MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IntTRSCompressionProof [EQUIVALENT, 0 ms] (4) IRSwT (5) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (6) IRSwT (7) TempFilterProof [SOUND, 20.0 s] (8) IRSwT (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTOrderProof [EQUIVALENT, 298 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 8077 ms] (19) IRSwT (20) IRSwTTerminationDigraphProof [EQUIVALENT, 50 ms] (21) IRSwT (22) IntTRSCompressionProof [EQUIVALENT, 0 ms] (23) IRSwT (24) IRSwT (25) IntTRSCompressionProof [EQUIVALENT, 0 ms] (26) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f731_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 1 = arg6P && arg2 = arg5P && 0 = arg3P && 2 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1 && 0 <= arg7P - 1 && 1 <= arg2 - 1 && -1 <= arg4P - 1 f731_0_main_GE(x, x1, x2, x3, x4, x5, x6) -> f731_0_main_GE(x7, x8, x9, x10, x11, x12, x13) :|: x4 = x11 && x3 = x10 && x2 + 1 = x9 && x5 + 2 <= x1 && x6 + 2 <= x1 && 0 <= x8 - 1 && 0 <= x7 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x7 <= x1 && x7 <= x && 0 <= x3 - 1 && 0 <= x6 - 1 && x2 <= x3 - 1 && 1 <= x4 - 1 f958_0_getNext_Return(x14, x15, x16, x17, x18, x19, x20) -> f731_0_main_GE(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x16 = x24 && x17 + 1 = x23 && x19 + 2 <= x15 && x20 + 2 <= x15 && 0 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x15 - 1 && 0 <= x14 - 1 && x22 <= x15 && x21 <= x15 && x21 <= x14 f731_0_main_GE(x28, x29, x30, x31, x32, x33, x34) -> f1280_0_getPowerOfKInSource_IntArithmetic(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x39 && x33 + 1 = x38 && x34 = x36 && x33 + 2 <= x29 && x34 + 2 <= x29 && 0 <= x35 - 1 && 0 <= x29 - 1 && 0 <= x28 - 1 && x35 - 1 <= x29 && 0 <= x34 - 1 && 0 <= x31 - 1 && x30 <= x31 - 1 && 1 <= x32 - 1 f873_0_findKthPrime_Return(x42, x43, x44, x45, x46, x47, x48) -> f1280_0_getPowerOfKInSource_IntArithmetic(x49, x50, x51, x52, x53, x54, x55) :|: x45 = x53 && x44 + 1 = x52 && x43 = x51 && x45 = x50 && x44 + 2 <= x42 && x45 + 2 <= x42 && 0 <= x49 - 1 && 0 <= x42 - 1 && x49 - 1 <= x42 f1280_0_getPowerOfKInSource_IntArithmetic(x56, x57, x58, x59, x60, x61, x62) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x63, x64, x65, x66, x67, x68, x69) :|: x57 - x58 * x70 = 0 && x71 <= x56 && 0 <= x56 - 1 && 0 <= x71 - 1 && x60 + 2 <= x56 && x59 + 2 <= x56 && x56 = x63 && x57 = x64 && x58 = x65 && x59 = x66 && x60 = x67 f1280_0_getPowerOfKInSource_IntArithmetic'(x72, x73, x74, x75, x78, x79, x80) -> f1280_0_getPowerOfKInSource_IntArithmetic(x81, x82, x83, x84, x86, x87, x88) :|: x73 - x74 * x89 = 0 && x81 <= x72 && 0 <= x72 - 1 && 0 <= x81 - 1 && x75 + 2 <= x72 && x78 + 2 <= x72 && 0 <= x73 - x74 * x82 && x73 - x74 * x82 <= x74 - 1 && x73 - x74 * x89 <= x74 - 1 && 0 <= x73 - x74 * x89 && x74 = x83 && x75 = x84 && x78 = x86 f731_0_main_GE(x91, x92, x93, x94, x96, x97, x98) -> f1029_0_findKthPrime_GE(x99, x101, x102, x103, x104, x106, x107) :|: x97 = x102 && 0 = x101 && 1 = x99 && x97 + 2 <= x92 && x98 + 2 <= x92 && 0 <= x92 - 1 && 0 <= x91 - 1 && 0 <= x98 - 1 && 0 <= x94 - 1 && x93 <= x94 - 1 && 1 <= x96 - 1 f1029_0_findKthPrime_GE(x108, x109, x111, x112, x113, x114, x115) -> f1209_0_checkPrime_GE(x116, x117, x118, x119, x120, x121, x122) :|: x108 + 1 = x119 && 2 = x118 && x109 = x117 && x111 = x116 && 0 <= x108 - 1 && x109 <= x111 - 1 f1209_0_checkPrime_GE(x123, x124, x125, x126, x127, x128, x129) -> f1209_0_checkPrime_GE'(x130, x131, x132, x133, x134, x135, x136) :|: x125 <= x126 - 1 && x126 - x125 * x137 <= -1 && x123 = x130 && x124 = x131 && x125 = x132 && x126 = x133 f1209_0_checkPrime_GE(x138, x139, x140, x141, x142, x143, x144) -> f1209_0_checkPrime_GE'(x145, x146, x147, x148, x149, x150, x151) :|: x140 <= x141 - 1 && 0 <= x141 - x140 * x152 - 1 && x138 = x145 && x139 = x146 && x140 = x147 && x141 = x148 f1209_0_checkPrime_GE'(x153, x154, x155, x156, x157, x158, x159) -> f1209_0_checkPrime_GE(x160, x161, x162, x163, x164, x165, x166) :|: 0 <= x156 - x155 * x167 - 1 && x156 - x155 * x167 <= x155 - 1 && x155 <= x156 - 1 && x153 = x160 && x154 = x161 && x155 + 1 = x162 && x156 = x163 f1209_0_checkPrime_GE(x168, x169, x170, x171, x172, x173, x174) -> f1029_0_findKthPrime_GE(x175, x176, x177, x178, x179, x180, x181) :|: x168 = x177 && x169 + 1 = x176 && x171 = x175 && x171 <= x170 f1029_0_findKthPrime_GE(x182, x183, x184, x185, x186, x187, x188) -> f1029_0_findKthPrime_GE(x189, x190, x191, x192, x193, x194, x195) :|: x184 = x191 && x183 = x190 && x182 + 1 = x189 && x182 <= 0 && x183 <= x184 - 1 f1209_0_checkPrime_GE(x196, x197, x198, x199, x200, x201, x202) -> f1209_0_checkPrime_GE'(x203, x204, x205, x206, x207, x208, x209) :|: x198 <= x199 - 1 && x199 - x198 * x210 = 0 && x196 = x203 && x197 = x204 && x198 = x205 && x199 = x206 f1209_0_checkPrime_GE'(x211, x212, x213, x214, x215, x216, x217) -> f1029_0_findKthPrime_GE(x218, x219, x220, x221, x222, x223, x224) :|: x214 - x213 * x225 = 0 && x213 <= x214 - 1 && x214 - x213 * x225 <= x213 - 1 && 0 <= x214 - x213 * x225 && x214 = x218 && x212 = x219 && x211 = x220 __init(x226, x227, x228, x229, x230, x231, x232) -> f1_0_main_Load(x233, x234, x235, x236, x237, x238, x239) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f731_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: 1 = arg6P && arg2 = arg5P && 0 = arg3P && 2 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg1P <= arg1 && 0 <= arg7P - 1 && 1 <= arg2 - 1 && -1 <= arg4P - 1 f731_0_main_GE(x, x1, x2, x3, x4, x5, x6) -> f731_0_main_GE(x7, x8, x9, x10, x11, x12, x13) :|: x4 = x11 && x3 = x10 && x2 + 1 = x9 && x5 + 2 <= x1 && x6 + 2 <= x1 && 0 <= x8 - 1 && 0 <= x7 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x7 <= x1 && x7 <= x && 0 <= x3 - 1 && 0 <= x6 - 1 && x2 <= x3 - 1 && 1 <= x4 - 1 f958_0_getNext_Return(x14, x15, x16, x17, x18, x19, x20) -> f731_0_main_GE(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x16 = x24 && x17 + 1 = x23 && x19 + 2 <= x15 && x20 + 2 <= x15 && 0 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x15 - 1 && 0 <= x14 - 1 && x22 <= x15 && x21 <= x15 && x21 <= x14 f731_0_main_GE(x28, x29, x30, x31, x32, x33, x34) -> f1280_0_getPowerOfKInSource_IntArithmetic(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x39 && x33 + 1 = x38 && x34 = x36 && x33 + 2 <= x29 && x34 + 2 <= x29 && 0 <= x35 - 1 && 0 <= x29 - 1 && 0 <= x28 - 1 && x35 - 1 <= x29 && 0 <= x34 - 1 && 0 <= x31 - 1 && x30 <= x31 - 1 && 1 <= x32 - 1 f873_0_findKthPrime_Return(x42, x43, x44, x45, x46, x47, x48) -> f1280_0_getPowerOfKInSource_IntArithmetic(x49, x50, x51, x52, x53, x54, x55) :|: x45 = x53 && x44 + 1 = x52 && x43 = x51 && x45 = x50 && x44 + 2 <= x42 && x45 + 2 <= x42 && 0 <= x49 - 1 && 0 <= x42 - 1 && x49 - 1 <= x42 f1280_0_getPowerOfKInSource_IntArithmetic(x56, x57, x58, x59, x60, x61, x62) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x63, x64, x65, x66, x67, x68, x69) :|: x57 - x58 * x70 = 0 && x71 <= x56 && 0 <= x56 - 1 && 0 <= x71 - 1 && x60 + 2 <= x56 && x59 + 2 <= x56 && x56 = x63 && x57 = x64 && x58 = x65 && x59 = x66 && x60 = x67 f1280_0_getPowerOfKInSource_IntArithmetic'(x72, x73, x74, x75, x78, x79, x80) -> f1280_0_getPowerOfKInSource_IntArithmetic(x81, x82, x83, x84, x86, x87, x88) :|: x73 - x74 * x89 = 0 && x81 <= x72 && 0 <= x72 - 1 && 0 <= x81 - 1 && x75 + 2 <= x72 && x78 + 2 <= x72 && 0 <= x73 - x74 * x82 && x73 - x74 * x82 <= x74 - 1 && x73 - x74 * x89 <= x74 - 1 && 0 <= x73 - x74 * x89 && x74 = x83 && x75 = x84 && x78 = x86 f731_0_main_GE(x91, x92, x93, x94, x96, x97, x98) -> f1029_0_findKthPrime_GE(x99, x101, x102, x103, x104, x106, x107) :|: x97 = x102 && 0 = x101 && 1 = x99 && x97 + 2 <= x92 && x98 + 2 <= x92 && 0 <= x92 - 1 && 0 <= x91 - 1 && 0 <= x98 - 1 && 0 <= x94 - 1 && x93 <= x94 - 1 && 1 <= x96 - 1 f1029_0_findKthPrime_GE(x108, x109, x111, x112, x113, x114, x115) -> f1209_0_checkPrime_GE(x116, x117, x118, x119, x120, x121, x122) :|: x108 + 1 = x119 && 2 = x118 && x109 = x117 && x111 = x116 && 0 <= x108 - 1 && x109 <= x111 - 1 f1209_0_checkPrime_GE(x123, x124, x125, x126, x127, x128, x129) -> f1209_0_checkPrime_GE'(x130, x131, x132, x133, x134, x135, x136) :|: x125 <= x126 - 1 && x126 - x125 * x137 <= -1 && x123 = x130 && x124 = x131 && x125 = x132 && x126 = x133 f1209_0_checkPrime_GE(x138, x139, x140, x141, x142, x143, x144) -> f1209_0_checkPrime_GE'(x145, x146, x147, x148, x149, x150, x151) :|: x140 <= x141 - 1 && 0 <= x141 - x140 * x152 - 1 && x138 = x145 && x139 = x146 && x140 = x147 && x141 = x148 f1209_0_checkPrime_GE'(x153, x154, x155, x156, x157, x158, x159) -> f1209_0_checkPrime_GE(x160, x161, x162, x163, x164, x165, x166) :|: 0 <= x156 - x155 * x167 - 1 && x156 - x155 * x167 <= x155 - 1 && x155 <= x156 - 1 && x153 = x160 && x154 = x161 && x155 + 1 = x162 && x156 = x163 f1209_0_checkPrime_GE(x168, x169, x170, x171, x172, x173, x174) -> f1029_0_findKthPrime_GE(x175, x176, x177, x178, x179, x180, x181) :|: x168 = x177 && x169 + 1 = x176 && x171 = x175 && x171 <= x170 f1029_0_findKthPrime_GE(x182, x183, x184, x185, x186, x187, x188) -> f1029_0_findKthPrime_GE(x189, x190, x191, x192, x193, x194, x195) :|: x184 = x191 && x183 = x190 && x182 + 1 = x189 && x182 <= 0 && x183 <= x184 - 1 f1209_0_checkPrime_GE(x196, x197, x198, x199, x200, x201, x202) -> f1209_0_checkPrime_GE'(x203, x204, x205, x206, x207, x208, x209) :|: x198 <= x199 - 1 && x199 - x198 * x210 = 0 && x196 = x203 && x197 = x204 && x198 = x205 && x199 = x206 f1209_0_checkPrime_GE'(x211, x212, x213, x214, x215, x216, x217) -> f1029_0_findKthPrime_GE(x218, x219, x220, x221, x222, x223, x224) :|: x214 - x213 * x225 = 0 && x213 <= x214 - 1 && x214 - x213 * x225 <= x213 - 1 && 0 <= x214 - x213 * x225 && x214 = x218 && x212 = x219 && x211 = x220 __init(x226, x227, x228, x229, x230, x231, x232) -> f1_0_main_Load(x233, x234, x235, x236, x237, x238, x239) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) ---------------------------------------- (3) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (4) Obligation: Rules: f873_0_findKthPrime_Return(x42:0, x43:0, x44:0, x45:0, x46:0, x47:0, x48:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x49:0, x45:0, x43:0, x44:0 + 1, x45:0, x68:0, x69:0) :|: x42:0 > 0 && x49:0 - 1 <= x42:0 && x45:0 + 2 <= x42:0 && x44:0 + 2 <= x42:0 && x49:0 >= x44:0 + 3 && x49:0 >= x45:0 + 2 && x71:0 > 0 && x49:0 > 0 && x71:0 <= x49:0 && x45:0 - x43:0 * x70:0 = 0 f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4, x5, x6) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4, x9, x10) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0, x215:0, x216:0, x217:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0, x221:0, x222:0, x223:0, x224:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, x17:0 + 1, x16:0, x18:0, x19:0, x20:0) :|: x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0, x185:0, x186:0, x187:0, x188:0) -> f1029_0_findKthPrime_GE(x182:0 + 1, x183:0, x184:0, x192:0, x193:0, x194:0, x195:0) :|: x184:0 - 1 >= x183:0 && x182:0 < 1 f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, x19 + 1, x20, x23, x24) :|: x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0 f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0, x172:0, x173:0, x174:0) -> f1029_0_findKthPrime_GE(x171:0, x169:0 + 1, x168:0, x178:0, x179:0, x180:0, x181:0) :|: x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0, x142:0, x143:0, x144:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0, x149:0, x150:0, x151:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0, x200:0, x201:0, x202:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0, x207:0, x208:0, x209:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, 0, arg4P:0, arg5P:0, 1, arg7P:0) :|: arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0 f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(1, 0, x102:0, x103:0, x104:0, x106:0, x107:0) :|: x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0, x127:0, x128:0, x129:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0, x134:0, x135:0, x136:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, x2:0 + 1, x10:0, x11:0, x12:0, x13:0) :|: x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, 2, x108:0 + 1, x120:0, x121:0, x122:0) :|: x111:0 - 1 >= x109:0 && x108:0 > 0 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0, x157:0, x158:0, x159:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, x155:0 + 1, x156:0, x164:0, x165:0, x166:0) :|: x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) ---------------------------------------- (5) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f873_0_findKthPrime_Return(x1, x2, x3, x4, x5, x6, x7) -> f873_0_findKthPrime_Return(x1, x2, x3, x4) f1280_0_getPowerOfKInSource_IntArithmetic'(x1, x2, x3, x4, x5, x6, x7) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x1, x2, x3, x4, x5) f1209_0_checkPrime_GE'(x1, x2, x3, x4, x5, x6, x7) -> f1209_0_checkPrime_GE'(x1, x2, x3, x4) f1029_0_findKthPrime_GE(x1, x2, x3, x4, x5, x6, x7) -> f1029_0_findKthPrime_GE(x1, x2, x3) f1209_0_checkPrime_GE(x1, x2, x3, x4, x5, x6, x7) -> f1209_0_checkPrime_GE(x1, x2, x3, x4) ---------------------------------------- (6) Obligation: Rules: f873_0_findKthPrime_Return(x42:0, x43:0, x44:0, x45:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x49:0, x45:0, x43:0, x44:0 + 1, x45:0) :|: x42:0 > 0 && x49:0 - 1 <= x42:0 && x45:0 + 2 <= x42:0 && x44:0 + 2 <= x42:0 && x49:0 >= x44:0 + 3 && x49:0 >= x45:0 + 2 && x71:0 > 0 && x49:0 > 0 && x71:0 <= x49:0 && x45:0 - x43:0 * x70:0 = 0 f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, x17:0 + 1, x16:0, x18:0, x19:0, x20:0) :|: x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(x182:0 + 1, x183:0, x184:0) :|: x184:0 - 1 >= x183:0 && x182:0 < 1 f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, x19 + 1, x20) :|: x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0 f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, x169:0 + 1, x168:0) :|: x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, 0, arg4P:0, arg5P:0, 1, arg7P:0) :|: arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0 f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(1, 0, x102:0) :|: x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, x2:0 + 1, x10:0, x11:0, x12:0, x13:0) :|: x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, 2, x108:0 + 1) :|: x111:0 - 1 >= x109:0 && x108:0 > 0 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, x155:0 + 1, x156:0) :|: x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) ---------------------------------------- (7) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f873_0_findKthPrime_Return(INTEGER, INTEGER, INTEGER, INTEGER) f1280_0_getPowerOfKInSource_IntArithmetic'(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) f1209_0_checkPrime_GE'(VARIABLE, VARIABLE, INTEGER, INTEGER) f1029_0_findKthPrime_GE(VARIABLE, VARIABLE, VARIABLE) f958_0_getNext_Return(INTEGER, INTEGER, VARIABLE, VARIABLE, VARIABLE, INTEGER, INTEGER) f731_0_main_GE(INTEGER, INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) f1209_0_checkPrime_GE(VARIABLE, VARIABLE, VARIABLE, INTEGER) __init(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: f873_0_findKthPrime_Return(x42:0, x43:0, x44:0, x45:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x49:0, x45:0, x43:0, c, x45:0) :|: c = x44:0 + 1 && (x42:0 > 0 && x49:0 - 1 <= x42:0 && x45:0 + 2 <= x42:0 && x44:0 + 2 <= x42:0 && x49:0 >= x44:0 + 3 && x49:0 >= x45:0 + 2 && x71:0 > 0 && x49:0 > 0 && x71:0 <= x49:0 && x45:0 - x43:0 * x70:0 = 0) f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, c1, x16:0, x18:0, x19:0, x20:0) :|: c1 = x17:0 + 1 && (x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0) f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, c3, x20) :|: c3 = x19 + 1 && (x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) Found the following polynomial interpretation: [f873_0_findKthPrime_Return(x, x1, x2, x3)] = 1 [f1280_0_getPowerOfKInSource_IntArithmetic'(x4, x5, x6, x7, x8)] = 0 [f1209_0_checkPrime_GE'(x9, x10, x11, x12)] = 0 [f1029_0_findKthPrime_GE(x13, x14, x15)] = 0 [f958_0_getNext_Return(x16, x17, x18, x19, x20, x21, x22)] = 0 [f731_0_main_GE(x23, x24, x25, x26, x27, x28, x29)] = 0 [f1209_0_checkPrime_GE(x30, x31, x32, x33)] = 0 [__init(x34, x35, x36, x37, x38, x39, x40)] = 0 The following rules are decreasing: f873_0_findKthPrime_Return(x42:0, x43:0, x44:0, x45:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x49:0, x45:0, x43:0, c, x45:0) :|: c = x44:0 + 1 && (x42:0 > 0 && x49:0 - 1 <= x42:0 && x45:0 + 2 <= x42:0 && x44:0 + 2 <= x42:0 && x49:0 >= x44:0 + 3 && x49:0 >= x45:0 + 2 && x71:0 > 0 && x49:0 > 0 && x71:0 <= x49:0 && x45:0 - x43:0 * x70:0 = 0) The following rules are bounded: f873_0_findKthPrime_Return(x42:0, x43:0, x44:0, x45:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x49:0, x45:0, x43:0, c, x45:0) :|: c = x44:0 + 1 && (x42:0 > 0 && x49:0 - 1 <= x42:0 && x45:0 + 2 <= x42:0 && x44:0 + 2 <= x42:0 && x49:0 >= x44:0 + 3 && x49:0 >= x45:0 + 2 && x71:0 > 0 && x49:0 > 0 && x71:0 <= x49:0 && x45:0 - x43:0 * x70:0 = 0) f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, c1, x16:0, x18:0, x19:0, x20:0) :|: c1 = x17:0 + 1 && (x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0) f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, c3, x20) :|: c3 = x19 + 1 && (x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, c1, x16:0, x18:0, x19:0, x20:0) :|: c1 = x17:0 + 1 && (x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0) f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, c3, x20) :|: c3 = x19 + 1 && (x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = -1 [f1209_0_checkPrime_GE'(x5, x6, x7, x8)] = -1 [f1029_0_findKthPrime_GE(x9, x10, x11)] = -1 [f958_0_getNext_Return(x12, x13, x14, x15, x16, x17, x18)] = 0 [f731_0_main_GE(x19, x20, x21, x22, x23, x24, x25)] = -1 [f1209_0_checkPrime_GE(x26, x27, x28, x29)] = -1 [__init(x30, x31, x32, x33, x34, x35, x36)] = -1 The following rules are decreasing: f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, c1, x16:0, x18:0, x19:0, x20:0) :|: c1 = x17:0 + 1 && (x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0) The following rules are bounded: f958_0_getNext_Return(x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f731_0_main_GE(x21:0, x22:0, c1, x16:0, x18:0, x19:0, x20:0) :|: c1 = x17:0 + 1 && (x21:0 <= x15:0 && x21:0 <= x14:0 && x22:0 <= x15:0 && x14:0 > 0 && x15:0 > 0 && x21:0 > 0 && x22:0 > 0 && x19:0 + 2 <= x15:0 && x20:0 + 2 <= x15:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, c3, x20) :|: c3 = x19 + 1 && (x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 0 [f1209_0_checkPrime_GE'(x5, x6, x7, x8)] = 1 [f1029_0_findKthPrime_GE(x9, x10, x11)] = 1 [f731_0_main_GE(x12, x13, x14, x15, x16, x17, x18)] = 1 [f1209_0_checkPrime_GE(x19, x20, x21, x22)] = 1 [__init(x23, x24, x25, x26, x27, x28, x29)] = 1 The following rules are decreasing: f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, c3, x20) :|: c3 = x19 + 1 && (x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f731_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x21, x20, x22, c3, x20) :|: c3 = x19 + 1 && (x17 - 1 >= x16 && x18 > 1 && x17 > 0 && x20 > 0 && x21 - 1 <= x15 && x14 > 0 && x21 >= x19 + 3 && x15 > 0 && x21 >= x20 + 2 && x25 > 0 && x20 + 2 <= x15 && x21 > 0 && x19 + 2 <= x15 && x25 <= x21 && x20 - x22 * x26 = 0) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 0 [f1209_0_checkPrime_GE'(x5, x6, x7, x8)] = 0 [f1029_0_findKthPrime_GE(x9, x10, x11)] = 0 [f1209_0_checkPrime_GE(x12, x13, x14, x15)] = 0 [__init(x16, x17, x18, x19, x20, x21, x22)] = 1 [f731_0_main_GE(x23, x24, x25, x26, x27, x28, x29)] = 0 The following rules are decreasing: __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 __init(x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0) -> f731_0_main_GE(arg1P:0, arg2P:0, c5, arg4P:0, arg5P:0, c6, arg7P:0) :|: c6 = 1 && c5 = 0 && (arg5P:0 > 1 && arg4P:0 > -1 && arg7P:0 > 0 && x233:0 >= arg1P:0 && x233:0 > 0 && arg2P:0 > 2 && arg1P:0 > 0) f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 2*x2 + x3 + x4 [f1209_0_checkPrime_GE'(x5, x6, x7, x8)] = 0 [f1029_0_findKthPrime_GE(x9, x10, x11)] = 0 [f1209_0_checkPrime_GE(x12, x13, x14, x15)] = 0 [f731_0_main_GE(x16, x17, x18, x19, x20, x21, x22)] = -2 + x16 - x18 + x19 The following rules are decreasing: f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) The following rules are bounded: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Interpretation: [ f1280_0_getPowerOfKInSource_IntArithmetic' ] = 0 [ f1209_0_checkPrime_GE' ] = -1 [ f1029_0_findKthPrime_GE ] = -1 [ f1209_0_checkPrime_GE ] = -1 [ f731_0_main_GE ] = 0 The following rules are decreasing: f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f731_0_main_GE(x91:0, x92:0, x93:0, x94:0, x96:0, x102:0, x98:0) -> f1029_0_findKthPrime_GE(c7, c8, x102:0) :|: c8 = 0 && c7 = 1 && (x94:0 - 1 >= x93:0 && x96:0 > 1 && x94:0 > 0 && x98:0 > 0 && x91:0 > 0 && x92:0 > 0 && x92:0 >= x102:0 + 2 && x98:0 + 2 <= x92:0) f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 0 [f1209_0_checkPrime_GE'(x5, x6, x7, x8)] = -1 + x5 - x6 [f1029_0_findKthPrime_GE(x9, x10, x11)] = -1 - x10 + x11 [f1209_0_checkPrime_GE(x12, x13, x14, x15)] = -1 + x12 - x13 The following rules are decreasing: f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 0 [f1209_0_checkPrime_GE'(x5, x6, x7, x8)] = -3 + 2*x5 - x6 - x8 [f1029_0_findKthPrime_GE(x9, x10, x11)] = -3 - x10 + 2*x11 - x9 [f1209_0_checkPrime_GE(x12, x13, x14, x15)] = -3 + 2*x12 - x13 - x15 The following rules are decreasing: f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - IntTRS - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Interpretation: [ f1280_0_getPowerOfKInSource_IntArithmetic' ] = 0 [ f1209_0_checkPrime_GE' ] = 2*f1209_0_checkPrime_GE'_4 + -2*f1209_0_checkPrime_GE'_3 + -1 [ f1029_0_findKthPrime_GE ] = -1 [ f1209_0_checkPrime_GE ] = 2*f1209_0_checkPrime_GE_4 + -2*f1209_0_checkPrime_GE_3 The following rules are decreasing: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - IntTRS - IntTRS - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - IntTRS Rules: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Interpretation: [ f1209_0_checkPrime_GE' ] = -7*f1209_0_checkPrime_GE'_4 + -2*f1209_0_checkPrime_GE'_2 + 2*f1209_0_checkPrime_GE'_1 + 1 [ f1029_0_findKthPrime_GE ] = -7*f1029_0_findKthPrime_GE_1 + -2*f1029_0_findKthPrime_GE_2 + 2*f1029_0_findKthPrime_GE_3 [ f1209_0_checkPrime_GE ] = -7*f1209_0_checkPrime_GE_4 + 2*f1209_0_checkPrime_GE_1 + -2*f1209_0_checkPrime_GE_2 + 1 The following rules are decreasing: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) The following rules are bounded: f1029_0_findKthPrime_GE(x182:0, x183:0, x184:0) -> f1029_0_findKthPrime_GE(c2, x183:0, x184:0) :|: c2 = x182:0 + 1 && (x184:0 - 1 >= x183:0 && x182:0 < 1) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - IntTRS - IntTRS Rules: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, c10, c11) :|: c11 = x108:0 + 1 && c10 = 2 && (x111:0 - 1 >= x109:0 && x108:0 > 0) f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Found the following polynomial interpretation: [f1209_0_checkPrime_GE'(x, x1, x2, x3)] = 0 [f1029_0_findKthPrime_GE(x4, x5, x6)] = -1 [f1209_0_checkPrime_GE(x7, x8, x9, x10)] = 0 The following rules are decreasing: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 The following rules are bounded: f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x168:0, x169:0, x170:0, x171:0) -> f1029_0_findKthPrime_GE(x171:0, c4, x168:0) :|: c4 = x169:0 + 1 && x171:0 <= x170:0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof - IntTRS Rules: f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) Interpretation: [ f1209_0_checkPrime_GE ] = 2*f1209_0_checkPrime_GE_4 + -2*f1209_0_checkPrime_GE_3 + 1 [ f1209_0_checkPrime_GE' ] = -2*f1209_0_checkPrime_GE'_3 + 2*f1209_0_checkPrime_GE'_4 The following rules are decreasing: f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) The following rules are bounded: f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, c12, x156:0) :|: c12 = x155:0 + 1 && (x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 0 [f731_0_main_GE(x5, x6, x7, x8, x9, x10, x11)] = -x7 + x8 The following rules are decreasing: f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f731_0_main_GE(x:0, x1:0, x2:0, x10:0, x11:0, x5:0, x6:0) -> f731_0_main_GE(x7:0, x8:0, c9, x10:0, x11:0, x12:0, x13:0) :|: c9 = x2:0 + 1 && (x2:0 <= x10:0 - 1 && x11:0 > 1 && x6:0 > 0 && x10:0 > 0 && x:0 >= x7:0 && x7:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x8:0 > 0 && x5:0 + 2 <= x1:0 && x6:0 + 2 <= x1:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 ---------------------------------------- (8) Obligation: Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7, x8, x2, x3, x4) :|: x1 - x2 * x11 <= x2 - 1 && x1 - x2 * x11 >= 0 && x1 - x2 * x8 <= x2 - 1 && x3 + 2 <= x7 && x1 - x2 * x8 >= 0 && x4 + 2 <= x7 && x >= x4 + 2 && x12 > 0 && x >= x3 + 2 && x7 > 0 && x8 - x2 * x13 = 0 && x12 <= x7 && x > 0 && x >= x7 && x1 - x2 * x11 = 0 f1209_0_checkPrime_GE'(x211:0, x212:0, x213:0, x214:0) -> f1029_0_findKthPrime_GE(x214:0, x212:0, x211:0) :|: x214:0 - x213:0 * x225:0 <= x213:0 - 1 && x214:0 - x213:0 * x225:0 >= 0 && x214:0 - 1 >= x213:0 && x214:0 - x213:0 * x225:0 = 0 f1209_0_checkPrime_GE(x138:0, x139:0, x140:0, x141:0) -> f1209_0_checkPrime_GE'(x138:0, x139:0, x140:0, x141:0) :|: x141:0 - 1 >= x140:0 && x141:0 - x140:0 * x152:0 >= 1 f1209_0_checkPrime_GE(x196:0, x197:0, x198:0, x199:0) -> f1209_0_checkPrime_GE'(x196:0, x197:0, x198:0, x199:0) :|: x199:0 - 1 >= x198:0 && x199:0 - x198:0 * x210:0 = 0 f1209_0_checkPrime_GE(x123:0, x124:0, x125:0, x126:0) -> f1209_0_checkPrime_GE'(x123:0, x124:0, x125:0, x126:0) :|: x126:0 - 1 >= x125:0 && x126:0 - x125:0 * x137:0 <= -1 f1029_0_findKthPrime_GE(x108:0, x109:0, x111:0) -> f1209_0_checkPrime_GE(x111:0, x109:0, 2, x108:0 + 1) :|: x111:0 - 1 >= x109:0 && x108:0 > 0 f1209_0_checkPrime_GE'(x153:0, x154:0, x155:0, x156:0) -> f1209_0_checkPrime_GE(x153:0, x154:0, x155:0 + 1, x156:0) :|: x156:0 - x155:0 * x167:0 >= 1 && x156:0 - x155:0 * x167:0 <= x155:0 - 1 && x156:0 - 1 >= x155:0 ---------------------------------------- (9) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (10) Obligation: Rules: f1209_0_checkPrime_GE(x123:0:0, x124:0:0, x125:0:0, x126:0:0) -> f1209_0_checkPrime_GE'(x123:0:0, x124:0:0, x125:0:0, x126:0:0) :|: x126:0:0 - 1 >= x125:0:0 && x126:0:0 - x125:0:0 * x137:0:0 <= -1 f1280_0_getPowerOfKInSource_IntArithmetic'(x:0, x1:0, x2:0, x3:0, x4:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0, x8:0, x2:0, x3:0, x4:0) :|: x:0 >= x7:0 && x1:0 - x2:0 * x11:0 = 0 && x:0 > 0 && x7:0 >= x12:0 && x8:0 - x2:0 * x13:0 = 0 && x7:0 > 0 && x:0 >= x3:0 + 2 && x12:0 > 0 && x:0 >= x4:0 + 2 && x7:0 >= x4:0 + 2 && x1:0 - x2:0 * x8:0 >= 0 && x7:0 >= x3:0 + 2 && x2:0 - 1 >= x1:0 - x2:0 * x8:0 && x1:0 - x2:0 * x11:0 >= 0 && x2:0 - 1 >= x1:0 - x2:0 * x11:0 f1209_0_checkPrime_GE'(x153:0:0, x154:0:0, x155:0:0, x156:0:0) -> f1209_0_checkPrime_GE(x153:0:0, x154:0:0, x155:0:0 + 1, x156:0:0) :|: x156:0:0 - x155:0:0 * x167:0:0 >= 1 && x156:0:0 - x155:0:0 * x167:0:0 <= x155:0:0 - 1 && x156:0:0 - 1 >= x155:0:0 f1209_0_checkPrime_GE(x138:0:0, x139:0:0, x140:0:0, x141:0:0) -> f1209_0_checkPrime_GE'(x138:0:0, x139:0:0, x140:0:0, x141:0:0) :|: x141:0:0 - 1 >= x140:0:0 && x141:0:0 - x140:0:0 * x152:0:0 >= 1 f1209_0_checkPrime_GE(x196:0:0, x197:0:0, x198:0:0, x199:0:0) -> f1209_0_checkPrime_GE'(x196:0:0, x197:0:0, x198:0:0, x199:0:0) :|: x199:0:0 - 1 >= x198:0:0 && x199:0:0 - x198:0:0 * x210:0:0 = 0 f1209_0_checkPrime_GE'(x211:0:0, x212:0:0, x213:0:0, x214:0:0) -> f1209_0_checkPrime_GE(x211:0:0, x212:0:0, 2, x214:0:0 + 1) :|: x212:0:0 <= x211:0:0 - 1 && x214:0:0 - x213:0:0 * x225:0:0 = 0 && x214:0:0 > 0 && x214:0:0 - 1 >= x213:0:0 && x214:0:0 - x213:0:0 * x225:0:0 >= 0 && x214:0:0 - x213:0:0 * x225:0:0 <= x213:0:0 - 1 ---------------------------------------- (11) IRSwTOrderProof (EQUIVALENT) [f1209_0_checkPrime_GE(x, x1, x2, x3)] = -8 + 0*x + 0*x1 + 0*x2 + -1*x3 [f1209_0_checkPrime_GE'(x4, x5, x6, x7)] = -8 + 0*x4 + 0*x5 + 0*x6 + -1*x7 [f1280_0_getPowerOfKInSource_IntArithmetic'(x8, x9, x10, x11, x12)] = -3 + 0*x10 + -1*x11 + 0*x12 + 2*x8 + 0*x9 The following rules are decreasing: f1209_0_checkPrime_GE'(x211:0:0, x212:0:0, x213:0:0, x214:0:0) -> f1209_0_checkPrime_GE(x211:0:0, x212:0:0, 2, x214:0:0 + 1) :|: x212:0:0 <= x211:0:0 - 1 && x214:0:0 - x213:0:0 * x225:0:0 = 0 && x214:0:0 > 0 && x214:0:0 - 1 >= x213:0:0 && x214:0:0 - x213:0:0 * x225:0:0 >= 0 && x214:0:0 - x213:0:0 * x225:0:0 <= x213:0:0 - 1 The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0, x1:0, x2:0, x3:0, x4:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0, x8:0, x2:0, x3:0, x4:0) :|: x:0 >= x7:0 && x1:0 - x2:0 * x11:0 = 0 && x:0 > 0 && x7:0 >= x12:0 && x8:0 - x2:0 * x13:0 = 0 && x7:0 > 0 && x:0 >= x3:0 + 2 && x12:0 > 0 && x:0 >= x4:0 + 2 && x7:0 >= x4:0 + 2 && x1:0 - x2:0 * x8:0 >= 0 && x7:0 >= x3:0 + 2 && x2:0 - 1 >= x1:0 - x2:0 * x8:0 && x1:0 - x2:0 * x11:0 >= 0 && x2:0 - 1 >= x1:0 - x2:0 * x11:0 ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Rules: f1209_0_checkPrime_GE(x123:0:0, x124:0:0, x125:0:0, x126:0:0) -> f1209_0_checkPrime_GE'(x123:0:0, x124:0:0, x125:0:0, x126:0:0) :|: x126:0:0 - 1 >= x125:0:0 && x126:0:0 - x125:0:0 * x137:0:0 <= -1 f1280_0_getPowerOfKInSource_IntArithmetic'(x:0, x1:0, x2:0, x3:0, x4:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0, x8:0, x2:0, x3:0, x4:0) :|: x:0 >= x7:0 && x1:0 - x2:0 * x11:0 = 0 && x:0 > 0 && x7:0 >= x12:0 && x8:0 - x2:0 * x13:0 = 0 && x7:0 > 0 && x:0 >= x3:0 + 2 && x12:0 > 0 && x:0 >= x4:0 + 2 && x7:0 >= x4:0 + 2 && x1:0 - x2:0 * x8:0 >= 0 && x7:0 >= x3:0 + 2 && x2:0 - 1 >= x1:0 - x2:0 * x8:0 && x1:0 - x2:0 * x11:0 >= 0 && x2:0 - 1 >= x1:0 - x2:0 * x11:0 f1209_0_checkPrime_GE'(x153:0:0, x154:0:0, x155:0:0, x156:0:0) -> f1209_0_checkPrime_GE(x153:0:0, x154:0:0, x155:0:0 + 1, x156:0:0) :|: x156:0:0 - x155:0:0 * x167:0:0 >= 1 && x156:0:0 - x155:0:0 * x167:0:0 <= x155:0:0 - 1 && x156:0:0 - 1 >= x155:0:0 f1209_0_checkPrime_GE(x138:0:0, x139:0:0, x140:0:0, x141:0:0) -> f1209_0_checkPrime_GE'(x138:0:0, x139:0:0, x140:0:0, x141:0:0) :|: x141:0:0 - 1 >= x140:0:0 && x141:0:0 - x140:0:0 * x152:0:0 >= 1 f1209_0_checkPrime_GE(x196:0:0, x197:0:0, x198:0:0, x199:0:0) -> f1209_0_checkPrime_GE'(x196:0:0, x197:0:0, x198:0:0, x199:0:0) :|: x199:0:0 - 1 >= x198:0:0 && x199:0:0 - x198:0:0 * x210:0:0 = 0 ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 f1209_0_checkPrime_GE(x123:0:0:0, x124:0:0:0, x125:0:0:0, x126:0:0:0) -> f1209_0_checkPrime_GE(x123:0:0:0, x124:0:0:0, x125:0:0:0 + 1, x126:0:0:0) :|: x126:0:0:0 - x125:0:0:0 * x137:0:0:0 <= -1 && x126:0:0:0 - 1 >= x125:0:0:0 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 <= x125:0:0:0 - 1 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 >= 1 f1209_0_checkPrime_GE(x, x1, x2, x3) -> f1209_0_checkPrime_GE(x, x1, x2 + 1, x3) :|: x3 - x2 * x4 = 0 && x3 - 1 >= x2 && x3 - x2 * x5 <= x2 - 1 && x3 - x2 * x5 >= 1 f1209_0_checkPrime_GE(x6, x7, x8, x9) -> f1209_0_checkPrime_GE(x6, x7, x8 + 1, x9) :|: x9 - x8 * x10 >= 1 && x9 - 1 >= x8 && x9 - x8 * x11 <= x8 - 1 && x9 - x8 * x11 >= 1 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1209_0_checkPrime_GE(x1, x2, x3, x4) -> f1209_0_checkPrime_GE(x3, x4) ---------------------------------------- (17) Obligation: Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 f1209_0_checkPrime_GE(x125:0:0:0, x126:0:0:0) -> f1209_0_checkPrime_GE(x125:0:0:0 + 1, x126:0:0:0) :|: x126:0:0:0 - x125:0:0:0 * x137:0:0:0 <= -1 && x126:0:0:0 - 1 >= x125:0:0:0 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 <= x125:0:0:0 - 1 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 >= 1 f1209_0_checkPrime_GE(x2, x3) -> f1209_0_checkPrime_GE(x2 + 1, x3) :|: x3 - x2 * x4 = 0 && x3 - 1 >= x2 && x3 - x2 * x5 <= x2 - 1 && x3 - x2 * x5 >= 1 f1209_0_checkPrime_GE(x8, x9) -> f1209_0_checkPrime_GE(x8 + 1, x9) :|: x9 - x8 * x10 >= 1 && x9 - 1 >= x8 && x9 - x8 * x11 <= x8 - 1 && x9 - x8 * x11 >= 1 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1280_0_getPowerOfKInSource_IntArithmetic'(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) f1209_0_checkPrime_GE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 f1209_0_checkPrime_GE(x125:0:0:0, x126:0:0:0) -> f1209_0_checkPrime_GE(c, x126:0:0:0) :|: c = x125:0:0:0 + 1 && (x126:0:0:0 - x125:0:0:0 * x137:0:0:0 <= -1 && x126:0:0:0 - 1 >= x125:0:0:0 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 <= x125:0:0:0 - 1 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 >= 1) f1209_0_checkPrime_GE(x2, x3) -> f1209_0_checkPrime_GE(c1, x3) :|: c1 = x2 + 1 && (x3 - x2 * x4 = 0 && x3 - 1 >= x2 && x3 - x2 * x5 <= x2 - 1 && x3 - x2 * x5 >= 1) f1209_0_checkPrime_GE(x8, x9) -> f1209_0_checkPrime_GE(c2, x9) :|: c2 = x8 + 1 && (x9 - x8 * x10 >= 1 && x9 - 1 >= x8 && x9 - x8 * x11 <= x8 - 1 && x9 - x8 * x11 >= 1) Found the following polynomial interpretation: [f1280_0_getPowerOfKInSource_IntArithmetic'(x, x1, x2, x3, x4)] = 0 [f1209_0_checkPrime_GE(x5, x6)] = -x5 + x6 The following rules are decreasing: f1209_0_checkPrime_GE(x125:0:0:0, x126:0:0:0) -> f1209_0_checkPrime_GE(c, x126:0:0:0) :|: c = x125:0:0:0 + 1 && (x126:0:0:0 - x125:0:0:0 * x137:0:0:0 <= -1 && x126:0:0:0 - 1 >= x125:0:0:0 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 <= x125:0:0:0 - 1 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 >= 1) f1209_0_checkPrime_GE(x2, x3) -> f1209_0_checkPrime_GE(c1, x3) :|: c1 = x2 + 1 && (x3 - x2 * x4 = 0 && x3 - 1 >= x2 && x3 - x2 * x5 <= x2 - 1 && x3 - x2 * x5 >= 1) f1209_0_checkPrime_GE(x8, x9) -> f1209_0_checkPrime_GE(c2, x9) :|: c2 = x8 + 1 && (x9 - x8 * x10 >= 1 && x9 - 1 >= x8 && x9 - x8 * x11 <= x8 - 1 && x9 - x8 * x11 >= 1) The following rules are bounded: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 f1209_0_checkPrime_GE(x125:0:0:0, x126:0:0:0) -> f1209_0_checkPrime_GE(c, x126:0:0:0) :|: c = x125:0:0:0 + 1 && (x126:0:0:0 - x125:0:0:0 * x137:0:0:0 <= -1 && x126:0:0:0 - 1 >= x125:0:0:0 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 <= x125:0:0:0 - 1 && x126:0:0:0 - x125:0:0:0 * x167:0:0:0 >= 1) f1209_0_checkPrime_GE(x2, x3) -> f1209_0_checkPrime_GE(c1, x3) :|: c1 = x2 + 1 && (x3 - x2 * x4 = 0 && x3 - 1 >= x2 && x3 - x2 * x5 <= x2 - 1 && x3 - x2 * x5 >= 1) f1209_0_checkPrime_GE(x8, x9) -> f1209_0_checkPrime_GE(c2, x9) :|: c2 = x8 + 1 && (x9 - x8 * x10 >= 1 && x9 - 1 >= x8 && x9 - x8 * x11 <= x8 - 1 && x9 - x8 * x11 >= 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 ---------------------------------------- (19) Obligation: Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 ---------------------------------------- (20) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) Obligation: Termination digraph: Nodes: (1) f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0, x1:0:0, x2:0:0, x3:0:0, x4:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0, x8:0:0, x2:0:0, x3:0:0, x4:0:0) :|: x1:0:0 - x2:0:0 * x11:0:0 >= 0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x11:0:0 && x2:0:0 - 1 >= x1:0:0 - x2:0:0 * x8:0:0 && x7:0:0 >= x3:0:0 + 2 && x1:0:0 - x2:0:0 * x8:0:0 >= 0 && x7:0:0 >= x4:0:0 + 2 && x:0:0 >= x4:0:0 + 2 && x12:0:0 > 0 && x:0:0 >= x3:0:0 + 2 && x7:0:0 > 0 && x8:0:0 - x2:0:0 * x13:0:0 = 0 && x7:0:0 >= x12:0:0 && x:0:0 > 0 && x1:0:0 - x2:0:0 * x11:0:0 = 0 && x:0:0 >= x7:0:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (22) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (23) Obligation: Rules: f1280_0_getPowerOfKInSource_IntArithmetic'(x:0:0:0, x1:0:0:0, x2:0:0:0, x3:0:0:0, x4:0:0:0) -> f1280_0_getPowerOfKInSource_IntArithmetic'(x7:0:0:0, x8:0:0:0, x2:0:0:0, x3:0:0:0, x4:0:0:0) :|: x1:0:0:0 - x2:0:0:0 * x11:0:0:0 = 0 && x:0:0:0 >= x7:0:0:0 && x:0:0:0 > 0 && x7:0:0:0 >= x12:0:0:0 && x8:0:0:0 - x2:0:0:0 * x13:0:0:0 = 0 && x7:0:0:0 > 0 && x:0:0:0 >= x3:0:0:0 + 2 && x12:0:0:0 > 0 && x:0:0:0 >= x4:0:0:0 + 2 && x7:0:0:0 >= x4:0:0:0 + 2 && x1:0:0:0 - x2:0:0:0 * x8:0:0:0 >= 0 && x7:0:0:0 >= x3:0:0:0 + 2 && x2:0:0:0 - 1 >= x1:0:0:0 - x2:0:0:0 * x8:0:0:0 && x2:0:0:0 - 1 >= x1:0:0:0 - x2:0:0:0 * x11:0:0:0 && x1:0:0:0 - x2:0:0:0 * x11:0:0:0 >= 0 ---------------------------------------- (24) Obligation: Rules: f1209_0_checkPrime_GE(x123:0:0, x124:0:0, x125:0:0, x126:0:0) -> f1209_0_checkPrime_GE'(x123:0:0, x124:0:0, x125:0:0, x126:0:0) :|: x126:0:0 - 1 >= x125:0:0 && x126:0:0 - x125:0:0 * x137:0:0 <= -1 f1209_0_checkPrime_GE'(x153:0:0, x154:0:0, x155:0:0, x156:0:0) -> f1209_0_checkPrime_GE(x153:0:0, x154:0:0, x155:0:0 + 1, x156:0:0) :|: x156:0:0 - x155:0:0 * x167:0:0 >= 1 && x156:0:0 - x155:0:0 * x167:0:0 <= x155:0:0 - 1 && x156:0:0 - 1 >= x155:0:0 f1209_0_checkPrime_GE(x138:0:0, x139:0:0, x140:0:0, x141:0:0) -> f1209_0_checkPrime_GE'(x138:0:0, x139:0:0, x140:0:0, x141:0:0) :|: x141:0:0 - 1 >= x140:0:0 && x141:0:0 - x140:0:0 * x152:0:0 >= 1 f1209_0_checkPrime_GE(x196:0:0, x197:0:0, x198:0:0, x199:0:0) -> f1209_0_checkPrime_GE'(x196:0:0, x197:0:0, x198:0:0, x199:0:0) :|: x199:0:0 - 1 >= x198:0:0 && x199:0:0 - x198:0:0 * x210:0:0 = 0 f1209_0_checkPrime_GE'(x211:0:0, x212:0:0, x213:0:0, x214:0:0) -> f1209_0_checkPrime_GE(x211:0:0, x212:0:0, 2, x214:0:0 + 1) :|: x212:0:0 <= x211:0:0 - 1 && x214:0:0 - x213:0:0 * x225:0:0 = 0 && x214:0:0 > 0 && x214:0:0 - 1 >= x213:0:0 && x214:0:0 - x213:0:0 * x225:0:0 >= 0 && x214:0:0 - x213:0:0 * x225:0:0 <= x213:0:0 - 1 ---------------------------------------- (25) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (26) Obligation: Rules: f1209_0_checkPrime_GE(x123:0:0:0, x124:0:0:0, x125:0:0:0, x126:0:0:0) -> f1209_0_checkPrime_GE'(x123:0:0:0, x124:0:0:0, x125:0:0:0, x126:0:0:0) :|: x126:0:0:0 - 1 >= x125:0:0:0 && x126:0:0:0 - x125:0:0:0 * x137:0:0:0 <= -1 f1209_0_checkPrime_GE'(x211:0:0:0, x212:0:0:0, x213:0:0:0, x214:0:0:0) -> f1209_0_checkPrime_GE(x211:0:0:0, x212:0:0:0, 2, x214:0:0:0 + 1) :|: x214:0:0:0 - x213:0:0:0 * x225:0:0:0 >= 0 && x214:0:0:0 - x213:0:0:0 * x225:0:0:0 <= x213:0:0:0 - 1 && x214:0:0:0 - 1 >= x213:0:0:0 && x214:0:0:0 > 0 && x214:0:0:0 - x213:0:0:0 * x225:0:0:0 = 0 && x212:0:0:0 <= x211:0:0:0 - 1 f1209_0_checkPrime_GE'(x153:0:0:0, x154:0:0:0, x155:0:0:0, x156:0:0:0) -> f1209_0_checkPrime_GE(x153:0:0:0, x154:0:0:0, x155:0:0:0 + 1, x156:0:0:0) :|: x156:0:0:0 - x155:0:0:0 * x167:0:0:0 >= 1 && x156:0:0:0 - x155:0:0:0 * x167:0:0:0 <= x155:0:0:0 - 1 && x156:0:0:0 - 1 >= x155:0:0:0 f1209_0_checkPrime_GE(x138:0:0:0, x139:0:0:0, x140:0:0:0, x141:0:0:0) -> f1209_0_checkPrime_GE'(x138:0:0:0, x139:0:0:0, x140:0:0:0, x141:0:0:0) :|: x141:0:0:0 - 1 >= x140:0:0:0 && x141:0:0:0 - x140:0:0:0 * x152:0:0:0 >= 1 f1209_0_checkPrime_GE(x196:0:0:0, x197:0:0:0, x198:0:0:0, x199:0:0:0) -> f1209_0_checkPrime_GE'(x196:0:0:0, x197:0:0:0, x198:0:0:0, x199:0:0:0) :|: x199:0:0:0 - 1 >= x198:0:0:0 && x199:0:0:0 - x198:0:0:0 * x210:0:0:0 = 0