YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1642 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 62 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 591 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 40 ms] (12) IntTRS (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (14) AND (15) IntTRS (16) RankingReductionPairProof [EQUIVALENT, 18 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 18 ms] (19) IntTRS (20) RankingReductionPairProof [EQUIVALENT, 0 ms] (21) IntTRS (22) RankingReductionPairProof [EQUIVALENT, 0 ms] (23) IntTRS (24) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (25) IntTRS (26) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (27) YES (28) IntTRS (29) PolynomialOrderProcessor [EQUIVALENT, 12 ms] (30) IntTRS (31) PolynomialOrderProcessor [EQUIVALENT, 16 ms] (32) IntTRS (33) RankingReductionPairProof [EQUIVALENT, 0 ms] (34) IntTRS (35) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (36) AND (37) IntTRS (38) RankingReductionPairProof [EQUIVALENT, 0 ms] (39) YES (40) IntTRS (41) RankingReductionPairProof [EQUIVALENT, 0 ms] (42) IntTRS (43) PolynomialOrderProcessor [EQUIVALENT, 2 ms] (44) YES ---------------------------------------- (0) Obligation: Rules: f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9) -> f101_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P, arg8P, arg9P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f101_0_main_GE(x, x1, x2, x3, x4, x5, x6, x7, x8) -> f255_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x2 = x13 && 2 * x1 = x12 && 0 = x11 && x1 = x10 && 0 <= x9 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x9 <= x f255_0_main_GE(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f101_0_main_GE(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x22 = x29 && x19 + 1 = x28 && 0 <= x27 - 1 && 0 <= x18 - 1 && x27 <= x18 && -1 <= x22 - 1 && x21 <= x20 f255_0_main_GE(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f292_0_main_LT(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x40 = x50 && x37 + x38 = x49 && x38 = x48 && x39 = x47 && x37 = x46 && 0 <= x45 - 1 && 0 <= x36 - 1 && x45 <= x36 && -1 <= x37 - 1 && -1 <= x38 - 1 && x38 <= x39 - 1 f292_0_main_LT(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> f255_0_main_GE(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x67 && x56 = x66 && x57 + 1 = x65 && x55 = x64 && 0 <= x63 - 1 && 0 <= x54 - 1 && x58 <= -1 && x63 <= x54 f292_0_main_LT(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> f422_0_main_GE(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x88 && 2 * x73 + 3 * x75 + 4 * x76 = x87 && 0 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && 0 <= x81 - 1 && 0 <= x72 - 1 && x81 <= x72 && 0 <= 4 * x76 && 0 <= 2 * x73 + 3 * x75 && 0 <= 2 * x73 && -1 <= x76 - 1 && 0 <= 3 * x75 f422_0_main_GE(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> f292_0_main_LT(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x97 = x104 && x94 - 1 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && 0 <= x99 - 1 && 0 <= x90 - 1 && x96 <= x95 && x99 <= x90 f422_0_main_GE(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> f448_0_main_LT(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x115 = x125 && 1000 * x109 + 100 * x111 + 10 * x112 + x113 = x124 && x113 = x123 && x114 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && 0 <= x117 - 1 && 0 <= x108 - 1 && x117 <= x108 && -1 <= x113 - 1 && 0 <= 1000 * x109 + 100 * x111 + 10 * x112 && 0 <= 1000 * x109 + 100 * x111 && 0 <= 10 * x112 && 0 <= 1000 * x109 && x113 <= x114 - 1 && 0 <= 100 * x111 f448_0_main_LT(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> f422_0_main_GE(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x142 && x131 = x141 && x132 + 1 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && 0 <= x135 - 1 && 0 <= x126 - 1 && x133 <= -1 && x135 <= x126 f448_0_main_LT(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> f448_0_main_LT(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 - 1 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && 0 <= x153 - 1 && 0 <= x144 - 1 && -1 <= x151 - 1 && x153 <= x144 __init(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> f1_0_main_ConstantStackPush(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9) -> f101_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P, arg8P, arg9P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f101_0_main_GE(x, x1, x2, x3, x4, x5, x6, x7, x8) -> f255_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x2 = x13 && 2 * x1 = x12 && 0 = x11 && x1 = x10 && 0 <= x9 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x9 <= x f255_0_main_GE(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f101_0_main_GE(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x22 = x29 && x19 + 1 = x28 && 0 <= x27 - 1 && 0 <= x18 - 1 && x27 <= x18 && -1 <= x22 - 1 && x21 <= x20 f255_0_main_GE(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f292_0_main_LT(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x40 = x50 && x37 + x38 = x49 && x38 = x48 && x39 = x47 && x37 = x46 && 0 <= x45 - 1 && 0 <= x36 - 1 && x45 <= x36 && -1 <= x37 - 1 && -1 <= x38 - 1 && x38 <= x39 - 1 f292_0_main_LT(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> f255_0_main_GE(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x67 && x56 = x66 && x57 + 1 = x65 && x55 = x64 && 0 <= x63 - 1 && 0 <= x54 - 1 && x58 <= -1 && x63 <= x54 f292_0_main_LT(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> f422_0_main_GE(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x88 && 2 * x73 + 3 * x75 + 4 * x76 = x87 && 0 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && 0 <= x81 - 1 && 0 <= x72 - 1 && x81 <= x72 && 0 <= 4 * x76 && 0 <= 2 * x73 + 3 * x75 && 0 <= 2 * x73 && -1 <= x76 - 1 && 0 <= 3 * x75 f422_0_main_GE(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> f292_0_main_LT(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x97 = x104 && x94 - 1 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && 0 <= x99 - 1 && 0 <= x90 - 1 && x96 <= x95 && x99 <= x90 f422_0_main_GE(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> f448_0_main_LT(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x115 = x125 && 1000 * x109 + 100 * x111 + 10 * x112 + x113 = x124 && x113 = x123 && x114 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && 0 <= x117 - 1 && 0 <= x108 - 1 && x117 <= x108 && -1 <= x113 - 1 && 0 <= 1000 * x109 + 100 * x111 + 10 * x112 && 0 <= 1000 * x109 + 100 * x111 && 0 <= 10 * x112 && 0 <= 1000 * x109 && x113 <= x114 - 1 && 0 <= 100 * x111 f448_0_main_LT(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> f422_0_main_GE(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x142 && x131 = x141 && x132 + 1 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && 0 <= x135 - 1 && 0 <= x126 - 1 && x133 <= -1 && x135 <= x126 f448_0_main_LT(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> f448_0_main_LT(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 - 1 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && 0 <= x153 - 1 && 0 <= x144 - 1 && -1 <= x151 - 1 && x153 <= x144 __init(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> f1_0_main_ConstantStackPush(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9) -> f101_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P, arg8P, arg9P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 (2) f101_0_main_GE(x, x1, x2, x3, x4, x5, x6, x7, x8) -> f255_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x2 = x13 && 2 * x1 = x12 && 0 = x11 && x1 = x10 && 0 <= x9 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x9 <= x (3) f255_0_main_GE(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f101_0_main_GE(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x22 = x29 && x19 + 1 = x28 && 0 <= x27 - 1 && 0 <= x18 - 1 && x27 <= x18 && -1 <= x22 - 1 && x21 <= x20 (4) f255_0_main_GE(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f292_0_main_LT(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x40 = x50 && x37 + x38 = x49 && x38 = x48 && x39 = x47 && x37 = x46 && 0 <= x45 - 1 && 0 <= x36 - 1 && x45 <= x36 && -1 <= x37 - 1 && -1 <= x38 - 1 && x38 <= x39 - 1 (5) f292_0_main_LT(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> f255_0_main_GE(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x67 && x56 = x66 && x57 + 1 = x65 && x55 = x64 && 0 <= x63 - 1 && 0 <= x54 - 1 && x58 <= -1 && x63 <= x54 (6) f292_0_main_LT(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> f422_0_main_GE(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x88 && 2 * x73 + 3 * x75 + 4 * x76 = x87 && 0 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && 0 <= x81 - 1 && 0 <= x72 - 1 && x81 <= x72 && 0 <= 4 * x76 && 0 <= 2 * x73 + 3 * x75 && 0 <= 2 * x73 && -1 <= x76 - 1 && 0 <= 3 * x75 (7) f422_0_main_GE(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> f292_0_main_LT(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x97 = x104 && x94 - 1 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && 0 <= x99 - 1 && 0 <= x90 - 1 && x96 <= x95 && x99 <= x90 (8) f422_0_main_GE(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> f448_0_main_LT(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x115 = x125 && 1000 * x109 + 100 * x111 + 10 * x112 + x113 = x124 && x113 = x123 && x114 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && 0 <= x117 - 1 && 0 <= x108 - 1 && x117 <= x108 && -1 <= x113 - 1 && 0 <= 1000 * x109 + 100 * x111 + 10 * x112 && 0 <= 1000 * x109 + 100 * x111 && 0 <= 10 * x112 && 0 <= 1000 * x109 && x113 <= x114 - 1 && 0 <= 100 * x111 (9) f448_0_main_LT(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> f422_0_main_GE(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x142 && x131 = x141 && x132 + 1 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && 0 <= x135 - 1 && 0 <= x126 - 1 && x133 <= -1 && x135 <= x126 (10) f448_0_main_LT(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> f448_0_main_LT(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 - 1 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && 0 <= x153 - 1 && 0 <= x144 - 1 && -1 <= x151 - 1 && x153 <= x144 (11) __init(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> f1_0_main_ConstantStackPush(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 0 <= 0 Arcs: (1) -> (2) (2) -> (3), (4) (3) -> (2) (4) -> (6) (5) -> (3), (4) (6) -> (7), (8) (7) -> (5), (6) (8) -> (10) (9) -> (7), (8) (10) -> (9), (10) (11) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f101_0_main_GE(x, x1, x2, x3, x4, x5, x6, x7, x8) -> f255_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x2 = x13 && 2 * x1 = x12 && 0 = x11 && x1 = x10 && 0 <= x9 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x9 <= x (2) f255_0_main_GE(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> f101_0_main_GE(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x22 = x29 && x19 + 1 = x28 && 0 <= x27 - 1 && 0 <= x18 - 1 && x27 <= x18 && -1 <= x22 - 1 && x21 <= x20 (3) f292_0_main_LT(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> f255_0_main_GE(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x67 && x56 = x66 && x57 + 1 = x65 && x55 = x64 && 0 <= x63 - 1 && 0 <= x54 - 1 && x58 <= -1 && x63 <= x54 (4) f422_0_main_GE(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> f292_0_main_LT(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x97 = x104 && x94 - 1 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && 0 <= x99 - 1 && 0 <= x90 - 1 && x96 <= x95 && x99 <= x90 (5) f448_0_main_LT(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> f422_0_main_GE(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x142 && x131 = x141 && x132 + 1 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && 0 <= x135 - 1 && 0 <= x126 - 1 && x133 <= -1 && x135 <= x126 (6) f448_0_main_LT(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> f448_0_main_LT(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 - 1 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && 0 <= x153 - 1 && 0 <= x144 - 1 && -1 <= x151 - 1 && x153 <= x144 (7) f422_0_main_GE(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> f448_0_main_LT(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x115 = x125 && 1000 * x109 + 100 * x111 + 10 * x112 + x113 = x124 && x113 = x123 && x114 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && 0 <= x117 - 1 && 0 <= x108 - 1 && x117 <= x108 && -1 <= x113 - 1 && 0 <= 1000 * x109 + 100 * x111 + 10 * x112 && 0 <= 1000 * x109 + 100 * x111 && 0 <= 10 * x112 && 0 <= 1000 * x109 && x113 <= x114 - 1 && 0 <= 100 * x111 (8) f292_0_main_LT(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> f422_0_main_GE(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x88 && 2 * x73 + 3 * x75 + 4 * x76 = x87 && 0 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && 0 <= x81 - 1 && 0 <= x72 - 1 && x81 <= x72 && 0 <= 4 * x76 && 0 <= 2 * x73 + 3 * x75 && 0 <= 2 * x73 && -1 <= x76 - 1 && 0 <= 3 * x75 (9) f255_0_main_GE(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f292_0_main_LT(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x40 = x50 && x37 + x38 = x49 && x38 = x48 && x39 = x47 && x37 = x46 && 0 <= x45 - 1 && 0 <= x36 - 1 && x45 <= x36 && -1 <= x37 - 1 && -1 <= x38 - 1 && x38 <= x39 - 1 Arcs: (1) -> (2), (9) (2) -> (1) (3) -> (2), (9) (4) -> (3), (8) (5) -> (4), (7) (6) -> (5), (6) (7) -> (6) (8) -> (4), (7) (9) -> (8) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, x132:0 + 1, x131:0, x134:0, x143:0) :|: x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0 f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0, x78:0, x79:0, x80:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, 0, 2 * x73:0 + 3 * x75:0 + 4 * x76:0, x77:0, x89:0) :|: x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0 f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0, x98:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, x94:0 - 1, x104:0, x105:0, x106:0, x107:0) :|: x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0 f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0, x60:0, x61:0, x62:0) -> f255_0_main_GE(x63:0, x55:0, x57:0 + 1, x56:0, x59:0, x68:0, x69:0, x70:0, x71:0) :|: x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0 f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0, x115:0) :|: x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0 f255_0_main_GE(x18:0, x19:0, x20:0, x21:0, x13:0, x23:0, x24:0, x25:0, x26:0) -> f255_0_main_GE(x9:0, x19:0 + 1, 0, 2 * (x19:0 + 1), x13:0, x14:0, x15:0, x16:0, x17:0) :|: x9:0 <= x27:0 && x21:0 <= x20:0 && x13:0 > -1 && x19:0 + 1 <= x13:0 - 1 && x27:0 <= x18:0 && x18:0 > 0 && x27:0 > 0 && x9:0 > 0 f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0 - 1, x152:0) :|: x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0 f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0, x42:0, x43:0, x44:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, x37:0 + x38:0, x40:0, x51:0, x52:0, x53:0) :|: x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f292_0_main_LT(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f292_0_main_LT(x1, x2, x3, x4, x5, x6) f422_0_main_GE(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f422_0_main_GE(x1, x2, x3, x4, x5, x6, x7, x8) f255_0_main_GE(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f255_0_main_GE(x1, x2, x3, x4, x5) ---------------------------------------- (8) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, x132:0 + 1, x131:0, x134:0) :|: x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0 f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, 0, 2 * x73:0 + 3 * x75:0 + 4 * x76:0, x77:0) :|: x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0 f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, x94:0 - 1, x104:0) :|: x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0 f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, x57:0 + 1, x56:0, x59:0) :|: x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0 f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0, x115:0) :|: x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0 f255_0_main_GE(x18:0, x19:0, x20:0, x21:0, x13:0) -> f255_0_main_GE(x9:0, x19:0 + 1, 0, 2 * (x19:0 + 1), x13:0) :|: x9:0 <= x27:0 && x21:0 <= x20:0 && x13:0 > -1 && x19:0 + 1 <= x13:0 - 1 && x27:0 <= x18:0 && x18:0 > 0 && x27:0 > 0 && x9:0 > 0 f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0 - 1, x152:0) :|: x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0 f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, x37:0 + x38:0, x40:0) :|: x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f448_0_main_LT(INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, INTEGER, VARIABLE) f422_0_main_GE(INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) f292_0_main_LT(INTEGER, VARIABLE, VARIABLE, VARIABLE, INTEGER, VARIABLE) f255_0_main_GE(INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, c4, x56:0, x59:0) :|: c4 = x57:0 + 1 && (x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f255_0_main_GE(x18:0, x19:0, x20:0, x21:0, x13:0) -> f255_0_main_GE(x9:0, c6, c7, c8, x13:0) :|: c8 = 2 * (x19:0 + 1) && (c7 = 0 && c6 = x19:0 + 1) && (x9:0 <= x27:0 && x21:0 <= x20:0 && x13:0 > -1 && x19:0 + 1 <= x13:0 - 1 && x27:0 <= x18:0 && x18:0 > 0 && x27:0 > 0 && x9:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, c10, x40:0) :|: c10 = x37:0 + x38:0 && (x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0) ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = -1 - x1 + x8 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = -1 - x10 + x16 [f292_0_main_LT(x17, x18, x19, x20, x21, x22)] = -1 - x18 + x22 [f255_0_main_GE(x23, x24, x25, x26, x27)] = -1 - x24 + x27 The following rules are decreasing: f255_0_main_GE(x18:0, x19:0, x20:0, x21:0, x13:0) -> f255_0_main_GE(x9:0, c6, c7, c8, x13:0) :|: c8 = 2 * (x19:0 + 1) && (c7 = 0 && c6 = x19:0 + 1) && (x9:0 <= x27:0 && x21:0 <= x20:0 && x13:0 > -1 && x19:0 + 1 <= x13:0 - 1 && x27:0 <= x18:0 && x18:0 > 0 && x27:0 > 0 && x9:0 > 0) The following rules are bounded: f255_0_main_GE(x18:0, x19:0, x20:0, x21:0, x13:0) -> f255_0_main_GE(x9:0, c6, c7, c8, x13:0) :|: c8 = 2 * (x19:0 + 1) && (c7 = 0 && c6 = x19:0 + 1) && (x9:0 <= x27:0 && x21:0 <= x20:0 && x13:0 > -1 && x19:0 + 1 <= x13:0 - 1 && x27:0 <= x18:0 && x18:0 > 0 && x27:0 > 0 && x9:0 > 0) ---------------------------------------- (12) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, c4, x56:0, x59:0) :|: c4 = x57:0 + 1 && (x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, c10, x40:0) :|: c10 = x37:0 + x38:0 && (x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0) ---------------------------------------- (13) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = -1 + x1 + x2 - x3 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = -1 + x10 + x11 - x12 [f292_0_main_LT(x17, x18, x19, x20, x21, x22)] = -1 + x18 + x19 - x20 [f255_0_main_GE(x23, x24, x25, x26, x27)] = -1 + x24 - x25 + x26 The following rules are decreasing: f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, c4, x56:0, x59:0) :|: c4 = x57:0 + 1 && (x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0) The following rules are bounded: f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, c10, x40:0) :|: c10 = x37:0 + x38:0 && (x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0) ---------------------------------------- (14) Complex Obligation (AND) ---------------------------------------- (15) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, c10, x40:0) :|: c10 = x37:0 + x38:0 && (x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0) ---------------------------------------- (16) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f448_0_main_LT ] = 0 [ f422_0_main_GE ] = 0 [ f292_0_main_LT ] = 0 [ f255_0_main_GE ] = f255_0_main_GE_1 The following rules are decreasing: f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, c10, x40:0) :|: c10 = x37:0 + x38:0 && (x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0) The following rules are bounded: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) f255_0_main_GE(x36:0, x37:0, x38:0, x39:0, x40:0) -> f292_0_main_LT(x45:0, x37:0, x39:0, x38:0, c10, x40:0) :|: c10 = x37:0 + x38:0 && (x38:0 > -1 && x39:0 - 1 >= x38:0 && x37:0 > -1 && x45:0 <= x36:0 && x45:0 > 0 && x36:0 > 0) ---------------------------------------- (17) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = -1 + 9*x1 + x3 + x4 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = -1 + 9*x10 + x12 + x13 [f292_0_main_LT(x17, x18, x19, x20, x21, x22)] = 9*x18 + x20 + x21 The following rules are decreasing: f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) The following rules are bounded: f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) ---------------------------------------- (19) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (20) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f448_0_main_LT ] = 0 [ f422_0_main_GE ] = 0 [ f292_0_main_LT ] = -1*f292_0_main_LT_1 The following rules are decreasing: f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) The following rules are bounded: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (21) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (22) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f448_0_main_LT ] = 2*f448_0_main_LT_2 + 2*f448_0_main_LT_4 + 2*f448_0_main_LT_5 + 2*f448_0_main_LT_6 + -2*f448_0_main_LT_7 + -1 [ f422_0_main_GE ] = 2*f422_0_main_GE_2 + 2*f422_0_main_GE_4 + 2*f422_0_main_GE_5 + 2*f422_0_main_GE_7 + -2*f422_0_main_GE_6 The following rules are decreasing: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) The following rules are bounded: f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) ---------------------------------------- (23) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (24) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = 1 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = 0 The following rules are decreasing: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) The following rules are bounded: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (25) Obligation: Rules: f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (26) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = x7 The following rules are decreasing: f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) The following rules are bounded: f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (27) YES ---------------------------------------- (28) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, c4, x56:0, x59:0) :|: c4 = x57:0 + 1 && (x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (29) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = 1 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = 1 [f292_0_main_LT(x17, x18, x19, x20, x21, x22)] = 1 [f255_0_main_GE(x23, x24, x25, x26, x27)] = 0 The following rules are decreasing: f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, c4, x56:0, x59:0) :|: c4 = x57:0 + 1 && (x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0) The following rules are bounded: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f292_0_main_LT(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f255_0_main_GE(x63:0, x55:0, c4, x56:0, x59:0) :|: c4 = x57:0 + 1 && (x58:0 < 0 && x63:0 <= x54:0 && x63:0 > 0 && x54:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (30) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (31) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = -1 + 9*x1 + x3 + x4 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = -1 + 9*x10 + x12 + x13 [f292_0_main_LT(x17, x18, x19, x20, x21, x22)] = 9*x18 + x20 + x21 The following rules are decreasing: f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) The following rules are bounded: f292_0_main_LT(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0) -> f422_0_main_GE(x81:0, x73:0, x74:0, x75:0, x76:0, c1, c2, x77:0) :|: c2 = 2 * x73:0 + 3 * x75:0 + 4 * x76:0 && c1 = 0 && (x76:0 > -1 && 3 * x75:0 >= 0 && 2 * x73:0 >= 0 && 2 * x73:0 + 3 * x75:0 >= 0 && 4 * x76:0 >= 0 && x81:0 <= x72:0 && x81:0 > 0 && x72:0 > 0) ---------------------------------------- (32) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (33) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f448_0_main_LT ] = 0 [ f422_0_main_GE ] = 0 [ f292_0_main_LT ] = -1*f292_0_main_LT_1 The following rules are decreasing: f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) The following rules are bounded: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x90:0, x100:0, x101:0, x102:0, x94:0, x95:0, x96:0, x104:0) -> f292_0_main_LT(x99:0, x100:0, x101:0, x102:0, c3, x104:0) :|: c3 = x94:0 - 1 && (x96:0 <= x95:0 && x99:0 <= x90:0 && x99:0 > 0 && x90:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (34) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (35) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = -1 + 10*x1 + x3 + x4 + x5 - x6 [f422_0_main_GE(x9, x10, x11, x12, x13, x14, x15, x16)] = -1 + 10*x10 + x12 + x13 - x14 + x15 The following rules are decreasing: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) The following rules are bounded: f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) ---------------------------------------- (36) Complex Obligation (AND) ---------------------------------------- (37) Obligation: Rules: f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (38) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f422_0_main_GE ] = f422_0_main_GE_6 + 100*f422_0_main_GE_4 + 1000*f422_0_main_GE_2 + 10*f422_0_main_GE_5 + f422_0_main_GE_1 [ f448_0_main_LT ] = f448_0_main_LT_8 The following rules are decreasing: f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) The following rules are bounded: f422_0_main_GE(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f448_0_main_LT(x117:0, x109:0, x110:0, x111:0, x112:0, x114:0, x113:0, c5, x115:0) :|: c5 = 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 + x113:0 && (x114:0 - 1 >= x113:0 && 100 * x111:0 >= 0 && 1000 * x109:0 >= 0 && 10 * x112:0 >= 0 && 1000 * x109:0 + 100 * x111:0 >= 0 && 1000 * x109:0 + 100 * x111:0 + 10 * x112:0 >= 0 && x113:0 > -1 && x117:0 <= x108:0 && x117:0 > 0 && x108:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (39) YES ---------------------------------------- (40) Obligation: Rules: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (41) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f448_0_main_LT ] = 0 [ f422_0_main_GE ] = -1*f422_0_main_GE_1 The following rules are decreasing: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) The following rules are bounded: f448_0_main_LT(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> f422_0_main_GE(x135:0, x127:0, x128:0, x129:0, x130:0, c, x131:0, x134:0) :|: c = x132:0 + 1 && (x133:0 < 0 && x135:0 <= x126:0 && x135:0 > 0 && x126:0 > 0) f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (42) Obligation: Rules: f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (43) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f448_0_main_LT(x, x1, x2, x3, x4, x5, x6, x7, x8)] = x7 The following rules are decreasing: f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) The following rules are bounded: f448_0_main_LT(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> f448_0_main_LT(x153:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, c9, x152:0) :|: c9 = x151:0 - 1 && (x151:0 > -1 && x153:0 <= x144:0 && x153:0 > 0 && x144:0 > 0) ---------------------------------------- (44) YES