LTS Termination Proof

Input

Integer Transition System

Initial Location: f566_0_sin_InvokeMethod, f342_0_exp_GT, f638_0_exp_InvokeMethod, f452_0_main_GE, f276_0_sin_GT, f453_0_fact_GT, f1_0_main_ConstantStackPush, f697_0_main_GE, f342_0_exp_GT', __init, f566_0_sin_InvokeMethod', f552_0_cos_InvokeMethod, f452_0_main_GE', f552_0_cos_InvokeMethod', f345_0_power_GT, f307_0_cos_GT

Transitions: (pre-variables and post-variables)

f1_0_main_ConstantStackPush	1	f452_0_main_GE:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ _arg2 = _arg3P ∧ 0 = _arg2P ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg2 − 1 ∧ _arg1P ≤ _arg1
f452_0_main_GE	2	f452_0_main_GE':	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x1 = _x4 ∧ x2 = _x5 ∧ x3 = _x6 ∧ x4 = _x7 ∧ _x1 ≤ _x2 − 1 ∧ 0 ≤ _x2 − 1 ∧ _x1 − 2⋅_x8 = 0 ∧ 0 ≤ _x − 1 ∧ _x = _x4 ∧ _x1 = _x5 ∧ _x2 = _x6
f452_0_main_GE'	3	f276_0_sin_GT:	x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ x4 = _x12 ∧ x1 = _x13 ∧ x2 = _x14 ∧ x3 = _x15 ∧ x4 = _x16 ∧ _x10 ≤ _x11 − 1 ∧ 0 ≤ _x11 − 1 ∧ _x10 − 2⋅_x17 = 0 ∧ 0 ≤ _x9 − 1 ∧ _x10 − 2⋅_x17 ≤ 1 ∧ 0 ≤ _x10 − 2⋅_x17 ∧ _x11 = _x13 ∧ _x10 = _x14
f452_0_main_GE	4	f452_0_main_GE':	x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x4 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ x3 = _x24 ∧ x4 = _x25 ∧ _x19 ≤ _x20 − 1 ∧ 0 ≤ _x20 − 1 ∧ _x19 − 2⋅_x26 = 1 ∧ _x19 − 3⋅_x27 = 0 ∧ 0 ≤ _x18 − 1 ∧ _x18 = _x22 ∧ _x19 = _x23 ∧ _x20 = _x24
f452_0_main_GE'	5	f307_0_cos_GT:	x1 = _x28 ∧ x2 = _x29 ∧ x3 = _x30 ∧ x4 = _x31 ∧ x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x4 = _x35 ∧ _x29 ≤ _x30 − 1 ∧ 0 ≤ _x30 − 1 ∧ _x29 − 2⋅_x36 = 1 ∧ _x29 − 3⋅_x37 = 0 ∧ 0 ≤ _x28 − 1 ∧ 0 ≤ _x29 − 2⋅_x36 ∧ _x29 − 2⋅_x36 ≤ 1 ∧ _x29 − 3⋅_x37 ≤ 2 ∧ 0 ≤ _x29 − 3⋅_x37 ∧ _x30 = _x32 ∧ _x29 = _x33
f452_0_main_GE	6	f452_0_main_GE':	x1 = _x38 ∧ x2 = _x39 ∧ x3 = _x40 ∧ x4 = _x41 ∧ x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x4 = _x45 ∧ _x39 ≤ _x40 − 1 ∧ 0 ≤ _x40 − 1 ∧ _x39 − 2⋅_x46 = 1 ∧ 0 ≤ _x39 − 3⋅_x47 − 1 ∧ _x39 − 5⋅_x48 = 0 ∧ 0 ≤ _x38 − 1 ∧ _x38 = _x42 ∧ _x39 = _x43 ∧ _x40 = _x44
f452_0_main_GE'	7	f342_0_exp_GT:	x1 = _x49 ∧ x2 = _x50 ∧ x3 = _x51 ∧ x4 = _x52 ∧ x1 = _x53 ∧ x2 = _x54 ∧ x3 = _x55 ∧ x4 = _x56 ∧ 0 ≤ _x50 − 3⋅_x57 − 1 ∧ _x50 ≤ _x51 − 1 ∧ 0 ≤ _x51 − 1 ∧ _x50 − 2⋅_x58 = 1 ∧ _x50 − 5⋅_x59 = 0 ∧ 0 ≤ _x49 − 1 ∧ 0 ≤ _x50 − 2⋅_x58 ∧ _x50 − 2⋅_x58 ≤ 1 ∧ _x50 − 3⋅_x57 ≤ 2 ∧ _x50 − 5⋅_x59 ≤ 4 ∧ 0 ≤ _x50 − 5⋅_x59 ∧ _x51 = _x53 ∧ _x50 = _x54
f452_0_main_GE	8	f452_0_main_GE':	x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x1 = _x64 ∧ x2 = _x65 ∧ x3 = _x66 ∧ x4 = _x67 ∧ _x61 − 2⋅_x68 = 1 ∧ _x61 ≤ _x62 − 1 ∧ 0 ≤ _x61 − 5⋅_x69 − 1 ∧ 0 ≤ _x61 − 3⋅_x70 − 1 ∧ _x71 ≤ _x60 ∧ 0 ≤ _x60 − 1 ∧ 0 ≤ _x71 − 1 ∧ _x60 = _x64 ∧ _x61 = _x65 ∧ _x62 = _x66
f452_0_main_GE'	9	f697_0_main_GE:	x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x1 = _x76 ∧ x2 = _x77 ∧ x3 = _x78 ∧ x4 = _x79 ∧ 0 ≤ _x73 − 5⋅_x80 − 1 ∧ 0 ≤ _x73 − 3⋅_x81 − 1 ∧ _x73 − 2⋅_x82 = 1 ∧ _x73 ≤ _x74 − 1 ∧ _x76 ≤ _x72 ∧ 0 ≤ _x72 − 1 ∧ 0 ≤ _x76 − 1 ∧ 0 ≤ _x73 − 2⋅_x82 ∧ _x73 − 2⋅_x82 ≤ 1 ∧ _x73 − 3⋅_x81 ≤ 2 ∧ _x73 − 5⋅_x80 ≤ 4 ∧ _x73 = _x77 ∧ 0 = _x78 ∧ _x74 = _x79
f697_0_main_GE	10	f697_0_main_GE:	x1 = _x83 ∧ x2 = _x84 ∧ x3 = _x85 ∧ x4 = _x86 ∧ x1 = _x87 ∧ x2 = _x88 ∧ x3 = _x89 ∧ x4 = _x90 ∧ _x86 = _x90 ∧ _x85 + 1 = _x89 ∧ _x84 = _x88 ∧ 0 ≤ _x87 − 1 ∧ 0 ≤ _x83 − 1 ∧ _x85 ≤ 99 ∧ _x87 ≤ _x83
f452_0_main_GE	11	f452_0_main_GE:	x1 = _x92 ∧ x2 = _x93 ∧ x3 = _x94 ∧ x4 = _x96 ∧ x1 = _x97 ∧ x2 = _x98 ∧ x3 = _x101 ∧ x4 = _x102 ∧ _x94 = _x101 ∧ 1 = _x98 ∧ 0 = _x93 ∧ 0 ≤ _x97 − 1 ∧ 0 ≤ _x92 − 1 ∧ 0 ≤ _x94 − 1 ∧ _x97 ≤ _x92
f697_0_main_GE	12	f452_0_main_GE:	x1 = _x103 ∧ x2 = _x106 ∧ x3 = _x107 ∧ x4 = _x108 ∧ x1 = _x112 ∧ x2 = _x113 ∧ x3 = _x114 ∧ x4 = _x118 ∧ _x108 = _x114 ∧ _x106 + 1 = _x113 ∧ 0 ≤ _x112 − 1 ∧ 0 ≤ _x103 − 1 ∧ _x112 ≤ _x103 ∧ 99 ≤ _x107 − 1 ∧ −1 ≤ _x108 − 1
f452_0_main_GE	13	f452_0_main_GE':	x1 = _x119 ∧ x2 = _x120 ∧ x3 = _x125 ∧ x4 = _x126 ∧ x1 = _x127 ∧ x2 = _x128 ∧ x3 = _x132 ∧ x4 = _x133 ∧ _x120 ≤ _x125 − 1 ∧ 0 ≤ _x125 − 1 ∧ _x120 − 2⋅_x134 = 1 ∧ 0 ≤ _x120 − 3⋅_x139 − 1 ∧ _x120 − 5⋅_x140 = 0 ∧ _x141 ≤ _x119 ∧ 0 ≤ _x119 − 1 ∧ 0 ≤ _x141 − 1 ∧ _x119 = _x127 ∧ _x120 = _x128 ∧ _x125 = _x132
f452_0_main_GE'	14	f452_0_main_GE:	x1 = _x142 ∧ x2 = _x146 ∧ x3 = _x147 ∧ x4 = _x148 ∧ x1 = _x152 ∧ x2 = _x153 ∧ x3 = _x154 ∧ x4 = _x155 ∧ 0 ≤ _x146 − 3⋅_x158 − 1 ∧ _x146 ≤ _x147 − 1 ∧ 0 ≤ _x147 − 1 ∧ _x146 − 2⋅_x159 = 1 ∧ _x146 − 5⋅_x160 = 0 ∧ _x152 ≤ _x142 ∧ 0 ≤ _x142 − 1 ∧ 0 ≤ _x152 − 1 ∧ 0 ≤ _x146 − 2⋅_x159 ∧ _x146 − 2⋅_x159 ≤ 1 ∧ _x146 − 3⋅_x158 ≤ 2 ∧ _x146 − 5⋅_x160 ≤ 4 ∧ 0 ≤ _x146 − 5⋅_x160 ∧ _x146 + 1 = _x153 ∧ _x147 = _x154
f452_0_main_GE	15	f452_0_main_GE':	x1 = _x163 ∧ x2 = _x164 ∧ x3 = _x165 ∧ x4 = _x166 ∧ x1 = _x168 ∧ x2 = _x169 ∧ x3 = _x170 ∧ x4 = _x174 ∧ _x164 ≤ _x165 − 1 ∧ 0 ≤ _x165 − 1 ∧ _x164 − 2⋅_x175 = 1 ∧ _x164 − 3⋅_x176 = 0 ∧ _x180 ≤ _x163 ∧ 0 ≤ _x163 − 1 ∧ 0 ≤ _x180 − 1 ∧ _x163 = _x168 ∧ _x164 = _x169 ∧ _x165 = _x170
f452_0_main_GE'	16	f452_0_main_GE:	x1 = _x181 ∧ x2 = _x185 ∧ x3 = _x186 ∧ x4 = _x190 ∧ x1 = _x191 ∧ x2 = _x192 ∧ x3 = _x193 ∧ x4 = _x194 ∧ _x185 ≤ _x186 − 1 ∧ 0 ≤ _x186 − 1 ∧ _x185 − 2⋅_x195 = 1 ∧ _x185 − 3⋅_x196 = 0 ∧ _x191 ≤ _x181 ∧ 0 ≤ _x181 − 1 ∧ 0 ≤ _x191 − 1 ∧ 0 ≤ _x185 − 2⋅_x195 ∧ _x185 − 2⋅_x195 ≤ 1 ∧ _x185 − 3⋅_x196 ≤ 2 ∧ 0 ≤ _x185 − 3⋅_x196 ∧ _x185 + 1 = _x192 ∧ _x186 = _x193
f452_0_main_GE	17	f452_0_main_GE':	x1 = _x197 ∧ x2 = _x198 ∧ x3 = _x199 ∧ x4 = _x200 ∧ x1 = _x201 ∧ x2 = _x202 ∧ x3 = _x203 ∧ x4 = _x204 ∧ _x198 ≤ _x199 − 1 ∧ 0 ≤ _x199 − 1 ∧ _x198 − 2⋅_x205 = 0 ∧ _x206 ≤ _x197 ∧ 0 ≤ _x197 − 1 ∧ 0 ≤ _x206 − 1 ∧ _x197 = _x201 ∧ _x198 = _x202 ∧ _x199 = _x203
f452_0_main_GE'	18	f452_0_main_GE:	x1 = _x207 ∧ x2 = _x208 ∧ x3 = _x209 ∧ x4 = _x210 ∧ x1 = _x211 ∧ x2 = _x212 ∧ x3 = _x213 ∧ x4 = _x214 ∧ _x208 ≤ _x209 − 1 ∧ 0 ≤ _x209 − 1 ∧ _x208 − 2⋅_x215 = 0 ∧ _x211 ≤ _x207 ∧ 0 ≤ _x207 − 1 ∧ 0 ≤ _x211 − 1 ∧ _x208 − 2⋅_x215 ≤ 1 ∧ 0 ≤ _x208 − 2⋅_x215 ∧ _x208 + 1 = _x212 ∧ _x209 = _x213
f276_0_sin_GT	19	f345_0_power_GT:	x1 = _x216 ∧ x2 = _x217 ∧ x3 = _x218 ∧ x4 = _x219 ∧ x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ x4 = _x223 ∧ _x217 = _x220 ∧ 0 ≤ _x216 − 1 ∧ 0 ≤ _x217 − 1
f276_0_sin_GT	20	f566_0_sin_InvokeMethod:	x1 = _x224 ∧ x2 = _x225 ∧ x3 = _x226 ∧ x4 = _x227 ∧ x1 = _x228 ∧ x2 = _x229 ∧ x3 = _x230 ∧ x4 = _x231 ∧ 2⋅_x225 + 1 = _x230 ∧ _x224 = _x229 ∧ _x225 = _x228 ∧ 0 ≤ _x225 − 1 ∧ 0 ≤ 2⋅_x225 − 1 ∧ 0 ≤ _x224 − 1
f566_0_sin_InvokeMethod	21	f345_0_power_GT:	x1 = _x232 ∧ x2 = _x233 ∧ x3 = _x234 ∧ x4 = _x235 ∧ x1 = _x236 ∧ x2 = _x237 ∧ x3 = _x238 ∧ x4 = _x239 ∧ _x234 = _x236 ∧ 0 ≤ _x232 − 1 ∧ 1 ≤ _x234 − 1 ∧ 0 ≤ _x233 − 1
f566_0_sin_InvokeMethod	22	f453_0_fact_GT:	x1 = _x240 ∧ x2 = _x241 ∧ x3 = _x242 ∧ x4 = _x243 ∧ x1 = _x244 ∧ x2 = _x245 ∧ x3 = _x246 ∧ x4 = _x247 ∧ 2⋅_x240 + 1 = _x244 ∧ 1 ≤ _x242 − 1 ∧ 0 ≤ 2⋅_x240 − 1 ∧ 0 ≤ _x240 − 1 ∧ 0 ≤ _x241 − 1
f566_0_sin_InvokeMethod	23	f566_0_sin_InvokeMethod':	x1 = _x248 ∧ x2 = _x249 ∧ x3 = _x250 ∧ x4 = _x251 ∧ x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ _x250 = _x254 ∧ _x249 = _x253 ∧ _x248 = _x252 ∧ 0 ≤ 2⋅_x248 − 1 ∧ _x248 − 1 ≤ _x248 − 1 ∧ 1 ≤ _x250 − 1 ∧ 0 ≤ _x248 − 1 ∧ 0 ≤ _x249 − 1
f566_0_sin_InvokeMethod'	24	f276_0_sin_GT:	x1 = _x256 ∧ x2 = _x257 ∧ x3 = _x258 ∧ x4 = _x259 ∧ x1 = _x260 ∧ x2 = _x261 ∧ x3 = _x262 ∧ x4 = _x263 ∧ 0 ≤ _x257 − 1 ∧ 0 ≤ _x256 − 1 ∧ 1 ≤ _x258 − 1 ∧ 0 ≤ 2⋅_x256 − 1 ∧ _x256 − 1 ≤ _x256 − 1 ∧ _x264 − _x265⋅_x266 ≤ _x265 − 1 ∧ 0 ≤ _x264 − _x265⋅_x266 ∧ _x257 = _x260 ∧ _x256 − 1 = _x261
f307_0_cos_GT	25	f345_0_power_GT:	x1 = _x267 ∧ x2 = _x268 ∧ x3 = _x269 ∧ x4 = _x270 ∧ x1 = _x271 ∧ x2 = _x272 ∧ x3 = _x273 ∧ x4 = _x274 ∧ _x268 = _x271 ∧ 0 ≤ _x267 − 1 ∧ 0 ≤ _x268 − 1
f307_0_cos_GT	26	f552_0_cos_InvokeMethod:	x1 = _x275 ∧ x2 = _x276 ∧ x3 = _x277 ∧ x4 = _x278 ∧ x1 = _x279 ∧ x2 = _x280 ∧ x3 = _x281 ∧ x4 = _x282 ∧ 2⋅_x276 = _x281 ∧ _x275 = _x280 ∧ _x276 = _x279 ∧ 0 ≤ _x275 − 1 ∧ 0 ≤ _x276 − 1
f552_0_cos_InvokeMethod	27	f345_0_power_GT:	x1 = _x283 ∧ x2 = _x284 ∧ x3 = _x285 ∧ x4 = _x286 ∧ x1 = _x287 ∧ x2 = _x288 ∧ x3 = _x289 ∧ x4 = _x290 ∧ _x285 = _x287 ∧ 0 ≤ _x283 − 1 ∧ 0 ≤ _x284 − 1 ∧ 1 ≤ _x285 − 1
f552_0_cos_InvokeMethod	28	f453_0_fact_GT:	x1 = _x291 ∧ x2 = _x292 ∧ x3 = _x293 ∧ x4 = _x294 ∧ x1 = _x295 ∧ x2 = _x296 ∧ x3 = _x297 ∧ x4 = _x298 ∧ 2⋅_x291 = _x295 ∧ 1 ≤ _x293 − 1 ∧ 1 ≤ 2⋅_x291 − 1 ∧ 0 ≤ _x291 − 1 ∧ 0 ≤ _x292 − 1
f552_0_cos_InvokeMethod	29	f552_0_cos_InvokeMethod':	x1 = _x299 ∧ x2 = _x300 ∧ x3 = _x301 ∧ x4 = _x302 ∧ x1 = _x303 ∧ x2 = _x304 ∧ x3 = _x305 ∧ x4 = _x306 ∧ _x301 = _x305 ∧ _x300 = _x304 ∧ _x299 = _x303 ∧ 1 ≤ 2⋅_x299 − 1 ∧ _x299 − 1 ≤ _x299 − 1 ∧ 1 ≤ _x301 − 1 ∧ 0 ≤ _x299 − 1 ∧ 0 ≤ _x300 − 1
f552_0_cos_InvokeMethod'	30	f307_0_cos_GT:	x1 = _x307 ∧ x2 = _x308 ∧ x3 = _x309 ∧ x4 = _x310 ∧ x1 = _x311 ∧ x2 = _x312 ∧ x3 = _x313 ∧ x4 = _x314 ∧ 0 ≤ _x308 − 1 ∧ 0 ≤ _x307 − 1 ∧ 1 ≤ _x309 − 1 ∧ 1 ≤ 2⋅_x307 − 1 ∧ _x307 − 1 ≤ _x307 − 1 ∧ _x315 − _x316⋅_x317 ≤ _x316 − 1 ∧ 0 ≤ _x315 − _x316⋅_x317 ∧ _x308 = _x311 ∧ _x307 − 1 = _x312
f342_0_exp_GT	31	f345_0_power_GT:	x1 = _x318 ∧ x2 = _x319 ∧ x3 = _x320 ∧ x4 = _x321 ∧ x1 = _x322 ∧ x2 = _x323 ∧ x3 = _x324 ∧ x4 = _x325 ∧ _x319 = _x322 ∧ 0 ≤ _x318 − 1 ∧ 0 ≤ _x319 − 1
f638_0_exp_InvokeMethod	32	f342_0_exp_GT:	x1 = _x326 ∧ x2 = _x327 ∧ x3 = _x328 ∧ x4 = _x329 ∧ x1 = _x330 ∧ x2 = _x331 ∧ x3 = _x332 ∧ x4 = _x333 ∧ _x328 = _x331 ∧ _x327 = _x330 ∧ 0 ≤ _x326 − 1 ∧ 0 ≤ _x327 − 1 ∧ _x328 ≤ _x326 − 1
f345_0_power_GT	33	f345_0_power_GT:	x1 = _x334 ∧ x2 = _x335 ∧ x3 = _x336 ∧ x4 = _x337 ∧ x1 = _x338 ∧ x2 = _x339 ∧ x3 = _x340 ∧ x4 = _x341 ∧ _x334 − 1 = _x338 ∧ 0 ≤ _x334 − 1
f453_0_fact_GT	34	f453_0_fact_GT:	x1 = _x342 ∧ x2 = _x343 ∧ x3 = _x344 ∧ x4 = _x345 ∧ x1 = _x346 ∧ x2 = _x347 ∧ x3 = _x348 ∧ x4 = _x349 ∧ _x342 − 1 = _x346 ∧ _x342 − 1 ≤ _x342 − 1 ∧ 0 ≤ _x342 − 1
f342_0_exp_GT	35	f453_0_fact_GT:	x1 = _x350 ∧ x2 = _x351 ∧ x3 = _x352 ∧ x4 = _x353 ∧ x1 = _x354 ∧ x2 = _x355 ∧ x3 = _x356 ∧ x4 = _x357 ∧ _x351 = _x354 ∧ 0 ≤ _x350 − 1 ∧ 0 ≤ _x351 − 1
f342_0_exp_GT	36	f342_0_exp_GT':	x1 = _x358 ∧ x2 = _x359 ∧ x3 = _x360 ∧ x4 = _x361 ∧ x1 = _x362 ∧ x2 = _x363 ∧ x3 = _x364 ∧ x4 = _x365 ∧ _x359 = _x363 ∧ _x358 = _x362 ∧ 0 ≤ _x358 − 1 ∧ 0 ≤ _x359 − 1
f342_0_exp_GT'	37	f638_0_exp_InvokeMethod:	x1 = _x366 ∧ x2 = _x367 ∧ x3 = _x368 ∧ x4 = _x369 ∧ x1 = _x370 ∧ x2 = _x371 ∧ x3 = _x372 ∧ x4 = _x373 ∧ 0 ≤ _x366 − 1 ∧ 0 ≤ _x367 − 1 ∧ _x374 − _x375⋅_x376 ≤ _x375 − 1 ∧ 0 ≤ _x374 − _x375⋅_x376 ∧ _x367 = _x370 ∧ _x366 = _x371 ∧ _x367 − 1 = _x372
f342_0_exp_GT	38	f342_0_exp_GT':	x1 = _x377 ∧ x2 = _x378 ∧ x3 = _x379 ∧ x4 = _x380 ∧ x1 = _x381 ∧ x2 = _x382 ∧ x3 = _x383 ∧ x4 = _x384 ∧ _x378 = _x382 ∧ _x377 = _x381 ∧ 0 ≤ _x378 − 1 ∧ 0 ≤ _x377 − 1
f342_0_exp_GT'	39	f638_0_exp_InvokeMethod:	x1 = _x385 ∧ x2 = _x386 ∧ x3 = _x387 ∧ x4 = _x388 ∧ x1 = _x389 ∧ x2 = _x390 ∧ x3 = _x391 ∧ x4 = _x392 ∧ 0 ≤ _x386 − 1 ∧ 0 ≤ _x385 − 1 ∧ _x393 − _x394⋅_x395 ≤ _x394 − 1 ∧ 0 ≤ _x393 − _x394⋅_x395 ∧ _x386 = _x389 ∧ _x385 = _x390 ∧ _x386 − 1 = _x391
__init	40	f1_0_main_ConstantStackPush:	x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x1 = _x400 ∧ x2 = _x401 ∧ x3 = _x402 ∧ x4 = _x403 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

f566_0_sin_InvokeMethod	f566_0_sin_InvokeMethod	f566_0_sin_InvokeMethod:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f342_0_exp_GT	f342_0_exp_GT	f342_0_exp_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f638_0_exp_InvokeMethod	f638_0_exp_InvokeMethod	f638_0_exp_InvokeMethod:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f452_0_main_GE	f452_0_main_GE	f452_0_main_GE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f276_0_sin_GT	f276_0_sin_GT	f276_0_sin_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f453_0_fact_GT	f453_0_fact_GT	f453_0_fact_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f1_0_main_ConstantStackPush	f1_0_main_ConstantStackPush	f1_0_main_ConstantStackPush:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f697_0_main_GE	f697_0_main_GE	f697_0_main_GE:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f342_0_exp_GT'	f342_0_exp_GT'	f342_0_exp_GT':	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
__init	__init	__init:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f566_0_sin_InvokeMethod'	f566_0_sin_InvokeMethod'	f566_0_sin_InvokeMethod':	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f552_0_cos_InvokeMethod	f552_0_cos_InvokeMethod	f552_0_cos_InvokeMethod:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f452_0_main_GE'	f452_0_main_GE'	f452_0_main_GE':	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f552_0_cos_InvokeMethod'	f552_0_cos_InvokeMethod'	f552_0_cos_InvokeMethod':	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f345_0_power_GT	f345_0_power_GT	f345_0_power_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4
f307_0_cos_GT	f307_0_cos_GT	f307_0_cos_GT:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4

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 { f452_0_main_GE, f452_0_main_GE', f697_0_main_GE }.

2.1.1 Transition Removal

We remove transitions 2, 11, 9, 4, 14, 6, 16, 8, 18, 17, 15, 13 using the following ranking functions, which are bounded by 0.

f452_0_main_GE:	1 − 2⋅x2 + 2⋅x3
f452_0_main_GE':	−2⋅x2 + 2⋅x3
f697_0_main_GE:	−1 − 2⋅x2 + 2⋅x4

2.1.2 Transition Removal

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

f697_0_main_GE:	x4
f452_0_main_GE:	−1 + x3

2.1.3 Transition Removal

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

f697_0_main_GE:

99 − x3

2.1.4 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 { f342_0_exp_GT, f638_0_exp_InvokeMethod, f342_0_exp_GT' }.

2.2.1 Transition Removal

We remove transitions 36, 32, 39, 37, 38 using the following ranking functions, which are bounded by 0.

f342_0_exp_GT:	2 + 3⋅x2
f342_0_exp_GT':	1 + 3⋅x2
f638_0_exp_InvokeMethod:	3⋅x1

2.2.2 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 { f552_0_cos_InvokeMethod, f552_0_cos_InvokeMethod', f307_0_cos_GT }.

2.3.1 Transition Removal

We remove transitions 26, 30, 29 using the following ranking functions, which are bounded by 0.

f307_0_cos_GT:	3⋅x2 + 2
f552_0_cos_InvokeMethod:	3⋅x1 + 1
f552_0_cos_InvokeMethod':	3⋅x1

2.3.2 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 { f566_0_sin_InvokeMethod, f276_0_sin_GT, f566_0_sin_InvokeMethod' }.

2.4.1 Transition Removal

We remove transitions 20, 24, 23 using the following ranking functions, which are bounded by 0.

f276_0_sin_GT:	3⋅x2 + 2
f566_0_sin_InvokeMethod:	3⋅x1 + 1
f566_0_sin_InvokeMethod':	3⋅x1

2.4.2 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 { f453_0_fact_GT }.

2.5.1 Transition Removal

We remove transition 34 using the following ranking functions, which are bounded by 0.

f453_0_fact_GT:

2.5.2 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 { f345_0_power_GT }.

2.6.1 Transition Removal

We remove transition 33 using the following ranking functions, which are bounded by 0.

f345_0_power_GT:

2.6.2 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 % (22 real / 0 unknown / 0 assumptions / 22 total proof steps)