MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1533 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 57 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 544 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 30 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(a4HAT0, aHAT0, answerHAT0, b5HAT0, bHAT0, ret_complex6HAT0) -> l1(a4HATpost, aHATpost, answerHATpost, b5HATpost, bHATpost, ret_complex6HATpost) :|: b5HAT0 = b5HATpost && bHAT0 = bHATpost && a4HAT0 = a4HATpost && aHAT0 = aHATpost && answerHATpost = ret_complex6HATpost && ret_complex6HATpost = 1 && 30 <= a4HAT0 l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x = x6 && x1 = x7 && 1 + x <= 30 l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x12 = x18 && x13 = x19 l2(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x24 = x30 && x25 = x31 l5(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x42 = 1 + x36 && 13 <= x39 l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x54 = 10 + x48 && x51 <= 12 l6(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x66 = 1 + x60 && 1 + x63 <= 10 l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x72 = x78 && x73 = x79 && 10 <= x75 l7(x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x84 = x90 && x85 = x91 && x93 = 2 + x87 && x87 <= 5 l7(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x96 = x102 && x97 = x103 && x105 = x105 && 6 <= x99 l4(x108, x109, x110, x111, x112, x113) -> l3(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x109 = x115 && x117 = -10 + x111 && x114 = 2 + x108 && x108 <= x111 l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x120 = x126 && x121 = x127 && 1 + x123 <= x120 l8(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x141 = x142 && x138 = x139 && x140 = 0 && x142 = 1 && x139 = 1 l9(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x147 = x153 && x148 = x154 && x146 = x152 && x144 = x150 && x145 = x151 Start term: l9(a4HAT0, aHAT0, answerHAT0, b5HAT0, bHAT0, ret_complex6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(a4HAT0, aHAT0, answerHAT0, b5HAT0, bHAT0, ret_complex6HAT0) -> l1(a4HATpost, aHATpost, answerHATpost, b5HATpost, bHATpost, ret_complex6HATpost) :|: b5HAT0 = b5HATpost && bHAT0 = bHATpost && a4HAT0 = a4HATpost && aHAT0 = aHATpost && answerHATpost = ret_complex6HATpost && ret_complex6HATpost = 1 && 30 <= a4HAT0 l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x = x6 && x1 = x7 && 1 + x <= 30 l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x12 = x18 && x13 = x19 l2(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x24 = x30 && x25 = x31 l5(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x42 = 1 + x36 && 13 <= x39 l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x54 = 10 + x48 && x51 <= 12 l6(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x66 = 1 + x60 && 1 + x63 <= 10 l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x72 = x78 && x73 = x79 && 10 <= x75 l7(x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x84 = x90 && x85 = x91 && x93 = 2 + x87 && x87 <= 5 l7(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x96 = x102 && x97 = x103 && x105 = x105 && 6 <= x99 l4(x108, x109, x110, x111, x112, x113) -> l3(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x109 = x115 && x117 = -10 + x111 && x114 = 2 + x108 && x108 <= x111 l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x120 = x126 && x121 = x127 && 1 + x123 <= x120 l8(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x141 = x142 && x138 = x139 && x140 = 0 && x142 = 1 && x139 = 1 l9(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x147 = x153 && x148 = x154 && x146 = x152 && x144 = x150 && x145 = x151 Start term: l9(a4HAT0, aHAT0, answerHAT0, b5HAT0, bHAT0, ret_complex6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(a4HAT0, aHAT0, answerHAT0, b5HAT0, bHAT0, ret_complex6HAT0) -> l1(a4HATpost, aHATpost, answerHATpost, b5HATpost, bHATpost, ret_complex6HATpost) :|: b5HAT0 = b5HATpost && bHAT0 = bHATpost && a4HAT0 = a4HATpost && aHAT0 = aHATpost && answerHATpost = ret_complex6HATpost && ret_complex6HATpost = 1 && 30 <= a4HAT0 (2) l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x = x6 && x1 = x7 && 1 + x <= 30 (3) l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x12 = x18 && x13 = x19 (4) l2(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x24 = x30 && x25 = x31 (5) l5(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x42 = 1 + x36 && 13 <= x39 (6) l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x54 = 10 + x48 && x51 <= 12 (7) l6(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x66 = 1 + x60 && 1 + x63 <= 10 (8) l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x72 = x78 && x73 = x79 && 10 <= x75 (9) l7(x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x84 = x90 && x85 = x91 && x93 = 2 + x87 && x87 <= 5 (10) l7(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x96 = x102 && x97 = x103 && x105 = x105 && 6 <= x99 (11) l4(x108, x109, x110, x111, x112, x113) -> l3(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x109 = x115 && x117 = -10 + x111 && x114 = 2 + x108 && x108 <= x111 (12) l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x120 = x126 && x121 = x127 && 1 + x123 <= x120 (13) l8(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x141 = x142 && x138 = x139 && x140 = 0 && x142 = 1 && x139 = 1 (14) l9(x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x147 = x153 && x148 = x154 && x146 = x152 && x144 = x150 && x145 = x151 Arcs: (2) -> (4) (3) -> (1), (2) (4) -> (11), (12) (5) -> (4) (6) -> (4) (7) -> (4) (8) -> (5), (6) (9) -> (7) (10) -> (7), (8) (11) -> (3) (12) -> (9), (10) (13) -> (3) (14) -> (13) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4, x5) -> l2(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x3 = x9 && x4 = x10 && x2 = x8 && x = x6 && x1 = x7 && 1 + x <= 30 (2) l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x15 = x21 && x16 = x22 && x14 = x20 && x12 = x18 && x13 = x19 (3) l4(x108, x109, x110, x111, x112, x113) -> l3(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x109 = x115 && x117 = -10 + x111 && x114 = 2 + x108 && x108 <= x111 (4) l2(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x27 = x33 && x28 = x34 && x26 = x32 && x24 = x30 && x25 = x31 (5) l6(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x63 = x69 && x64 = x70 && x62 = x68 && x61 = x67 && x66 = 1 + x60 && 1 + x63 <= 10 (6) l7(x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x84 = x90 && x85 = x91 && x93 = 2 + x87 && x87 <= 5 (7) l5(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x51 = x57 && x52 = x58 && x50 = x56 && x49 = x55 && x54 = 10 + x48 && x51 <= 12 (8) l5(x36, x37, x38, x39, x40, x41) -> l2(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x39 = x45 && x40 = x46 && x38 = x44 && x37 = x43 && x42 = 1 + x36 && 13 <= x39 (9) l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x75 = x81 && x76 = x82 && x74 = x80 && x72 = x78 && x73 = x79 && 10 <= x75 (10) l7(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x96 = x102 && x97 = x103 && x105 = x105 && 6 <= x99 (11) l4(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x123 = x129 && x124 = x130 && x122 = x128 && x120 = x126 && x121 = x127 && 1 + x123 <= x120 Arcs: (1) -> (4) (2) -> (1) (3) -> (2) (4) -> (3), (11) (5) -> (4) (6) -> (5) (7) -> (4) (8) -> (4) (9) -> (7), (8) (10) -> (5), (9) (11) -> (6), (10) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l4(x108:0, x109:0, x110:0, x111:0, x10:0, x113:0) -> l4(2 + x108:0, x109:0, x110:0, -10 + x111:0, x10:0, x113:0) :|: x111:0 >= x108:0 && x108:0 < 28 l4(x120:0, x121:0, x122:0, x123:0, x124:0, x125:0) -> l6(x120:0, x121:0, x122:0, 2 + x123:0, x124:0, x125:0) :|: x120:0 >= 1 + x123:0 && x123:0 < 6 l6(x72:0, x31:0, x32:0, x33:0, x34:0, x35:0) -> l4(1 + x72:0, x31:0, x32:0, x33:0, x34:0, x35:0) :|: x33:0 > 12 l6(x, x1, x2, x3, x4, x5) -> l4(1 + x, x1, x2, x3, x4, x5) :|: x3 < 10 l4(x6, x7, x8, x9, x10, x11) -> l6(x6, x7, x8, x12, x10, x11) :|: x6 >= 1 + x9 && x9 > 5 l6(x13, x14, x15, x16, x17, x18) -> l4(10 + x13, x14, x15, x16, x17, x18) :|: x16 > 9 && x16 < 13 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l4(x1, x2, x3, x4, x5, x6) -> l4(x1, x4) l6(x1, x2, x3, x4, x5, x6) -> l6(x1, x4) ---------------------------------------- (8) Obligation: Rules: l4(x108:0, x111:0) -> l4(2 + x108:0, -10 + x111:0) :|: x111:0 >= x108:0 && x108:0 < 28 l4(x120:0, x123:0) -> l6(x120:0, 2 + x123:0) :|: x120:0 >= 1 + x123:0 && x123:0 < 6 l6(x72:0, x33:0) -> l4(1 + x72:0, x33:0) :|: x33:0 > 12 l6(x, x3) -> l4(1 + x, x3) :|: x3 < 10 l4(x6, x9) -> l6(x6, x12) :|: x6 >= 1 + x9 && x9 > 5 l6(x13, x16) -> l4(10 + x13, x16) :|: x16 > 9 && x16 < 13 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER, INTEGER) l6(VARIABLE, VARIABLE) 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: l4(x108:0, x111:0) -> l4(c, c1) :|: c1 = -10 + x111:0 && c = 2 + x108:0 && (x111:0 >= x108:0 && x108:0 < 28) l4(x120:0, x123:0) -> l6(x120:0, c2) :|: c2 = 2 + x123:0 && (x120:0 >= 1 + x123:0 && x123:0 < 6) l6(x72:0, x33:0) -> l4(c3, x33:0) :|: c3 = 1 + x72:0 && x33:0 > 12 l6(x, x3) -> l4(c4, x3) :|: c4 = 1 + x && x3 < 10 l4(x6, x9) -> l6(x6, x12) :|: x6 >= 1 + x9 && x9 > 5 l6(x13, x16) -> l4(c5, x16) :|: c5 = 10 + x13 && (x16 > 9 && x16 < 13) Found the following polynomial interpretation: [l4(x, x1)] = 27 - x [l6(x2, x3)] = 27 - x2 The following rules are decreasing: l4(x108:0, x111:0) -> l4(c, c1) :|: c1 = -10 + x111:0 && c = 2 + x108:0 && (x111:0 >= x108:0 && x108:0 < 28) l6(x72:0, x33:0) -> l4(c3, x33:0) :|: c3 = 1 + x72:0 && x33:0 > 12 l6(x, x3) -> l4(c4, x3) :|: c4 = 1 + x && x3 < 10 l6(x13, x16) -> l4(c5, x16) :|: c5 = 10 + x13 && (x16 > 9 && x16 < 13) The following rules are bounded: l4(x108:0, x111:0) -> l4(c, c1) :|: c1 = -10 + x111:0 && c = 2 + x108:0 && (x111:0 >= x108:0 && x108:0 < 28) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l4(x120:0, x123:0) -> l6(x120:0, c2) :|: c2 = 2 + x123:0 && (x120:0 >= 1 + x123:0 && x123:0 < 6) l6(x72:0, x33:0) -> l4(c3, x33:0) :|: c3 = 1 + x72:0 && x33:0 > 12 l6(x, x3) -> l4(c4, x3) :|: c4 = 1 + x && x3 < 10 l4(x6, x9) -> l6(x6, x12) :|: x6 >= 1 + x9 && x9 > 5 l6(x13, x16) -> l4(c5, x16) :|: c5 = 10 + x13 && (x16 > 9 && x16 < 13) ---------------------------------------- (10) Obligation: Rules: l4(x120:0, x123:0) -> l6(x120:0, 2 + x123:0) :|: x120:0 >= 1 + x123:0 && x123:0 < 6 l6(x72:0, x33:0) -> l4(1 + x72:0, x33:0) :|: x33:0 > 12 l6(x, x3) -> l4(1 + x, x3) :|: x3 < 10 l4(x6, x9) -> l6(x6, x12) :|: x6 >= 1 + x9 && x9 > 5 l6(x13, x16) -> l4(10 + x13, x16) :|: x16 > 9 && x16 < 13 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l4(x120:0, x123:0) -> l6(x120:0, 2 + x123:0) :|: x120:0 >= 1 + x123:0 && x123:0 < 6 (2) l6(x72:0, x33:0) -> l4(1 + x72:0, x33:0) :|: x33:0 > 12 (3) l6(x, x3) -> l4(1 + x, x3) :|: x3 < 10 (4) l4(x6, x9) -> l6(x6, x12) :|: x6 >= 1 + x9 && x9 > 5 (5) l6(x13, x16) -> l4(10 + x13, x16) :|: x16 > 9 && x16 < 13 Arcs: (1) -> (3) (2) -> (4) (3) -> (1), (4) (4) -> (2), (3), (5) (5) -> (4) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l4(x120:0, x123:0) -> l6(x120:0, 2 + x123:0) :|: x120:0 >= 1 + x123:0 && x123:0 < 6 (2) l6(x, x3) -> l4(1 + x, x3) :|: x3 < 10 (3) l4(x6, x9) -> l6(x6, x12) :|: x6 >= 1 + x9 && x9 > 5 (4) l6(x13, x16) -> l4(10 + x13, x16) :|: x16 > 9 && x16 < 13 (5) l6(x72:0, x33:0) -> l4(1 + x72:0, x33:0) :|: x33:0 > 12 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2), (4), (5) (4) -> (3) (5) -> (3) This digraph is fully evaluated!