NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 4214 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 46 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 61 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 31 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 0 ms] (25) IRSwT (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (27) IRSwT (28) FilterProof [EQUIVALENT, 0 ms] (29) IntTRS (30) IntTRSCompressionProof [EQUIVALENT, 0 ms] (31) IntTRS (32) IntTRSPeriodicNontermProof [COMPLETE, 8 ms] (33) NO ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f962_0_main_LE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 1 = arg4P && -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P + 1 <= arg1 && arg1P <= arg1 && -1 <= arg3P - 1 && -1 <= arg2 - 1 f962_0_main_LE(x, x1, x2, x3, x4, x6) -> f962_0_main_LE(x7, x8, x9, x10, x11, x12) :|: 0 <= x2 - 1 && 0 <= x14 - 1 && x7 <= x && x7 - 1 <= x1 && x8 - 2 <= x1 && 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x7 - 1 && 1 <= x8 - 1 && x2 - 1 = x9 f962_0_main_LE(x15, x16, x17, x18, x19, x20) -> f962_0_main_LE(x21, x22, x23, x24, x25, x26) :|: 0 <= x17 - 1 && 0 <= x27 - 1 && x21 <= x15 && x21 - 1 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x21 - 1 && 2 <= x22 - 1 && x17 - 1 = x23 f1714_0_createTree_Return(x28, x29, x31, x32, x33, x34) -> f962_0_main_LE(x35, x36, x37, x38, x39, x40) :|: x33 = x38 && x31 - 1 = x37 && x34 + 2 <= x32 && 3 <= x36 - 1 && 0 <= x35 - 1 && 1 <= x32 - 1 && 0 <= x28 - 1 && x35 + 1 <= x32 && x35 <= x28 f962_0_main_LE(x41, x42, x43, x44, x45, x47) -> f1548_0_flatten_NULL(x48, x49, x50, x51, x52, x53) :|: x48 <= x42 && 0 <= x54 - 1 && x49 <= x42 && 0 <= x41 - 1 && -1 <= x42 - 1 && -1 <= x48 - 1 && -1 <= x49 - 1 && 0 = x43 f1548_0_flatten_NULL(x55, x56, x57, x58, x59, x60) -> f1548_0_flatten_NULL(x61, x62, x63, x64, x65, x66) :|: -1 <= x62 - 1 && -1 <= x61 - 1 && 1 <= x56 - 1 && 1 <= x55 - 1 && x62 + 2 <= x56 && x62 + 2 <= x55 && x61 + 2 <= x56 && x61 + 2 <= x55 f1548_0_flatten_NULL(x68, x69, x70, x71, x72, x73) -> f1548_0_flatten_NULL(x74, x76, x77, x78, x79, x80) :|: 2 <= x76 - 1 && 2 <= x74 - 1 && 2 <= x69 - 1 && 2 <= x68 - 1 && x76 - 2 <= x69 && x76 - 2 <= x68 && x74 - 2 <= x69 && x74 - 2 <= x68 f962_0_main_LE(x81, x82, x83, x84, x85, x86) -> f2482_0_createTree_LE(x87, x88, x89, x90, x91, x92) :|: 0 <= x89 - 1 && 0 <= x93 - 1 && 0 <= x83 - 1 && -1 <= x84 - 1 && x87 - 1 <= x81 && x87 - 2 <= x82 && x88 - 1 <= x81 && x88 - 2 <= x82 && 0 <= x81 - 1 && -1 <= x82 - 1 && 1 <= x87 - 1 && 1 <= x88 - 1 f2482_0_createTree_LE(x94, x95, x96, x99, x100, x101) -> f2482_0_createTree_LE(x102, x103, x105, x106, x107, x108) :|: x99 + 1 = x106 && x96 - 1 = x105 && 0 <= x103 - 1 && 0 <= x102 - 1 && 2 <= x95 - 1 && 0 <= x94 - 1 && x103 + 2 <= x95 && x102 <= x94 && 0 <= x96 - 1 && -1 <= x99 - 1 f2482_0_createTree_LE(x109, x110, x111, x112, x113, x114) -> f2482_0_createTree_LE(x115, x116, x118, x119, x120, x121) :|: 0 <= x111 - 1 && 0 <= x122 - 1 && -1 <= x112 - 1 && x115 <= x109 && x116 + 2 <= x110 && 0 <= x109 - 1 && 2 <= x110 - 1 && 0 <= x115 - 1 && 0 <= x116 - 1 && x111 - 1 = x118 && x112 + 1 = x119 f2482_0_createTree_LE(x123, x124, x125, x126, x127, x128) -> f2482_0_createTree_LE(x129, x130, x131, x132, x133, x134) :|: -1 <= x126 - 1 && 0 <= x135 - 1 && 0 <= x125 - 1 && 0 <= x123 - 1 && 1 <= x124 - 1 && 0 <= x129 - 1 && 0 <= x130 - 1 && x125 - 1 = x131 f2482_0_createTree_LE(x136, x137, x138, x139, x140, x141) -> f2482_0_createTree_LE(x142, x143, x144, x145, x146, x147) :|: x138 - 1 = x144 && 0 <= x143 - 1 && 0 <= x142 - 1 && 1 <= x137 - 1 && 0 <= x136 - 1 && -1 <= x139 - 1 && 0 <= x138 - 1 f2482_0_createTree_LE(x148, x149, x150, x151, x152, x153) -> f2482_0_createTree_LE(x154, x155, x156, x157, x158, x159) :|: x150 - 1 = x156 && 3 <= x155 - 1 && 3 <= x154 - 1 && 1 <= x149 - 1 && 1 <= x148 - 1 && x155 - 2 <= x149 && x155 - 2 <= x148 && x154 - 2 <= x149 && x154 - 2 <= x148 && -1 <= x151 - 1 && 0 <= x150 - 1 f2482_0_createTree_LE(x160, x161, x162, x163, x164, x165) -> f2482_0_createTree_LE(x166, x167, x168, x169, x170, x171) :|: -1 <= x163 - 1 && 0 <= x172 - 1 && 0 <= x162 - 1 && x166 - 2 <= x160 && x166 - 2 <= x161 && x167 - 2 <= x160 && x167 - 2 <= x161 && 1 <= x160 - 1 && 1 <= x161 - 1 && 3 <= x166 - 1 && 3 <= x167 - 1 && x162 - 1 = x168 f962_0_main_LE(x173, x174, x175, x176, x177, x178) -> f1223_0_random_ArrayAccess(x179, x180, x181, x182, x183, x184) :|: 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x175 - 1 && -1 <= x176 - 1 && x179 <= x173 && x179 - 1 <= x174 && 0 <= x173 - 1 && -1 <= x174 - 1 && 0 <= x179 - 1 && x176 + 1 = x180 f2482_0_createTree_LE(x187, x188, x189, x190, x191, x192) -> f1223_0_random_ArrayAccess(x193, x194, x195, x196, x197, x198) :|: x190 + 1 = x194 && 0 <= x193 - 1 && 1 <= x188 - 1 && 0 <= x187 - 1 && x193 + 1 <= x188 && x193 <= x187 && -1 <= x190 - 1 && 0 <= x189 - 1 f2482_0_createTree_LE(x199, x200, x201, x202, x203, x204) -> f1223_0_random_ArrayAccess(x205, x206, x207, x208, x209, x210) :|: -1 <= x202 - 1 && 0 <= x211 - 1 && 0 <= x201 - 1 && x205 <= x199 && x205 + 1 <= x200 && 0 <= x199 - 1 && 1 <= x200 - 1 && 0 <= x205 - 1 && x202 + 1 = x206 __init(x212, x213, x214, x215, x216, x217) -> f1_0_main_Load(x218, x219, x220, x221, x222, x223) :|: 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) -> f962_0_main_LE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 1 = arg4P && -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P + 1 <= arg1 && arg1P <= arg1 && -1 <= arg3P - 1 && -1 <= arg2 - 1 f962_0_main_LE(x, x1, x2, x3, x4, x6) -> f962_0_main_LE(x7, x8, x9, x10, x11, x12) :|: 0 <= x2 - 1 && 0 <= x14 - 1 && x7 <= x && x7 - 1 <= x1 && x8 - 2 <= x1 && 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x7 - 1 && 1 <= x8 - 1 && x2 - 1 = x9 f962_0_main_LE(x15, x16, x17, x18, x19, x20) -> f962_0_main_LE(x21, x22, x23, x24, x25, x26) :|: 0 <= x17 - 1 && 0 <= x27 - 1 && x21 <= x15 && x21 - 1 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x21 - 1 && 2 <= x22 - 1 && x17 - 1 = x23 f1714_0_createTree_Return(x28, x29, x31, x32, x33, x34) -> f962_0_main_LE(x35, x36, x37, x38, x39, x40) :|: x33 = x38 && x31 - 1 = x37 && x34 + 2 <= x32 && 3 <= x36 - 1 && 0 <= x35 - 1 && 1 <= x32 - 1 && 0 <= x28 - 1 && x35 + 1 <= x32 && x35 <= x28 f962_0_main_LE(x41, x42, x43, x44, x45, x47) -> f1548_0_flatten_NULL(x48, x49, x50, x51, x52, x53) :|: x48 <= x42 && 0 <= x54 - 1 && x49 <= x42 && 0 <= x41 - 1 && -1 <= x42 - 1 && -1 <= x48 - 1 && -1 <= x49 - 1 && 0 = x43 f1548_0_flatten_NULL(x55, x56, x57, x58, x59, x60) -> f1548_0_flatten_NULL(x61, x62, x63, x64, x65, x66) :|: -1 <= x62 - 1 && -1 <= x61 - 1 && 1 <= x56 - 1 && 1 <= x55 - 1 && x62 + 2 <= x56 && x62 + 2 <= x55 && x61 + 2 <= x56 && x61 + 2 <= x55 f1548_0_flatten_NULL(x68, x69, x70, x71, x72, x73) -> f1548_0_flatten_NULL(x74, x76, x77, x78, x79, x80) :|: 2 <= x76 - 1 && 2 <= x74 - 1 && 2 <= x69 - 1 && 2 <= x68 - 1 && x76 - 2 <= x69 && x76 - 2 <= x68 && x74 - 2 <= x69 && x74 - 2 <= x68 f962_0_main_LE(x81, x82, x83, x84, x85, x86) -> f2482_0_createTree_LE(x87, x88, x89, x90, x91, x92) :|: 0 <= x89 - 1 && 0 <= x93 - 1 && 0 <= x83 - 1 && -1 <= x84 - 1 && x87 - 1 <= x81 && x87 - 2 <= x82 && x88 - 1 <= x81 && x88 - 2 <= x82 && 0 <= x81 - 1 && -1 <= x82 - 1 && 1 <= x87 - 1 && 1 <= x88 - 1 f2482_0_createTree_LE(x94, x95, x96, x99, x100, x101) -> f2482_0_createTree_LE(x102, x103, x105, x106, x107, x108) :|: x99 + 1 = x106 && x96 - 1 = x105 && 0 <= x103 - 1 && 0 <= x102 - 1 && 2 <= x95 - 1 && 0 <= x94 - 1 && x103 + 2 <= x95 && x102 <= x94 && 0 <= x96 - 1 && -1 <= x99 - 1 f2482_0_createTree_LE(x109, x110, x111, x112, x113, x114) -> f2482_0_createTree_LE(x115, x116, x118, x119, x120, x121) :|: 0 <= x111 - 1 && 0 <= x122 - 1 && -1 <= x112 - 1 && x115 <= x109 && x116 + 2 <= x110 && 0 <= x109 - 1 && 2 <= x110 - 1 && 0 <= x115 - 1 && 0 <= x116 - 1 && x111 - 1 = x118 && x112 + 1 = x119 f2482_0_createTree_LE(x123, x124, x125, x126, x127, x128) -> f2482_0_createTree_LE(x129, x130, x131, x132, x133, x134) :|: -1 <= x126 - 1 && 0 <= x135 - 1 && 0 <= x125 - 1 && 0 <= x123 - 1 && 1 <= x124 - 1 && 0 <= x129 - 1 && 0 <= x130 - 1 && x125 - 1 = x131 f2482_0_createTree_LE(x136, x137, x138, x139, x140, x141) -> f2482_0_createTree_LE(x142, x143, x144, x145, x146, x147) :|: x138 - 1 = x144 && 0 <= x143 - 1 && 0 <= x142 - 1 && 1 <= x137 - 1 && 0 <= x136 - 1 && -1 <= x139 - 1 && 0 <= x138 - 1 f2482_0_createTree_LE(x148, x149, x150, x151, x152, x153) -> f2482_0_createTree_LE(x154, x155, x156, x157, x158, x159) :|: x150 - 1 = x156 && 3 <= x155 - 1 && 3 <= x154 - 1 && 1 <= x149 - 1 && 1 <= x148 - 1 && x155 - 2 <= x149 && x155 - 2 <= x148 && x154 - 2 <= x149 && x154 - 2 <= x148 && -1 <= x151 - 1 && 0 <= x150 - 1 f2482_0_createTree_LE(x160, x161, x162, x163, x164, x165) -> f2482_0_createTree_LE(x166, x167, x168, x169, x170, x171) :|: -1 <= x163 - 1 && 0 <= x172 - 1 && 0 <= x162 - 1 && x166 - 2 <= x160 && x166 - 2 <= x161 && x167 - 2 <= x160 && x167 - 2 <= x161 && 1 <= x160 - 1 && 1 <= x161 - 1 && 3 <= x166 - 1 && 3 <= x167 - 1 && x162 - 1 = x168 f962_0_main_LE(x173, x174, x175, x176, x177, x178) -> f1223_0_random_ArrayAccess(x179, x180, x181, x182, x183, x184) :|: 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x175 - 1 && -1 <= x176 - 1 && x179 <= x173 && x179 - 1 <= x174 && 0 <= x173 - 1 && -1 <= x174 - 1 && 0 <= x179 - 1 && x176 + 1 = x180 f2482_0_createTree_LE(x187, x188, x189, x190, x191, x192) -> f1223_0_random_ArrayAccess(x193, x194, x195, x196, x197, x198) :|: x190 + 1 = x194 && 0 <= x193 - 1 && 1 <= x188 - 1 && 0 <= x187 - 1 && x193 + 1 <= x188 && x193 <= x187 && -1 <= x190 - 1 && 0 <= x189 - 1 f2482_0_createTree_LE(x199, x200, x201, x202, x203, x204) -> f1223_0_random_ArrayAccess(x205, x206, x207, x208, x209, x210) :|: -1 <= x202 - 1 && 0 <= x211 - 1 && 0 <= x201 - 1 && x205 <= x199 && x205 + 1 <= x200 && 0 <= x199 - 1 && 1 <= x200 - 1 && 0 <= x205 - 1 && x202 + 1 = x206 __init(x212, x213, x214, x215, x216, x217) -> f1_0_main_Load(x218, x219, x220, x221, x222, x223) :|: 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) -> f962_0_main_LE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: 1 = arg4P && -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P + 1 <= arg1 && arg1P <= arg1 && -1 <= arg3P - 1 && -1 <= arg2 - 1 (2) f962_0_main_LE(x, x1, x2, x3, x4, x6) -> f962_0_main_LE(x7, x8, x9, x10, x11, x12) :|: 0 <= x2 - 1 && 0 <= x14 - 1 && x7 <= x && x7 - 1 <= x1 && x8 - 2 <= x1 && 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x7 - 1 && 1 <= x8 - 1 && x2 - 1 = x9 (3) f962_0_main_LE(x15, x16, x17, x18, x19, x20) -> f962_0_main_LE(x21, x22, x23, x24, x25, x26) :|: 0 <= x17 - 1 && 0 <= x27 - 1 && x21 <= x15 && x21 - 1 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x21 - 1 && 2 <= x22 - 1 && x17 - 1 = x23 (4) f1714_0_createTree_Return(x28, x29, x31, x32, x33, x34) -> f962_0_main_LE(x35, x36, x37, x38, x39, x40) :|: x33 = x38 && x31 - 1 = x37 && x34 + 2 <= x32 && 3 <= x36 - 1 && 0 <= x35 - 1 && 1 <= x32 - 1 && 0 <= x28 - 1 && x35 + 1 <= x32 && x35 <= x28 (5) f962_0_main_LE(x41, x42, x43, x44, x45, x47) -> f1548_0_flatten_NULL(x48, x49, x50, x51, x52, x53) :|: x48 <= x42 && 0 <= x54 - 1 && x49 <= x42 && 0 <= x41 - 1 && -1 <= x42 - 1 && -1 <= x48 - 1 && -1 <= x49 - 1 && 0 = x43 (6) f1548_0_flatten_NULL(x55, x56, x57, x58, x59, x60) -> f1548_0_flatten_NULL(x61, x62, x63, x64, x65, x66) :|: -1 <= x62 - 1 && -1 <= x61 - 1 && 1 <= x56 - 1 && 1 <= x55 - 1 && x62 + 2 <= x56 && x62 + 2 <= x55 && x61 + 2 <= x56 && x61 + 2 <= x55 (7) f1548_0_flatten_NULL(x68, x69, x70, x71, x72, x73) -> f1548_0_flatten_NULL(x74, x76, x77, x78, x79, x80) :|: 2 <= x76 - 1 && 2 <= x74 - 1 && 2 <= x69 - 1 && 2 <= x68 - 1 && x76 - 2 <= x69 && x76 - 2 <= x68 && x74 - 2 <= x69 && x74 - 2 <= x68 (8) f962_0_main_LE(x81, x82, x83, x84, x85, x86) -> f2482_0_createTree_LE(x87, x88, x89, x90, x91, x92) :|: 0 <= x89 - 1 && 0 <= x93 - 1 && 0 <= x83 - 1 && -1 <= x84 - 1 && x87 - 1 <= x81 && x87 - 2 <= x82 && x88 - 1 <= x81 && x88 - 2 <= x82 && 0 <= x81 - 1 && -1 <= x82 - 1 && 1 <= x87 - 1 && 1 <= x88 - 1 (9) f2482_0_createTree_LE(x94, x95, x96, x99, x100, x101) -> f2482_0_createTree_LE(x102, x103, x105, x106, x107, x108) :|: x99 + 1 = x106 && x96 - 1 = x105 && 0 <= x103 - 1 && 0 <= x102 - 1 && 2 <= x95 - 1 && 0 <= x94 - 1 && x103 + 2 <= x95 && x102 <= x94 && 0 <= x96 - 1 && -1 <= x99 - 1 (10) f2482_0_createTree_LE(x109, x110, x111, x112, x113, x114) -> f2482_0_createTree_LE(x115, x116, x118, x119, x120, x121) :|: 0 <= x111 - 1 && 0 <= x122 - 1 && -1 <= x112 - 1 && x115 <= x109 && x116 + 2 <= x110 && 0 <= x109 - 1 && 2 <= x110 - 1 && 0 <= x115 - 1 && 0 <= x116 - 1 && x111 - 1 = x118 && x112 + 1 = x119 (11) f2482_0_createTree_LE(x123, x124, x125, x126, x127, x128) -> f2482_0_createTree_LE(x129, x130, x131, x132, x133, x134) :|: -1 <= x126 - 1 && 0 <= x135 - 1 && 0 <= x125 - 1 && 0 <= x123 - 1 && 1 <= x124 - 1 && 0 <= x129 - 1 && 0 <= x130 - 1 && x125 - 1 = x131 (12) f2482_0_createTree_LE(x136, x137, x138, x139, x140, x141) -> f2482_0_createTree_LE(x142, x143, x144, x145, x146, x147) :|: x138 - 1 = x144 && 0 <= x143 - 1 && 0 <= x142 - 1 && 1 <= x137 - 1 && 0 <= x136 - 1 && -1 <= x139 - 1 && 0 <= x138 - 1 (13) f2482_0_createTree_LE(x148, x149, x150, x151, x152, x153) -> f2482_0_createTree_LE(x154, x155, x156, x157, x158, x159) :|: x150 - 1 = x156 && 3 <= x155 - 1 && 3 <= x154 - 1 && 1 <= x149 - 1 && 1 <= x148 - 1 && x155 - 2 <= x149 && x155 - 2 <= x148 && x154 - 2 <= x149 && x154 - 2 <= x148 && -1 <= x151 - 1 && 0 <= x150 - 1 (14) f2482_0_createTree_LE(x160, x161, x162, x163, x164, x165) -> f2482_0_createTree_LE(x166, x167, x168, x169, x170, x171) :|: -1 <= x163 - 1 && 0 <= x172 - 1 && 0 <= x162 - 1 && x166 - 2 <= x160 && x166 - 2 <= x161 && x167 - 2 <= x160 && x167 - 2 <= x161 && 1 <= x160 - 1 && 1 <= x161 - 1 && 3 <= x166 - 1 && 3 <= x167 - 1 && x162 - 1 = x168 (15) f962_0_main_LE(x173, x174, x175, x176, x177, x178) -> f1223_0_random_ArrayAccess(x179, x180, x181, x182, x183, x184) :|: 0 <= x185 - 1 && 0 <= x186 - 1 && 0 <= x175 - 1 && -1 <= x176 - 1 && x179 <= x173 && x179 - 1 <= x174 && 0 <= x173 - 1 && -1 <= x174 - 1 && 0 <= x179 - 1 && x176 + 1 = x180 (16) f2482_0_createTree_LE(x187, x188, x189, x190, x191, x192) -> f1223_0_random_ArrayAccess(x193, x194, x195, x196, x197, x198) :|: x190 + 1 = x194 && 0 <= x193 - 1 && 1 <= x188 - 1 && 0 <= x187 - 1 && x193 + 1 <= x188 && x193 <= x187 && -1 <= x190 - 1 && 0 <= x189 - 1 (17) f2482_0_createTree_LE(x199, x200, x201, x202, x203, x204) -> f1223_0_random_ArrayAccess(x205, x206, x207, x208, x209, x210) :|: -1 <= x202 - 1 && 0 <= x211 - 1 && 0 <= x201 - 1 && x205 <= x199 && x205 + 1 <= x200 && 0 <= x199 - 1 && 1 <= x200 - 1 && 0 <= x205 - 1 && x202 + 1 = x206 (18) __init(x212, x213, x214, x215, x216, x217) -> f1_0_main_Load(x218, x219, x220, x221, x222, x223) :|: 0 <= 0 Arcs: (1) -> (2), (3), (5), (8), (15) (2) -> (2), (3), (5), (8), (15) (3) -> (2), (3), (5), (8), (15) (4) -> (2), (3), (5), (8), (15) (5) -> (6), (7) (6) -> (6), (7) (7) -> (6), (7) (8) -> (9), (10), (11), (12), (13), (14), (16), (17) (9) -> (9), (10), (11), (12), (13), (14), (16), (17) (10) -> (9), (10), (11), (12), (13), (14), (16), (17) (11) -> (9), (10), (11), (12), (13), (14), (16), (17) (12) -> (9), (10), (11), (12), (13), (14), (16), (17) (13) -> (9), (10), (11), (12), (13), (14), (16), (17) (14) -> (9), (10), (11), (12), (13), (14), (16), (17) (18) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f962_0_main_LE(x, x1, x2, x3, x4, x6) -> f962_0_main_LE(x7, x8, x9, x10, x11, x12) :|: 0 <= x2 - 1 && 0 <= x14 - 1 && x7 <= x && x7 - 1 <= x1 && x8 - 2 <= x1 && 0 <= x - 1 && -1 <= x1 - 1 && 0 <= x7 - 1 && 1 <= x8 - 1 && x2 - 1 = x9 (2) f962_0_main_LE(x15, x16, x17, x18, x19, x20) -> f962_0_main_LE(x21, x22, x23, x24, x25, x26) :|: 0 <= x17 - 1 && 0 <= x27 - 1 && x21 <= x15 && x21 - 1 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x21 - 1 && 2 <= x22 - 1 && x17 - 1 = x23 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f962_0_main_LE(x:0, x1:0, x2:0, x3:0, x4:0, x6:0) -> f962_0_main_LE(x7:0, x8:0, x2:0 - 1, x10:0, x11:0, x12:0) :|: x7:0 > 0 && x8:0 > 1 && x1:0 > -1 && x:0 > 0 && x8:0 - 2 <= x1:0 && x7:0 - 1 <= x1:0 && x:0 >= x7:0 && x14:0 > 0 && x2:0 > 0 f962_0_main_LE(x15:0, x16:0, x17:0, x18:0, x19:0, x20:0) -> f962_0_main_LE(x21:0, x22:0, x17:0 - 1, x24:0, x25:0, x26:0) :|: x21:0 > 0 && x22:0 > 2 && x16:0 > -1 && x15:0 > 0 && x21:0 - 1 <= x16:0 && x21:0 <= x15:0 && x27:0 > 0 && x17:0 > 0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f962_0_main_LE(x1, x2, x3, x4, x5, x6) -> f962_0_main_LE(x1, x2, x3) ---------------------------------------- (9) Obligation: Rules: f962_0_main_LE(x:0, x1:0, x2:0) -> f962_0_main_LE(x7:0, x8:0, x2:0 - 1) :|: x7:0 > 0 && x8:0 > 1 && x1:0 > -1 && x:0 > 0 && x8:0 - 2 <= x1:0 && x7:0 - 1 <= x1:0 && x:0 >= x7:0 && x14:0 > 0 && x2:0 > 0 f962_0_main_LE(x15:0, x16:0, x17:0) -> f962_0_main_LE(x21:0, x22:0, x17:0 - 1) :|: x21:0 > 0 && x22:0 > 2 && x16:0 > -1 && x15:0 > 0 && x21:0 - 1 <= x16:0 && x21:0 <= x15:0 && x27:0 > 0 && x17:0 > 0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f962_0_main_LE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: f962_0_main_LE(x:0, x1:0, x2:0) -> f962_0_main_LE(x7:0, x8:0, c) :|: c = x2:0 - 1 && (x7:0 > 0 && x8:0 > 1 && x1:0 > -1 && x:0 > 0 && x8:0 - 2 <= x1:0 && x7:0 - 1 <= x1:0 && x:0 >= x7:0 && x14:0 > 0 && x2:0 > 0) f962_0_main_LE(x15:0, x16:0, x17:0) -> f962_0_main_LE(x21:0, x22:0, c1) :|: c1 = x17:0 - 1 && (x21:0 > 0 && x22:0 > 2 && x16:0 > -1 && x15:0 > 0 && x21:0 - 1 <= x16:0 && x21:0 <= x15:0 && x27:0 > 0 && x17:0 > 0) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f962_0_main_LE(x, x1, x2)] = -1 + x2 The following rules are decreasing: f962_0_main_LE(x:0, x1:0, x2:0) -> f962_0_main_LE(x7:0, x8:0, c) :|: c = x2:0 - 1 && (x7:0 > 0 && x8:0 > 1 && x1:0 > -1 && x:0 > 0 && x8:0 - 2 <= x1:0 && x7:0 - 1 <= x1:0 && x:0 >= x7:0 && x14:0 > 0 && x2:0 > 0) f962_0_main_LE(x15:0, x16:0, x17:0) -> f962_0_main_LE(x21:0, x22:0, c1) :|: c1 = x17:0 - 1 && (x21:0 > 0 && x22:0 > 2 && x16:0 > -1 && x15:0 > 0 && x21:0 - 1 <= x16:0 && x21:0 <= x15:0 && x27:0 > 0 && x17:0 > 0) The following rules are bounded: f962_0_main_LE(x:0, x1:0, x2:0) -> f962_0_main_LE(x7:0, x8:0, c) :|: c = x2:0 - 1 && (x7:0 > 0 && x8:0 > 1 && x1:0 > -1 && x:0 > 0 && x8:0 - 2 <= x1:0 && x7:0 - 1 <= x1:0 && x:0 >= x7:0 && x14:0 > 0 && x2:0 > 0) f962_0_main_LE(x15:0, x16:0, x17:0) -> f962_0_main_LE(x21:0, x22:0, c1) :|: c1 = x17:0 - 1 && (x21:0 > 0 && x22:0 > 2 && x16:0 > -1 && x15:0 > 0 && x21:0 - 1 <= x16:0 && x21:0 <= x15:0 && x27:0 > 0 && x17:0 > 0) ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) f2482_0_createTree_LE(x94, x95, x96, x99, x100, x101) -> f2482_0_createTree_LE(x102, x103, x105, x106, x107, x108) :|: x99 + 1 = x106 && x96 - 1 = x105 && 0 <= x103 - 1 && 0 <= x102 - 1 && 2 <= x95 - 1 && 0 <= x94 - 1 && x103 + 2 <= x95 && x102 <= x94 && 0 <= x96 - 1 && -1 <= x99 - 1 (2) f2482_0_createTree_LE(x109, x110, x111, x112, x113, x114) -> f2482_0_createTree_LE(x115, x116, x118, x119, x120, x121) :|: 0 <= x111 - 1 && 0 <= x122 - 1 && -1 <= x112 - 1 && x115 <= x109 && x116 + 2 <= x110 && 0 <= x109 - 1 && 2 <= x110 - 1 && 0 <= x115 - 1 && 0 <= x116 - 1 && x111 - 1 = x118 && x112 + 1 = x119 (3) f2482_0_createTree_LE(x123, x124, x125, x126, x127, x128) -> f2482_0_createTree_LE(x129, x130, x131, x132, x133, x134) :|: -1 <= x126 - 1 && 0 <= x135 - 1 && 0 <= x125 - 1 && 0 <= x123 - 1 && 1 <= x124 - 1 && 0 <= x129 - 1 && 0 <= x130 - 1 && x125 - 1 = x131 (4) f2482_0_createTree_LE(x136, x137, x138, x139, x140, x141) -> f2482_0_createTree_LE(x142, x143, x144, x145, x146, x147) :|: x138 - 1 = x144 && 0 <= x143 - 1 && 0 <= x142 - 1 && 1 <= x137 - 1 && 0 <= x136 - 1 && -1 <= x139 - 1 && 0 <= x138 - 1 (5) f2482_0_createTree_LE(x148, x149, x150, x151, x152, x153) -> f2482_0_createTree_LE(x154, x155, x156, x157, x158, x159) :|: x150 - 1 = x156 && 3 <= x155 - 1 && 3 <= x154 - 1 && 1 <= x149 - 1 && 1 <= x148 - 1 && x155 - 2 <= x149 && x155 - 2 <= x148 && x154 - 2 <= x149 && x154 - 2 <= x148 && -1 <= x151 - 1 && 0 <= x150 - 1 (6) f2482_0_createTree_LE(x160, x161, x162, x163, x164, x165) -> f2482_0_createTree_LE(x166, x167, x168, x169, x170, x171) :|: -1 <= x163 - 1 && 0 <= x172 - 1 && 0 <= x162 - 1 && x166 - 2 <= x160 && x166 - 2 <= x161 && x167 - 2 <= x160 && x167 - 2 <= x161 && 1 <= x160 - 1 && 1 <= x161 - 1 && 3 <= x166 - 1 && 3 <= x167 - 1 && x162 - 1 = x168 Arcs: (1) -> (1), (2), (3), (4), (5), (6) (2) -> (1), (2), (3), (4), (5), (6) (3) -> (1), (2), (3), (4), (5), (6) (4) -> (1), (2), (3), (4), (5), (6) (5) -> (1), (2), (3), (4), (5), (6) (6) -> (1), (2), (3), (4), (5), (6) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: f2482_0_createTree_LE(x109:0, x110:0, x111:0, x112:0, x113:0, x114:0) -> f2482_0_createTree_LE(x115:0, x116:0, x111:0 - 1, x112:0 + 1, x120:0, x121:0) :|: x115:0 > 0 && x116:0 > 0 && x110:0 > 2 && x109:0 > 0 && x116:0 + 2 <= x110:0 && x115:0 <= x109:0 && x112:0 > -1 && x122:0 > 0 && x111:0 > 0 f2482_0_createTree_LE(x123:0, x124:0, x125:0, x126:0, x127:0, x128:0) -> f2482_0_createTree_LE(x129:0, x130:0, x125:0 - 1, x132:0, x133:0, x134:0) :|: x129:0 > 0 && x130:0 > 0 && x124:0 > 1 && x123:0 > 0 && x125:0 > 0 && x135:0 > 0 && x126:0 > -1 f2482_0_createTree_LE(x160:0, x161:0, x162:0, x163:0, x164:0, x165:0) -> f2482_0_createTree_LE(x166:0, x167:0, x162:0 - 1, x169:0, x170:0, x171:0) :|: x166:0 > 3 && x167:0 > 3 && x161:0 > 1 && x160:0 > 1 && x167:0 - 2 <= x161:0 && x167:0 - 2 <= x160:0 && x166:0 - 2 <= x161:0 && x166:0 - 2 <= x160:0 && x162:0 > 0 && x172:0 > 0 && x163:0 > -1 f2482_0_createTree_LE(x148:0, x149:0, x150:0, x151:0, x152:0, x153:0) -> f2482_0_createTree_LE(x154:0, x155:0, x150:0 - 1, x157:0, x158:0, x159:0) :|: x151:0 > -1 && x150:0 > 0 && x154:0 - 2 <= x148:0 && x154:0 - 2 <= x149:0 && x155:0 - 2 <= x148:0 && x155:0 - 2 <= x149:0 && x148:0 > 1 && x149:0 > 1 && x155:0 > 3 && x154:0 > 3 f2482_0_createTree_LE(x136:0, x137:0, x138:0, x139:0, x140:0, x141:0) -> f2482_0_createTree_LE(x142:0, x143:0, x138:0 - 1, x145:0, x146:0, x147:0) :|: x139:0 > -1 && x138:0 > 0 && x136:0 > 0 && x137:0 > 1 && x143:0 > 0 && x142:0 > 0 f2482_0_createTree_LE(x94:0, x95:0, x96:0, x99:0, x100:0, x101:0) -> f2482_0_createTree_LE(x102:0, x103:0, x96:0 - 1, x99:0 + 1, x107:0, x108:0) :|: x96:0 > 0 && x99:0 > -1 && x94:0 >= x102:0 && x95:0 >= x103:0 + 2 && x94:0 > 0 && x95:0 > 2 && x103:0 > 0 && x102:0 > 0 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f2482_0_createTree_LE(x1, x2, x3, x4, x5, x6) -> f2482_0_createTree_LE(x1, x2, x3, x4) ---------------------------------------- (18) Obligation: Rules: f2482_0_createTree_LE(x109:0, x110:0, x111:0, x112:0) -> f2482_0_createTree_LE(x115:0, x116:0, x111:0 - 1, x112:0 + 1) :|: x115:0 > 0 && x116:0 > 0 && x110:0 > 2 && x109:0 > 0 && x116:0 + 2 <= x110:0 && x115:0 <= x109:0 && x112:0 > -1 && x122:0 > 0 && x111:0 > 0 f2482_0_createTree_LE(x123:0, x124:0, x125:0, x126:0) -> f2482_0_createTree_LE(x129:0, x130:0, x125:0 - 1, x132:0) :|: x129:0 > 0 && x130:0 > 0 && x124:0 > 1 && x123:0 > 0 && x125:0 > 0 && x135:0 > 0 && x126:0 > -1 f2482_0_createTree_LE(x160:0, x161:0, x162:0, x163:0) -> f2482_0_createTree_LE(x166:0, x167:0, x162:0 - 1, x169:0) :|: x166:0 > 3 && x167:0 > 3 && x161:0 > 1 && x160:0 > 1 && x167:0 - 2 <= x161:0 && x167:0 - 2 <= x160:0 && x166:0 - 2 <= x161:0 && x166:0 - 2 <= x160:0 && x162:0 > 0 && x172:0 > 0 && x163:0 > -1 f2482_0_createTree_LE(x148:0, x149:0, x150:0, x151:0) -> f2482_0_createTree_LE(x154:0, x155:0, x150:0 - 1, x157:0) :|: x151:0 > -1 && x150:0 > 0 && x154:0 - 2 <= x148:0 && x154:0 - 2 <= x149:0 && x155:0 - 2 <= x148:0 && x155:0 - 2 <= x149:0 && x148:0 > 1 && x149:0 > 1 && x155:0 > 3 && x154:0 > 3 f2482_0_createTree_LE(x136:0, x137:0, x138:0, x139:0) -> f2482_0_createTree_LE(x142:0, x143:0, x138:0 - 1, x145:0) :|: x139:0 > -1 && x138:0 > 0 && x136:0 > 0 && x137:0 > 1 && x143:0 > 0 && x142:0 > 0 f2482_0_createTree_LE(x94:0, x95:0, x96:0, x99:0) -> f2482_0_createTree_LE(x102:0, x103:0, x96:0 - 1, x99:0 + 1) :|: x96:0 > 0 && x99:0 > -1 && x94:0 >= x102:0 && x95:0 >= x103:0 + 2 && x94:0 > 0 && x95:0 > 2 && x103:0 > 0 && x102:0 > 0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f2482_0_createTree_LE(INTEGER, INTEGER, INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: f2482_0_createTree_LE(x109:0, x110:0, x111:0, x112:0) -> f2482_0_createTree_LE(x115:0, x116:0, c, c1) :|: c1 = x112:0 + 1 && c = x111:0 - 1 && (x115:0 > 0 && x116:0 > 0 && x110:0 > 2 && x109:0 > 0 && x116:0 + 2 <= x110:0 && x115:0 <= x109:0 && x112:0 > -1 && x122:0 > 0 && x111:0 > 0) f2482_0_createTree_LE(x123:0, x124:0, x125:0, x126:0) -> f2482_0_createTree_LE(x129:0, x130:0, c2, x132:0) :|: c2 = x125:0 - 1 && (x129:0 > 0 && x130:0 > 0 && x124:0 > 1 && x123:0 > 0 && x125:0 > 0 && x135:0 > 0 && x126:0 > -1) f2482_0_createTree_LE(x160:0, x161:0, x162:0, x163:0) -> f2482_0_createTree_LE(x166:0, x167:0, c3, x169:0) :|: c3 = x162:0 - 1 && (x166:0 > 3 && x167:0 > 3 && x161:0 > 1 && x160:0 > 1 && x167:0 - 2 <= x161:0 && x167:0 - 2 <= x160:0 && x166:0 - 2 <= x161:0 && x166:0 - 2 <= x160:0 && x162:0 > 0 && x172:0 > 0 && x163:0 > -1) f2482_0_createTree_LE(x148:0, x149:0, x150:0, x151:0) -> f2482_0_createTree_LE(x154:0, x155:0, c4, x157:0) :|: c4 = x150:0 - 1 && (x151:0 > -1 && x150:0 > 0 && x154:0 - 2 <= x148:0 && x154:0 - 2 <= x149:0 && x155:0 - 2 <= x148:0 && x155:0 - 2 <= x149:0 && x148:0 > 1 && x149:0 > 1 && x155:0 > 3 && x154:0 > 3) f2482_0_createTree_LE(x136:0, x137:0, x138:0, x139:0) -> f2482_0_createTree_LE(x142:0, x143:0, c5, x145:0) :|: c5 = x138:0 - 1 && (x139:0 > -1 && x138:0 > 0 && x136:0 > 0 && x137:0 > 1 && x143:0 > 0 && x142:0 > 0) f2482_0_createTree_LE(x94:0, x95:0, x96:0, x99:0) -> f2482_0_createTree_LE(x102:0, x103:0, c6, c7) :|: c7 = x99:0 + 1 && c6 = x96:0 - 1 && (x96:0 > 0 && x99:0 > -1 && x94:0 >= x102:0 && x95:0 >= x103:0 + 2 && x94:0 > 0 && x95:0 > 2 && x103:0 > 0 && x102:0 > 0) ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f2482_0_createTree_LE ] = f2482_0_createTree_LE_3 The following rules are decreasing: f2482_0_createTree_LE(x109:0, x110:0, x111:0, x112:0) -> f2482_0_createTree_LE(x115:0, x116:0, c, c1) :|: c1 = x112:0 + 1 && c = x111:0 - 1 && (x115:0 > 0 && x116:0 > 0 && x110:0 > 2 && x109:0 > 0 && x116:0 + 2 <= x110:0 && x115:0 <= x109:0 && x112:0 > -1 && x122:0 > 0 && x111:0 > 0) f2482_0_createTree_LE(x123:0, x124:0, x125:0, x126:0) -> f2482_0_createTree_LE(x129:0, x130:0, c2, x132:0) :|: c2 = x125:0 - 1 && (x129:0 > 0 && x130:0 > 0 && x124:0 > 1 && x123:0 > 0 && x125:0 > 0 && x135:0 > 0 && x126:0 > -1) f2482_0_createTree_LE(x160:0, x161:0, x162:0, x163:0) -> f2482_0_createTree_LE(x166:0, x167:0, c3, x169:0) :|: c3 = x162:0 - 1 && (x166:0 > 3 && x167:0 > 3 && x161:0 > 1 && x160:0 > 1 && x167:0 - 2 <= x161:0 && x167:0 - 2 <= x160:0 && x166:0 - 2 <= x161:0 && x166:0 - 2 <= x160:0 && x162:0 > 0 && x172:0 > 0 && x163:0 > -1) f2482_0_createTree_LE(x148:0, x149:0, x150:0, x151:0) -> f2482_0_createTree_LE(x154:0, x155:0, c4, x157:0) :|: c4 = x150:0 - 1 && (x151:0 > -1 && x150:0 > 0 && x154:0 - 2 <= x148:0 && x154:0 - 2 <= x149:0 && x155:0 - 2 <= x148:0 && x155:0 - 2 <= x149:0 && x148:0 > 1 && x149:0 > 1 && x155:0 > 3 && x154:0 > 3) f2482_0_createTree_LE(x136:0, x137:0, x138:0, x139:0) -> f2482_0_createTree_LE(x142:0, x143:0, c5, x145:0) :|: c5 = x138:0 - 1 && (x139:0 > -1 && x138:0 > 0 && x136:0 > 0 && x137:0 > 1 && x143:0 > 0 && x142:0 > 0) f2482_0_createTree_LE(x94:0, x95:0, x96:0, x99:0) -> f2482_0_createTree_LE(x102:0, x103:0, c6, c7) :|: c7 = x99:0 + 1 && c6 = x96:0 - 1 && (x96:0 > 0 && x99:0 > -1 && x94:0 >= x102:0 && x95:0 >= x103:0 + 2 && x94:0 > 0 && x95:0 > 2 && x103:0 > 0 && x102:0 > 0) The following rules are bounded: f2482_0_createTree_LE(x109:0, x110:0, x111:0, x112:0) -> f2482_0_createTree_LE(x115:0, x116:0, c, c1) :|: c1 = x112:0 + 1 && c = x111:0 - 1 && (x115:0 > 0 && x116:0 > 0 && x110:0 > 2 && x109:0 > 0 && x116:0 + 2 <= x110:0 && x115:0 <= x109:0 && x112:0 > -1 && x122:0 > 0 && x111:0 > 0) f2482_0_createTree_LE(x123:0, x124:0, x125:0, x126:0) -> f2482_0_createTree_LE(x129:0, x130:0, c2, x132:0) :|: c2 = x125:0 - 1 && (x129:0 > 0 && x130:0 > 0 && x124:0 > 1 && x123:0 > 0 && x125:0 > 0 && x135:0 > 0 && x126:0 > -1) f2482_0_createTree_LE(x160:0, x161:0, x162:0, x163:0) -> f2482_0_createTree_LE(x166:0, x167:0, c3, x169:0) :|: c3 = x162:0 - 1 && (x166:0 > 3 && x167:0 > 3 && x161:0 > 1 && x160:0 > 1 && x167:0 - 2 <= x161:0 && x167:0 - 2 <= x160:0 && x166:0 - 2 <= x161:0 && x166:0 - 2 <= x160:0 && x162:0 > 0 && x172:0 > 0 && x163:0 > -1) f2482_0_createTree_LE(x148:0, x149:0, x150:0, x151:0) -> f2482_0_createTree_LE(x154:0, x155:0, c4, x157:0) :|: c4 = x150:0 - 1 && (x151:0 > -1 && x150:0 > 0 && x154:0 - 2 <= x148:0 && x154:0 - 2 <= x149:0 && x155:0 - 2 <= x148:0 && x155:0 - 2 <= x149:0 && x148:0 > 1 && x149:0 > 1 && x155:0 > 3 && x154:0 > 3) f2482_0_createTree_LE(x136:0, x137:0, x138:0, x139:0) -> f2482_0_createTree_LE(x142:0, x143:0, c5, x145:0) :|: c5 = x138:0 - 1 && (x139:0 > -1 && x138:0 > 0 && x136:0 > 0 && x137:0 > 1 && x143:0 > 0 && x142:0 > 0) f2482_0_createTree_LE(x94:0, x95:0, x96:0, x99:0) -> f2482_0_createTree_LE(x102:0, x103:0, c6, c7) :|: c7 = x99:0 + 1 && c6 = x96:0 - 1 && (x96:0 > 0 && x99:0 > -1 && x94:0 >= x102:0 && x95:0 >= x103:0 + 2 && x94:0 > 0 && x95:0 > 2 && x103:0 > 0 && x102:0 > 0) ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) f1548_0_flatten_NULL(x55, x56, x57, x58, x59, x60) -> f1548_0_flatten_NULL(x61, x62, x63, x64, x65, x66) :|: -1 <= x62 - 1 && -1 <= x61 - 1 && 1 <= x56 - 1 && 1 <= x55 - 1 && x62 + 2 <= x56 && x62 + 2 <= x55 && x61 + 2 <= x56 && x61 + 2 <= x55 (2) f1548_0_flatten_NULL(x68, x69, x70, x71, x72, x73) -> f1548_0_flatten_NULL(x74, x76, x77, x78, x79, x80) :|: 2 <= x76 - 1 && 2 <= x74 - 1 && 2 <= x69 - 1 && 2 <= x68 - 1 && x76 - 2 <= x69 && x76 - 2 <= x68 && x74 - 2 <= x69 && x74 - 2 <= x68 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: f1548_0_flatten_NULL(x55:0, x56:0, x57:0, x58:0, x59:0, x60:0) -> f1548_0_flatten_NULL(x61:0, x62:0, x63:0, x64:0, x65:0, x66:0) :|: x61:0 + 2 <= x56:0 && x61:0 + 2 <= x55:0 && x62:0 + 2 <= x55:0 && x62:0 + 2 <= x56:0 && x55:0 > 1 && x56:0 > 1 && x61:0 > -1 && x62:0 > -1 f1548_0_flatten_NULL(x68:0, x69:0, x70:0, x71:0, x72:0, x73:0) -> f1548_0_flatten_NULL(x74:0, x76:0, x77:0, x78:0, x79:0, x80:0) :|: x74:0 - 2 <= x69:0 && x74:0 - 2 <= x68:0 && x76:0 - 2 <= x68:0 && x76:0 - 2 <= x69:0 && x68:0 > 2 && x69:0 > 2 && x74:0 > 2 && x76:0 > 2 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1548_0_flatten_NULL(x1, x2, x3, x4, x5, x6) -> f1548_0_flatten_NULL(x1, x2) ---------------------------------------- (27) Obligation: Rules: f1548_0_flatten_NULL(x55:0, x56:0) -> f1548_0_flatten_NULL(x61:0, x62:0) :|: x61:0 + 2 <= x56:0 && x61:0 + 2 <= x55:0 && x62:0 + 2 <= x55:0 && x62:0 + 2 <= x56:0 && x55:0 > 1 && x56:0 > 1 && x61:0 > -1 && x62:0 > -1 f1548_0_flatten_NULL(x68:0, x69:0) -> f1548_0_flatten_NULL(x74:0, x76:0) :|: x74:0 - 2 <= x69:0 && x74:0 - 2 <= x68:0 && x76:0 - 2 <= x68:0 && x76:0 - 2 <= x69:0 && x68:0 > 2 && x69:0 > 2 && x74:0 > 2 && x76:0 > 2 ---------------------------------------- (28) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f1548_0_flatten_NULL(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: f1548_0_flatten_NULL(x55:0, x56:0) -> f1548_0_flatten_NULL(x61:0, x62:0) :|: x61:0 + 2 <= x56:0 && x61:0 + 2 <= x55:0 && x62:0 + 2 <= x55:0 && x62:0 + 2 <= x56:0 && x55:0 > 1 && x56:0 > 1 && x61:0 > -1 && x62:0 > -1 f1548_0_flatten_NULL(x68:0, x69:0) -> f1548_0_flatten_NULL(x74:0, x76:0) :|: x74:0 - 2 <= x69:0 && x74:0 - 2 <= x68:0 && x76:0 - 2 <= x68:0 && x76:0 - 2 <= x69:0 && x68:0 > 2 && x69:0 > 2 && x74:0 > 2 && x76:0 > 2 ---------------------------------------- (30) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (31) Obligation: Rules: f1548_0_flatten_NULL(x68:0:0, x69:0:0) -> f1548_0_flatten_NULL(x74:0:0, x76:0:0) :|: x74:0:0 > 2 && x76:0:0 > 2 && x69:0:0 > 2 && x68:0:0 > 2 && x76:0:0 - 2 <= x69:0:0 && x76:0:0 - 2 <= x68:0:0 && x74:0:0 - 2 <= x68:0:0 && x74:0:0 - 2 <= x69:0:0 f1548_0_flatten_NULL(x55:0:0, x56:0:0) -> f1548_0_flatten_NULL(x61:0:0, x62:0:0) :|: x61:0:0 > -1 && x62:0:0 > -1 && x56:0:0 > 1 && x55:0:0 > 1 && x62:0:0 + 2 <= x56:0:0 && x62:0:0 + 2 <= x55:0:0 && x61:0:0 + 2 <= x55:0:0 && x61:0:0 + 2 <= x56:0:0 ---------------------------------------- (32) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x68:0:0, x69:0:0) -> f(1, x74:0:0, x76:0:0) :|: pc = 1 && (x74:0:0 > 2 && x76:0:0 > 2 && x69:0:0 > 2 && x68:0:0 > 2 && x76:0:0 - 2 <= x69:0:0 && x76:0:0 - 2 <= x68:0:0 && x74:0:0 - 2 <= x68:0:0 && x74:0:0 - 2 <= x69:0:0) f(pc, x55:0:0, x56:0:0) -> f(1, x61:0:0, x62:0:0) :|: pc = 1 && (x61:0:0 > -1 && x62:0:0 > -1 && x56:0:0 > 1 && x55:0:0 > 1 && x62:0:0 + 2 <= x56:0:0 && x62:0:0 + 2 <= x55:0:0 && x61:0:0 + 2 <= x55:0:0 && x61:0:0 + 2 <= x56:0:0) Witness term starting non-terminating reduction: f(1, 4, 4) ---------------------------------------- (33) NO