NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 2805 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 2 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 51 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 7 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 3 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 76 ms] (20) IntTRS (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 2 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, 4 ms] (33) NO ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6) -> f850_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 && 0 <= arg2 - 1 f850_0_main_LE(x, x1, x2, x3, x4, x6) -> f1962_0_flatten_NONNULL(x7, x8, x9, x11, x12, x13) :|: x7 <= x1 && 0 <= x14 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && -1 <= x7 - 1 && 0 = x2 f850_0_main_LE(x15, x16, x17, x19, x20, x21) -> f850_0_main_LE(x22, x23, x24, x25, x26, x27) :|: 0 <= x17 - 1 && 0 <= x28 - 1 && x22 <= x15 && x22 - 1 <= x16 && x23 - 2 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x22 - 1 && 1 <= x23 - 1 && x17 - 1 = x24 f850_0_main_LE(x29, x30, x31, x32, x33, x34) -> f850_0_main_LE(x35, x36, x37, x38, x39, x40) :|: 0 <= x31 - 1 && 0 <= x41 - 1 && x35 <= x29 && x35 - 1 <= x30 && 0 <= x29 - 1 && -1 <= x30 - 1 && 0 <= x35 - 1 && 4 <= x36 - 1 && x31 - 1 = x37 f1367_0_createTree_Return(x42, x43, x44, x45, x46, x47) -> f850_0_main_LE(x48, x49, x50, x51, x52, x53) :|: x46 = x51 && x44 - 1 = x50 && x47 + 2 <= x45 && 4 <= x49 - 1 && 0 <= x48 - 1 && 2 <= x45 - 1 && 0 <= x42 - 1 && x48 + 2 <= x45 && x48 <= x42 f1962_0_flatten_NONNULL(x54, x55, x56, x57, x58, x59) -> f1962_0_flatten_NONNULL(x60, x61, x62, x64, x65, x66) :|: -1 <= x60 - 1 && 1 <= x54 - 1 && x60 + 2 <= x54 f1962_0_flatten_NONNULL(x67, x68, x69, x70, x72, x73) -> f1962_0_flatten_NONNULL(x74, x75, x76, x77, x78, x79) :|: 2 <= x74 - 1 && 2 <= x67 - 1 && x74 - 2 <= x67 f850_0_main_LE(x80, x81, x82, x83, x84, x85) -> f2618_0_createTree_LE(x86, x87, x88, x89, x90, x91) :|: x83 + 1 = x90 && 2 <= x87 - 1 && 2 <= x86 - 1 && -1 <= x81 - 1 && 0 <= x80 - 1 && x87 - 3 <= x81 && x87 - 2 <= x80 && x86 - 3 <= x81 && x86 - 2 <= x80 && -1 <= x83 - 1 && x83 <= x89 - 1 && 0 <= x82 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 f2618_0_createTree_LE(x92, x94, x95, x96, x97, x98) -> f2618_0_createTree_LE(x99, x100, x101, x102, x103, x104) :|: x97 + 1 = x103 && x96 = x102 && x95 - 1 = x101 && 0 <= x100 - 1 && 2 <= x99 - 1 && 2 <= x94 - 1 && 2 <= x92 - 1 && x100 + 2 <= x94 && x99 <= x92 && x97 <= x96 - 1 && -1 <= x97 - 1 && 0 <= x95 - 1 f2618_0_createTree_LE(x105, x106, x107, x108, x109, x110) -> f2618_0_createTree_LE(x111, x112, x113, x114, x115, x116) :|: -1 <= x109 - 1 && 0 <= x117 - 1 && 0 <= x107 - 1 && x109 <= x108 - 1 && x111 <= x105 && x112 + 2 <= x106 && 2 <= x105 - 1 && 2 <= x106 - 1 && 2 <= x111 - 1 && 0 <= x112 - 1 && x107 - 1 = x113 && x108 = x114 && x109 + 1 = x115 f2618_0_createTree_LE(x118, x119, x120, x121, x122, x123) -> f2618_0_createTree_LE(x124, x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && 0 <= x130 - 1 && 0 <= x120 - 1 && x122 <= x121 - 1 && 2 <= x118 - 1 && 1 <= x119 - 1 && 2 <= x124 - 1 && 2 <= x125 - 1 && x120 - 1 = x126 && x121 = x127 && x122 + 1 = x128 f2618_0_createTree_LE(x131, x132, x133, x134, x135, x136) -> f2618_0_createTree_LE(x137, x138, x139, x140, x141, x142) :|: x135 + 1 = x141 && x134 = x140 && x133 - 1 = x139 && 2 <= x138 - 1 && 2 <= x137 - 1 && 1 <= x132 - 1 && 2 <= x131 - 1 && x135 <= x134 - 1 && -1 <= x135 - 1 && 0 <= x133 - 1 f2618_0_createTree_LE(x143, x144, x145, x146, x147, x148) -> f2618_0_createTree_LE(x149, x150, x151, x152, x153, x154) :|: x147 + 1 = x153 && x146 = x152 && x145 - 1 = x151 && 4 <= x150 - 1 && 4 <= x149 - 1 && 2 <= x144 - 1 && 2 <= x143 - 1 && x150 - 2 <= x144 && x150 - 2 <= x143 && x149 - 2 <= x144 && x149 - 2 <= x143 && x147 <= x146 - 1 && -1 <= x147 - 1 && 0 <= x145 - 1 f2618_0_createTree_LE(x155, x156, x157, x158, x159, x160) -> f2618_0_createTree_LE(x161, x162, x163, x164, x165, x166) :|: -1 <= x159 - 1 && 0 <= x167 - 1 && 0 <= x157 - 1 && x159 <= x158 - 1 && x161 - 2 <= x155 && x161 - 2 <= x156 && x162 - 2 <= x155 && x162 - 2 <= x156 && 2 <= x155 - 1 && 2 <= x156 - 1 && 4 <= x161 - 1 && 4 <= x162 - 1 && x157 - 1 = x163 && x158 = x164 && x159 + 1 = x165 __init(x168, x169, x170, x171, x172, x173) -> f1_0_main_Load(x174, x175, x176, x177, x178, x179) :|: 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) -> f850_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 && 0 <= arg2 - 1 f850_0_main_LE(x, x1, x2, x3, x4, x6) -> f1962_0_flatten_NONNULL(x7, x8, x9, x11, x12, x13) :|: x7 <= x1 && 0 <= x14 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && -1 <= x7 - 1 && 0 = x2 f850_0_main_LE(x15, x16, x17, x19, x20, x21) -> f850_0_main_LE(x22, x23, x24, x25, x26, x27) :|: 0 <= x17 - 1 && 0 <= x28 - 1 && x22 <= x15 && x22 - 1 <= x16 && x23 - 2 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x22 - 1 && 1 <= x23 - 1 && x17 - 1 = x24 f850_0_main_LE(x29, x30, x31, x32, x33, x34) -> f850_0_main_LE(x35, x36, x37, x38, x39, x40) :|: 0 <= x31 - 1 && 0 <= x41 - 1 && x35 <= x29 && x35 - 1 <= x30 && 0 <= x29 - 1 && -1 <= x30 - 1 && 0 <= x35 - 1 && 4 <= x36 - 1 && x31 - 1 = x37 f1367_0_createTree_Return(x42, x43, x44, x45, x46, x47) -> f850_0_main_LE(x48, x49, x50, x51, x52, x53) :|: x46 = x51 && x44 - 1 = x50 && x47 + 2 <= x45 && 4 <= x49 - 1 && 0 <= x48 - 1 && 2 <= x45 - 1 && 0 <= x42 - 1 && x48 + 2 <= x45 && x48 <= x42 f1962_0_flatten_NONNULL(x54, x55, x56, x57, x58, x59) -> f1962_0_flatten_NONNULL(x60, x61, x62, x64, x65, x66) :|: -1 <= x60 - 1 && 1 <= x54 - 1 && x60 + 2 <= x54 f1962_0_flatten_NONNULL(x67, x68, x69, x70, x72, x73) -> f1962_0_flatten_NONNULL(x74, x75, x76, x77, x78, x79) :|: 2 <= x74 - 1 && 2 <= x67 - 1 && x74 - 2 <= x67 f850_0_main_LE(x80, x81, x82, x83, x84, x85) -> f2618_0_createTree_LE(x86, x87, x88, x89, x90, x91) :|: x83 + 1 = x90 && 2 <= x87 - 1 && 2 <= x86 - 1 && -1 <= x81 - 1 && 0 <= x80 - 1 && x87 - 3 <= x81 && x87 - 2 <= x80 && x86 - 3 <= x81 && x86 - 2 <= x80 && -1 <= x83 - 1 && x83 <= x89 - 1 && 0 <= x82 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 f2618_0_createTree_LE(x92, x94, x95, x96, x97, x98) -> f2618_0_createTree_LE(x99, x100, x101, x102, x103, x104) :|: x97 + 1 = x103 && x96 = x102 && x95 - 1 = x101 && 0 <= x100 - 1 && 2 <= x99 - 1 && 2 <= x94 - 1 && 2 <= x92 - 1 && x100 + 2 <= x94 && x99 <= x92 && x97 <= x96 - 1 && -1 <= x97 - 1 && 0 <= x95 - 1 f2618_0_createTree_LE(x105, x106, x107, x108, x109, x110) -> f2618_0_createTree_LE(x111, x112, x113, x114, x115, x116) :|: -1 <= x109 - 1 && 0 <= x117 - 1 && 0 <= x107 - 1 && x109 <= x108 - 1 && x111 <= x105 && x112 + 2 <= x106 && 2 <= x105 - 1 && 2 <= x106 - 1 && 2 <= x111 - 1 && 0 <= x112 - 1 && x107 - 1 = x113 && x108 = x114 && x109 + 1 = x115 f2618_0_createTree_LE(x118, x119, x120, x121, x122, x123) -> f2618_0_createTree_LE(x124, x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && 0 <= x130 - 1 && 0 <= x120 - 1 && x122 <= x121 - 1 && 2 <= x118 - 1 && 1 <= x119 - 1 && 2 <= x124 - 1 && 2 <= x125 - 1 && x120 - 1 = x126 && x121 = x127 && x122 + 1 = x128 f2618_0_createTree_LE(x131, x132, x133, x134, x135, x136) -> f2618_0_createTree_LE(x137, x138, x139, x140, x141, x142) :|: x135 + 1 = x141 && x134 = x140 && x133 - 1 = x139 && 2 <= x138 - 1 && 2 <= x137 - 1 && 1 <= x132 - 1 && 2 <= x131 - 1 && x135 <= x134 - 1 && -1 <= x135 - 1 && 0 <= x133 - 1 f2618_0_createTree_LE(x143, x144, x145, x146, x147, x148) -> f2618_0_createTree_LE(x149, x150, x151, x152, x153, x154) :|: x147 + 1 = x153 && x146 = x152 && x145 - 1 = x151 && 4 <= x150 - 1 && 4 <= x149 - 1 && 2 <= x144 - 1 && 2 <= x143 - 1 && x150 - 2 <= x144 && x150 - 2 <= x143 && x149 - 2 <= x144 && x149 - 2 <= x143 && x147 <= x146 - 1 && -1 <= x147 - 1 && 0 <= x145 - 1 f2618_0_createTree_LE(x155, x156, x157, x158, x159, x160) -> f2618_0_createTree_LE(x161, x162, x163, x164, x165, x166) :|: -1 <= x159 - 1 && 0 <= x167 - 1 && 0 <= x157 - 1 && x159 <= x158 - 1 && x161 - 2 <= x155 && x161 - 2 <= x156 && x162 - 2 <= x155 && x162 - 2 <= x156 && 2 <= x155 - 1 && 2 <= x156 - 1 && 4 <= x161 - 1 && 4 <= x162 - 1 && x157 - 1 = x163 && x158 = x164 && x159 + 1 = x165 __init(x168, x169, x170, x171, x172, x173) -> f1_0_main_Load(x174, x175, x176, x177, x178, x179) :|: 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) -> f850_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 && 0 <= arg2 - 1 (2) f850_0_main_LE(x, x1, x2, x3, x4, x6) -> f1962_0_flatten_NONNULL(x7, x8, x9, x11, x12, x13) :|: x7 <= x1 && 0 <= x14 - 1 && 0 <= x - 1 && -1 <= x1 - 1 && -1 <= x7 - 1 && 0 = x2 (3) f850_0_main_LE(x15, x16, x17, x19, x20, x21) -> f850_0_main_LE(x22, x23, x24, x25, x26, x27) :|: 0 <= x17 - 1 && 0 <= x28 - 1 && x22 <= x15 && x22 - 1 <= x16 && x23 - 2 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x22 - 1 && 1 <= x23 - 1 && x17 - 1 = x24 (4) f850_0_main_LE(x29, x30, x31, x32, x33, x34) -> f850_0_main_LE(x35, x36, x37, x38, x39, x40) :|: 0 <= x31 - 1 && 0 <= x41 - 1 && x35 <= x29 && x35 - 1 <= x30 && 0 <= x29 - 1 && -1 <= x30 - 1 && 0 <= x35 - 1 && 4 <= x36 - 1 && x31 - 1 = x37 (5) f1367_0_createTree_Return(x42, x43, x44, x45, x46, x47) -> f850_0_main_LE(x48, x49, x50, x51, x52, x53) :|: x46 = x51 && x44 - 1 = x50 && x47 + 2 <= x45 && 4 <= x49 - 1 && 0 <= x48 - 1 && 2 <= x45 - 1 && 0 <= x42 - 1 && x48 + 2 <= x45 && x48 <= x42 (6) f1962_0_flatten_NONNULL(x54, x55, x56, x57, x58, x59) -> f1962_0_flatten_NONNULL(x60, x61, x62, x64, x65, x66) :|: -1 <= x60 - 1 && 1 <= x54 - 1 && x60 + 2 <= x54 (7) f1962_0_flatten_NONNULL(x67, x68, x69, x70, x72, x73) -> f1962_0_flatten_NONNULL(x74, x75, x76, x77, x78, x79) :|: 2 <= x74 - 1 && 2 <= x67 - 1 && x74 - 2 <= x67 (8) f850_0_main_LE(x80, x81, x82, x83, x84, x85) -> f2618_0_createTree_LE(x86, x87, x88, x89, x90, x91) :|: x83 + 1 = x90 && 2 <= x87 - 1 && 2 <= x86 - 1 && -1 <= x81 - 1 && 0 <= x80 - 1 && x87 - 3 <= x81 && x87 - 2 <= x80 && x86 - 3 <= x81 && x86 - 2 <= x80 && -1 <= x83 - 1 && x83 <= x89 - 1 && 0 <= x82 - 1 && 0 <= x89 - 1 && 0 <= x88 - 1 (9) f2618_0_createTree_LE(x92, x94, x95, x96, x97, x98) -> f2618_0_createTree_LE(x99, x100, x101, x102, x103, x104) :|: x97 + 1 = x103 && x96 = x102 && x95 - 1 = x101 && 0 <= x100 - 1 && 2 <= x99 - 1 && 2 <= x94 - 1 && 2 <= x92 - 1 && x100 + 2 <= x94 && x99 <= x92 && x97 <= x96 - 1 && -1 <= x97 - 1 && 0 <= x95 - 1 (10) f2618_0_createTree_LE(x105, x106, x107, x108, x109, x110) -> f2618_0_createTree_LE(x111, x112, x113, x114, x115, x116) :|: -1 <= x109 - 1 && 0 <= x117 - 1 && 0 <= x107 - 1 && x109 <= x108 - 1 && x111 <= x105 && x112 + 2 <= x106 && 2 <= x105 - 1 && 2 <= x106 - 1 && 2 <= x111 - 1 && 0 <= x112 - 1 && x107 - 1 = x113 && x108 = x114 && x109 + 1 = x115 (11) f2618_0_createTree_LE(x118, x119, x120, x121, x122, x123) -> f2618_0_createTree_LE(x124, x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && 0 <= x130 - 1 && 0 <= x120 - 1 && x122 <= x121 - 1 && 2 <= x118 - 1 && 1 <= x119 - 1 && 2 <= x124 - 1 && 2 <= x125 - 1 && x120 - 1 = x126 && x121 = x127 && x122 + 1 = x128 (12) f2618_0_createTree_LE(x131, x132, x133, x134, x135, x136) -> f2618_0_createTree_LE(x137, x138, x139, x140, x141, x142) :|: x135 + 1 = x141 && x134 = x140 && x133 - 1 = x139 && 2 <= x138 - 1 && 2 <= x137 - 1 && 1 <= x132 - 1 && 2 <= x131 - 1 && x135 <= x134 - 1 && -1 <= x135 - 1 && 0 <= x133 - 1 (13) f2618_0_createTree_LE(x143, x144, x145, x146, x147, x148) -> f2618_0_createTree_LE(x149, x150, x151, x152, x153, x154) :|: x147 + 1 = x153 && x146 = x152 && x145 - 1 = x151 && 4 <= x150 - 1 && 4 <= x149 - 1 && 2 <= x144 - 1 && 2 <= x143 - 1 && x150 - 2 <= x144 && x150 - 2 <= x143 && x149 - 2 <= x144 && x149 - 2 <= x143 && x147 <= x146 - 1 && -1 <= x147 - 1 && 0 <= x145 - 1 (14) f2618_0_createTree_LE(x155, x156, x157, x158, x159, x160) -> f2618_0_createTree_LE(x161, x162, x163, x164, x165, x166) :|: -1 <= x159 - 1 && 0 <= x167 - 1 && 0 <= x157 - 1 && x159 <= x158 - 1 && x161 - 2 <= x155 && x161 - 2 <= x156 && x162 - 2 <= x155 && x162 - 2 <= x156 && 2 <= x155 - 1 && 2 <= x156 - 1 && 4 <= x161 - 1 && 4 <= x162 - 1 && x157 - 1 = x163 && x158 = x164 && x159 + 1 = x165 (15) __init(x168, x169, x170, x171, x172, x173) -> f1_0_main_Load(x174, x175, x176, x177, x178, x179) :|: 0 <= 0 Arcs: (1) -> (2), (3), (4), (8) (2) -> (6), (7) (3) -> (2), (3), (4), (8) (4) -> (2), (3), (4), (8) (5) -> (2), (3), (4), (8) (6) -> (6), (7) (7) -> (6), (7) (8) -> (9), (10), (11), (12), (13), (14) (9) -> (9), (10), (11), (12), (13), (14) (10) -> (9), (10), (11), (12), (13), (14) (11) -> (9), (10), (11), (12), (13), (14) (12) -> (9), (10), (11), (12), (13), (14) (13) -> (9), (10), (11), (12), (13), (14) (14) -> (9), (10), (11), (12), (13), (14) (15) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f850_0_main_LE(x15, x16, x17, x19, x20, x21) -> f850_0_main_LE(x22, x23, x24, x25, x26, x27) :|: 0 <= x17 - 1 && 0 <= x28 - 1 && x22 <= x15 && x22 - 1 <= x16 && x23 - 2 <= x16 && 0 <= x15 - 1 && -1 <= x16 - 1 && 0 <= x22 - 1 && 1 <= x23 - 1 && x17 - 1 = x24 (2) f850_0_main_LE(x29, x30, x31, x32, x33, x34) -> f850_0_main_LE(x35, x36, x37, x38, x39, x40) :|: 0 <= x31 - 1 && 0 <= x41 - 1 && x35 <= x29 && x35 - 1 <= x30 && 0 <= x29 - 1 && -1 <= x30 - 1 && 0 <= x35 - 1 && 4 <= x36 - 1 && x31 - 1 = x37 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f850_0_main_LE(x15:0, x16:0, x17:0, x19:0, x20:0, x21:0) -> f850_0_main_LE(x22:0, x23:0, x17:0 - 1, x25:0, x26:0, x27:0) :|: x22:0 > 0 && x23:0 > 1 && x16:0 > -1 && x15:0 > 0 && x23:0 - 2 <= x16:0 && x22:0 - 1 <= x16:0 && x22:0 <= x15:0 && x28:0 > 0 && x17:0 > 0 f850_0_main_LE(x29:0, x30:0, x31:0, x32:0, x33:0, x34:0) -> f850_0_main_LE(x35:0, x36:0, x31:0 - 1, x38:0, x39:0, x40:0) :|: x35:0 > 0 && x36:0 > 4 && x30:0 > -1 && x29:0 > 0 && x35:0 - 1 <= x30:0 && x35:0 <= x29:0 && x41:0 > 0 && x31:0 > 0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f850_0_main_LE(x1, x2, x3, x4, x5, x6) -> f850_0_main_LE(x1, x2, x3) ---------------------------------------- (9) Obligation: Rules: f850_0_main_LE(x15:0, x16:0, x17:0) -> f850_0_main_LE(x22:0, x23:0, x17:0 - 1) :|: x22:0 > 0 && x23:0 > 1 && x16:0 > -1 && x15:0 > 0 && x23:0 - 2 <= x16:0 && x22:0 - 1 <= x16:0 && x22:0 <= x15:0 && x28:0 > 0 && x17:0 > 0 f850_0_main_LE(x29:0, x30:0, x31:0) -> f850_0_main_LE(x35:0, x36:0, x31:0 - 1) :|: x35:0 > 0 && x36:0 > 4 && x30:0 > -1 && x29:0 > 0 && x35:0 - 1 <= x30:0 && x35:0 <= x29:0 && x41:0 > 0 && x31:0 > 0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f850_0_main_LE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: f850_0_main_LE(x15:0, x16:0, x17:0) -> f850_0_main_LE(x22:0, x23:0, c) :|: c = x17:0 - 1 && (x22:0 > 0 && x23:0 > 1 && x16:0 > -1 && x15:0 > 0 && x23:0 - 2 <= x16:0 && x22:0 - 1 <= x16:0 && x22:0 <= x15:0 && x28:0 > 0 && x17:0 > 0) f850_0_main_LE(x29:0, x30:0, x31:0) -> f850_0_main_LE(x35:0, x36:0, c1) :|: c1 = x31:0 - 1 && (x35:0 > 0 && x36:0 > 4 && x30:0 > -1 && x29:0 > 0 && x35:0 - 1 <= x30:0 && x35:0 <= x29:0 && x41:0 > 0 && x31:0 > 0) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f850_0_main_LE(x, x1, x2)] = -1 + x2 The following rules are decreasing: f850_0_main_LE(x15:0, x16:0, x17:0) -> f850_0_main_LE(x22:0, x23:0, c) :|: c = x17:0 - 1 && (x22:0 > 0 && x23:0 > 1 && x16:0 > -1 && x15:0 > 0 && x23:0 - 2 <= x16:0 && x22:0 - 1 <= x16:0 && x22:0 <= x15:0 && x28:0 > 0 && x17:0 > 0) f850_0_main_LE(x29:0, x30:0, x31:0) -> f850_0_main_LE(x35:0, x36:0, c1) :|: c1 = x31:0 - 1 && (x35:0 > 0 && x36:0 > 4 && x30:0 > -1 && x29:0 > 0 && x35:0 - 1 <= x30:0 && x35:0 <= x29:0 && x41:0 > 0 && x31:0 > 0) The following rules are bounded: f850_0_main_LE(x15:0, x16:0, x17:0) -> f850_0_main_LE(x22:0, x23:0, c) :|: c = x17:0 - 1 && (x22:0 > 0 && x23:0 > 1 && x16:0 > -1 && x15:0 > 0 && x23:0 - 2 <= x16:0 && x22:0 - 1 <= x16:0 && x22:0 <= x15:0 && x28:0 > 0 && x17:0 > 0) f850_0_main_LE(x29:0, x30:0, x31:0) -> f850_0_main_LE(x35:0, x36:0, c1) :|: c1 = x31:0 - 1 && (x35:0 > 0 && x36:0 > 4 && x30:0 > -1 && x29:0 > 0 && x35:0 - 1 <= x30:0 && x35:0 <= x29:0 && x41:0 > 0 && x31:0 > 0) ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) f2618_0_createTree_LE(x92, x94, x95, x96, x97, x98) -> f2618_0_createTree_LE(x99, x100, x101, x102, x103, x104) :|: x97 + 1 = x103 && x96 = x102 && x95 - 1 = x101 && 0 <= x100 - 1 && 2 <= x99 - 1 && 2 <= x94 - 1 && 2 <= x92 - 1 && x100 + 2 <= x94 && x99 <= x92 && x97 <= x96 - 1 && -1 <= x97 - 1 && 0 <= x95 - 1 (2) f2618_0_createTree_LE(x105, x106, x107, x108, x109, x110) -> f2618_0_createTree_LE(x111, x112, x113, x114, x115, x116) :|: -1 <= x109 - 1 && 0 <= x117 - 1 && 0 <= x107 - 1 && x109 <= x108 - 1 && x111 <= x105 && x112 + 2 <= x106 && 2 <= x105 - 1 && 2 <= x106 - 1 && 2 <= x111 - 1 && 0 <= x112 - 1 && x107 - 1 = x113 && x108 = x114 && x109 + 1 = x115 (3) f2618_0_createTree_LE(x118, x119, x120, x121, x122, x123) -> f2618_0_createTree_LE(x124, x125, x126, x127, x128, x129) :|: -1 <= x122 - 1 && 0 <= x130 - 1 && 0 <= x120 - 1 && x122 <= x121 - 1 && 2 <= x118 - 1 && 1 <= x119 - 1 && 2 <= x124 - 1 && 2 <= x125 - 1 && x120 - 1 = x126 && x121 = x127 && x122 + 1 = x128 (4) f2618_0_createTree_LE(x131, x132, x133, x134, x135, x136) -> f2618_0_createTree_LE(x137, x138, x139, x140, x141, x142) :|: x135 + 1 = x141 && x134 = x140 && x133 - 1 = x139 && 2 <= x138 - 1 && 2 <= x137 - 1 && 1 <= x132 - 1 && 2 <= x131 - 1 && x135 <= x134 - 1 && -1 <= x135 - 1 && 0 <= x133 - 1 (5) f2618_0_createTree_LE(x143, x144, x145, x146, x147, x148) -> f2618_0_createTree_LE(x149, x150, x151, x152, x153, x154) :|: x147 + 1 = x153 && x146 = x152 && x145 - 1 = x151 && 4 <= x150 - 1 && 4 <= x149 - 1 && 2 <= x144 - 1 && 2 <= x143 - 1 && x150 - 2 <= x144 && x150 - 2 <= x143 && x149 - 2 <= x144 && x149 - 2 <= x143 && x147 <= x146 - 1 && -1 <= x147 - 1 && 0 <= x145 - 1 (6) f2618_0_createTree_LE(x155, x156, x157, x158, x159, x160) -> f2618_0_createTree_LE(x161, x162, x163, x164, x165, x166) :|: -1 <= x159 - 1 && 0 <= x167 - 1 && 0 <= x157 - 1 && x159 <= x158 - 1 && x161 - 2 <= x155 && x161 - 2 <= x156 && x162 - 2 <= x155 && x162 - 2 <= x156 && 2 <= x155 - 1 && 2 <= x156 - 1 && 4 <= x161 - 1 && 4 <= x162 - 1 && x157 - 1 = x163 && x158 = x164 && x159 + 1 = x165 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: f2618_0_createTree_LE(x131:0, x132:0, x133:0, x134:0, x135:0, x136:0) -> f2618_0_createTree_LE(x137:0, x138:0, x133:0 - 1, x134:0, x135:0 + 1, x142:0) :|: x135:0 > -1 && x133:0 > 0 && x135:0 <= x134:0 - 1 && x131:0 > 2 && x132:0 > 1 && x138:0 > 2 && x137:0 > 2 f2618_0_createTree_LE(x155:0, x156:0, x157:0, x158:0, x159:0, x160:0) -> f2618_0_createTree_LE(x161:0, x162:0, x157:0 - 1, x158:0, x159:0 + 1, x166:0) :|: x161:0 > 4 && x162:0 > 4 && x156:0 > 2 && x155:0 > 2 && x162:0 - 2 <= x156:0 && x162:0 - 2 <= x155:0 && x161:0 - 2 <= x156:0 && x161:0 - 2 <= x155:0 && x159:0 <= x158:0 - 1 && x157:0 > 0 && x167:0 > 0 && x159:0 > -1 f2618_0_createTree_LE(x118:0, x119:0, x120:0, x121:0, x122:0, x123:0) -> f2618_0_createTree_LE(x124:0, x125:0, x120:0 - 1, x121:0, x122:0 + 1, x129:0) :|: x124:0 > 2 && x125:0 > 2 && x119:0 > 1 && x118:0 > 2 && x122:0 <= x121:0 - 1 && x120:0 > 0 && x130:0 > 0 && x122:0 > -1 f2618_0_createTree_LE(x105:0, x106:0, x107:0, x108:0, x109:0, x110:0) -> f2618_0_createTree_LE(x111:0, x112:0, x107:0 - 1, x108:0, x109:0 + 1, x116:0) :|: x111:0 > 2 && x112:0 > 0 && x106:0 > 2 && x105:0 > 2 && x112:0 + 2 <= x106:0 && x111:0 <= x105:0 && x109:0 <= x108:0 - 1 && x107:0 > 0 && x117:0 > 0 && x109:0 > -1 f2618_0_createTree_LE(x143:0, x144:0, x145:0, x146:0, x147:0, x148:0) -> f2618_0_createTree_LE(x149:0, x150:0, x145:0 - 1, x146:0, x147:0 + 1, x154:0) :|: x147:0 > -1 && x145:0 > 0 && x147:0 <= x146:0 - 1 && x149:0 - 2 <= x143:0 && x149:0 - 2 <= x144:0 && x150:0 - 2 <= x143:0 && x150:0 - 2 <= x144:0 && x143:0 > 2 && x144:0 > 2 && x150:0 > 4 && x149:0 > 4 f2618_0_createTree_LE(x92:0, x94:0, x95:0, x102:0, x97:0, x98:0) -> f2618_0_createTree_LE(x99:0, x100:0, x95:0 - 1, x102:0, x97:0 + 1, x104:0) :|: x97:0 > -1 && x95:0 > 0 && x97:0 <= x102:0 - 1 && x99:0 <= x92:0 && x94:0 >= x100:0 + 2 && x92:0 > 2 && x94:0 > 2 && x100:0 > 0 && x99:0 > 2 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f2618_0_createTree_LE(x1, x2, x3, x4, x5, x6) -> f2618_0_createTree_LE(x1, x2, x3, x4, x5) ---------------------------------------- (18) Obligation: Rules: f2618_0_createTree_LE(x131:0, x132:0, x133:0, x134:0, x135:0) -> f2618_0_createTree_LE(x137:0, x138:0, x133:0 - 1, x134:0, x135:0 + 1) :|: x135:0 > -1 && x133:0 > 0 && x135:0 <= x134:0 - 1 && x131:0 > 2 && x132:0 > 1 && x138:0 > 2 && x137:0 > 2 f2618_0_createTree_LE(x155:0, x156:0, x157:0, x158:0, x159:0) -> f2618_0_createTree_LE(x161:0, x162:0, x157:0 - 1, x158:0, x159:0 + 1) :|: x161:0 > 4 && x162:0 > 4 && x156:0 > 2 && x155:0 > 2 && x162:0 - 2 <= x156:0 && x162:0 - 2 <= x155:0 && x161:0 - 2 <= x156:0 && x161:0 - 2 <= x155:0 && x159:0 <= x158:0 - 1 && x157:0 > 0 && x167:0 > 0 && x159:0 > -1 f2618_0_createTree_LE(x118:0, x119:0, x120:0, x121:0, x122:0) -> f2618_0_createTree_LE(x124:0, x125:0, x120:0 - 1, x121:0, x122:0 + 1) :|: x124:0 > 2 && x125:0 > 2 && x119:0 > 1 && x118:0 > 2 && x122:0 <= x121:0 - 1 && x120:0 > 0 && x130:0 > 0 && x122:0 > -1 f2618_0_createTree_LE(x105:0, x106:0, x107:0, x108:0, x109:0) -> f2618_0_createTree_LE(x111:0, x112:0, x107:0 - 1, x108:0, x109:0 + 1) :|: x111:0 > 2 && x112:0 > 0 && x106:0 > 2 && x105:0 > 2 && x112:0 + 2 <= x106:0 && x111:0 <= x105:0 && x109:0 <= x108:0 - 1 && x107:0 > 0 && x117:0 > 0 && x109:0 > -1 f2618_0_createTree_LE(x143:0, x144:0, x145:0, x146:0, x147:0) -> f2618_0_createTree_LE(x149:0, x150:0, x145:0 - 1, x146:0, x147:0 + 1) :|: x147:0 > -1 && x145:0 > 0 && x147:0 <= x146:0 - 1 && x149:0 - 2 <= x143:0 && x149:0 - 2 <= x144:0 && x150:0 - 2 <= x143:0 && x150:0 - 2 <= x144:0 && x143:0 > 2 && x144:0 > 2 && x150:0 > 4 && x149:0 > 4 f2618_0_createTree_LE(x92:0, x94:0, x95:0, x102:0, x97:0) -> f2618_0_createTree_LE(x99:0, x100:0, x95:0 - 1, x102:0, x97:0 + 1) :|: x97:0 > -1 && x95:0 > 0 && x97:0 <= x102:0 - 1 && x99:0 <= x92:0 && x94:0 >= x100:0 + 2 && x92:0 > 2 && x94:0 > 2 && x100:0 > 0 && x99:0 > 2 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f2618_0_createTree_LE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: f2618_0_createTree_LE(x131:0, x132:0, x133:0, x134:0, x135:0) -> f2618_0_createTree_LE(x137:0, x138:0, c, x134:0, c1) :|: c1 = x135:0 + 1 && c = x133:0 - 1 && (x135:0 > -1 && x133:0 > 0 && x135:0 <= x134:0 - 1 && x131:0 > 2 && x132:0 > 1 && x138:0 > 2 && x137:0 > 2) f2618_0_createTree_LE(x155:0, x156:0, x157:0, x158:0, x159:0) -> f2618_0_createTree_LE(x161:0, x162:0, c2, x158:0, c3) :|: c3 = x159:0 + 1 && c2 = x157:0 - 1 && (x161:0 > 4 && x162:0 > 4 && x156:0 > 2 && x155:0 > 2 && x162:0 - 2 <= x156:0 && x162:0 - 2 <= x155:0 && x161:0 - 2 <= x156:0 && x161:0 - 2 <= x155:0 && x159:0 <= x158:0 - 1 && x157:0 > 0 && x167:0 > 0 && x159:0 > -1) f2618_0_createTree_LE(x118:0, x119:0, x120:0, x121:0, x122:0) -> f2618_0_createTree_LE(x124:0, x125:0, c4, x121:0, c5) :|: c5 = x122:0 + 1 && c4 = x120:0 - 1 && (x124:0 > 2 && x125:0 > 2 && x119:0 > 1 && x118:0 > 2 && x122:0 <= x121:0 - 1 && x120:0 > 0 && x130:0 > 0 && x122:0 > -1) f2618_0_createTree_LE(x105:0, x106:0, x107:0, x108:0, x109:0) -> f2618_0_createTree_LE(x111:0, x112:0, c6, x108:0, c7) :|: c7 = x109:0 + 1 && c6 = x107:0 - 1 && (x111:0 > 2 && x112:0 > 0 && x106:0 > 2 && x105:0 > 2 && x112:0 + 2 <= x106:0 && x111:0 <= x105:0 && x109:0 <= x108:0 - 1 && x107:0 > 0 && x117:0 > 0 && x109:0 > -1) f2618_0_createTree_LE(x143:0, x144:0, x145:0, x146:0, x147:0) -> f2618_0_createTree_LE(x149:0, x150:0, c8, x146:0, c9) :|: c9 = x147:0 + 1 && c8 = x145:0 - 1 && (x147:0 > -1 && x145:0 > 0 && x147:0 <= x146:0 - 1 && x149:0 - 2 <= x143:0 && x149:0 - 2 <= x144:0 && x150:0 - 2 <= x143:0 && x150:0 - 2 <= x144:0 && x143:0 > 2 && x144:0 > 2 && x150:0 > 4 && x149:0 > 4) f2618_0_createTree_LE(x92:0, x94:0, x95:0, x102:0, x97:0) -> f2618_0_createTree_LE(x99:0, x100:0, c10, x102:0, c11) :|: c11 = x97:0 + 1 && c10 = x95:0 - 1 && (x97:0 > -1 && x95:0 > 0 && x97:0 <= x102:0 - 1 && x99:0 <= x92:0 && x94:0 >= x100:0 + 2 && x92:0 > 2 && x94:0 > 2 && x100:0 > 0 && x99:0 > 2) ---------------------------------------- (21) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f2618_0_createTree_LE(x, x1, x2, x3, x4)] = x2 The following rules are decreasing: f2618_0_createTree_LE(x131:0, x132:0, x133:0, x134:0, x135:0) -> f2618_0_createTree_LE(x137:0, x138:0, c, x134:0, c1) :|: c1 = x135:0 + 1 && c = x133:0 - 1 && (x135:0 > -1 && x133:0 > 0 && x135:0 <= x134:0 - 1 && x131:0 > 2 && x132:0 > 1 && x138:0 > 2 && x137:0 > 2) f2618_0_createTree_LE(x155:0, x156:0, x157:0, x158:0, x159:0) -> f2618_0_createTree_LE(x161:0, x162:0, c2, x158:0, c3) :|: c3 = x159:0 + 1 && c2 = x157:0 - 1 && (x161:0 > 4 && x162:0 > 4 && x156:0 > 2 && x155:0 > 2 && x162:0 - 2 <= x156:0 && x162:0 - 2 <= x155:0 && x161:0 - 2 <= x156:0 && x161:0 - 2 <= x155:0 && x159:0 <= x158:0 - 1 && x157:0 > 0 && x167:0 > 0 && x159:0 > -1) f2618_0_createTree_LE(x118:0, x119:0, x120:0, x121:0, x122:0) -> f2618_0_createTree_LE(x124:0, x125:0, c4, x121:0, c5) :|: c5 = x122:0 + 1 && c4 = x120:0 - 1 && (x124:0 > 2 && x125:0 > 2 && x119:0 > 1 && x118:0 > 2 && x122:0 <= x121:0 - 1 && x120:0 > 0 && x130:0 > 0 && x122:0 > -1) f2618_0_createTree_LE(x105:0, x106:0, x107:0, x108:0, x109:0) -> f2618_0_createTree_LE(x111:0, x112:0, c6, x108:0, c7) :|: c7 = x109:0 + 1 && c6 = x107:0 - 1 && (x111:0 > 2 && x112:0 > 0 && x106:0 > 2 && x105:0 > 2 && x112:0 + 2 <= x106:0 && x111:0 <= x105:0 && x109:0 <= x108:0 - 1 && x107:0 > 0 && x117:0 > 0 && x109:0 > -1) f2618_0_createTree_LE(x143:0, x144:0, x145:0, x146:0, x147:0) -> f2618_0_createTree_LE(x149:0, x150:0, c8, x146:0, c9) :|: c9 = x147:0 + 1 && c8 = x145:0 - 1 && (x147:0 > -1 && x145:0 > 0 && x147:0 <= x146:0 - 1 && x149:0 - 2 <= x143:0 && x149:0 - 2 <= x144:0 && x150:0 - 2 <= x143:0 && x150:0 - 2 <= x144:0 && x143:0 > 2 && x144:0 > 2 && x150:0 > 4 && x149:0 > 4) f2618_0_createTree_LE(x92:0, x94:0, x95:0, x102:0, x97:0) -> f2618_0_createTree_LE(x99:0, x100:0, c10, x102:0, c11) :|: c11 = x97:0 + 1 && c10 = x95:0 - 1 && (x97:0 > -1 && x95:0 > 0 && x97:0 <= x102:0 - 1 && x99:0 <= x92:0 && x94:0 >= x100:0 + 2 && x92:0 > 2 && x94:0 > 2 && x100:0 > 0 && x99:0 > 2) The following rules are bounded: f2618_0_createTree_LE(x131:0, x132:0, x133:0, x134:0, x135:0) -> f2618_0_createTree_LE(x137:0, x138:0, c, x134:0, c1) :|: c1 = x135:0 + 1 && c = x133:0 - 1 && (x135:0 > -1 && x133:0 > 0 && x135:0 <= x134:0 - 1 && x131:0 > 2 && x132:0 > 1 && x138:0 > 2 && x137:0 > 2) f2618_0_createTree_LE(x155:0, x156:0, x157:0, x158:0, x159:0) -> f2618_0_createTree_LE(x161:0, x162:0, c2, x158:0, c3) :|: c3 = x159:0 + 1 && c2 = x157:0 - 1 && (x161:0 > 4 && x162:0 > 4 && x156:0 > 2 && x155:0 > 2 && x162:0 - 2 <= x156:0 && x162:0 - 2 <= x155:0 && x161:0 - 2 <= x156:0 && x161:0 - 2 <= x155:0 && x159:0 <= x158:0 - 1 && x157:0 > 0 && x167:0 > 0 && x159:0 > -1) f2618_0_createTree_LE(x118:0, x119:0, x120:0, x121:0, x122:0) -> f2618_0_createTree_LE(x124:0, x125:0, c4, x121:0, c5) :|: c5 = x122:0 + 1 && c4 = x120:0 - 1 && (x124:0 > 2 && x125:0 > 2 && x119:0 > 1 && x118:0 > 2 && x122:0 <= x121:0 - 1 && x120:0 > 0 && x130:0 > 0 && x122:0 > -1) f2618_0_createTree_LE(x105:0, x106:0, x107:0, x108:0, x109:0) -> f2618_0_createTree_LE(x111:0, x112:0, c6, x108:0, c7) :|: c7 = x109:0 + 1 && c6 = x107:0 - 1 && (x111:0 > 2 && x112:0 > 0 && x106:0 > 2 && x105:0 > 2 && x112:0 + 2 <= x106:0 && x111:0 <= x105:0 && x109:0 <= x108:0 - 1 && x107:0 > 0 && x117:0 > 0 && x109:0 > -1) f2618_0_createTree_LE(x143:0, x144:0, x145:0, x146:0, x147:0) -> f2618_0_createTree_LE(x149:0, x150:0, c8, x146:0, c9) :|: c9 = x147:0 + 1 && c8 = x145:0 - 1 && (x147:0 > -1 && x145:0 > 0 && x147:0 <= x146:0 - 1 && x149:0 - 2 <= x143:0 && x149:0 - 2 <= x144:0 && x150:0 - 2 <= x143:0 && x150:0 - 2 <= x144:0 && x143:0 > 2 && x144:0 > 2 && x150:0 > 4 && x149:0 > 4) f2618_0_createTree_LE(x92:0, x94:0, x95:0, x102:0, x97:0) -> f2618_0_createTree_LE(x99:0, x100:0, c10, x102:0, c11) :|: c11 = x97:0 + 1 && c10 = x95:0 - 1 && (x97:0 > -1 && x95:0 > 0 && x97:0 <= x102:0 - 1 && x99:0 <= x92:0 && x94:0 >= x100:0 + 2 && x92:0 > 2 && x94:0 > 2 && x100:0 > 0 && x99:0 > 2) ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) f1962_0_flatten_NONNULL(x54, x55, x56, x57, x58, x59) -> f1962_0_flatten_NONNULL(x60, x61, x62, x64, x65, x66) :|: -1 <= x60 - 1 && 1 <= x54 - 1 && x60 + 2 <= x54 (2) f1962_0_flatten_NONNULL(x67, x68, x69, x70, x72, x73) -> f1962_0_flatten_NONNULL(x74, x75, x76, x77, x78, x79) :|: 2 <= x74 - 1 && 2 <= x67 - 1 && x74 - 2 <= x67 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: f1962_0_flatten_NONNULL(x67:0, x68:0, x69:0, x70:0, x72:0, x73:0) -> f1962_0_flatten_NONNULL(x74:0, x75:0, x76:0, x77:0, x78:0, x79:0) :|: x74:0 > 2 && x67:0 > 2 && x74:0 - 2 <= x67:0 f1962_0_flatten_NONNULL(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0) -> f1962_0_flatten_NONNULL(x60:0, x61:0, x62:0, x64:0, x65:0, x66:0) :|: x60:0 > -1 && x54:0 > 1 && x60:0 + 2 <= x54:0 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1962_0_flatten_NONNULL(x1, x2, x3, x4, x5, x6) -> f1962_0_flatten_NONNULL(x1) ---------------------------------------- (27) Obligation: Rules: f1962_0_flatten_NONNULL(x67:0) -> f1962_0_flatten_NONNULL(x74:0) :|: x74:0 > 2 && x67:0 > 2 && x74:0 - 2 <= x67:0 f1962_0_flatten_NONNULL(x54:0) -> f1962_0_flatten_NONNULL(x60:0) :|: x60:0 > -1 && x54:0 > 1 && x60:0 + 2 <= x54:0 ---------------------------------------- (28) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f1962_0_flatten_NONNULL(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: f1962_0_flatten_NONNULL(x67:0) -> f1962_0_flatten_NONNULL(x74:0) :|: x74:0 > 2 && x67:0 > 2 && x74:0 - 2 <= x67:0 f1962_0_flatten_NONNULL(x54:0) -> f1962_0_flatten_NONNULL(x60:0) :|: x60:0 > -1 && x54:0 > 1 && x60:0 + 2 <= x54:0 ---------------------------------------- (30) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (31) Obligation: Rules: f1962_0_flatten_NONNULL(x67:0:0) -> f1962_0_flatten_NONNULL(x74:0:0) :|: x74:0:0 > 2 && x67:0:0 > 2 && x74:0:0 - 2 <= x67:0:0 f1962_0_flatten_NONNULL(x54:0:0) -> f1962_0_flatten_NONNULL(x60:0:0) :|: x60:0:0 > -1 && x54:0:0 > 1 && x60:0:0 + 2 <= x54:0:0 ---------------------------------------- (32) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x67:0:0) -> f(1, x74:0:0) :|: pc = 1 && (x74:0:0 > 2 && x67:0:0 > 2 && x74:0:0 - 2 <= x67:0:0) f(pc, x54:0:0) -> f(1, x60:0:0) :|: pc = 1 && (x60:0:0 > -1 && x54:0:0 > 1 && x60:0:0 + 2 <= x54:0:0) Witness term starting non-terminating reduction: f(1, 5) ---------------------------------------- (33) NO