MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 2267 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 10 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 90 ms] (11) IRSwT (12) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (13) IRSwT (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 23 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 27 ms] (20) IntTRS (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Rules: l0(__const_100HAT0, iHAT0, jHAT0, kHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_100HATpost, iHATpost, jHATpost, kHATpost, tmpHATpost, tmp___0HATpost) :|: tmpHAT0 = tmpHATpost && kHAT0 = kHATpost && jHAT0 = jHATpost && __const_100HAT0 = __const_100HATpost && iHATpost = 0 && tmp___0HATpost = tmp___0HATpost && kHAT0 <= __const_100HAT0 l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && 1 + x <= x3 l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 && 1 <= x15 l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 l1(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x38 = x44 && x37 = x43 && x36 = x42 l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54 && x49 <= x50 l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x61 = x67 && x60 = x66 && x68 = 1 + x62 && 1 + x62 <= x61 l7(x72, x73, x74, x75, x76, x77) -> l6(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x75 = x81 && x72 = x78 && x80 = 0 && x79 = -1 + x73 l6(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 l8(x96, x97, x98, x99, x100, x101) -> l1(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x96 = x102 && x103 = 1 + x97 l8(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x111 = x117 && x110 = x116 && x109 = x115 && x108 = x114 l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x123 = x129 && x122 = x128 && x121 = x127 && x120 = x126 && x123 <= x121 && x121 <= x123 l4(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x135 = x141 && x134 = x140 && x133 = x139 && x132 = x138 && 1 + x135 <= x133 l4(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x147 = x153 && x146 = x152 && x145 = x151 && x144 = x150 && 1 + x145 <= x147 l9(x156, x157, x158, x159, x160, x161) -> l3(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x158 = x164 && x157 = x163 && x156 = x162 && x165 = x166 && x166 = x166 l10(x168, x169, x170, x171, x172, x173) -> l9(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x172 = x178 && x171 = x177 && x170 = x176 && x169 = x175 && x168 = x174 Start term: l10(__const_100HAT0, iHAT0, jHAT0, kHAT0, tmpHAT0, tmp___0HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__const_100HAT0, iHAT0, jHAT0, kHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_100HATpost, iHATpost, jHATpost, kHATpost, tmpHATpost, tmp___0HATpost) :|: tmpHAT0 = tmpHATpost && kHAT0 = kHATpost && jHAT0 = jHATpost && __const_100HAT0 = __const_100HATpost && iHATpost = 0 && tmp___0HATpost = tmp___0HATpost && kHAT0 <= __const_100HAT0 l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && 1 + x <= x3 l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 && 1 <= x15 l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 l1(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x38 = x44 && x37 = x43 && x36 = x42 l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54 && x49 <= x50 l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x61 = x67 && x60 = x66 && x68 = 1 + x62 && 1 + x62 <= x61 l7(x72, x73, x74, x75, x76, x77) -> l6(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x75 = x81 && x72 = x78 && x80 = 0 && x79 = -1 + x73 l6(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 l8(x96, x97, x98, x99, x100, x101) -> l1(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x96 = x102 && x103 = 1 + x97 l8(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x111 = x117 && x110 = x116 && x109 = x115 && x108 = x114 l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x123 = x129 && x122 = x128 && x121 = x127 && x120 = x126 && x123 <= x121 && x121 <= x123 l4(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x135 = x141 && x134 = x140 && x133 = x139 && x132 = x138 && 1 + x135 <= x133 l4(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x147 = x153 && x146 = x152 && x145 = x151 && x144 = x150 && 1 + x145 <= x147 l9(x156, x157, x158, x159, x160, x161) -> l3(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x158 = x164 && x157 = x163 && x156 = x162 && x165 = x166 && x166 = x166 l10(x168, x169, x170, x171, x172, x173) -> l9(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x172 = x178 && x171 = x177 && x170 = x176 && x169 = x175 && x168 = x174 Start term: l10(__const_100HAT0, iHAT0, jHAT0, kHAT0, tmpHAT0, tmp___0HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_100HAT0, iHAT0, jHAT0, kHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_100HATpost, iHATpost, jHATpost, kHATpost, tmpHATpost, tmp___0HATpost) :|: tmpHAT0 = tmpHATpost && kHAT0 = kHATpost && jHAT0 = jHATpost && __const_100HAT0 = __const_100HATpost && iHATpost = 0 && tmp___0HATpost = tmp___0HATpost && kHAT0 <= __const_100HAT0 (2) l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && 1 + x <= x3 (3) l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 && 1 <= x15 (4) l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 && x27 <= 0 (5) l1(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x38 = x44 && x37 = x43 && x36 = x42 (6) l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x49 = x55 && x48 = x54 && x49 <= x50 (7) l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x61 = x67 && x60 = x66 && x68 = 1 + x62 && 1 + x62 <= x61 (8) l7(x72, x73, x74, x75, x76, x77) -> l6(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x75 = x81 && x72 = x78 && x80 = 0 && x79 = -1 + x73 (9) l6(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 (10) l8(x96, x97, x98, x99, x100, x101) -> l1(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x96 = x102 && x103 = 1 + x97 (11) l8(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x111 = x117 && x110 = x116 && x109 = x115 && x108 = x114 (12) l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x123 = x129 && x122 = x128 && x121 = x127 && x120 = x126 && x123 <= x121 && x121 <= x123 (13) l4(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x135 = x141 && x134 = x140 && x133 = x139 && x132 = x138 && 1 + x135 <= x133 (14) l4(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x147 = x153 && x146 = x152 && x145 = x151 && x144 = x150 && 1 + x145 <= x147 (15) l9(x156, x157, x158, x159, x160, x161) -> l3(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x158 = x164 && x157 = x163 && x156 = x162 && x165 = x166 && x166 = x166 (16) l10(x168, x169, x170, x171, x172, x173) -> l9(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x172 = x178 && x171 = x177 && x170 = x176 && x169 = x175 && x168 = x174 Arcs: (1) -> (5) (3) -> (1), (2) (5) -> (12), (13), (14) (7) -> (9) (8) -> (9) (9) -> (6), (7) (10) -> (5) (11) -> (8) (12) -> (8) (13) -> (10), (11) (14) -> (10), (11) (15) -> (3), (4) (16) -> (15) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l1(x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x39 = x45 && x38 = x44 && x37 = x43 && x36 = x42 (2) l8(x96, x97, x98, x99, x100, x101) -> l1(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x96 = x102 && x103 = 1 + x97 (3) l4(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x147 = x153 && x146 = x152 && x145 = x151 && x144 = x150 && 1 + x145 <= x147 (4) l4(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x135 = x141 && x134 = x140 && x133 = x139 && x132 = x138 && 1 + x135 <= x133 Arcs: (1) -> (3), (4) (2) -> (1) (3) -> (2) (4) -> (2) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l8(x102:0, x97:0, x104:0, x105:0, x100:0, x101:0) -> l8(x102:0, 1 + x97:0, x104:0, x105:0, x100:0, x101:0) :|: 1 + x97:0 >= 1 + x105:0 l8(x, x1, x2, x3, x4, x5) -> l8(x, 1 + x1, x2, x3, x4, x5) :|: x3 >= 1 + (1 + x1) ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l8(x1, x2, x3, x4, x5, x6) -> l8(x2, x4) ---------------------------------------- (9) Obligation: Rules: l8(x97:0, x105:0) -> l8(1 + x97:0, x105:0) :|: 1 + x97:0 >= 1 + x105:0 l8(x1, x3) -> l8(1 + x1, x3) :|: x3 >= 1 + (1 + x1) ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l8(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: l8(x97:0, x105:0) -> l8(c, x105:0) :|: c = 1 + x97:0 && 1 + x97:0 >= 1 + x105:0 l8(x1, x3) -> l8(c1, x3) :|: c1 = 1 + x1 && x3 >= 1 + (1 + x1) Found the following polynomial interpretation: [l8(x, x1)] = -1 - x + x1 The following rules are decreasing: l8(x97:0, x105:0) -> l8(c, x105:0) :|: c = 1 + x97:0 && 1 + x97:0 >= 1 + x105:0 l8(x1, x3) -> l8(c1, x3) :|: c1 = 1 + x1 && x3 >= 1 + (1 + x1) The following rules are bounded: l8(x1, x3) -> l8(c1, x3) :|: c1 = 1 + x1 && x3 >= 1 + (1 + x1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l8(x97:0, x105:0) -> l8(c, x105:0) :|: c = 1 + x97:0 && 1 + x97:0 >= 1 + x105:0 ---------------------------------------- (11) Obligation: Rules: l8(x97:0, x105:0) -> l8(1 + x97:0, x105:0) :|: 1 + x97:0 >= 1 + x105:0 ---------------------------------------- (12) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l8(x97:0, x105:0) -> l8(1 + x97:0, x105:0) :|: 1 + x97:0 >= 1 + x105:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) l8(x97:0, x105:0) -> l8(1 + x97:0, x105:0) :|: 1 + x97:0 >= 1 + x105:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) l6(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 (2) l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x61 = x67 && x60 = x66 && x68 = 1 + x62 && 1 + x62 <= x61 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: l6(x66:0, x67:0, x86:0, x69:0, x70:0, x71:0) -> l6(x66:0, x67:0, 1 + x86:0, x69:0, x70:0, x71:0) :|: x67:0 >= 1 + x86:0 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l6(x1, x2, x3, x4, x5, x6) -> l6(x2, x3) ---------------------------------------- (18) Obligation: Rules: l6(x67:0, x86:0) -> l6(x67:0, 1 + x86:0) :|: x67:0 >= 1 + x86:0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l6(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l6(x67:0, x86:0) -> l6(x67:0, c) :|: c = 1 + x86:0 && x67:0 >= 1 + x86:0 ---------------------------------------- (21) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l6(x, x1)] = x - x1 The following rules are decreasing: l6(x67:0, x86:0) -> l6(x67:0, c) :|: c = 1 + x86:0 && x67:0 >= 1 + x86:0 The following rules are bounded: l6(x67:0, x86:0) -> l6(x67:0, c) :|: c = 1 + x86:0 && x67:0 >= 1 + x86:0 ---------------------------------------- (22) YES