MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 1535 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 54 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 2045 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 8 ms] (12) IRSwT (13) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(__const_100HAT0, __const_10HAT0, __const_11HAT0, copiedHAT0, eHAT0, nHAT0, oldeHAT0, oldnHAT0) -> l1(__const_100HATpost, __const_10HATpost, __const_11HATpost, copiedHATpost, eHATpost, nHATpost, oldeHATpost, oldnHATpost) :|: oldnHAT0 = oldnHATpost && oldeHAT0 = oldeHATpost && nHAT0 = nHATpost && eHAT0 = eHATpost && copiedHAT0 = copiedHATpost && __const_11HAT0 = __const_11HATpost && __const_100HAT0 = __const_100HATpost && __const_10HAT0 = __const_10HATpost && nHAT0 <= oldnHAT0 && oldeHAT0 <= eHAT0 && 1 <= copiedHAT0 l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x2 = x10 && x = x8 && x1 = x9 && x12 = 1 + x4 && x13 = x2 + x5 && x5 <= x && 1 <= x4 && x14 = x4 && x15 = x5 && x11 = 1 && x3 <= 0 l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x17 = x25 l0(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x34 = x42 && x32 = x40 && x33 = x41 && x44 = -1 + x36 && x45 = -1 * x33 + x37 && 1 + x32 <= x37 && 1 <= x36 && x46 = x36 && x47 = x37 && x43 = 1 && x35 <= 0 l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l0(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x48 = x56 && x49 = x57 l0(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x67 = x75 && x66 = x74 && x64 = x72 && x65 = x73 && x76 = 1 + x68 && x77 = x66 + x69 && x69 <= x64 && 1 <= x68 l4(x80, x81, x82, x83, x84, x85, x86, x87) -> l0(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x80 = x88 && x81 = x89 l0(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x99 = x107 && x98 = x106 && x96 = x104 && x97 = x105 && x108 = -1 + x100 && x109 = -1 * x97 + x101 && 1 + x96 <= x101 && 1 <= x100 l5(x112, x113, x114, x115, x116, x117, x118, x119) -> l0(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x112 = x120 && x113 = x121 l6(x128, x129, x130, x131, x132, x133, x134, x135) -> l0(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x130 = x138 && x128 = x136 && x129 = x137 && x139 = 0 && x140 = 1 && x141 = x141 l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l6(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x144 = x152 && x145 = x153 Start term: l7(__const_100HAT0, __const_10HAT0, __const_11HAT0, copiedHAT0, eHAT0, nHAT0, oldeHAT0, oldnHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__const_100HAT0, __const_10HAT0, __const_11HAT0, copiedHAT0, eHAT0, nHAT0, oldeHAT0, oldnHAT0) -> l1(__const_100HATpost, __const_10HATpost, __const_11HATpost, copiedHATpost, eHATpost, nHATpost, oldeHATpost, oldnHATpost) :|: oldnHAT0 = oldnHATpost && oldeHAT0 = oldeHATpost && nHAT0 = nHATpost && eHAT0 = eHATpost && copiedHAT0 = copiedHATpost && __const_11HAT0 = __const_11HATpost && __const_100HAT0 = __const_100HATpost && __const_10HAT0 = __const_10HATpost && nHAT0 <= oldnHAT0 && oldeHAT0 <= eHAT0 && 1 <= copiedHAT0 l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x2 = x10 && x = x8 && x1 = x9 && x12 = 1 + x4 && x13 = x2 + x5 && x5 <= x && 1 <= x4 && x14 = x4 && x15 = x5 && x11 = 1 && x3 <= 0 l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x17 = x25 l0(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x34 = x42 && x32 = x40 && x33 = x41 && x44 = -1 + x36 && x45 = -1 * x33 + x37 && 1 + x32 <= x37 && 1 <= x36 && x46 = x36 && x47 = x37 && x43 = 1 && x35 <= 0 l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l0(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x48 = x56 && x49 = x57 l0(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x67 = x75 && x66 = x74 && x64 = x72 && x65 = x73 && x76 = 1 + x68 && x77 = x66 + x69 && x69 <= x64 && 1 <= x68 l4(x80, x81, x82, x83, x84, x85, x86, x87) -> l0(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x80 = x88 && x81 = x89 l0(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x99 = x107 && x98 = x106 && x96 = x104 && x97 = x105 && x108 = -1 + x100 && x109 = -1 * x97 + x101 && 1 + x96 <= x101 && 1 <= x100 l5(x112, x113, x114, x115, x116, x117, x118, x119) -> l0(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x112 = x120 && x113 = x121 l6(x128, x129, x130, x131, x132, x133, x134, x135) -> l0(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x130 = x138 && x128 = x136 && x129 = x137 && x139 = 0 && x140 = 1 && x141 = x141 l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l6(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x144 = x152 && x145 = x153 Start term: l7(__const_100HAT0, __const_10HAT0, __const_11HAT0, copiedHAT0, eHAT0, nHAT0, oldeHAT0, oldnHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_100HAT0, __const_10HAT0, __const_11HAT0, copiedHAT0, eHAT0, nHAT0, oldeHAT0, oldnHAT0) -> l1(__const_100HATpost, __const_10HATpost, __const_11HATpost, copiedHATpost, eHATpost, nHATpost, oldeHATpost, oldnHATpost) :|: oldnHAT0 = oldnHATpost && oldeHAT0 = oldeHATpost && nHAT0 = nHATpost && eHAT0 = eHATpost && copiedHAT0 = copiedHATpost && __const_11HAT0 = __const_11HATpost && __const_100HAT0 = __const_100HATpost && __const_10HAT0 = __const_10HATpost && nHAT0 <= oldnHAT0 && oldeHAT0 <= eHAT0 && 1 <= copiedHAT0 (2) l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x2 = x10 && x = x8 && x1 = x9 && x12 = 1 + x4 && x13 = x2 + x5 && x5 <= x && 1 <= x4 && x14 = x4 && x15 = x5 && x11 = 1 && x3 <= 0 (3) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x17 = x25 (4) l0(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x34 = x42 && x32 = x40 && x33 = x41 && x44 = -1 + x36 && x45 = -1 * x33 + x37 && 1 + x32 <= x37 && 1 <= x36 && x46 = x36 && x47 = x37 && x43 = 1 && x35 <= 0 (5) l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l0(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x48 = x56 && x49 = x57 (6) l0(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x67 = x75 && x66 = x74 && x64 = x72 && x65 = x73 && x76 = 1 + x68 && x77 = x66 + x69 && x69 <= x64 && 1 <= x68 (7) l4(x80, x81, x82, x83, x84, x85, x86, x87) -> l0(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x80 = x88 && x81 = x89 (8) l0(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x99 = x107 && x98 = x106 && x96 = x104 && x97 = x105 && x108 = -1 + x100 && x109 = -1 * x97 + x101 && 1 + x96 <= x101 && 1 <= x100 (9) l5(x112, x113, x114, x115, x116, x117, x118, x119) -> l0(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x112 = x120 && x113 = x121 (10) l6(x128, x129, x130, x131, x132, x133, x134, x135) -> l0(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x130 = x138 && x128 = x136 && x129 = x137 && x139 = 0 && x140 = 1 && x141 = x141 (11) l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l6(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x146 = x154 && x144 = x152 && x145 = x153 Arcs: (2) -> (3) (3) -> (1), (2), (4), (6), (8) (4) -> (5) (5) -> (1), (2), (4), (6), (8) (6) -> (7) (7) -> (1), (2), (4), (6), (8) (8) -> (9) (9) -> (1), (2), (4), (6), (8) (10) -> (2), (4), (6), (8) (11) -> (10) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x2 = x10 && x = x8 && x1 = x9 && x12 = 1 + x4 && x13 = x2 + x5 && x5 <= x && 1 <= x4 && x14 = x4 && x15 = x5 && x11 = 1 && x3 <= 0 (2) l3(x48, x49, x50, x51, x52, x53, x54, x55) -> l0(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x48 = x56 && x49 = x57 (3) l0(x32, x33, x34, x35, x36, x37, x38, x39) -> l3(x40, x41, x42, x43, x44, x45, x46, x47) :|: x34 = x42 && x32 = x40 && x33 = x41 && x44 = -1 + x36 && x45 = -1 * x33 + x37 && 1 + x32 <= x37 && 1 <= x36 && x46 = x36 && x47 = x37 && x43 = 1 && x35 <= 0 (4) l4(x80, x81, x82, x83, x84, x85, x86, x87) -> l0(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x82 = x90 && x80 = x88 && x81 = x89 (5) l0(x64, x65, x66, x67, x68, x69, x70, x71) -> l4(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x67 = x75 && x66 = x74 && x64 = x72 && x65 = x73 && x76 = 1 + x68 && x77 = x66 + x69 && x69 <= x64 && 1 <= x68 (6) l5(x112, x113, x114, x115, x116, x117, x118, x119) -> l0(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x112 = x120 && x113 = x121 (7) l0(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x99 = x107 && x98 = x106 && x96 = x104 && x97 = x105 && x108 = -1 + x100 && x109 = -1 * x97 + x101 && 1 + x96 <= x101 && 1 <= x100 (8) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x18 = x26 && x16 = x24 && x17 = x25 Arcs: (1) -> (8) (2) -> (1), (3), (5), (7) (3) -> (2) (4) -> (1), (3), (5), (7) (5) -> (4) (6) -> (1), (3), (5), (7) (7) -> (6) (8) -> (1), (3), (5), (7) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0, x102:0, x103:0) -> l0(x104:0, x105:0, x106:0, x107:0, -1 + x100:0, -1 * x105:0 + x101:0, x102:0, x103:0) :|: x100:0 > 0 && x101:0 >= 1 + x104:0 l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0, x70:0, x71:0) -> l0(x64:0, x65:0, x66:0, x67:0, 1 + x68:0, x66:0 + x69:0, x70:0, x71:0) :|: x68:0 > 0 && x69:0 <= x64:0 l0(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0, x38:0, x39:0) -> l0(x32:0, x33:0, x34:0, 1, -1 + x36:0, -1 * x33:0 + x37:0, x36:0, x37:0) :|: x36:0 > 0 && x37:0 >= 1 + x32:0 && x35:0 < 1 l0(x24:0, x1:0, x10:0, x3:0, x14:0, x15:0, x6:0, x7:0) -> l0(x24:0, x1:0, x10:0, 1, 1 + x14:0, x10:0 + x15:0, x14:0, x15:0) :|: x14:0 > 0 && x24:0 >= x15:0 && x3:0 < 1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x1, x2, x3, x4, x5, x6) ---------------------------------------- (8) Obligation: Rules: l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, x107:0, -1 + x100:0, -1 * x105:0 + x101:0) :|: x100:0 > 0 && x101:0 >= 1 + x104:0 l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, x67:0, 1 + x68:0, x66:0 + x69:0) :|: x68:0 > 0 && x69:0 <= x64:0 l0(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0) -> l0(x32:0, x33:0, x34:0, 1, -1 + x36:0, -1 * x33:0 + x37:0) :|: x36:0 > 0 && x37:0 >= 1 + x32:0 && x35:0 < 1 l0(x24:0, x1:0, x10:0, x3:0, x14:0, x15:0) -> l0(x24:0, x1:0, x10:0, 1, 1 + x14:0, x10:0 + x15:0) :|: x14:0 > 0 && x24:0 >= x15:0 && x3:0 < 1 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER, VARIABLE, VARIABLE, VARIABLE, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, x107:0, c, c1) :|: c1 = -1 * x105:0 + x101:0 && c = -1 + x100:0 && (x100:0 > 0 && x101:0 >= 1 + x104:0) l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, x67:0, c2, c3) :|: c3 = x66:0 + x69:0 && c2 = 1 + x68:0 && (x68:0 > 0 && x69:0 <= x64:0) l0(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0) -> l0(x32:0, x33:0, x34:0, c4, c5, c6) :|: c6 = -1 * x33:0 + x37:0 && (c5 = -1 + x36:0 && c4 = 1) && (x36:0 > 0 && x37:0 >= 1 + x32:0 && x35:0 < 1) l0(x24:0, x1:0, x10:0, x3:0, x14:0, x15:0) -> l0(x24:0, x1:0, x10:0, c7, c8, c9) :|: c9 = x10:0 + x15:0 && (c8 = 1 + x14:0 && c7 = 1) && (x14:0 > 0 && x24:0 >= x15:0 && x3:0 < 1) Found the following polynomial interpretation: [l0(x, x1, x2, x3, x4, x5)] = -x3 The following rules are decreasing: l0(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0) -> l0(x32:0, x33:0, x34:0, c4, c5, c6) :|: c6 = -1 * x33:0 + x37:0 && (c5 = -1 + x36:0 && c4 = 1) && (x36:0 > 0 && x37:0 >= 1 + x32:0 && x35:0 < 1) l0(x24:0, x1:0, x10:0, x3:0, x14:0, x15:0) -> l0(x24:0, x1:0, x10:0, c7, c8, c9) :|: c9 = x10:0 + x15:0 && (c8 = 1 + x14:0 && c7 = 1) && (x14:0 > 0 && x24:0 >= x15:0 && x3:0 < 1) The following rules are bounded: l0(x32:0, x33:0, x34:0, x35:0, x36:0, x37:0) -> l0(x32:0, x33:0, x34:0, c4, c5, c6) :|: c6 = -1 * x33:0 + x37:0 && (c5 = -1 + x36:0 && c4 = 1) && (x36:0 > 0 && x37:0 >= 1 + x32:0 && x35:0 < 1) l0(x24:0, x1:0, x10:0, x3:0, x14:0, x15:0) -> l0(x24:0, x1:0, x10:0, c7, c8, c9) :|: c9 = x10:0 + x15:0 && (c8 = 1 + x14:0 && c7 = 1) && (x14:0 > 0 && x24:0 >= x15:0 && x3:0 < 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, x107:0, c, c1) :|: c1 = -1 * x105:0 + x101:0 && c = -1 + x100:0 && (x100:0 > 0 && x101:0 >= 1 + x104:0) l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, x67:0, c2, c3) :|: c3 = x66:0 + x69:0 && c2 = 1 + x68:0 && (x68:0 > 0 && x69:0 <= x64:0) ---------------------------------------- (10) Obligation: Rules: l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, x107:0, -1 + x100:0, -1 * x105:0 + x101:0) :|: x100:0 > 0 && x101:0 >= 1 + x104:0 l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, x67:0, 1 + x68:0, x66:0 + x69:0) :|: x68:0 > 0 && x69:0 <= x64:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, x107:0, -1 + x100:0, -1 * x105:0 + x101:0) :|: x100:0 > 0 && x101:0 >= 1 + x104:0 (2) l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, x67:0, 1 + x68:0, x66:0 + x69:0) :|: x68:0 > 0 && x69:0 <= x64:0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, x107:0, -1 + x100:0, -1 * x105:0 + x101:0) :|: x100:0 > 0 && x101:0 >= 1 + x104:0 (2) l0(x64:0, x65:0, x66:0, x67:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, x67:0, 1 + x68:0, x66:0 + x69:0) :|: x68:0 > 0 && x69:0 <= x64:0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5, x6) -> l0(x1, x2, x3, x5, x6) ---------------------------------------- (14) Obligation: Rules: l0(x104:0, x105:0, x106:0, x100:0, x101:0) -> l0(x104:0, x105:0, x106:0, -1 + x100:0, -1 * x105:0 + x101:0) :|: x100:0 > 0 && x101:0 >= 1 + x104:0 l0(x64:0, x65:0, x66:0, x68:0, x69:0) -> l0(x64:0, x65:0, x66:0, 1 + x68:0, x66:0 + x69:0) :|: x68:0 > 0 && x69:0 <= x64:0