LTS Termination Proof

Input

Integer Transition System

Initial Location: f648_0_create_GT, f3952_0_extendMatchingSubstitution_NULL, f3684_0_extendMatchingSubstitution_EQ, f1260_0_create_Return, f2576_0_create_GE, f1_0_main_Load, f1262_0_create_Return, f3568_0_extendMatchingSubstitution_CheckCast, f2800_0_random_ArrayAccess, __init

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f2800_0_random_ArrayAccess:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ −1 ≤ _x6 − 1 ∧ 0 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 ∧ 3 ≤ _arg1P − 1 ∧ _arg2 = _arg2P
f1260_0_create_Return	2	f2800_0_random_ArrayAccess:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x7 ∧ x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x4 = _x11 ∧ x5 = _x12 ∧ x6 = _x13 ∧ x7 = _x14 ∧ _x4 = _x11 ∧ _x3 = _x10 ∧ _x3 + 5 ≤ _x1 ∧ _x4 + 5 ≤ _x1 ∧ 3 ≤ _x8 − 1 ∧ 3 ≤ _x1 − 1 ∧ 0 ≤ _x − 1 ∧ _x8 ≤ _x1
f1_0_main_Load	3	f2894_0_extendMatchingSubstitution_InvokeMethod:	x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ x4 = _x21 ∧ x5 = _x22 ∧ x6 = _x23 ∧ x7 = _x24 ∧ x1 = _x25 ∧ x2 = _x27 ∧ x3 = _x28 ∧ x4 = _x29 ∧ x5 = _x30 ∧ x6 = _x31 ∧ x7 = _x32 ∧ −1 ≤ _x33 − 1 ∧ 0 ≤ _x16 − 1 ∧ 0 ≤ _x35 − 1 ∧ _x35 ≤ _x16 − 1 ∧ −1 ≤ _x37 − 1 ∧ _x25 ≤ _x15 ∧ 0 ≤ _x15 − 1 ∧ 0 ≤ _x25 − 1
f1262_0_create_Return	4	f2894_0_extendMatchingSubstitution_InvokeMethod:	x1 = _x38 ∧ x2 = _x39 ∧ x3 = _x40 ∧ x4 = _x41 ∧ x5 = _x42 ∧ x6 = _x43 ∧ x7 = _x45 ∧ x1 = _x46 ∧ x2 = _x47 ∧ x3 = _x48 ∧ x4 = _x49 ∧ x5 = _x51 ∧ x6 = _x53 ∧ x7 = _x55 ∧ 0 ≤ _x46 − 1 ∧ 0 ≤ _x38 − 1 ∧ _x46 ≤ _x38
f2800_0_random_ArrayAccess	5	f3568_0_extendMatchingSubstitution_CheckCast:	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 ∧ _x70 ≤ _x57 − 1 ∧ 0 ≤ _x70 − 1 ∧ 0 ≤ _x57 − 1 ∧ −1 ≤ _x71 − 1 ∧ 1 ≤ _x66 − 1 ∧ _x63 ≤ _x56 ∧ _x64 + 3 ≤ _x56 ∧ _x65 + 3 ≤ _x56 ∧ 3 ≤ _x56 − 1 ∧ 3 ≤ _x63 − 1 ∧ 0 ≤ _x64 − 1 ∧ 0 ≤ _x65 − 1 ∧ _x59 + 5 ≤ _x56 ∧ _x58 + 5 ≤ _x56
f2800_0_random_ArrayAccess	6	f3568_0_extendMatchingSubstitution_CheckCast:	x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x1 = _x79 ∧ x2 = _x80 ∧ x3 = _x81 ∧ x4 = _x82 ∧ x5 = _x83 ∧ x6 = _x84 ∧ x7 = _x85 ∧ _x86 ≤ _x73 − 1 ∧ 0 ≤ _x86 − 1 ∧ 0 ≤ _x73 − 1 ∧ −1 ≤ _x87 − 1 ∧ 1 ≤ _x82 − 1 ∧ _x79 ≤ _x72 ∧ 3 ≤ _x72 − 1 ∧ 3 ≤ _x79 − 1 ∧ 3 ≤ _x80 − 1 ∧ 3 ≤ _x81 − 1 ∧ _x75 + 5 ≤ _x72 ∧ _x74 + 5 ≤ _x72
f1_0_main_Load	7	f648_0_create_GT:	x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ x4 = _x91 ∧ x5 = _x92 ∧ x6 = _x93 ∧ x7 = _x94 ∧ x1 = _x95 ∧ x2 = _x96 ∧ x3 = _x97 ∧ x4 = _x98 ∧ x5 = _x99 ∧ x6 = _x100 ∧ x7 = _x101 ∧ 1 = _x97 ∧ _x89 = _x96 ∧ 0 ≤ _x88 − 1 ∧ 0 ≤ _x89 − 1 ∧ −1 ≤ _x95 − 1
f1_0_main_Load	8	f648_0_create_GT:	x1 = _x102 ∧ x2 = _x103 ∧ x3 = _x104 ∧ x4 = _x105 ∧ x5 = _x106 ∧ x6 = _x107 ∧ x7 = _x108 ∧ x1 = _x109 ∧ x2 = _x110 ∧ x3 = _x111 ∧ x4 = _x112 ∧ x5 = _x113 ∧ x6 = _x114 ∧ x7 = _x115 ∧ −1 ≤ _x116 − 1 ∧ 0 ≤ _x103 − 1 ∧ 0 ≤ _x117 − 1 ∧ _x117 ≤ _x103 − 1 ∧ −1 ≤ _x109 − 1 ∧ 0 ≤ _x102 − 1 ∧ _x103 = _x110 ∧ _x117 + 1 = _x111
f2800_0_random_ArrayAccess	9	f648_0_create_GT:	x1 = _x118 ∧ x2 = _x119 ∧ x3 = _x120 ∧ x4 = _x121 ∧ x5 = _x122 ∧ x6 = _x123 ∧ x7 = _x124 ∧ x1 = _x125 ∧ x2 = _x126 ∧ x3 = _x127 ∧ x4 = _x128 ∧ x5 = _x129 ∧ x6 = _x130 ∧ x7 = _x131 ∧ _x132 ≤ _x119 − 1 ∧ 0 ≤ _x132 − 1 ∧ 0 ≤ _x119 − 1 ∧ −1 ≤ _x125 − 1 ∧ 3 ≤ _x118 − 1 ∧ _x121 + 5 ≤ _x118 ∧ _x120 + 5 ≤ _x118 ∧ _x119 = _x126 ∧ _x132 + 1 = _x127
f648_0_create_GT	10	f2576_0_create_GE:	x1 = _x133 ∧ x2 = _x134 ∧ x3 = _x135 ∧ x4 = _x136 ∧ x5 = _x137 ∧ x6 = _x138 ∧ x7 = _x139 ∧ x1 = _x140 ∧ x2 = _x141 ∧ x3 = _x142 ∧ x4 = _x143 ∧ x5 = _x144 ∧ x6 = _x145 ∧ x7 = _x146 ∧ _x135 + 1 = _x144 ∧ _x134 = _x143 ∧ 0 = _x141 ∧ _x133 = _x140 ∧ −1 ≤ _x142 − 1 ∧ _x135 ≤ _x134 − 1 ∧ 0 ≤ _x135 − 1 ∧ 1 ≤ _x133 − 1 ∧ −1 ≤ _x134 − 1
f2576_0_create_GE	11	f648_0_create_GT:	x1 = _x147 ∧ x2 = _x148 ∧ x3 = _x149 ∧ x4 = _x150 ∧ x5 = _x151 ∧ x6 = _x152 ∧ x7 = _x153 ∧ x1 = _x154 ∧ x2 = _x155 ∧ x3 = _x156 ∧ x4 = _x157 ∧ x5 = _x158 ∧ x6 = _x159 ∧ x7 = _x160 ∧ _x151 = _x156 ∧ _x150 = _x155 ∧ _x147 − 1 = _x154 ∧ _x147 − 1 ≤ _x147 − 1 ∧ 1 ≤ _x151 − 1 ∧ 0 ≤ _x149 − 1 ∧ 1 ≤ _x147 − 1 ∧ _x148 ≤ _x149 − 1
f2576_0_create_GE	12	f2576_0_create_GE:	x1 = _x161 ∧ x2 = _x162 ∧ x3 = _x163 ∧ x4 = _x164 ∧ x5 = _x165 ∧ x6 = _x166 ∧ x7 = _x167 ∧ x1 = _x168 ∧ x2 = _x169 ∧ x3 = _x170 ∧ x4 = _x171 ∧ x5 = _x172 ∧ x6 = _x173 ∧ x7 = _x174 ∧ _x164 = _x171 ∧ _x163 = _x170 ∧ _x162 + 1 = _x169 ∧ _x161 = _x168 ∧ _x161 − 1 ≤ _x161 − 1 ∧ 1 ≤ _x165 − 1 ∧ 0 ≤ _x163 − 1 ∧ 1 ≤ _x161 − 1 ∧ _x162 ≤ _x163 − 1
f3568_0_extendMatchingSubstitution_CheckCast	13	f3684_0_extendMatchingSubstitution_EQ:	x1 = _x175 ∧ x2 = _x176 ∧ x3 = _x177 ∧ x4 = _x178 ∧ x5 = _x179 ∧ x6 = _x180 ∧ x7 = _x181 ∧ x1 = _x182 ∧ x2 = _x183 ∧ x3 = _x184 ∧ x4 = _x185 ∧ x5 = _x186 ∧ x6 = _x187 ∧ x7 = _x188 ∧ _x178 = _x186 ∧ 0 = _x184 ∧ −1 ≤ _x188 − 1 ∧ −1 ≤ _x187 − 1 ∧ 0 ≤ _x183 − 1 ∧ 0 ≤ _x182 − 1 ∧ 0 ≤ _x177 − 1 ∧ 0 ≤ _x176 − 1 ∧ 0 ≤ _x175 − 1 ∧ _x188 + 1 ≤ _x177 ∧ _x188 + 1 ≤ _x176 ∧ _x187 + 1 ≤ _x175 ∧ _x183 ≤ _x177 ∧ _x183 ≤ _x176 ∧ 1 ≤ _x178 − 1 ∧ _x182 ≤ _x175
f3568_0_extendMatchingSubstitution_CheckCast	14	f3684_0_extendMatchingSubstitution_EQ:	x1 = _x189 ∧ x2 = _x190 ∧ x3 = _x191 ∧ x4 = _x192 ∧ x5 = _x193 ∧ x6 = _x194 ∧ x7 = _x195 ∧ x1 = _x196 ∧ x2 = _x197 ∧ x3 = _x198 ∧ x4 = _x199 ∧ x5 = _x200 ∧ x6 = _x201 ∧ x7 = _x202 ∧ _x192 = _x200 ∧ 1 = _x198 ∧ −1 ≤ _x202 − 1 ∧ −1 ≤ _x201 − 1 ∧ 0 ≤ _x197 − 1 ∧ 0 ≤ _x196 − 1 ∧ 0 ≤ _x191 − 1 ∧ 0 ≤ _x190 − 1 ∧ 0 ≤ _x189 − 1 ∧ _x202 + 1 ≤ _x191 ∧ _x202 + 1 ≤ _x190 ∧ _x201 + 1 ≤ _x189 ∧ _x197 ≤ _x191 ∧ _x197 ≤ _x190 ∧ 1 ≤ _x192 − 1 ∧ _x196 ≤ _x189
f3684_0_extendMatchingSubstitution_EQ	15	f3952_0_extendMatchingSubstitution_NULL:	x1 = _x203 ∧ x2 = _x204 ∧ x3 = _x205 ∧ x4 = _x206 ∧ x5 = _x207 ∧ x6 = _x208 ∧ x7 = _x209 ∧ x1 = _x210 ∧ x2 = _x211 ∧ x3 = _x212 ∧ x4 = _x213 ∧ x5 = _x214 ∧ x6 = _x215 ∧ x7 = _x216 ∧ _x207 = _x213 ∧ _x206 = _x212 ∧ 1 = _x205 ∧ −1 ≤ _x211 − 1 ∧ −1 ≤ _x210 − 1 ∧ −1 ≤ _x209 − 1 ∧ −1 ≤ _x208 − 1 ∧ 0 ≤ _x204 − 1 ∧ 0 ≤ _x203 − 1 ∧ _x211 ≤ _x208 ∧ _x211 + 1 ≤ _x203 ∧ _x210 ≤ _x209 ∧ _x210 + 1 ≤ _x204
f3952_0_extendMatchingSubstitution_NULL	16	f3568_0_extendMatchingSubstitution_CheckCast:	x1 = _x217 ∧ x2 = _x218 ∧ x3 = _x219 ∧ x4 = _x220 ∧ x5 = _x221 ∧ x6 = _x222 ∧ x7 = _x223 ∧ x1 = _x224 ∧ x2 = _x225 ∧ x3 = _x226 ∧ x4 = _x227 ∧ x5 = _x228 ∧ x6 = _x229 ∧ x7 = _x230 ∧ _x220 = _x227 ∧ −1 ≤ _x226 − 1 ∧ −1 ≤ _x225 − 1 ∧ 0 ≤ _x224 − 1 ∧ 2 ≤ _x218 − 1 ∧ 1 ≤ _x217 − 1 ∧ _x226 + 3 ≤ _x218 ∧ _x226 + 2 ≤ _x217 ∧ _x225 + 3 ≤ _x218 ∧ _x225 + 2 ≤ _x217 ∧ 1 ≤ _x220 − 1 ∧ _x224 + 2 ≤ _x218
f3952_0_extendMatchingSubstitution_NULL	17	f3568_0_extendMatchingSubstitution_CheckCast:	x1 = _x231 ∧ x2 = _x232 ∧ x3 = _x233 ∧ x4 = _x234 ∧ x5 = _x235 ∧ x6 = _x236 ∧ x7 = _x237 ∧ x1 = _x238 ∧ x2 = _x239 ∧ x3 = _x240 ∧ x4 = _x241 ∧ x5 = _x242 ∧ x6 = _x243 ∧ x7 = _x244 ∧ _x234 = _x241 ∧ 0 ≤ _x240 − 1 ∧ 0 ≤ _x239 − 1 ∧ 0 ≤ _x238 − 1 ∧ 2 ≤ _x232 − 1 ∧ 2 ≤ _x231 − 1 ∧ _x240 + 2 ≤ _x231 ∧ _x239 + 2 ≤ _x231 ∧ 1 ≤ _x234 − 1 ∧ _x238 + 2 ≤ _x232
f3952_0_extendMatchingSubstitution_NULL	18	f3952_0_extendMatchingSubstitution_NULL:	x1 = _x245 ∧ x2 = _x246 ∧ x3 = _x247 ∧ x4 = _x248 ∧ x5 = _x249 ∧ x6 = _x250 ∧ x7 = _x251 ∧ x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ _x248 = _x255 ∧ _x247 = _x254 ∧ −1 ≤ _x253 − 1 ∧ −1 ≤ _x252 − 1 ∧ 2 ≤ _x246 − 1 ∧ 2 ≤ _x245 − 1 ∧ _x253 + 2 ≤ _x246 ∧ 1 ≤ _x248 − 1 ∧ _x252 + 2 ≤ _x245
f3952_0_extendMatchingSubstitution_NULL	19	f3952_0_extendMatchingSubstitution_NULL:	x1 = _x259 ∧ x2 = _x260 ∧ x3 = _x261 ∧ x4 = _x262 ∧ x5 = _x263 ∧ x6 = _x264 ∧ x7 = _x265 ∧ x1 = _x266 ∧ x2 = _x267 ∧ x3 = _x268 ∧ x4 = _x269 ∧ x5 = _x270 ∧ x6 = _x271 ∧ x7 = _x272 ∧ _x262 = _x269 ∧ _x261 = _x268 ∧ −1 ≤ _x267 − 1 ∧ −1 ≤ _x266 − 1 ∧ 2 ≤ _x260 − 1 ∧ 1 ≤ _x259 − 1 ∧ _x267 + 2 ≤ _x260 ∧ 1 ≤ _x262 − 1 ∧ _x266 + 2 ≤ _x259
__init	20	f1_0_main_Load:	x1 = _x273 ∧ x2 = _x274 ∧ x3 = _x275 ∧ x4 = _x276 ∧ x5 = _x277 ∧ x6 = _x278 ∧ x7 = _x279 ∧ x1 = _x280 ∧ x2 = _x281 ∧ x3 = _x282 ∧ x4 = _x283 ∧ x5 = _x284 ∧ x6 = _x285 ∧ x7 = _x286 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f648_0_create_GT	f648_0_create_GT	f648_0_create_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f3952_0_extendMatchingSubstitution_NULL	f3952_0_extendMatchingSubstitution_NULL	f3952_0_extendMatchingSubstitution_NULL:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f3684_0_extendMatchingSubstitution_EQ	f3684_0_extendMatchingSubstitution_EQ	f3684_0_extendMatchingSubstitution_EQ:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f1260_0_create_Return	f1260_0_create_Return	f1260_0_create_Return:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f2576_0_create_GE	f2576_0_create_GE	f2576_0_create_GE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f1_0_main_Load	f1_0_main_Load	f1_0_main_Load:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f1262_0_create_Return	f1262_0_create_Return	f1262_0_create_Return:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f3568_0_extendMatchingSubstitution_CheckCast	f3568_0_extendMatchingSubstitution_CheckCast	f3568_0_extendMatchingSubstitution_CheckCast:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
f2800_0_random_ArrayAccess	f2800_0_random_ArrayAccess	f2800_0_random_ArrayAccess:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
__init	__init	__init:	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 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { f648_0_create_GT, f2576_0_create_GE }.

2.1.1 Transition Removal

We remove transitions 10, 11 using the following ranking functions, which are bounded by 0.

f648_0_create_GT:	1 + 2⋅x1
f2576_0_create_GE:	2⋅x1

2.1.2 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by 0.

f2576_0_create_GE:

− x2 + x3

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 2/2

Here we consider the SCC { f3952_0_extendMatchingSubstitution_NULL, f3684_0_extendMatchingSubstitution_EQ, f3568_0_extendMatchingSubstitution_CheckCast }.

2.2.1 Transition Removal

We remove transitions 13, 16, 15, 14, 17, 18, 19 using the following ranking functions, which are bounded by 0.

f3568_0_extendMatchingSubstitution_CheckCast:	1 + x1
f3684_0_extendMatchingSubstitution_EQ:	x1
f3952_0_extendMatchingSubstitution_NULL:	x2

2.2.2 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 % (9 real / 0 unknown / 0 assumptions / 9 total proof steps)