NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 6414 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 12 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 107 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 0 ms] (13) IntTRS (14) RankingReductionPairProof [EQUIVALENT, 0 ms] (15) IntTRS (16) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 4 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 16 ms] (22) IRSwT (23) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 26 ms] (26) IntTRS (27) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (28) YES (29) IRSwT (30) IntTRSCompressionProof [EQUIVALENT, 0 ms] (31) IRSwT (32) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (33) IRSwT (34) TempFilterProof [SOUND, 31 ms] (35) IntTRS (36) RankingReductionPairProof [EQUIVALENT, 0 ms] (37) YES (38) IRSwT (39) IntTRSCompressionProof [EQUIVALENT, 0 ms] (40) IRSwT (41) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (42) IRSwT (43) FilterProof [EQUIVALENT, 0 ms] (44) IntTRS (45) IntTRSCompressionProof [EQUIVALENT, 0 ms] (46) IntTRS (47) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (48) NO ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f975_0_random_GT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f121_0_createList_Return(x, x1, x2, x3, x4, x6) -> f975_0_random_GT(x7, x8, x9, x11, x12, x13) :|: x7 <= x && -1 <= x14 - 1 && x8 + 1 <= x && 0 <= x - 1 && 0 <= x7 - 1 && -1 <= x8 - 1 f975_0_random_GT(x15, x17, x18, x19, x20, x21) -> f998_0_main_InvokeMethod(x22, x25, x26, x27, x28, x29) :|: x22 <= x15 && x30 <= x26 && x22 - 1 <= x17 && x25 <= x17 && 0 <= x15 - 1 && -1 <= x17 - 1 && 0 <= x22 - 1 && -1 <= x25 - 1 f998_0_main_InvokeMethod(x31, x32, x33, x36, x37, x38) -> f1099_0_get_InvokeMethod(x39, x40, x41, x42, x43, x44) :|: x39 <= x31 && x45 <= x33 && x39 <= x32 && 0 <= x31 - 1 && 0 <= x32 - 1 && 0 <= x39 - 1 && 1 <= x40 - 1 f975_0_random_GT(x46, x47, x48, x49, x50, x51) -> f998_0_main_InvokeMethod(x52, x53, x54, x55, x56, x57) :|: x58 <= x59 - 1 && -1 <= x58 - 1 && x52 <= x46 && x52 - 1 <= x47 && x53 <= x47 && 0 <= x46 - 1 && -1 <= x47 - 1 && 0 <= x52 - 1 && -1 <= x53 - 1 && x58 + 1 = x54 f1099_0_get_InvokeMethod(x60, x61, x62, x63, x64, x65) -> f983_0_getR_EQ(x66, x67, x68, x69, x70, x71) :|: 0 = x67 && x62 + 2 <= x61 && 1 <= x66 - 1 && 1 <= x61 - 1 && 0 <= x60 - 1 && x66 <= x61 f975_0_random_GT(x72, x73, x74, x76, x77, x78) -> f983_0_getR_EQ(x79, x80, x81, x82, x83, x84) :|: x85 <= x86 - 1 && -1 <= x85 - 1 && 0 <= x86 - 1 && x85 + 1 <= x86 && -1 <= x80 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && 1 <= x79 - 1 f1_0_main_Load(x87, x88, x89, x91, x92, x93) -> f1248_0_createList_GE(x94, x95, x96, x99, x100, x101) :|: 0 = x100 && 0 = x99 && 0 = x96 && 0 = x95 && 0 = x88 && -1 <= x94 - 1 && 0 <= x87 - 1 && x94 + 1 <= x87 f1_0_main_Load(x102, x103, x105, x106, x107, x108) -> f1248_0_createList_GE(x109, x110, x111, x112, x113, x114) :|: 1 = x113 && x103 = x112 && 0 = x111 && 0 = x110 && -1 <= x109 - 1 && 0 <= x102 - 1 && 0 <= x103 - 1 && x109 + 1 <= x102 f1_0_main_Load(x115, x116, x117, x118, x119, x120) -> f1248_0_createList_GE(x121, x122, x123, x124, x125, x126) :|: 1 = x125 && x116 = x124 && 0 = x122 && -1 <= x121 - 1 && 0 <= x115 - 1 && x121 + 1 <= x115 && 0 <= x116 - 1 && -1 <= x123 - 1 f1248_0_createList_GE(x127, x128, x129, x130, x131, x132) -> f1248_0_createList_GE(x133, x134, x135, x136, x137, x138) :|: x131 = x137 && x130 = x136 && x129 = x135 && x128 + 1 = x134 && 1 <= x133 - 1 && -1 <= x127 - 1 && x133 - 2 <= x127 && x128 <= x129 - 1 && -1 <= x130 - 1 && x130 <= x131 f1248_0_createList_GE(x139, x140, x141, x142, x143, x144) -> f1248_0_createList_GE(x145, x146, x147, x148, x149, x150) :|: x143 = x149 && x142 = x148 && x141 = x147 && x140 + 1 = x146 && 4 <= x145 - 1 && 0 <= x139 - 1 && x140 <= x141 - 1 && -1 <= x142 - 1 && x142 <= x143 f1248_0_createList_GE(x151, x152, x153, x154, x155, x156) -> f1379_0_createList_NULL(x157, x158, x159, x160, x161, x162) :|: x155 + 1 = x162 && x154 = x161 && x152 = x159 && x153 = x157 && -1 <= x160 - 1 && 1 <= x158 - 1 && -1 <= x151 - 1 && x160 <= x151 && -1 <= x155 - 1 && x155 <= x154 - 1 && -1 <= x154 - 1 && x152 <= x153 - 1 f1248_0_createList_GE(x163, x164, x165, x166, x167, x168) -> f1379_0_createList_NULL(x169, x170, x171, x172, x173, x174) :|: x164 <= x165 - 1 && -1 <= x166 - 1 && x167 <= x166 - 1 && -1 <= x167 - 1 && -1 <= x175 - 1 && x172 <= x163 && -1 <= x163 - 1 && 1 <= x170 - 1 && -1 <= x172 - 1 && x165 = x169 && x164 = x171 && x166 = x173 && x167 + 1 = x174 f1379_0_createList_NULL(x176, x177, x178, x179, x180, x181) -> f1248_0_createList_GE(x182, x183, x184, x185, x186, x187) :|: x181 = x186 && x180 = x185 && x176 = x184 && x178 + 1 = x183 && 1 <= x182 - 1 && -1 <= x179 - 1 && 1 <= x177 - 1 && x182 - 2 <= x179 && x182 <= x177 f1379_0_createList_NULL(x188, x189, x190, x191, x192, x193) -> f1248_0_createList_GE(x194, x195, x196, x197, x198, x199) :|: x193 = x198 && x192 = x197 && x188 = x196 && x190 + 1 = x195 && 4 <= x194 - 1 && 0 <= x191 - 1 && 2 <= x189 - 1 f998_0_main_InvokeMethod(x200, x201, x202, x203, x204, x205) -> f739_0_getFirst_NONNULL(x206, x207, x208, x209, x210, x211) :|: x206 <= x201 && x212 <= x202 && 0 <= x200 - 1 && 0 <= x201 - 1 && 0 <= x206 - 1 && -1 <= x207 - 1 && x208 + 2 <= x201 f975_0_random_GT(x213, x214, x215, x216, x217, x218) -> f739_0_getFirst_NONNULL(x219, x220, x221, x222, x223, x224) :|: x225 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x226 - 1 && -1 <= x227 - 1 && x225 + 1 <= x226 && x219 <= x214 && 0 <= x213 - 1 && 0 <= x214 - 1 && 0 <= x219 - 1 && -1 <= x220 - 1 && x221 + 2 <= x214 f739_0_getFirst_NONNULL(x228, x229, x230, x231, x232, x233) -> f739_0_getFirst_NONNULL(x234, x235, x236, x237, x238, x239) :|: x230 + 2 <= x228 && -1 <= x235 - 1 && 0 <= x234 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1 f983_0_getR_EQ(x240, x241, x242, x243, x244, x245) -> f983_0_getR_EQ(x246, x247, x248, x249, x250, x251) :|: x241 - 1 = x247 && 0 <= x246 - 1 && 2 <= x240 - 1 && 0 <= x241 - 1 && x241 - 1 <= x241 - 1 __init(x252, x253, x254, x255, x256, x257) -> f1_0_main_Load(x258, x259, x260, x261, x262, x263) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6) ---------------------------------------- (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) -> f975_0_random_GT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f121_0_createList_Return(x, x1, x2, x3, x4, x6) -> f975_0_random_GT(x7, x8, x9, x11, x12, x13) :|: x7 <= x && -1 <= x14 - 1 && x8 + 1 <= x && 0 <= x - 1 && 0 <= x7 - 1 && -1 <= x8 - 1 f975_0_random_GT(x15, x17, x18, x19, x20, x21) -> f998_0_main_InvokeMethod(x22, x25, x26, x27, x28, x29) :|: x22 <= x15 && x30 <= x26 && x22 - 1 <= x17 && x25 <= x17 && 0 <= x15 - 1 && -1 <= x17 - 1 && 0 <= x22 - 1 && -1 <= x25 - 1 f998_0_main_InvokeMethod(x31, x32, x33, x36, x37, x38) -> f1099_0_get_InvokeMethod(x39, x40, x41, x42, x43, x44) :|: x39 <= x31 && x45 <= x33 && x39 <= x32 && 0 <= x31 - 1 && 0 <= x32 - 1 && 0 <= x39 - 1 && 1 <= x40 - 1 f975_0_random_GT(x46, x47, x48, x49, x50, x51) -> f998_0_main_InvokeMethod(x52, x53, x54, x55, x56, x57) :|: x58 <= x59 - 1 && -1 <= x58 - 1 && x52 <= x46 && x52 - 1 <= x47 && x53 <= x47 && 0 <= x46 - 1 && -1 <= x47 - 1 && 0 <= x52 - 1 && -1 <= x53 - 1 && x58 + 1 = x54 f1099_0_get_InvokeMethod(x60, x61, x62, x63, x64, x65) -> f983_0_getR_EQ(x66, x67, x68, x69, x70, x71) :|: 0 = x67 && x62 + 2 <= x61 && 1 <= x66 - 1 && 1 <= x61 - 1 && 0 <= x60 - 1 && x66 <= x61 f975_0_random_GT(x72, x73, x74, x76, x77, x78) -> f983_0_getR_EQ(x79, x80, x81, x82, x83, x84) :|: x85 <= x86 - 1 && -1 <= x85 - 1 && 0 <= x86 - 1 && x85 + 1 <= x86 && -1 <= x80 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && 1 <= x79 - 1 f1_0_main_Load(x87, x88, x89, x91, x92, x93) -> f1248_0_createList_GE(x94, x95, x96, x99, x100, x101) :|: 0 = x100 && 0 = x99 && 0 = x96 && 0 = x95 && 0 = x88 && -1 <= x94 - 1 && 0 <= x87 - 1 && x94 + 1 <= x87 f1_0_main_Load(x102, x103, x105, x106, x107, x108) -> f1248_0_createList_GE(x109, x110, x111, x112, x113, x114) :|: 1 = x113 && x103 = x112 && 0 = x111 && 0 = x110 && -1 <= x109 - 1 && 0 <= x102 - 1 && 0 <= x103 - 1 && x109 + 1 <= x102 f1_0_main_Load(x115, x116, x117, x118, x119, x120) -> f1248_0_createList_GE(x121, x122, x123, x124, x125, x126) :|: 1 = x125 && x116 = x124 && 0 = x122 && -1 <= x121 - 1 && 0 <= x115 - 1 && x121 + 1 <= x115 && 0 <= x116 - 1 && -1 <= x123 - 1 f1248_0_createList_GE(x127, x128, x129, x130, x131, x132) -> f1248_0_createList_GE(x133, x134, x135, x136, x137, x138) :|: x131 = x137 && x130 = x136 && x129 = x135 && x128 + 1 = x134 && 1 <= x133 - 1 && -1 <= x127 - 1 && x133 - 2 <= x127 && x128 <= x129 - 1 && -1 <= x130 - 1 && x130 <= x131 f1248_0_createList_GE(x139, x140, x141, x142, x143, x144) -> f1248_0_createList_GE(x145, x146, x147, x148, x149, x150) :|: x143 = x149 && x142 = x148 && x141 = x147 && x140 + 1 = x146 && 4 <= x145 - 1 && 0 <= x139 - 1 && x140 <= x141 - 1 && -1 <= x142 - 1 && x142 <= x143 f1248_0_createList_GE(x151, x152, x153, x154, x155, x156) -> f1379_0_createList_NULL(x157, x158, x159, x160, x161, x162) :|: x155 + 1 = x162 && x154 = x161 && x152 = x159 && x153 = x157 && -1 <= x160 - 1 && 1 <= x158 - 1 && -1 <= x151 - 1 && x160 <= x151 && -1 <= x155 - 1 && x155 <= x154 - 1 && -1 <= x154 - 1 && x152 <= x153 - 1 f1248_0_createList_GE(x163, x164, x165, x166, x167, x168) -> f1379_0_createList_NULL(x169, x170, x171, x172, x173, x174) :|: x164 <= x165 - 1 && -1 <= x166 - 1 && x167 <= x166 - 1 && -1 <= x167 - 1 && -1 <= x175 - 1 && x172 <= x163 && -1 <= x163 - 1 && 1 <= x170 - 1 && -1 <= x172 - 1 && x165 = x169 && x164 = x171 && x166 = x173 && x167 + 1 = x174 f1379_0_createList_NULL(x176, x177, x178, x179, x180, x181) -> f1248_0_createList_GE(x182, x183, x184, x185, x186, x187) :|: x181 = x186 && x180 = x185 && x176 = x184 && x178 + 1 = x183 && 1 <= x182 - 1 && -1 <= x179 - 1 && 1 <= x177 - 1 && x182 - 2 <= x179 && x182 <= x177 f1379_0_createList_NULL(x188, x189, x190, x191, x192, x193) -> f1248_0_createList_GE(x194, x195, x196, x197, x198, x199) :|: x193 = x198 && x192 = x197 && x188 = x196 && x190 + 1 = x195 && 4 <= x194 - 1 && 0 <= x191 - 1 && 2 <= x189 - 1 f998_0_main_InvokeMethod(x200, x201, x202, x203, x204, x205) -> f739_0_getFirst_NONNULL(x206, x207, x208, x209, x210, x211) :|: x206 <= x201 && x212 <= x202 && 0 <= x200 - 1 && 0 <= x201 - 1 && 0 <= x206 - 1 && -1 <= x207 - 1 && x208 + 2 <= x201 f975_0_random_GT(x213, x214, x215, x216, x217, x218) -> f739_0_getFirst_NONNULL(x219, x220, x221, x222, x223, x224) :|: x225 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x226 - 1 && -1 <= x227 - 1 && x225 + 1 <= x226 && x219 <= x214 && 0 <= x213 - 1 && 0 <= x214 - 1 && 0 <= x219 - 1 && -1 <= x220 - 1 && x221 + 2 <= x214 f739_0_getFirst_NONNULL(x228, x229, x230, x231, x232, x233) -> f739_0_getFirst_NONNULL(x234, x235, x236, x237, x238, x239) :|: x230 + 2 <= x228 && -1 <= x235 - 1 && 0 <= x234 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1 f983_0_getR_EQ(x240, x241, x242, x243, x244, x245) -> f983_0_getR_EQ(x246, x247, x248, x249, x250, x251) :|: x241 - 1 = x247 && 0 <= x246 - 1 && 2 <= x240 - 1 && 0 <= x241 - 1 && x241 - 1 <= x241 - 1 __init(x252, x253, x254, x255, x256, x257) -> f1_0_main_Load(x258, x259, x260, x261, x262, x263) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f975_0_random_GT(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 (2) f121_0_createList_Return(x, x1, x2, x3, x4, x6) -> f975_0_random_GT(x7, x8, x9, x11, x12, x13) :|: x7 <= x && -1 <= x14 - 1 && x8 + 1 <= x && 0 <= x - 1 && 0 <= x7 - 1 && -1 <= x8 - 1 (3) f975_0_random_GT(x15, x17, x18, x19, x20, x21) -> f998_0_main_InvokeMethod(x22, x25, x26, x27, x28, x29) :|: x22 <= x15 && x30 <= x26 && x22 - 1 <= x17 && x25 <= x17 && 0 <= x15 - 1 && -1 <= x17 - 1 && 0 <= x22 - 1 && -1 <= x25 - 1 (4) f998_0_main_InvokeMethod(x31, x32, x33, x36, x37, x38) -> f1099_0_get_InvokeMethod(x39, x40, x41, x42, x43, x44) :|: x39 <= x31 && x45 <= x33 && x39 <= x32 && 0 <= x31 - 1 && 0 <= x32 - 1 && 0 <= x39 - 1 && 1 <= x40 - 1 (5) f975_0_random_GT(x46, x47, x48, x49, x50, x51) -> f998_0_main_InvokeMethod(x52, x53, x54, x55, x56, x57) :|: x58 <= x59 - 1 && -1 <= x58 - 1 && x52 <= x46 && x52 - 1 <= x47 && x53 <= x47 && 0 <= x46 - 1 && -1 <= x47 - 1 && 0 <= x52 - 1 && -1 <= x53 - 1 && x58 + 1 = x54 (6) f1099_0_get_InvokeMethod(x60, x61, x62, x63, x64, x65) -> f983_0_getR_EQ(x66, x67, x68, x69, x70, x71) :|: 0 = x67 && x62 + 2 <= x61 && 1 <= x66 - 1 && 1 <= x61 - 1 && 0 <= x60 - 1 && x66 <= x61 (7) f975_0_random_GT(x72, x73, x74, x76, x77, x78) -> f983_0_getR_EQ(x79, x80, x81, x82, x83, x84) :|: x85 <= x86 - 1 && -1 <= x85 - 1 && 0 <= x86 - 1 && x85 + 1 <= x86 && -1 <= x80 - 1 && 0 <= x72 - 1 && 0 <= x73 - 1 && 1 <= x79 - 1 (8) f1_0_main_Load(x87, x88, x89, x91, x92, x93) -> f1248_0_createList_GE(x94, x95, x96, x99, x100, x101) :|: 0 = x100 && 0 = x99 && 0 = x96 && 0 = x95 && 0 = x88 && -1 <= x94 - 1 && 0 <= x87 - 1 && x94 + 1 <= x87 (9) f1_0_main_Load(x102, x103, x105, x106, x107, x108) -> f1248_0_createList_GE(x109, x110, x111, x112, x113, x114) :|: 1 = x113 && x103 = x112 && 0 = x111 && 0 = x110 && -1 <= x109 - 1 && 0 <= x102 - 1 && 0 <= x103 - 1 && x109 + 1 <= x102 (10) f1_0_main_Load(x115, x116, x117, x118, x119, x120) -> f1248_0_createList_GE(x121, x122, x123, x124, x125, x126) :|: 1 = x125 && x116 = x124 && 0 = x122 && -1 <= x121 - 1 && 0 <= x115 - 1 && x121 + 1 <= x115 && 0 <= x116 - 1 && -1 <= x123 - 1 (11) f1248_0_createList_GE(x127, x128, x129, x130, x131, x132) -> f1248_0_createList_GE(x133, x134, x135, x136, x137, x138) :|: x131 = x137 && x130 = x136 && x129 = x135 && x128 + 1 = x134 && 1 <= x133 - 1 && -1 <= x127 - 1 && x133 - 2 <= x127 && x128 <= x129 - 1 && -1 <= x130 - 1 && x130 <= x131 (12) f1248_0_createList_GE(x139, x140, x141, x142, x143, x144) -> f1248_0_createList_GE(x145, x146, x147, x148, x149, x150) :|: x143 = x149 && x142 = x148 && x141 = x147 && x140 + 1 = x146 && 4 <= x145 - 1 && 0 <= x139 - 1 && x140 <= x141 - 1 && -1 <= x142 - 1 && x142 <= x143 (13) f1248_0_createList_GE(x151, x152, x153, x154, x155, x156) -> f1379_0_createList_NULL(x157, x158, x159, x160, x161, x162) :|: x155 + 1 = x162 && x154 = x161 && x152 = x159 && x153 = x157 && -1 <= x160 - 1 && 1 <= x158 - 1 && -1 <= x151 - 1 && x160 <= x151 && -1 <= x155 - 1 && x155 <= x154 - 1 && -1 <= x154 - 1 && x152 <= x153 - 1 (14) f1248_0_createList_GE(x163, x164, x165, x166, x167, x168) -> f1379_0_createList_NULL(x169, x170, x171, x172, x173, x174) :|: x164 <= x165 - 1 && -1 <= x166 - 1 && x167 <= x166 - 1 && -1 <= x167 - 1 && -1 <= x175 - 1 && x172 <= x163 && -1 <= x163 - 1 && 1 <= x170 - 1 && -1 <= x172 - 1 && x165 = x169 && x164 = x171 && x166 = x173 && x167 + 1 = x174 (15) f1379_0_createList_NULL(x176, x177, x178, x179, x180, x181) -> f1248_0_createList_GE(x182, x183, x184, x185, x186, x187) :|: x181 = x186 && x180 = x185 && x176 = x184 && x178 + 1 = x183 && 1 <= x182 - 1 && -1 <= x179 - 1 && 1 <= x177 - 1 && x182 - 2 <= x179 && x182 <= x177 (16) f1379_0_createList_NULL(x188, x189, x190, x191, x192, x193) -> f1248_0_createList_GE(x194, x195, x196, x197, x198, x199) :|: x193 = x198 && x192 = x197 && x188 = x196 && x190 + 1 = x195 && 4 <= x194 - 1 && 0 <= x191 - 1 && 2 <= x189 - 1 (17) f998_0_main_InvokeMethod(x200, x201, x202, x203, x204, x205) -> f739_0_getFirst_NONNULL(x206, x207, x208, x209, x210, x211) :|: x206 <= x201 && x212 <= x202 && 0 <= x200 - 1 && 0 <= x201 - 1 && 0 <= x206 - 1 && -1 <= x207 - 1 && x208 + 2 <= x201 (18) f975_0_random_GT(x213, x214, x215, x216, x217, x218) -> f739_0_getFirst_NONNULL(x219, x220, x221, x222, x223, x224) :|: x225 <= x226 - 1 && -1 <= x225 - 1 && 0 <= x226 - 1 && -1 <= x227 - 1 && x225 + 1 <= x226 && x219 <= x214 && 0 <= x213 - 1 && 0 <= x214 - 1 && 0 <= x219 - 1 && -1 <= x220 - 1 && x221 + 2 <= x214 (19) f739_0_getFirst_NONNULL(x228, x229, x230, x231, x232, x233) -> f739_0_getFirst_NONNULL(x234, x235, x236, x237, x238, x239) :|: x230 + 2 <= x228 && -1 <= x235 - 1 && 0 <= x234 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1 (20) f983_0_getR_EQ(x240, x241, x242, x243, x244, x245) -> f983_0_getR_EQ(x246, x247, x248, x249, x250, x251) :|: x241 - 1 = x247 && 0 <= x246 - 1 && 2 <= x240 - 1 && 0 <= x241 - 1 && x241 - 1 <= x241 - 1 (21) __init(x252, x253, x254, x255, x256, x257) -> f1_0_main_Load(x258, x259, x260, x261, x262, x263) :|: 0 <= 0 Arcs: (1) -> (3), (5), (7), (18) (2) -> (3), (5), (7), (18) (3) -> (4), (17) (4) -> (6) (5) -> (4), (17) (7) -> (20) (10) -> (11), (12), (13), (14) (11) -> (11), (12) (12) -> (11), (12) (13) -> (15), (16) (14) -> (15), (16) (15) -> (11), (12), (13), (14) (16) -> (11), (12), (13), (14) (17) -> (19) (18) -> (19) (19) -> (19) (20) -> (20) (21) -> (1), (8), (9), (10) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f1248_0_createList_GE(x151, x152, x153, x154, x155, x156) -> f1379_0_createList_NULL(x157, x158, x159, x160, x161, x162) :|: x155 + 1 = x162 && x154 = x161 && x152 = x159 && x153 = x157 && -1 <= x160 - 1 && 1 <= x158 - 1 && -1 <= x151 - 1 && x160 <= x151 && -1 <= x155 - 1 && x155 <= x154 - 1 && -1 <= x154 - 1 && x152 <= x153 - 1 (2) f1379_0_createList_NULL(x176, x177, x178, x179, x180, x181) -> f1248_0_createList_GE(x182, x183, x184, x185, x186, x187) :|: x181 = x186 && x180 = x185 && x176 = x184 && x178 + 1 = x183 && 1 <= x182 - 1 && -1 <= x179 - 1 && 1 <= x177 - 1 && x182 - 2 <= x179 && x182 <= x177 (3) f1248_0_createList_GE(x163, x164, x165, x166, x167, x168) -> f1379_0_createList_NULL(x169, x170, x171, x172, x173, x174) :|: x164 <= x165 - 1 && -1 <= x166 - 1 && x167 <= x166 - 1 && -1 <= x167 - 1 && -1 <= x175 - 1 && x172 <= x163 && -1 <= x163 - 1 && 1 <= x170 - 1 && -1 <= x172 - 1 && x165 = x169 && x164 = x171 && x166 = x173 && x167 + 1 = x174 (4) f1379_0_createList_NULL(x188, x189, x190, x191, x192, x193) -> f1248_0_createList_GE(x194, x195, x196, x197, x198, x199) :|: x193 = x198 && x192 = x197 && x188 = x196 && x190 + 1 = x195 && 4 <= x194 - 1 && 0 <= x191 - 1 && 2 <= x189 - 1 Arcs: (1) -> (2), (4) (2) -> (1), (3) (3) -> (2), (4) (4) -> (1), (3) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f1248_0_createList_GE(x151:0, x152:0, x153:0, x154:0, x155:0, x156:0) -> f1379_0_createList_NULL(x153:0, x158:0, x152:0, x160:0, x154:0, x155:0 + 1) :|: x154:0 > -1 && x153:0 - 1 >= x152:0 && x155:0 <= x154:0 - 1 && x155:0 > -1 && x160:0 <= x151:0 && x151:0 > -1 && x160:0 > -1 && x158:0 > 1 f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, x190:0 + 1, x188:0, x192:0, x193:0, x199:0) :|: x191:0 > 0 && x194:0 > 4 && x189:0 > 2 f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, x178:0 + 1, x176:0, x180:0, x181:0, x187:0) :|: x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1 f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0, x168:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, x167:0 + 1) :|: x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1248_0_createList_GE(x1, x2, x3, x4, x5, x6) -> f1248_0_createList_GE(x1, x2, x3, x4, x5) ---------------------------------------- (9) Obligation: Rules: f1248_0_createList_GE(x151:0, x152:0, x153:0, x154:0, x155:0) -> f1379_0_createList_NULL(x153:0, x158:0, x152:0, x160:0, x154:0, x155:0 + 1) :|: x154:0 > -1 && x153:0 - 1 >= x152:0 && x155:0 <= x154:0 - 1 && x155:0 > -1 && x160:0 <= x151:0 && x151:0 > -1 && x160:0 > -1 && x158:0 > 1 f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, x190:0 + 1, x188:0, x192:0, x193:0) :|: x191:0 > 0 && x194:0 > 4 && x189:0 > 2 f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, x178:0 + 1, x176:0, x180:0, x181:0) :|: x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1 f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, x167:0 + 1) :|: x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1248_0_createList_GE(INTEGER, INTEGER, VARIABLE, VARIABLE, VARIABLE) f1379_0_createList_NULL(VARIABLE, INTEGER, VARIABLE, INTEGER, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: f1248_0_createList_GE(x151:0, x152:0, x153:0, x154:0, x155:0) -> f1379_0_createList_NULL(x153:0, x158:0, x152:0, x160:0, x154:0, c) :|: c = x155:0 + 1 && (x154:0 > -1 && x153:0 - 1 >= x152:0 && x155:0 <= x154:0 - 1 && x155:0 > -1 && x160:0 <= x151:0 && x151:0 > -1 && x160:0 > -1 && x158:0 > 1) f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, c3) :|: c3 = x167:0 + 1 && (x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0) ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1248_0_createList_GE ] = 4*f1248_0_createList_GE_4 + 2*f1248_0_createList_GE_3 + -2*f1248_0_createList_GE_2 + -2*f1248_0_createList_GE_5 [ f1379_0_createList_NULL ] = 2*f1379_0_createList_NULL_1 + -2*f1379_0_createList_NULL_3 + 4*f1379_0_createList_NULL_5 + -2*f1379_0_createList_NULL_6 + -1 The following rules are decreasing: f1248_0_createList_GE(x151:0, x152:0, x153:0, x154:0, x155:0) -> f1379_0_createList_NULL(x153:0, x158:0, x152:0, x160:0, x154:0, c) :|: c = x155:0 + 1 && (x154:0 > -1 && x153:0 - 1 >= x152:0 && x155:0 <= x154:0 - 1 && x155:0 > -1 && x160:0 <= x151:0 && x151:0 > -1 && x160:0 > -1 && x158:0 > 1) f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, c3) :|: c3 = x167:0 + 1 && (x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0) The following rules are bounded: f1248_0_createList_GE(x151:0, x152:0, x153:0, x154:0, x155:0) -> f1379_0_createList_NULL(x153:0, x158:0, x152:0, x160:0, x154:0, c) :|: c = x155:0 + 1 && (x154:0 > -1 && x153:0 - 1 >= x152:0 && x155:0 <= x154:0 - 1 && x155:0 > -1 && x160:0 <= x151:0 && x151:0 > -1 && x160:0 > -1 && x158:0 > 1) ---------------------------------------- (13) Obligation: Rules: f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, c3) :|: c3 = x167:0 + 1 && (x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0) ---------------------------------------- (14) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1379_0_createList_NULL ] = 2*f1379_0_createList_NULL_1 + 2*f1379_0_createList_NULL_5 + -2*f1379_0_createList_NULL_3 + -1 [ f1248_0_createList_GE ] = 2*f1248_0_createList_GE_3 + 2*f1248_0_createList_GE_4 + -2*f1248_0_createList_GE_2 The following rules are decreasing: f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, c3) :|: c3 = x167:0 + 1 && (x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0) The following rules are bounded: f1248_0_createList_GE(x163:0, x164:0, x165:0, x166:0, x167:0) -> f1379_0_createList_NULL(x165:0, x170:0, x164:0, x172:0, x166:0, c3) :|: c3 = x167:0 + 1 && (x170:0 > 1 && x172:0 > -1 && x163:0 > -1 && x172:0 <= x163:0 && x175:0 > -1 && x167:0 > -1 && x167:0 <= x166:0 - 1 && x166:0 > -1 && x165:0 - 1 >= x164:0) ---------------------------------------- (15) Obligation: Rules: f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) ---------------------------------------- (16) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1379_0_createList_NULL(x, x1, x2, x3, x4, x5)] = x3 [f1248_0_createList_GE(x6, x7, x8, x9, x10)] = 0 The following rules are decreasing: f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) The following rules are bounded: f1379_0_createList_NULL(x188:0, x189:0, x190:0, x191:0, x192:0, x193:0) -> f1248_0_createList_GE(x194:0, c1, x188:0, x192:0, x193:0) :|: c1 = x190:0 + 1 && (x191:0 > 0 && x194:0 > 4 && x189:0 > 2) f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) ---------------------------------------- (17) Obligation: Rules: f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1379_0_createList_NULL(x, x1, x2, x3, x4, x5)] = 1 [f1248_0_createList_GE(x6, x7, x8, x9, x10)] = 0 The following rules are decreasing: f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) The following rules are bounded: f1379_0_createList_NULL(x176:0, x177:0, x178:0, x179:0, x180:0, x181:0) -> f1248_0_createList_GE(x182:0, c2, x176:0, x180:0, x181:0) :|: c2 = x178:0 + 1 && (x182:0 - 2 <= x179:0 && x182:0 <= x177:0 && x177:0 > 1 && x182:0 > 1 && x179:0 > -1) ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f1248_0_createList_GE(x127, x128, x129, x130, x131, x132) -> f1248_0_createList_GE(x133, x134, x135, x136, x137, x138) :|: x131 = x137 && x130 = x136 && x129 = x135 && x128 + 1 = x134 && 1 <= x133 - 1 && -1 <= x127 - 1 && x133 - 2 <= x127 && x128 <= x129 - 1 && -1 <= x130 - 1 && x130 <= x131 (2) f1248_0_createList_GE(x139, x140, x141, x142, x143, x144) -> f1248_0_createList_GE(x145, x146, x147, x148, x149, x150) :|: x143 = x149 && x142 = x148 && x141 = x147 && x140 + 1 = x146 && 4 <= x145 - 1 && 0 <= x139 - 1 && x140 <= x141 - 1 && -1 <= x142 - 1 && x142 <= x143 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f1248_0_createList_GE(x139:0, x140:0, x141:0, x142:0, x143:0, x144:0) -> f1248_0_createList_GE(x145:0, x140:0 + 1, x141:0, x142:0, x143:0, x150:0) :|: x142:0 > -1 && x143:0 >= x142:0 && x141:0 - 1 >= x140:0 && x145:0 > 4 && x139:0 > 0 f1248_0_createList_GE(x127:0, x128:0, x129:0, x130:0, x131:0, x132:0) -> f1248_0_createList_GE(x133:0, x128:0 + 1, x129:0, x130:0, x131:0, x138:0) :|: x130:0 > -1 && x131:0 >= x130:0 && x129:0 - 1 >= x128:0 && x133:0 - 2 <= x127:0 && x133:0 > 1 && x127:0 > -1 ---------------------------------------- (23) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1248_0_createList_GE(x1, x2, x3, x4, x5, x6) -> f1248_0_createList_GE(x1, x2, x3, x4, x5) ---------------------------------------- (24) Obligation: Rules: f1248_0_createList_GE(x139:0, x140:0, x141:0, x142:0, x143:0) -> f1248_0_createList_GE(x145:0, x140:0 + 1, x141:0, x142:0, x143:0) :|: x142:0 > -1 && x143:0 >= x142:0 && x141:0 - 1 >= x140:0 && x145:0 > 4 && x139:0 > 0 f1248_0_createList_GE(x127:0, x128:0, x129:0, x130:0, x131:0) -> f1248_0_createList_GE(x133:0, x128:0 + 1, x129:0, x130:0, x131:0) :|: x130:0 > -1 && x131:0 >= x130:0 && x129:0 - 1 >= x128:0 && x133:0 - 2 <= x127:0 && x133:0 > 1 && x127:0 > -1 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1248_0_createList_GE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f1248_0_createList_GE(x139:0, x140:0, x141:0, x142:0, x143:0) -> f1248_0_createList_GE(x145:0, c, x141:0, x142:0, x143:0) :|: c = x140:0 + 1 && (x142:0 > -1 && x143:0 >= x142:0 && x141:0 - 1 >= x140:0 && x145:0 > 4 && x139:0 > 0) f1248_0_createList_GE(x127:0, x128:0, x129:0, x130:0, x131:0) -> f1248_0_createList_GE(x133:0, c1, x129:0, x130:0, x131:0) :|: c1 = x128:0 + 1 && (x130:0 > -1 && x131:0 >= x130:0 && x129:0 - 1 >= x128:0 && x133:0 - 2 <= x127:0 && x133:0 > 1 && x127:0 > -1) ---------------------------------------- (27) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1248_0_createList_GE(x, x1, x2, x3, x4)] = -1 - x1 + x2 The following rules are decreasing: f1248_0_createList_GE(x139:0, x140:0, x141:0, x142:0, x143:0) -> f1248_0_createList_GE(x145:0, c, x141:0, x142:0, x143:0) :|: c = x140:0 + 1 && (x142:0 > -1 && x143:0 >= x142:0 && x141:0 - 1 >= x140:0 && x145:0 > 4 && x139:0 > 0) f1248_0_createList_GE(x127:0, x128:0, x129:0, x130:0, x131:0) -> f1248_0_createList_GE(x133:0, c1, x129:0, x130:0, x131:0) :|: c1 = x128:0 + 1 && (x130:0 > -1 && x131:0 >= x130:0 && x129:0 - 1 >= x128:0 && x133:0 - 2 <= x127:0 && x133:0 > 1 && x127:0 > -1) The following rules are bounded: f1248_0_createList_GE(x139:0, x140:0, x141:0, x142:0, x143:0) -> f1248_0_createList_GE(x145:0, c, x141:0, x142:0, x143:0) :|: c = x140:0 + 1 && (x142:0 > -1 && x143:0 >= x142:0 && x141:0 - 1 >= x140:0 && x145:0 > 4 && x139:0 > 0) f1248_0_createList_GE(x127:0, x128:0, x129:0, x130:0, x131:0) -> f1248_0_createList_GE(x133:0, c1, x129:0, x130:0, x131:0) :|: c1 = x128:0 + 1 && (x130:0 > -1 && x131:0 >= x130:0 && x129:0 - 1 >= x128:0 && x133:0 - 2 <= x127:0 && x133:0 > 1 && x127:0 > -1) ---------------------------------------- (28) YES ---------------------------------------- (29) Obligation: Termination digraph: Nodes: (1) f983_0_getR_EQ(x240, x241, x242, x243, x244, x245) -> f983_0_getR_EQ(x246, x247, x248, x249, x250, x251) :|: x241 - 1 = x247 && 0 <= x246 - 1 && 2 <= x240 - 1 && 0 <= x241 - 1 && x241 - 1 <= x241 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (30) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (31) Obligation: Rules: f983_0_getR_EQ(x240:0, x241:0, x242:0, x243:0, x244:0, x245:0) -> f983_0_getR_EQ(x246:0, x241:0 - 1, x248:0, x249:0, x250:0, x251:0) :|: x240:0 > 2 && x246:0 > 0 && x241:0 > 0 ---------------------------------------- (32) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f983_0_getR_EQ(x1, x2, x3, x4, x5, x6) -> f983_0_getR_EQ(x1, x2) ---------------------------------------- (33) Obligation: Rules: f983_0_getR_EQ(x240:0, x241:0) -> f983_0_getR_EQ(x246:0, x241:0 - 1) :|: x240:0 > 2 && x246:0 > 0 && x241:0 > 0 ---------------------------------------- (34) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f983_0_getR_EQ(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (35) Obligation: Rules: f983_0_getR_EQ(x240:0, x241:0) -> f983_0_getR_EQ(x246:0, c) :|: c = x241:0 - 1 && (x240:0 > 2 && x246:0 > 0 && x241:0 > 0) ---------------------------------------- (36) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f983_0_getR_EQ ] = f983_0_getR_EQ_2 The following rules are decreasing: f983_0_getR_EQ(x240:0, x241:0) -> f983_0_getR_EQ(x246:0, c) :|: c = x241:0 - 1 && (x240:0 > 2 && x246:0 > 0 && x241:0 > 0) The following rules are bounded: f983_0_getR_EQ(x240:0, x241:0) -> f983_0_getR_EQ(x246:0, c) :|: c = x241:0 - 1 && (x240:0 > 2 && x246:0 > 0 && x241:0 > 0) ---------------------------------------- (37) YES ---------------------------------------- (38) Obligation: Termination digraph: Nodes: (1) f739_0_getFirst_NONNULL(x228, x229, x230, x231, x232, x233) -> f739_0_getFirst_NONNULL(x234, x235, x236, x237, x238, x239) :|: x230 + 2 <= x228 && -1 <= x235 - 1 && 0 <= x234 - 1 && 0 <= x229 - 1 && 2 <= x228 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (39) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (40) Obligation: Rules: f739_0_getFirst_NONNULL(x228:0, x229:0, x230:0, x231:0, x232:0, x233:0) -> f739_0_getFirst_NONNULL(x234:0, x235:0, x236:0, x237:0, x238:0, x239:0) :|: x229:0 > 0 && x228:0 > 2 && x234:0 > 0 && x235:0 > -1 && x230:0 + 2 <= x228:0 ---------------------------------------- (41) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f739_0_getFirst_NONNULL(x1, x2, x3, x4, x5, x6) -> f739_0_getFirst_NONNULL(x1, x2, x3) ---------------------------------------- (42) Obligation: Rules: f739_0_getFirst_NONNULL(x228:0, x229:0, x230:0) -> f739_0_getFirst_NONNULL(x234:0, x235:0, x236:0) :|: x229:0 > 0 && x228:0 > 2 && x234:0 > 0 && x235:0 > -1 && x230:0 + 2 <= x228:0 ---------------------------------------- (43) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f739_0_getFirst_NONNULL(INTEGER, INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (44) Obligation: Rules: f739_0_getFirst_NONNULL(x228:0, x229:0, x230:0) -> f739_0_getFirst_NONNULL(x234:0, x235:0, x236:0) :|: x229:0 > 0 && x228:0 > 2 && x234:0 > 0 && x235:0 > -1 && x230:0 + 2 <= x228:0 ---------------------------------------- (45) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (46) Obligation: Rules: f739_0_getFirst_NONNULL(x228:0:0, x229:0:0, x230:0:0) -> f739_0_getFirst_NONNULL(x234:0:0, x235:0:0, x236:0:0) :|: x235:0:0 > -1 && x230:0:0 + 2 <= x228:0:0 && x234:0:0 > 0 && x228:0:0 > 2 && x229:0:0 > 0 ---------------------------------------- (47) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x228:0:0, x229:0:0, x230:0:0) -> f(1, x234:0:0, x235:0:0, x236:0:0) :|: pc = 1 && (x235:0:0 > -1 && x230:0:0 + 2 <= x228:0:0 && x234:0:0 > 0 && x228:0:0 > 2 && x229:0:0 > 0) Witness term starting non-terminating reduction: f(1, 15, 15, -8) ---------------------------------------- (48) NO