LTS Termination Proof

Input

Integer Transition System

Initial Location: l5, l4, l6, l1, l0, l2

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _head_16HAT0 ∧ x2 = _head_21HAT0 ∧ x3 = _head_SLAM_f_18HAT0 ∧ x4 = _i_19HAT0 ∧ x5 = _i_86HAT0 ∧ x6 = _length_17HAT0 ∧ x7 = _nondet_12HAT0 ∧ x8 = _rcd_50HAT0 ∧ x9 = _rcd_80HAT0 ∧ x10 = _result_11HAT0 ∧ x11 = _result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0 ∧ x12 = _result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0 ∧ x13 = _tail_14HAT0 ∧ x14 = _temp0_15HAT0 ∧ x15 = _temp0_20HAT0 ∧ x16 = _temp_26HAT0 ∧ x17 = _tmp_23HAT0 ∧ x1 = _head_16HATpost ∧ x2 = _head_21HATpost ∧ x3 = _head_SLAM_f_18HATpost ∧ x4 = _i_19HATpost ∧ x5 = _i_86HATpost ∧ x6 = _length_17HATpost ∧ x7 = _nondet_12HATpost ∧ x8 = _rcd_50HATpost ∧ x9 = _rcd_80HATpost ∧ x10 = _result_11HATpost ∧ x11 = _result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost ∧ x12 = _result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost ∧ x13 = _tail_14HATpost ∧ x14 = _temp0_15HATpost ∧ x15 = _temp0_20HATpost ∧ x16 = _temp_26HATpost ∧ x17 = _tmp_23HATpost ∧ _nondet_12HAT1 = _nondet_12HAT1 ∧ _result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = _nondet_12HAT1 ∧ _nondet_12HATpost = _nondet_12HATpost ∧ _length_17HATpost = _result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost ∧ _head_SLAM_f_18HATpost = _tail_14HAT0 ∧ _head_21HATpost = _head_SLAM_f_18HATpost ∧ _i_19HATpost = 0 ∧ 0 ≤ _i_19HATpost ∧ _i_19HATpost ≤ 0 ∧ _result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost ≤ _length_17HATpost ∧ _length_17HATpost ≤ _result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost ∧ _tail_14HAT0 ≤ _head_SLAM_f_18HATpost ∧ _head_SLAM_f_18HATpost ≤ _tail_14HAT0 ∧ _tail_14HAT0 ≤ _head_21HATpost ∧ _head_21HATpost ≤ _tail_14HAT0 ∧ _head_SLAM_f_18HATpost ≤ _head_21HATpost ∧ _head_21HATpost ≤ _head_SLAM_f_18HATpost ∧ _head_16HAT0 = _head_16HATpost ∧ _i_86HAT0 = _i_86HATpost ∧ _rcd_50HAT0 = _rcd_50HATpost ∧ _rcd_80HAT0 = _rcd_80HATpost ∧ _result_11HAT0 = _result_11HATpost ∧ _result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0 = _result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost ∧ _tail_14HAT0 = _tail_14HATpost ∧ _temp0_15HAT0 = _temp0_15HATpost ∧ _temp0_20HAT0 = _temp0_20HATpost ∧ _temp_26HAT0 = _temp_26HATpost ∧ _tmp_23HAT0 = _tmp_23HATpost
l2	2	l3:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x11 = _x10 ∧ x12 = _x11 ∧ x13 = _x12 ∧ x14 = _x13 ∧ x15 = _x14 ∧ x16 = _x15 ∧ x17 = _x16 ∧ x1 = _x17 ∧ x2 = _x18 ∧ x3 = _x19 ∧ x4 = _x20 ∧ x5 = _x21 ∧ x6 = _x22 ∧ x7 = _x23 ∧ x8 = _x24 ∧ x9 = _x25 ∧ x10 = _x26 ∧ x11 = _x27 ∧ x12 = _x28 ∧ x13 = _x29 ∧ x14 = _x30 ∧ x15 = _x31 ∧ x16 = _x32 ∧ x17 = _x33 ∧ _x28 = _x28 ∧ _x5 ≤ _x3 ∧ _x34 = _x1 ∧ _x35 = _x34 ∧ _x22 = _x22 ∧ _x19 = _x19 ∧ _x20 = _x20 ∧ _x31 = _x31 ∧ _x18 = _x18 ∧ _x27 = _x27 ∧ _x33 = _x33 ∧ _x32 = _x32 ∧ _x17 = _x35 ∧ _x36 = _x36 ∧ _x26 = _x13 ∧ 1 ≤ _x28 ∧ _x28 ≤ 1 ∧ 1 ≤ _x28 ∧ _x28 ≤ 1 ∧ _x4 = _x21 ∧ _x6 = _x23 ∧ _x7 = _x24 ∧ _x8 = _x25 ∧ _x12 = _x29 ∧ _x13 = _x30
l2	3	l4:	x1 = _x37 ∧ x2 = _x38 ∧ x3 = _x39 ∧ x4 = _x40 ∧ x5 = _x41 ∧ x6 = _x42 ∧ x7 = _x43 ∧ x8 = _x44 ∧ x9 = _x45 ∧ x10 = _x46 ∧ x11 = _x47 ∧ x12 = _x48 ∧ x13 = _x49 ∧ x14 = _x50 ∧ x15 = _x51 ∧ x16 = _x52 ∧ x17 = _x53 ∧ x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x4 = _x57 ∧ x5 = _x58 ∧ x6 = _x59 ∧ x7 = _x60 ∧ x8 = _x61 ∧ x9 = _x62 ∧ x10 = _x63 ∧ x11 = _x64 ∧ x12 = _x65 ∧ x13 = _x66 ∧ x14 = _x67 ∧ x15 = _x68 ∧ x16 = _x69 ∧ x17 = _x70 ∧ _x51 = _x68 ∧ _x50 = _x67 ∧ _x46 = _x63 ∧ _x45 = _x62 ∧ _x43 = _x60 ∧ _x42 = _x59 ∧ _x41 = _x58 ∧ _x37 = _x54 ∧ 2 ≤ _x42 ∧ 1 ≤ _x42 ∧ _x70 ≤ _x64 ∧ _x64 ≤ _x70 ∧ _x70 ≤ _x55 ∧ _x55 ≤ _x70 ∧ _x64 ≤ _x55 ∧ _x55 ≤ _x64 ∧ _x56 ≤ _x66 ∧ _x66 ≤ _x56 ∧ _x42 ≤ _x65 ∧ _x65 ≤ _x42 ∧ _x57 ≤ 2 ∧ 2 ≤ _x57 ∧ _x57 = 1 + _x40 ∧ _x55 = _x70 ∧ _x69 = _x69 ∧ _x70 = _x52 ∧ 1 + _x40 ≤ _x42 ∧ _x61 = _x61 ∧ _x64 = _x64 ∧ _x56 = _x56 ∧ _x66 = _x66 ∧ _x65 = _x65
l4	4	l3:	x1 = _x71 ∧ x2 = _x72 ∧ x3 = _x73 ∧ x4 = _x74 ∧ x5 = _x75 ∧ x6 = _x76 ∧ x7 = _x77 ∧ x8 = _x78 ∧ x9 = _x79 ∧ x10 = _x80 ∧ x11 = _x81 ∧ x12 = _x82 ∧ x13 = _x83 ∧ x14 = _x84 ∧ x15 = _x85 ∧ x16 = _x86 ∧ x17 = _x87 ∧ x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ x4 = _x91 ∧ x5 = _x92 ∧ x6 = _x93 ∧ x7 = _x94 ∧ x8 = _x95 ∧ x9 = _x96 ∧ x10 = _x97 ∧ x11 = _x98 ∧ x12 = _x99 ∧ x13 = _x100 ∧ x14 = _x101 ∧ x15 = _x102 ∧ x16 = _x103 ∧ x17 = _x104 ∧ 0 ≤ _x74 ∧ _x99 = _x99 ∧ _x76 ≤ _x74 ∧ _x105 = _x72 ∧ _x106 = _x105 ∧ _x93 = _x93 ∧ _x90 = _x90 ∧ _x91 = _x91 ∧ _x102 = _x102 ∧ _x89 = _x89 ∧ _x98 = _x98 ∧ _x104 = _x104 ∧ _x103 = _x103 ∧ _x88 = _x106 ∧ _x107 = _x107 ∧ _x97 = _x84 ∧ 1 ≤ _x99 ∧ 2 ≤ _x99 ∧ _x99 ≤ _x91 ∧ _x75 = _x92 ∧ _x77 = _x94 ∧ _x78 = _x95 ∧ _x79 = _x96 ∧ _x83 = _x100 ∧ _x84 = _x101
l4	5	l5:	x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x4 = _x111 ∧ x5 = _x112 ∧ x6 = _x113 ∧ x7 = _x114 ∧ x8 = _x115 ∧ x9 = _x116 ∧ x10 = _x117 ∧ x11 = _x118 ∧ x12 = _x119 ∧ x13 = _x120 ∧ x14 = _x121 ∧ x15 = _x122 ∧ x16 = _x123 ∧ x17 = _x124 ∧ x1 = _x125 ∧ x2 = _x126 ∧ x3 = _x127 ∧ x4 = _x128 ∧ x5 = _x129 ∧ x6 = _x130 ∧ x7 = _x131 ∧ x8 = _x132 ∧ x9 = _x133 ∧ x10 = _x134 ∧ x11 = _x135 ∧ x12 = _x136 ∧ x13 = _x137 ∧ x14 = _x138 ∧ x15 = _x139 ∧ x16 = _x140 ∧ x17 = _x141 ∧ _x122 = _x139 ∧ _x121 = _x138 ∧ _x120 = _x137 ∧ _x119 = _x136 ∧ _x118 = _x135 ∧ _x117 = _x134 ∧ _x115 = _x132 ∧ _x114 = _x131 ∧ _x113 = _x130 ∧ _x110 = _x127 ∧ _x108 = _x125 ∧ 1 + _x129 ≤ _x113 ∧ −1 + _x128 ≤ _x129 ∧ _x129 ≤ −1 + _x128 ∧ 1 + _x129 ≤ _x128 ∧ _x128 ≤ 1 + _x129 ∧ _x128 = 1 + _x111 ∧ _x126 = _x141 ∧ _x140 = _x140 ∧ _x141 = _x123 ∧ 1 + _x111 ≤ _x113 ∧ _x129 = _x129 ∧ _x133 = _x133 ∧ 0 ≤ _x111
l5	6	l4:	x1 = _x142 ∧ x2 = _x143 ∧ x3 = _x144 ∧ x4 = _x145 ∧ x5 = _x146 ∧ x6 = _x147 ∧ x7 = _x148 ∧ x8 = _x149 ∧ x9 = _x150 ∧ x10 = _x151 ∧ x11 = _x152 ∧ x12 = _x153 ∧ x13 = _x154 ∧ x14 = _x155 ∧ x15 = _x156 ∧ x16 = _x157 ∧ x17 = _x158 ∧ x1 = _x159 ∧ x2 = _x160 ∧ x3 = _x161 ∧ x4 = _x162 ∧ x5 = _x163 ∧ x6 = _x164 ∧ x7 = _x165 ∧ x8 = _x166 ∧ x9 = _x167 ∧ x10 = _x168 ∧ x11 = _x169 ∧ x12 = _x170 ∧ x13 = _x171 ∧ x14 = _x172 ∧ x15 = _x173 ∧ x16 = _x174 ∧ x17 = _x175 ∧ _x158 = _x175 ∧ _x157 = _x174 ∧ _x156 = _x173 ∧ _x155 = _x172 ∧ _x154 = _x171 ∧ _x153 = _x170 ∧ _x152 = _x169 ∧ _x151 = _x168 ∧ _x150 = _x167 ∧ _x149 = _x166 ∧ _x148 = _x165 ∧ _x147 = _x164 ∧ _x146 = _x163 ∧ _x145 = _x162 ∧ _x144 = _x161 ∧ _x143 = _x160 ∧ _x142 = _x159
l1	7	l3:	x1 = _x176 ∧ x2 = _x177 ∧ x3 = _x178 ∧ x4 = _x179 ∧ x5 = _x180 ∧ x6 = _x181 ∧ x7 = _x182 ∧ x8 = _x183 ∧ x9 = _x184 ∧ x10 = _x185 ∧ x11 = _x186 ∧ x12 = _x187 ∧ x13 = _x188 ∧ x14 = _x189 ∧ x15 = _x190 ∧ x16 = _x191 ∧ x17 = _x192 ∧ x1 = _x193 ∧ x2 = _x194 ∧ x3 = _x195 ∧ x4 = _x196 ∧ x5 = _x197 ∧ x6 = _x198 ∧ x7 = _x199 ∧ x8 = _x200 ∧ x9 = _x201 ∧ x10 = _x202 ∧ x11 = _x203 ∧ x12 = _x204 ∧ x13 = _x205 ∧ x14 = _x206 ∧ x15 = _x207 ∧ x16 = _x208 ∧ x17 = _x209 ∧ _x204 = _x204 ∧ _x181 ≤ _x179 ∧ _x210 = _x177 ∧ _x211 = _x210 ∧ _x198 = _x198 ∧ _x195 = _x195 ∧ _x196 = _x196 ∧ _x207 = _x207 ∧ _x194 = _x194 ∧ _x203 = _x203 ∧ _x209 = _x209 ∧ _x208 = _x208 ∧ _x193 = _x211 ∧ _x212 = _x212 ∧ _x202 = _x189 ∧ _x204 ≤ 0 ∧ _x180 = _x197 ∧ _x182 = _x199 ∧ _x183 = _x200 ∧ _x184 = _x201 ∧ _x188 = _x205 ∧ _x189 = _x206
l1	8	l2:	x1 = _x213 ∧ x2 = _x214 ∧ x3 = _x215 ∧ x4 = _x216 ∧ x5 = _x217 ∧ x6 = _x218 ∧ x7 = _x219 ∧ x8 = _x220 ∧ x9 = _x221 ∧ x10 = _x222 ∧ x11 = _x223 ∧ x12 = _x224 ∧ x13 = _x225 ∧ x14 = _x226 ∧ x15 = _x227 ∧ x16 = _x228 ∧ x17 = _x229 ∧ x1 = _x230 ∧ x2 = _x231 ∧ x3 = _x232 ∧ x4 = _x233 ∧ x5 = _x234 ∧ x6 = _x235 ∧ x7 = _x236 ∧ x8 = _x237 ∧ x9 = _x238 ∧ x10 = _x239 ∧ x11 = _x240 ∧ x12 = _x241 ∧ x13 = _x242 ∧ x14 = _x243 ∧ x15 = _x244 ∧ x16 = _x245 ∧ x17 = _x246 ∧ _x227 = _x244 ∧ _x226 = _x243 ∧ _x222 = _x239 ∧ _x221 = _x238 ∧ _x220 = _x237 ∧ _x219 = _x236 ∧ _x218 = _x235 ∧ _x217 = _x234 ∧ _x213 = _x230 ∧ 1 ≤ _x218 ∧ _x246 ≤ _x240 ∧ _x240 ≤ _x246 ∧ _x246 ≤ _x231 ∧ _x231 ≤ _x246 ∧ _x240 ≤ _x231 ∧ _x231 ≤ _x240 ∧ _x232 ≤ _x242 ∧ _x242 ≤ _x232 ∧ _x218 ≤ _x241 ∧ _x241 ≤ _x218 ∧ _x233 ≤ 1 ∧ 1 ≤ _x233 ∧ _x233 = 1 + _x216 ∧ _x231 = _x246 ∧ _x245 = _x245 ∧ _x246 = _x228 ∧ 1 + _x216 ≤ _x218 ∧ _x240 = _x240 ∧ _x232 = _x232 ∧ _x242 = _x242 ∧ _x241 = _x241
l6	9	l0:	x1 = _x247 ∧ x2 = _x248 ∧ x3 = _x249 ∧ x4 = _x250 ∧ x5 = _x251 ∧ x6 = _x252 ∧ x7 = _x253 ∧ x8 = _x254 ∧ x9 = _x255 ∧ x10 = _x256 ∧ x11 = _x257 ∧ x12 = _x258 ∧ x13 = _x259 ∧ x14 = _x260 ∧ x15 = _x261 ∧ x16 = _x262 ∧ x17 = _x263 ∧ x1 = _x264 ∧ x2 = _x265 ∧ x3 = _x266 ∧ x4 = _x267 ∧ x5 = _x268 ∧ x6 = _x269 ∧ x7 = _x270 ∧ x8 = _x271 ∧ x9 = _x272 ∧ x10 = _x273 ∧ x11 = _x274 ∧ x12 = _x275 ∧ x13 = _x276 ∧ x14 = _x277 ∧ x15 = _x278 ∧ x16 = _x279 ∧ x17 = _x280 ∧ _x263 = _x280 ∧ _x262 = _x279 ∧ _x261 = _x278 ∧ _x260 = _x277 ∧ _x259 = _x276 ∧ _x258 = _x275 ∧ _x257 = _x274 ∧ _x256 = _x273 ∧ _x255 = _x272 ∧ _x254 = _x271 ∧ _x253 = _x270 ∧ _x252 = _x269 ∧ _x251 = _x268 ∧ _x250 = _x267 ∧ _x249 = _x266 ∧ _x248 = _x265 ∧ _x247 = _x264

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 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17
l4	l4	l4:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17
l6	l6	l6:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17
l1	l1	l1:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17
l0	l0	l0:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17
l2	l2	l2:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17

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

2 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

2.1 SCC Subproblem 1/1

Here we consider the SCC { l5, l4 }.

2.1.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by 0.

l4:	−1 − x4 + x6
l5:	−1 − x4 + x6

2.1.2 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 0.

l5:	0
l4:	−1

2.1.3 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 % (6 real / 0 unknown / 0 assumptions / 6 total proof steps)