = _x268 ∧ _x259 = _x266 ∧ _x258 = _x265 ∧ _x257 = _x264 ∧ _x256 = _x263 ∧ _x260 = _x267

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

l5	l5	l5:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l7	l7	l7:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l11	l11	l11:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l1	l1	l1:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l13	l13	l13:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l2	l2	l2:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l9	l9	l9:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l14	l14	l14:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l4	l4	l4:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l10	l10	l10:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l6	l6	l6:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l8	l8	l8:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l0	l0	l0:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
l12	l12	l12:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7

and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 6 SCC(s) of the program graph.

2.1 SCC Subproblem 1/6

Here we consider the SCC { l1, l0 }.

2.1.1 Transition Removal

We remove transition 18 using the following ranking functions, which are bounded by 0.

l0:	49 − x3
l1:	49 − x3

2.1.2 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 0.

l0:	0
l1:	−1

2.1.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.2 SCC Subproblem 2/6

Here we consider the SCC { l5, l6 }.

2.2.1 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by 0.

l5:	49 − x4
l6:	49 − x4

2.2.2 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

l5:	0
l6:	−1

2.2.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.3 SCC Subproblem 3/6

Here we consider the SCC { l10, l9 }.

2.3.1 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by −98.

l9:	−2⋅x5 + 1
l10:	−2⋅x5

2.3.2 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 0.

l9:	0
l10:	−1

2.3.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.4 SCC Subproblem 4/6

Here we consider the SCC { l11, l12 }.

2.4.1 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by −98.

l12:	−2⋅x1 + 1
l11:	−2⋅x1

2.4.2 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 0.

l12:	0
l11:	−1

2.4.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.5 SCC Subproblem 5/6

Here we consider the SCC { l7, l8 }.

2.5.1 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by −98.

l8:	−2⋅x2 + 1
l7:	−2⋅x2

2.5.2 Transition Removal

We remove transition 13 using the following ranking functions, which are bounded by 0.

l8:	0
l7:	−1

2.5.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.6 SCC Subproblem 6/6

Here we consider the SCC { l4, l2 }.

2.6.1 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by −98.

l4:	−2⋅x5 + 1
l2:	−2⋅x5

2.6.2 Transition Removal

We remove transition 16 using the following ranking functions, which are bounded by 0.

l4:	0
l2:	−1

2.6.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

AProVE

version: AProVE Commit ID: unknown
strategy: Statistics for single proof: 100.00 % (20 real / 0 unknown / 0 assumptions / 20 total proof steps)