YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 2764 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 4 ms] (7) IRSwT (8) TempFilterProof [SOUND, 21 ms] (9) IntTRS (10) PolynomialOrderProcessor [EQUIVALENT, 8 ms] (11) YES (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 38 ms] (14) IRSwT (15) TempFilterProof [SOUND, 43 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 21 ms] (18) YES (19) IRSwT (20) IntTRSCompressionProof [EQUIVALENT, 5 ms] (21) IRSwT (22) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (23) IRSwT (24) TempFilterProof [SOUND, 32 ms] (25) IntTRS (26) RankingReductionPairProof [EQUIVALENT, 18 ms] (27) YES (28) IRSwT (29) IntTRSCompressionProof [EQUIVALENT, 6 ms] (30) IRSwT (31) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (32) IRSwT (33) TempFilterProof [SOUND, 37 ms] (34) IntTRS (35) RankingReductionPairProof [EQUIVALENT, 17 ms] (36) YES ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8) -> f795_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P, arg8P) :|: 0 = arg8P && 0 = arg7P && 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2 && 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P <= arg1 && arg1P <= arg1 f1_0_main_Load(x, x1, x2, x3, x4, x5, x7, x8) -> f795_0_main_GE(x9, x10, x13, x14, x15, x16, x17, x18) :|: x9 <= x && -1 <= x19 - 1 && x10 <= x && 0 <= x - 1 && 0 <= x9 - 1 && 0 <= x10 - 1 && 1 = x1 && 0 = x13 && 0 = x14 && 1 = x15 && 1 = x16 && 1 = x17 && 0 = x18 f1_0_main_Load(x20, x21, x22, x23, x24, x25, x26, x27) -> f795_0_main_GE(x28, x29, x30, x31, x32, x33, x34, x35) :|: -1 <= x36 - 1 && 1 <= x21 - 1 && 0 <= x36 * x37 && -1 <= x37 - 1 && x28 <= x20 && x29 <= x20 && 0 <= x20 - 1 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 = x30 && x36 * x37 = x31 && x21 = x32 && 2 = x33 && x21 = x34 && x36 * x37 = x35 f795_0_main_GE(x38, x39, x40, x41, x42, x43, x44, x45) -> f795_0_main_GE(x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x53 && x42 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 + 1 = x48 && x41 = x45 && x42 = x44 && 0 <= x47 - 1 && 0 <= x46 - 1 && 0 <= x39 - 1 && 0 <= x38 - 1 && x47 <= x39 && x47 <= x38 && x46 <= x39 && x46 <= x38 && -1 <= x41 - 1 && x42 <= x43 && -1 <= x42 - 1 && x40 <= x41 - 1 f795_0_main_GE(x54, x55, x56, x57, x58, x59, x60, x61) -> f795_0_main_GE(x62, x63, x64, x65, x66, x67, x70, x71) :|: x57 = x71 && x58 = x70 && x59 + 1 = x67 && x58 = x66 && x57 = x65 && x56 + 1 = x64 && x57 = x61 && x58 = x60 && 0 <= x63 - 1 && 0 <= x62 - 1 && 0 <= x55 - 1 && 0 <= x54 - 1 && x63 <= x55 && x63 <= x54 && x62 <= x55 && x62 <= x54 && -1 <= x57 - 1 && x59 <= x58 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x56 <= x57 - 1 f795_0_main_GE(x72, x73, x74, x75, x76, x79, x80, x81) -> f1421_0_sort_GE(x82, x83, x84, x85, x86, x87, x88, x89) :|: x75 = x86 && x75 = x85 && 1 = x84 && x75 = x81 && x76 = x80 && 0 <= x83 - 1 && 0 <= x82 - 1 && 0 <= x73 - 1 && 0 <= x72 - 1 && x83 <= x73 && x83 <= x72 && x82 <= x73 && x82 <= x72 && x75 <= x74 && -1 <= x75 - 1 f1421_0_sort_GE(x90, x91, x92, x93, x94, x95, x96, x97) -> f1421_0_sort_GE(x98, x99, x100, x101, x102, x103, x104, x105) :|: x94 = x102 && x93 = x101 && x92 + 1 = x100 && 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x91 - 1 && 0 <= x90 - 1 && x99 <= x91 && x99 <= x90 && x98 <= x91 && x98 <= x90 && x92 <= x93 - 1 && 0 <= x92 - 1 && 1 <= x93 - 1 && 1 <= x93 - x92 f1421_0_sort_GE(x106, x107, x108, x109, x110, x111, x112, x113) -> f1421_0_sort_GE(x114, x115, x116, x117, x118, x119, x120, x121) :|: x109 = x117 && x108 + 1 = x116 && 0 <= x115 - 1 && 0 <= x114 - 1 && 0 <= x107 - 1 && 0 <= x106 - 1 && x115 <= x107 && x115 <= x106 && x114 <= x107 && x114 <= x106 && x108 <= x109 - 1 && 0 <= x108 - 1 && 1 <= x109 - 1 && 1 <= x109 - x108 f1421_0_sort_GE(x122, x123, x124, x125, x126, x127, x128, x129) -> f1445_0_aux_LT(x130, x131, x132, x133, x134, x135, x136, x137) :|: x126 = x135 && x125 - x124 = x134 && 0 = x133 && 0 = x131 && 0 = x130 && 0 <= x132 - 1 && 0 <= x123 - 1 && 0 <= x122 - 1 && x132 <= x123 && x132 <= x122 && x124 <= x125 - 1 && 0 <= x124 - 1 && 1 <= x125 - 1 && 1 <= x125 - x124 f1445_0_aux_LT(x138, x139, x140, x141, x142, x143, x144, x145) -> f1611_0_aux_InvokeMethod(x146, x147, x148, x149, x150, x151, x152, x153) :|: -1 <= x139 - 1 && x139 + 1 <= x143 - 1 && x139 <= x142 - 1 && x154 <= x155 && x149 <= x140 && 0 <= x140 - 1 && 0 <= x149 - 1 && x139 = x141 && x138 = x146 && x139 + 1 = x147 && x142 = x148 && x143 = x151 f1445_0_aux_LT(x156, x157, x158, x159, x160, x161, x162, x163) -> f1611_0_aux_InvokeMethod(x164, x165, x166, x167, x168, x169, x170, x171) :|: -1 <= x157 - 1 && x157 + 1 <= x161 - 1 && x157 <= x160 - 1 && x172 <= x173 - 1 && x167 <= x158 && 0 <= x158 - 1 && 0 <= x167 - 1 && x157 = x159 && x156 = x164 && x157 + 1 = x165 && x160 = x166 && x161 = x169 f1611_0_aux_InvokeMethod(x174, x175, x176, x177, x178, x179, x180, x181) -> f1445_0_aux_LT(x182, x183, x184, x185, x186, x187, x188, x189) :|: x179 = x187 && x176 = x186 && x175 = x185 && x175 = x183 && x175 = x182 && 0 <= x184 - 1 && 0 <= x177 - 1 && x184 <= x177 && x174 <= x176 && x175 <= x176 && 0 <= x175 - 1 && 0 <= x176 - 1 __init(x190, x191, x192, x193, x194, x195, x196, x197) -> f1_0_main_Load(x198, x199, x200, x201, x202, x203, x204, x205) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8) ---------------------------------------- (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, arg8) -> f795_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P, arg8P) :|: 0 = arg8P && 0 = arg7P && 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2 && 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P <= arg1 && arg1P <= arg1 f1_0_main_Load(x, x1, x2, x3, x4, x5, x7, x8) -> f795_0_main_GE(x9, x10, x13, x14, x15, x16, x17, x18) :|: x9 <= x && -1 <= x19 - 1 && x10 <= x && 0 <= x - 1 && 0 <= x9 - 1 && 0 <= x10 - 1 && 1 = x1 && 0 = x13 && 0 = x14 && 1 = x15 && 1 = x16 && 1 = x17 && 0 = x18 f1_0_main_Load(x20, x21, x22, x23, x24, x25, x26, x27) -> f795_0_main_GE(x28, x29, x30, x31, x32, x33, x34, x35) :|: -1 <= x36 - 1 && 1 <= x21 - 1 && 0 <= x36 * x37 && -1 <= x37 - 1 && x28 <= x20 && x29 <= x20 && 0 <= x20 - 1 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 = x30 && x36 * x37 = x31 && x21 = x32 && 2 = x33 && x21 = x34 && x36 * x37 = x35 f795_0_main_GE(x38, x39, x40, x41, x42, x43, x44, x45) -> f795_0_main_GE(x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x53 && x42 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 + 1 = x48 && x41 = x45 && x42 = x44 && 0 <= x47 - 1 && 0 <= x46 - 1 && 0 <= x39 - 1 && 0 <= x38 - 1 && x47 <= x39 && x47 <= x38 && x46 <= x39 && x46 <= x38 && -1 <= x41 - 1 && x42 <= x43 && -1 <= x42 - 1 && x40 <= x41 - 1 f795_0_main_GE(x54, x55, x56, x57, x58, x59, x60, x61) -> f795_0_main_GE(x62, x63, x64, x65, x66, x67, x70, x71) :|: x57 = x71 && x58 = x70 && x59 + 1 = x67 && x58 = x66 && x57 = x65 && x56 + 1 = x64 && x57 = x61 && x58 = x60 && 0 <= x63 - 1 && 0 <= x62 - 1 && 0 <= x55 - 1 && 0 <= x54 - 1 && x63 <= x55 && x63 <= x54 && x62 <= x55 && x62 <= x54 && -1 <= x57 - 1 && x59 <= x58 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x56 <= x57 - 1 f795_0_main_GE(x72, x73, x74, x75, x76, x79, x80, x81) -> f1421_0_sort_GE(x82, x83, x84, x85, x86, x87, x88, x89) :|: x75 = x86 && x75 = x85 && 1 = x84 && x75 = x81 && x76 = x80 && 0 <= x83 - 1 && 0 <= x82 - 1 && 0 <= x73 - 1 && 0 <= x72 - 1 && x83 <= x73 && x83 <= x72 && x82 <= x73 && x82 <= x72 && x75 <= x74 && -1 <= x75 - 1 f1421_0_sort_GE(x90, x91, x92, x93, x94, x95, x96, x97) -> f1421_0_sort_GE(x98, x99, x100, x101, x102, x103, x104, x105) :|: x94 = x102 && x93 = x101 && x92 + 1 = x100 && 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x91 - 1 && 0 <= x90 - 1 && x99 <= x91 && x99 <= x90 && x98 <= x91 && x98 <= x90 && x92 <= x93 - 1 && 0 <= x92 - 1 && 1 <= x93 - 1 && 1 <= x93 - x92 f1421_0_sort_GE(x106, x107, x108, x109, x110, x111, x112, x113) -> f1421_0_sort_GE(x114, x115, x116, x117, x118, x119, x120, x121) :|: x109 = x117 && x108 + 1 = x116 && 0 <= x115 - 1 && 0 <= x114 - 1 && 0 <= x107 - 1 && 0 <= x106 - 1 && x115 <= x107 && x115 <= x106 && x114 <= x107 && x114 <= x106 && x108 <= x109 - 1 && 0 <= x108 - 1 && 1 <= x109 - 1 && 1 <= x109 - x108 f1421_0_sort_GE(x122, x123, x124, x125, x126, x127, x128, x129) -> f1445_0_aux_LT(x130, x131, x132, x133, x134, x135, x136, x137) :|: x126 = x135 && x125 - x124 = x134 && 0 = x133 && 0 = x131 && 0 = x130 && 0 <= x132 - 1 && 0 <= x123 - 1 && 0 <= x122 - 1 && x132 <= x123 && x132 <= x122 && x124 <= x125 - 1 && 0 <= x124 - 1 && 1 <= x125 - 1 && 1 <= x125 - x124 f1445_0_aux_LT(x138, x139, x140, x141, x142, x143, x144, x145) -> f1611_0_aux_InvokeMethod(x146, x147, x148, x149, x150, x151, x152, x153) :|: -1 <= x139 - 1 && x139 + 1 <= x143 - 1 && x139 <= x142 - 1 && x154 <= x155 && x149 <= x140 && 0 <= x140 - 1 && 0 <= x149 - 1 && x139 = x141 && x138 = x146 && x139 + 1 = x147 && x142 = x148 && x143 = x151 f1445_0_aux_LT(x156, x157, x158, x159, x160, x161, x162, x163) -> f1611_0_aux_InvokeMethod(x164, x165, x166, x167, x168, x169, x170, x171) :|: -1 <= x157 - 1 && x157 + 1 <= x161 - 1 && x157 <= x160 - 1 && x172 <= x173 - 1 && x167 <= x158 && 0 <= x158 - 1 && 0 <= x167 - 1 && x157 = x159 && x156 = x164 && x157 + 1 = x165 && x160 = x166 && x161 = x169 f1611_0_aux_InvokeMethod(x174, x175, x176, x177, x178, x179, x180, x181) -> f1445_0_aux_LT(x182, x183, x184, x185, x186, x187, x188, x189) :|: x179 = x187 && x176 = x186 && x175 = x185 && x175 = x183 && x175 = x182 && 0 <= x184 - 1 && 0 <= x177 - 1 && x184 <= x177 && x174 <= x176 && x175 <= x176 && 0 <= x175 - 1 && 0 <= x176 - 1 __init(x190, x191, x192, x193, x194, x195, x196, x197) -> f1_0_main_Load(x198, x199, x200, x201, x202, x203, x204, x205) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8) -> f795_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P, arg8P) :|: 0 = arg8P && 0 = arg7P && 0 = arg6P && 0 = arg5P && 0 = arg4P && 0 = arg3P && 0 = arg2 && 0 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P <= arg1 && arg1P <= arg1 (2) f1_0_main_Load(x, x1, x2, x3, x4, x5, x7, x8) -> f795_0_main_GE(x9, x10, x13, x14, x15, x16, x17, x18) :|: x9 <= x && -1 <= x19 - 1 && x10 <= x && 0 <= x - 1 && 0 <= x9 - 1 && 0 <= x10 - 1 && 1 = x1 && 0 = x13 && 0 = x14 && 1 = x15 && 1 = x16 && 1 = x17 && 0 = x18 (3) f1_0_main_Load(x20, x21, x22, x23, x24, x25, x26, x27) -> f795_0_main_GE(x28, x29, x30, x31, x32, x33, x34, x35) :|: -1 <= x36 - 1 && 1 <= x21 - 1 && 0 <= x36 * x37 && -1 <= x37 - 1 && x28 <= x20 && x29 <= x20 && 0 <= x20 - 1 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 = x30 && x36 * x37 = x31 && x21 = x32 && 2 = x33 && x21 = x34 && x36 * x37 = x35 (4) f795_0_main_GE(x38, x39, x40, x41, x42, x43, x44, x45) -> f795_0_main_GE(x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x53 && x42 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 + 1 = x48 && x41 = x45 && x42 = x44 && 0 <= x47 - 1 && 0 <= x46 - 1 && 0 <= x39 - 1 && 0 <= x38 - 1 && x47 <= x39 && x47 <= x38 && x46 <= x39 && x46 <= x38 && -1 <= x41 - 1 && x42 <= x43 && -1 <= x42 - 1 && x40 <= x41 - 1 (5) f795_0_main_GE(x54, x55, x56, x57, x58, x59, x60, x61) -> f795_0_main_GE(x62, x63, x64, x65, x66, x67, x70, x71) :|: x57 = x71 && x58 = x70 && x59 + 1 = x67 && x58 = x66 && x57 = x65 && x56 + 1 = x64 && x57 = x61 && x58 = x60 && 0 <= x63 - 1 && 0 <= x62 - 1 && 0 <= x55 - 1 && 0 <= x54 - 1 && x63 <= x55 && x63 <= x54 && x62 <= x55 && x62 <= x54 && -1 <= x57 - 1 && x59 <= x58 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x56 <= x57 - 1 (6) f795_0_main_GE(x72, x73, x74, x75, x76, x79, x80, x81) -> f1421_0_sort_GE(x82, x83, x84, x85, x86, x87, x88, x89) :|: x75 = x86 && x75 = x85 && 1 = x84 && x75 = x81 && x76 = x80 && 0 <= x83 - 1 && 0 <= x82 - 1 && 0 <= x73 - 1 && 0 <= x72 - 1 && x83 <= x73 && x83 <= x72 && x82 <= x73 && x82 <= x72 && x75 <= x74 && -1 <= x75 - 1 (7) f1421_0_sort_GE(x90, x91, x92, x93, x94, x95, x96, x97) -> f1421_0_sort_GE(x98, x99, x100, x101, x102, x103, x104, x105) :|: x94 = x102 && x93 = x101 && x92 + 1 = x100 && 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x91 - 1 && 0 <= x90 - 1 && x99 <= x91 && x99 <= x90 && x98 <= x91 && x98 <= x90 && x92 <= x93 - 1 && 0 <= x92 - 1 && 1 <= x93 - 1 && 1 <= x93 - x92 (8) f1421_0_sort_GE(x106, x107, x108, x109, x110, x111, x112, x113) -> f1421_0_sort_GE(x114, x115, x116, x117, x118, x119, x120, x121) :|: x109 = x117 && x108 + 1 = x116 && 0 <= x115 - 1 && 0 <= x114 - 1 && 0 <= x107 - 1 && 0 <= x106 - 1 && x115 <= x107 && x115 <= x106 && x114 <= x107 && x114 <= x106 && x108 <= x109 - 1 && 0 <= x108 - 1 && 1 <= x109 - 1 && 1 <= x109 - x108 (9) f1421_0_sort_GE(x122, x123, x124, x125, x126, x127, x128, x129) -> f1445_0_aux_LT(x130, x131, x132, x133, x134, x135, x136, x137) :|: x126 = x135 && x125 - x124 = x134 && 0 = x133 && 0 = x131 && 0 = x130 && 0 <= x132 - 1 && 0 <= x123 - 1 && 0 <= x122 - 1 && x132 <= x123 && x132 <= x122 && x124 <= x125 - 1 && 0 <= x124 - 1 && 1 <= x125 - 1 && 1 <= x125 - x124 (10) f1445_0_aux_LT(x138, x139, x140, x141, x142, x143, x144, x145) -> f1611_0_aux_InvokeMethod(x146, x147, x148, x149, x150, x151, x152, x153) :|: -1 <= x139 - 1 && x139 + 1 <= x143 - 1 && x139 <= x142 - 1 && x154 <= x155 && x149 <= x140 && 0 <= x140 - 1 && 0 <= x149 - 1 && x139 = x141 && x138 = x146 && x139 + 1 = x147 && x142 = x148 && x143 = x151 (11) f1445_0_aux_LT(x156, x157, x158, x159, x160, x161, x162, x163) -> f1611_0_aux_InvokeMethod(x164, x165, x166, x167, x168, x169, x170, x171) :|: -1 <= x157 - 1 && x157 + 1 <= x161 - 1 && x157 <= x160 - 1 && x172 <= x173 - 1 && x167 <= x158 && 0 <= x158 - 1 && 0 <= x167 - 1 && x157 = x159 && x156 = x164 && x157 + 1 = x165 && x160 = x166 && x161 = x169 (12) f1611_0_aux_InvokeMethod(x174, x175, x176, x177, x178, x179, x180, x181) -> f1445_0_aux_LT(x182, x183, x184, x185, x186, x187, x188, x189) :|: x179 = x187 && x176 = x186 && x175 = x185 && x175 = x183 && x175 = x182 && 0 <= x184 - 1 && 0 <= x177 - 1 && x184 <= x177 && x174 <= x176 && x175 <= x176 && 0 <= x175 - 1 && 0 <= x176 - 1 (13) __init(x190, x191, x192, x193, x194, x195, x196, x197) -> f1_0_main_Load(x198, x199, x200, x201, x202, x203, x204, x205) :|: 0 <= 0 Arcs: (1) -> (6) (2) -> (6) (3) -> (4), (5), (6) (4) -> (4), (6) (5) -> (4), (5), (6) (6) -> (7), (8), (9) (7) -> (7), (8), (9) (8) -> (7), (8), (9) (9) -> (10), (11) (10) -> (12) (11) -> (12) (12) -> (10), (11) (13) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f795_0_main_GE(x54, x55, x56, x57, x58, x59, x60, x61) -> f795_0_main_GE(x62, x63, x64, x65, x66, x67, x70, x71) :|: x57 = x71 && x58 = x70 && x59 + 1 = x67 && x58 = x66 && x57 = x65 && x56 + 1 = x64 && x57 = x61 && x58 = x60 && 0 <= x63 - 1 && 0 <= x62 - 1 && 0 <= x55 - 1 && 0 <= x54 - 1 && x63 <= x55 && x63 <= x54 && x62 <= x55 && x62 <= x54 && -1 <= x57 - 1 && x59 <= x58 - 1 && -1 <= x59 - 1 && -1 <= x58 - 1 && x56 <= x57 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f795_0_main_GE(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0, x58:0, x57:0) -> f795_0_main_GE(x62:0, x63:0, x56:0 + 1, x57:0, x58:0, x59:0 + 1, x58:0, x57:0) :|: x58:0 > -1 && x57:0 - 1 >= x56:0 && x59:0 > -1 && x59:0 <= x58:0 - 1 && x57:0 > -1 && x62:0 <= x54:0 && x62:0 <= x55:0 && x63:0 <= x54:0 && x63:0 <= x55:0 && x54:0 > 0 && x55:0 > 0 && x63:0 > 0 && x62:0 > 0 ---------------------------------------- (8) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f795_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (9) Obligation: Rules: f795_0_main_GE(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0, x58:0, x57:0) -> f795_0_main_GE(x62:0, x63:0, c, x57:0, x58:0, c1, x58:0, x57:0) :|: c1 = x59:0 + 1 && c = x56:0 + 1 && (x58:0 > -1 && x57:0 - 1 >= x56:0 && x59:0 > -1 && x59:0 <= x58:0 - 1 && x57:0 > -1 && x62:0 <= x54:0 && x62:0 <= x55:0 && x63:0 <= x54:0 && x63:0 <= x55:0 && x54:0 > 0 && x55:0 > 0 && x63:0 > 0 && x62:0 > 0) ---------------------------------------- (10) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f795_0_main_GE(x, x1, x2, x3, x4, x5, x6, x7)] = x4 - x5 The following rules are decreasing: f795_0_main_GE(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0, x58:0, x57:0) -> f795_0_main_GE(x62:0, x63:0, c, x57:0, x58:0, c1, x58:0, x57:0) :|: c1 = x59:0 + 1 && c = x56:0 + 1 && (x58:0 > -1 && x57:0 - 1 >= x56:0 && x59:0 > -1 && x59:0 <= x58:0 - 1 && x57:0 > -1 && x62:0 <= x54:0 && x62:0 <= x55:0 && x63:0 <= x54:0 && x63:0 <= x55:0 && x54:0 > 0 && x55:0 > 0 && x63:0 > 0 && x62:0 > 0) The following rules are bounded: f795_0_main_GE(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0, x58:0, x57:0) -> f795_0_main_GE(x62:0, x63:0, c, x57:0, x58:0, c1, x58:0, x57:0) :|: c1 = x59:0 + 1 && c = x56:0 + 1 && (x58:0 > -1 && x57:0 - 1 >= x56:0 && x59:0 > -1 && x59:0 <= x58:0 - 1 && x57:0 > -1 && x62:0 <= x54:0 && x62:0 <= x55:0 && x63:0 <= x54:0 && x63:0 <= x55:0 && x54:0 > 0 && x55:0 > 0 && x63:0 > 0 && x62:0 > 0) ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f795_0_main_GE(x38, x39, x40, x41, x42, x43, x44, x45) -> f795_0_main_GE(x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x53 && x42 = x52 && x43 = x51 && x42 = x50 && x41 = x49 && x40 + 1 = x48 && x41 = x45 && x42 = x44 && 0 <= x47 - 1 && 0 <= x46 - 1 && 0 <= x39 - 1 && 0 <= x38 - 1 && x47 <= x39 && x47 <= x38 && x46 <= x39 && x46 <= x38 && -1 <= x41 - 1 && x42 <= x43 && -1 <= x42 - 1 && x40 <= x41 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f795_0_main_GE(x38:0, x39:0, x40:0, x41:0, x42:0, x43:0, x42:0, x41:0) -> f795_0_main_GE(x46:0, x47:0, x40:0 + 1, x41:0, x42:0, x43:0, x42:0, x41:0) :|: x42:0 > -1 && x41:0 - 1 >= x40:0 && x43:0 >= x42:0 && x41:0 > -1 && x46:0 <= x38:0 && x46:0 <= x39:0 && x47:0 <= x38:0 && x47:0 <= x39:0 && x38:0 > 0 && x39:0 > 0 && x47:0 > 0 && x46:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f795_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f795_0_main_GE(x38:0, x39:0, x40:0, x41:0, x42:0, x43:0, x42:0, x41:0) -> f795_0_main_GE(x46:0, x47:0, c, x41:0, x42:0, x43:0, x42:0, x41:0) :|: c = x40:0 + 1 && (x42:0 > -1 && x41:0 - 1 >= x40:0 && x43:0 >= x42:0 && x41:0 > -1 && x46:0 <= x38:0 && x46:0 <= x39:0 && x47:0 <= x38:0 && x47:0 <= x39:0 && x38:0 > 0 && x39:0 > 0 && x47:0 > 0 && x46:0 > 0) ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f795_0_main_GE ] = f795_0_main_GE_8 + -1*f795_0_main_GE_3 The following rules are decreasing: f795_0_main_GE(x38:0, x39:0, x40:0, x41:0, x42:0, x43:0, x42:0, x41:0) -> f795_0_main_GE(x46:0, x47:0, c, x41:0, x42:0, x43:0, x42:0, x41:0) :|: c = x40:0 + 1 && (x42:0 > -1 && x41:0 - 1 >= x40:0 && x43:0 >= x42:0 && x41:0 > -1 && x46:0 <= x38:0 && x46:0 <= x39:0 && x47:0 <= x38:0 && x47:0 <= x39:0 && x38:0 > 0 && x39:0 > 0 && x47:0 > 0 && x46:0 > 0) The following rules are bounded: f795_0_main_GE(x38:0, x39:0, x40:0, x41:0, x42:0, x43:0, x42:0, x41:0) -> f795_0_main_GE(x46:0, x47:0, c, x41:0, x42:0, x43:0, x42:0, x41:0) :|: c = x40:0 + 1 && (x42:0 > -1 && x41:0 - 1 >= x40:0 && x43:0 >= x42:0 && x41:0 > -1 && x46:0 <= x38:0 && x46:0 <= x39:0 && x47:0 <= x38:0 && x47:0 <= x39:0 && x38:0 > 0 && x39:0 > 0 && x47:0 > 0 && x46:0 > 0) ---------------------------------------- (18) YES ---------------------------------------- (19) Obligation: Termination digraph: Nodes: (1) f1421_0_sort_GE(x90, x91, x92, x93, x94, x95, x96, x97) -> f1421_0_sort_GE(x98, x99, x100, x101, x102, x103, x104, x105) :|: x94 = x102 && x93 = x101 && x92 + 1 = x100 && 0 <= x99 - 1 && 0 <= x98 - 1 && 0 <= x91 - 1 && 0 <= x90 - 1 && x99 <= x91 && x99 <= x90 && x98 <= x91 && x98 <= x90 && x92 <= x93 - 1 && 0 <= x92 - 1 && 1 <= x93 - 1 && 1 <= x93 - x92 (2) f1421_0_sort_GE(x106, x107, x108, x109, x110, x111, x112, x113) -> f1421_0_sort_GE(x114, x115, x116, x117, x118, x119, x120, x121) :|: x109 = x117 && x108 + 1 = x116 && 0 <= x115 - 1 && 0 <= x114 - 1 && 0 <= x107 - 1 && 0 <= x106 - 1 && x115 <= x107 && x115 <= x106 && x114 <= x107 && x114 <= x106 && x108 <= x109 - 1 && 0 <= x108 - 1 && 1 <= x109 - 1 && 1 <= x109 - x108 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (20) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (21) Obligation: Rules: f1421_0_sort_GE(x90:0, x91:0, x92:0, x101:0, x102:0, x95:0, x96:0, x97:0) -> f1421_0_sort_GE(x98:0, x99:0, x92:0 + 1, x101:0, x102:0, x103:0, x104:0, x105:0) :|: x101:0 > 1 && x101:0 - x92:0 >= 1 && x92:0 > 0 && x92:0 <= x101:0 - 1 && x98:0 <= x90:0 && x98:0 <= x91:0 && x99:0 <= x90:0 && x99:0 <= x91:0 && x90:0 > 0 && x91:0 > 0 && x99:0 > 0 && x98:0 > 0 f1421_0_sort_GE(x106:0, x107:0, x108:0, x109:0, x110:0, x111:0, x112:0, x113:0) -> f1421_0_sort_GE(x114:0, x115:0, x108:0 + 1, x109:0, x118:0, x119:0, x120:0, x121:0) :|: x109:0 > 1 && x109:0 - x108:0 >= 1 && x108:0 > 0 && x109:0 - 1 >= x108:0 && x114:0 <= x106:0 && x114:0 <= x107:0 && x115:0 <= x106:0 && x115:0 <= x107:0 && x106:0 > 0 && x107:0 > 0 && x115:0 > 0 && x114:0 > 0 ---------------------------------------- (22) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1421_0_sort_GE(x1, x2, x3, x4, x5, x6, x7, x8) -> f1421_0_sort_GE(x1, x2, x3, x4) ---------------------------------------- (23) Obligation: Rules: f1421_0_sort_GE(x90:0, x91:0, x92:0, x101:0) -> f1421_0_sort_GE(x98:0, x99:0, x92:0 + 1, x101:0) :|: x101:0 > 1 && x101:0 - x92:0 >= 1 && x92:0 > 0 && x92:0 <= x101:0 - 1 && x98:0 <= x90:0 && x98:0 <= x91:0 && x99:0 <= x90:0 && x99:0 <= x91:0 && x90:0 > 0 && x91:0 > 0 && x99:0 > 0 && x98:0 > 0 f1421_0_sort_GE(x106:0, x107:0, x108:0, x109:0) -> f1421_0_sort_GE(x114:0, x115:0, x108:0 + 1, x109:0) :|: x109:0 > 1 && x109:0 - x108:0 >= 1 && x108:0 > 0 && x109:0 - 1 >= x108:0 && x114:0 <= x106:0 && x114:0 <= x107:0 && x115:0 <= x106:0 && x115:0 <= x107:0 && x106:0 > 0 && x107:0 > 0 && x115:0 > 0 && x114:0 > 0 ---------------------------------------- (24) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1421_0_sort_GE(INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (25) Obligation: Rules: f1421_0_sort_GE(x90:0, x91:0, x92:0, x101:0) -> f1421_0_sort_GE(x98:0, x99:0, c, x101:0) :|: c = x92:0 + 1 && (x101:0 > 1 && x101:0 - x92:0 >= 1 && x92:0 > 0 && x92:0 <= x101:0 - 1 && x98:0 <= x90:0 && x98:0 <= x91:0 && x99:0 <= x90:0 && x99:0 <= x91:0 && x90:0 > 0 && x91:0 > 0 && x99:0 > 0 && x98:0 > 0) f1421_0_sort_GE(x106:0, x107:0, x108:0, x109:0) -> f1421_0_sort_GE(x114:0, x115:0, c1, x109:0) :|: c1 = x108:0 + 1 && (x109:0 > 1 && x109:0 - x108:0 >= 1 && x108:0 > 0 && x109:0 - 1 >= x108:0 && x114:0 <= x106:0 && x114:0 <= x107:0 && x115:0 <= x106:0 && x115:0 <= x107:0 && x106:0 > 0 && x107:0 > 0 && x115:0 > 0 && x114:0 > 0) ---------------------------------------- (26) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1421_0_sort_GE ] = f1421_0_sort_GE_4 + -1*f1421_0_sort_GE_3 The following rules are decreasing: f1421_0_sort_GE(x90:0, x91:0, x92:0, x101:0) -> f1421_0_sort_GE(x98:0, x99:0, c, x101:0) :|: c = x92:0 + 1 && (x101:0 > 1 && x101:0 - x92:0 >= 1 && x92:0 > 0 && x92:0 <= x101:0 - 1 && x98:0 <= x90:0 && x98:0 <= x91:0 && x99:0 <= x90:0 && x99:0 <= x91:0 && x90:0 > 0 && x91:0 > 0 && x99:0 > 0 && x98:0 > 0) f1421_0_sort_GE(x106:0, x107:0, x108:0, x109:0) -> f1421_0_sort_GE(x114:0, x115:0, c1, x109:0) :|: c1 = x108:0 + 1 && (x109:0 > 1 && x109:0 - x108:0 >= 1 && x108:0 > 0 && x109:0 - 1 >= x108:0 && x114:0 <= x106:0 && x114:0 <= x107:0 && x115:0 <= x106:0 && x115:0 <= x107:0 && x106:0 > 0 && x107:0 > 0 && x115:0 > 0 && x114:0 > 0) The following rules are bounded: f1421_0_sort_GE(x90:0, x91:0, x92:0, x101:0) -> f1421_0_sort_GE(x98:0, x99:0, c, x101:0) :|: c = x92:0 + 1 && (x101:0 > 1 && x101:0 - x92:0 >= 1 && x92:0 > 0 && x92:0 <= x101:0 - 1 && x98:0 <= x90:0 && x98:0 <= x91:0 && x99:0 <= x90:0 && x99:0 <= x91:0 && x90:0 > 0 && x91:0 > 0 && x99:0 > 0 && x98:0 > 0) f1421_0_sort_GE(x106:0, x107:0, x108:0, x109:0) -> f1421_0_sort_GE(x114:0, x115:0, c1, x109:0) :|: c1 = x108:0 + 1 && (x109:0 > 1 && x109:0 - x108:0 >= 1 && x108:0 > 0 && x109:0 - 1 >= x108:0 && x114:0 <= x106:0 && x114:0 <= x107:0 && x115:0 <= x106:0 && x115:0 <= x107:0 && x106:0 > 0 && x107:0 > 0 && x115:0 > 0 && x114:0 > 0) ---------------------------------------- (27) YES ---------------------------------------- (28) Obligation: Termination digraph: Nodes: (1) f1445_0_aux_LT(x138, x139, x140, x141, x142, x143, x144, x145) -> f1611_0_aux_InvokeMethod(x146, x147, x148, x149, x150, x151, x152, x153) :|: -1 <= x139 - 1 && x139 + 1 <= x143 - 1 && x139 <= x142 - 1 && x154 <= x155 && x149 <= x140 && 0 <= x140 - 1 && 0 <= x149 - 1 && x139 = x141 && x138 = x146 && x139 + 1 = x147 && x142 = x148 && x143 = x151 (2) f1611_0_aux_InvokeMethod(x174, x175, x176, x177, x178, x179, x180, x181) -> f1445_0_aux_LT(x182, x183, x184, x185, x186, x187, x188, x189) :|: x179 = x187 && x176 = x186 && x175 = x185 && x175 = x183 && x175 = x182 && 0 <= x184 - 1 && 0 <= x177 - 1 && x184 <= x177 && x174 <= x176 && x175 <= x176 && 0 <= x175 - 1 && 0 <= x176 - 1 (3) f1445_0_aux_LT(x156, x157, x158, x159, x160, x161, x162, x163) -> f1611_0_aux_InvokeMethod(x164, x165, x166, x167, x168, x169, x170, x171) :|: -1 <= x157 - 1 && x157 + 1 <= x161 - 1 && x157 <= x160 - 1 && x172 <= x173 - 1 && x167 <= x158 && 0 <= x158 - 1 && 0 <= x167 - 1 && x157 = x159 && x156 = x164 && x157 + 1 = x165 && x160 = x166 && x161 = x169 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (29) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (30) Obligation: Rules: f1445_0_aux_LT(x138:0, x139:0, x140:0, x139:0, x142:0, x143:0, x144:0, x145:0) -> f1445_0_aux_LT(x139:0 + 1, x139:0 + 1, x184:0, x139:0 + 1, x142:0, x143:0, x188:0, x189:0) :|: x142:0 > 0 && x142:0 >= x139:0 + 1 && x142:0 >= x138:0 && x184:0 <= x149:0 && x149:0 > 0 && x140:0 > 0 && x184:0 > 0 && x149:0 <= x140:0 && x155:0 >= x154:0 && x142:0 - 1 >= x139:0 && x143:0 - 1 >= x139:0 + 1 && x139:0 > -1 f1445_0_aux_LT(x, x1, x2, x1, x3, x4, x5, x6) -> f1445_0_aux_LT(x1 + 1, x1 + 1, x7, x1 + 1, x3, x4, x8, x9) :|: x3 > 0 && x3 >= x1 + 1 && x3 >= x && x7 <= x10 && x10 > 0 && x2 > 0 && x7 > 0 && x10 <= x2 && x11 - 1 >= x12 && x3 - 1 >= x1 && x4 - 1 >= x1 + 1 && x1 > -1 ---------------------------------------- (31) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1445_0_aux_LT(x1, x2, x3, x4, x5, x6, x7, x8) -> f1445_0_aux_LT(x1, x2, x3, x4, x5, x6) ---------------------------------------- (32) Obligation: Rules: f1445_0_aux_LT(x138:0, x139:0, x140:0, x139:0, x142:0, x143:0) -> f1445_0_aux_LT(x139:0 + 1, x139:0 + 1, x184:0, x139:0 + 1, x142:0, x143:0) :|: x142:0 > 0 && x142:0 >= x139:0 + 1 && x142:0 >= x138:0 && x184:0 <= x149:0 && x149:0 > 0 && x140:0 > 0 && x184:0 > 0 && x149:0 <= x140:0 && x155:0 >= x154:0 && x142:0 - 1 >= x139:0 && x143:0 - 1 >= x139:0 + 1 && x139:0 > -1 f1445_0_aux_LT(x, x1, x2, x1, x3, x4) -> f1445_0_aux_LT(x1 + 1, x1 + 1, x7, x1 + 1, x3, x4) :|: x3 > 0 && x3 >= x1 + 1 && x3 >= x && x7 <= x10 && x10 > 0 && x2 > 0 && x7 > 0 && x10 <= x2 && x11 - 1 >= x12 && x3 - 1 >= x1 && x4 - 1 >= x1 + 1 && x1 > -1 ---------------------------------------- (33) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1445_0_aux_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (34) Obligation: Rules: f1445_0_aux_LT(x138:0, x139:0, x140:0, x139:0, x142:0, x143:0) -> f1445_0_aux_LT(c, c1, x184:0, c2, x142:0, x143:0) :|: c2 = x139:0 + 1 && (c1 = x139:0 + 1 && c = x139:0 + 1) && (x142:0 > 0 && x142:0 >= x139:0 + 1 && x142:0 >= x138:0 && x184:0 <= x149:0 && x149:0 > 0 && x140:0 > 0 && x184:0 > 0 && x149:0 <= x140:0 && x155:0 >= x154:0 && x142:0 - 1 >= x139:0 && x143:0 - 1 >= x139:0 + 1 && x139:0 > -1) f1445_0_aux_LT(x, x1, x2, x1, x3, x4) -> f1445_0_aux_LT(c3, c4, x7, c5, x3, x4) :|: c5 = x1 + 1 && (c4 = x1 + 1 && c3 = x1 + 1) && (x3 > 0 && x3 >= x1 + 1 && x3 >= x && x7 <= x10 && x10 > 0 && x2 > 0 && x7 > 0 && x10 <= x2 && x11 - 1 >= x12 && x3 - 1 >= x1 && x4 - 1 >= x1 + 1 && x1 > -1) ---------------------------------------- (35) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1445_0_aux_LT ] = f1445_0_aux_LT_5 + -1*f1445_0_aux_LT_4 The following rules are decreasing: f1445_0_aux_LT(x138:0, x139:0, x140:0, x139:0, x142:0, x143:0) -> f1445_0_aux_LT(c, c1, x184:0, c2, x142:0, x143:0) :|: c2 = x139:0 + 1 && (c1 = x139:0 + 1 && c = x139:0 + 1) && (x142:0 > 0 && x142:0 >= x139:0 + 1 && x142:0 >= x138:0 && x184:0 <= x149:0 && x149:0 > 0 && x140:0 > 0 && x184:0 > 0 && x149:0 <= x140:0 && x155:0 >= x154:0 && x142:0 - 1 >= x139:0 && x143:0 - 1 >= x139:0 + 1 && x139:0 > -1) f1445_0_aux_LT(x, x1, x2, x1, x3, x4) -> f1445_0_aux_LT(c3, c4, x7, c5, x3, x4) :|: c5 = x1 + 1 && (c4 = x1 + 1 && c3 = x1 + 1) && (x3 > 0 && x3 >= x1 + 1 && x3 >= x && x7 <= x10 && x10 > 0 && x2 > 0 && x7 > 0 && x10 <= x2 && x11 - 1 >= x12 && x3 - 1 >= x1 && x4 - 1 >= x1 + 1 && x1 > -1) The following rules are bounded: f1445_0_aux_LT(x138:0, x139:0, x140:0, x139:0, x142:0, x143:0) -> f1445_0_aux_LT(c, c1, x184:0, c2, x142:0, x143:0) :|: c2 = x139:0 + 1 && (c1 = x139:0 + 1 && c = x139:0 + 1) && (x142:0 > 0 && x142:0 >= x139:0 + 1 && x142:0 >= x138:0 && x184:0 <= x149:0 && x149:0 > 0 && x140:0 > 0 && x184:0 > 0 && x149:0 <= x140:0 && x155:0 >= x154:0 && x142:0 - 1 >= x139:0 && x143:0 - 1 >= x139:0 + 1 && x139:0 > -1) f1445_0_aux_LT(x, x1, x2, x1, x3, x4) -> f1445_0_aux_LT(c3, c4, x7, c5, x3, x4) :|: c5 = x1 + 1 && (c4 = x1 + 1 && c3 = x1 + 1) && (x3 > 0 && x3 >= x1 + 1 && x3 >= x && x7 <= x10 && x10 > 0 && x2 > 0 && x7 > 0 && x10 <= x2 && x11 - 1 >= x12 && x3 - 1 >= x1 && x4 - 1 >= x1 + 1 && x1 > -1) ---------------------------------------- (36) YES