NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1008 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 63 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) FilterProof [EQUIVALENT, 0 ms] (10) IntTRS (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IntTRS (13) IntTRSNonPeriodicNontermProof [COMPLETE, 0 ms] (14) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_16HATpost, lt_10HATpost, lt_9HATpost, p_7HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && tmp_8HAT0 = tmp_8HATpost && lt_9HAT0 = lt_9HATpost && lt_10HAT0 = lt_10HATpost && cnt_16HAT0 = cnt_16HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && -1 * x16 + x7 <= 0 && x10 = x10 && x8 = x8 && x1 = x9 && x3 = x11 && x4 = x12 && x5 = x13 && x6 = x14 && x7 = x15 l1(x17, x18, x19, x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29, x30, x31, x32) :|: x33 = x18 && 0 <= -1 - x33 + x24 && x27 = x27 && x30 = x30 && x30 <= 0 && 0 <= x30 && x17 = x25 && x18 = x26 && x20 = x28 && x21 = x29 && x23 = x31 && x24 = x32 l3(x34, x35, x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 l1(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x66 = x51 && 0 <= -1 - x66 + x57 && x60 = x60 && x63 = x63 && x50 = x58 && x51 = x59 && x53 = x61 && x54 = x62 && x56 = x64 && x57 = x65 l5(x67, x68, x69, x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79, x80, x81, x82) :|: x74 = x82 && x73 = x81 && x72 = x80 && x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && 1 + x72 <= 0 l5(x83, x84, x85, x86, x87, x88, x89, x90) -> l6(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && 1 <= x88 l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l4(x107, x108, x109, x110, x111, x112, x113, x114) :|: x115 = x100 && x110 = x110 && x99 = x107 && x100 = x108 && x101 = x109 && x103 = x111 && x104 = x112 && x105 = x113 && x106 = x114 l4(x116, x117, x118, x119, x120, x121, x122, x123) -> l1(x124, x125, x126, x127, x128, x129, x130, x131) :|: x123 = x131 && x122 = x130 && x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 l7(x132, x133, x134, x135, x136, x137, x138, x139) -> l0(x140, x141, x142, x143, x144, x145, x146, x147) :|: x139 = x147 && x138 = x146 && x137 = x145 && x136 = x144 && x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 Start term: l7(Result_4HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_16HATpost, lt_10HATpost, lt_9HATpost, p_7HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && tmp_8HAT0 = tmp_8HATpost && lt_9HAT0 = lt_9HATpost && lt_10HAT0 = lt_10HATpost && cnt_16HAT0 = cnt_16HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && -1 * x16 + x7 <= 0 && x10 = x10 && x8 = x8 && x1 = x9 && x3 = x11 && x4 = x12 && x5 = x13 && x6 = x14 && x7 = x15 l1(x17, x18, x19, x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29, x30, x31, x32) :|: x33 = x18 && 0 <= -1 - x33 + x24 && x27 = x27 && x30 = x30 && x30 <= 0 && 0 <= x30 && x17 = x25 && x18 = x26 && x20 = x28 && x21 = x29 && x23 = x31 && x24 = x32 l3(x34, x35, x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 l1(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x66 = x51 && 0 <= -1 - x66 + x57 && x60 = x60 && x63 = x63 && x50 = x58 && x51 = x59 && x53 = x61 && x54 = x62 && x56 = x64 && x57 = x65 l5(x67, x68, x69, x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79, x80, x81, x82) :|: x74 = x82 && x73 = x81 && x72 = x80 && x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && 1 + x72 <= 0 l5(x83, x84, x85, x86, x87, x88, x89, x90) -> l6(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && 1 <= x88 l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l4(x107, x108, x109, x110, x111, x112, x113, x114) :|: x115 = x100 && x110 = x110 && x99 = x107 && x100 = x108 && x101 = x109 && x103 = x111 && x104 = x112 && x105 = x113 && x106 = x114 l4(x116, x117, x118, x119, x120, x121, x122, x123) -> l1(x124, x125, x126, x127, x128, x129, x130, x131) :|: x123 = x131 && x122 = x130 && x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 l7(x132, x133, x134, x135, x136, x137, x138, x139) -> l0(x140, x141, x142, x143, x144, x145, x146, x147) :|: x139 = x147 && x138 = x146 && x137 = x145 && x136 = x144 && x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 Start term: l7(Result_4HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_16HATpost, lt_10HATpost, lt_9HATpost, p_7HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && tmp_8HAT0 = tmp_8HATpost && lt_9HAT0 = lt_9HATpost && lt_10HAT0 = lt_10HATpost && cnt_16HAT0 = cnt_16HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x8, x9, x10, x11, x12, x13, x14, x15) :|: x16 = x1 && -1 * x16 + x7 <= 0 && x10 = x10 && x8 = x8 && x1 = x9 && x3 = x11 && x4 = x12 && x5 = x13 && x6 = x14 && x7 = x15 (3) l1(x17, x18, x19, x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29, x30, x31, x32) :|: x33 = x18 && 0 <= -1 - x33 + x24 && x27 = x27 && x30 = x30 && x30 <= 0 && 0 <= x30 && x17 = x25 && x18 = x26 && x20 = x28 && x21 = x29 && x23 = x31 && x24 = x32 (4) l3(x34, x35, x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 (5) l1(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x66 = x51 && 0 <= -1 - x66 + x57 && x60 = x60 && x63 = x63 && x50 = x58 && x51 = x59 && x53 = x61 && x54 = x62 && x56 = x64 && x57 = x65 (6) l5(x67, x68, x69, x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79, x80, x81, x82) :|: x74 = x82 && x73 = x81 && x72 = x80 && x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && 1 + x72 <= 0 (7) l5(x83, x84, x85, x86, x87, x88, x89, x90) -> l6(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && 1 <= x88 (8) l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l4(x107, x108, x109, x110, x111, x112, x113, x114) :|: x115 = x100 && x110 = x110 && x99 = x107 && x100 = x108 && x101 = x109 && x103 = x111 && x104 = x112 && x105 = x113 && x106 = x114 (9) l4(x116, x117, x118, x119, x120, x121, x122, x123) -> l1(x124, x125, x126, x127, x128, x129, x130, x131) :|: x123 = x131 && x122 = x130 && x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 (10) l7(x132, x133, x134, x135, x136, x137, x138, x139) -> l0(x140, x141, x142, x143, x144, x145, x146, x147) :|: x139 = x147 && x138 = x146 && x137 = x145 && x136 = x144 && x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 Arcs: (1) -> (2), (3), (5) (3) -> (4) (4) -> (2), (3), (5) (5) -> (6), (7) (6) -> (8) (7) -> (8) (8) -> (9) (9) -> (2), (3), (5) (10) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x17, x18, x19, x20, x21, x22, x23, x24) -> l3(x25, x26, x27, x28, x29, x30, x31, x32) :|: x33 = x18 && 0 <= -1 - x33 + x24 && x27 = x27 && x30 = x30 && x30 <= 0 && 0 <= x30 && x17 = x25 && x18 = x26 && x20 = x28 && x21 = x29 && x23 = x31 && x24 = x32 (2) l4(x116, x117, x118, x119, x120, x121, x122, x123) -> l1(x124, x125, x126, x127, x128, x129, x130, x131) :|: x123 = x131 && x122 = x130 && x121 = x129 && x120 = x128 && x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 (3) l6(x99, x100, x101, x102, x103, x104, x105, x106) -> l4(x107, x108, x109, x110, x111, x112, x113, x114) :|: x115 = x100 && x110 = x110 && x99 = x107 && x100 = x108 && x101 = x109 && x103 = x111 && x104 = x112 && x105 = x113 && x106 = x114 (4) l5(x83, x84, x85, x86, x87, x88, x89, x90) -> l6(x91, x92, x93, x94, x95, x96, x97, x98) :|: x90 = x98 && x89 = x97 && x88 = x96 && x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && 1 <= x88 (5) l5(x67, x68, x69, x70, x71, x72, x73, x74) -> l6(x75, x76, x77, x78, x79, x80, x81, x82) :|: x74 = x82 && x73 = x81 && x72 = x80 && x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && 1 + x72 <= 0 (6) l1(x50, x51, x52, x53, x54, x55, x56, x57) -> l5(x58, x59, x60, x61, x62, x63, x64, x65) :|: x66 = x51 && 0 <= -1 - x66 + x57 && x60 = x60 && x63 = x63 && x50 = x58 && x51 = x59 && x53 = x61 && x54 = x62 && x56 = x64 && x57 = x65 (7) l3(x34, x35, x36, x37, x38, x39, x40, x41) -> l1(x42, x43, x44, x45, x46, x47, x48, x49) :|: x41 = x49 && x40 = x48 && x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 Arcs: (1) -> (7) (2) -> (1), (6) (3) -> (2) (4) -> (3) (5) -> (3) (6) -> (4), (5) (7) -> (1), (6) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x17:0, x18:0, x19:0, x20:0, x21:0, x22:0, x23:0, x24:0) -> l1(x17:0, x18:0, x27:0, x20:0, x21:0, x30:0, x23:0, x24:0) :|: x30:0 < 1 && 0 <= -1 - x18:0 + x24:0 && x30:0 > -1 l1(x107:0, x108:0, x52:0, x53:0, x111:0, x55:0, x113:0, x114:0) -> l1(x107:0, x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0) :|: x112:0 < 0 && 0 <= -1 - x108:0 + x114:0 l1(x, x1, x2, x3, x4, x5, x6, x7) -> l1(x, x1, x8, x9, x4, x10, x6, x7) :|: x10 > 0 && 0 <= -1 - x1 + x7 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x2, x8) ---------------------------------------- (8) Obligation: Rules: l1(x18:0, x24:0) -> l1(x18:0, x24:0) :|: x30:0 < 1 && 0 <= -1 - x18:0 + x24:0 && x30:0 > -1 l1(x108:0, x114:0) -> l1(x108:0, x114:0) :|: x112:0 < 0 && 0 <= -1 - x108:0 + x114:0 l1(x1, x7) -> l1(x1, x7) :|: x10 > 0 && 0 <= -1 - x1 + x7 ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l1(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l1(x18:0, x24:0) -> l1(x18:0, x24:0) :|: x30:0 < 1 && 0 <= -1 - x18:0 + x24:0 && x30:0 > -1 l1(x108:0, x114:0) -> l1(x108:0, x114:0) :|: x112:0 < 0 && 0 <= -1 - x108:0 + x114:0 l1(x1, x7) -> l1(x1, x7) :|: x10 > 0 && 0 <= -1 - x1 + x7 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l1(x108:0:0, x114:0:0) -> l1(x108:0:0, x114:0:0) :|: x112:0:0 < 0 && 0 <= -1 - x108:0:0 + x114:0:0 l1(x1:0, x7:0) -> l1(x1:0, x7:0) :|: x10:0 > 0 && 0 <= -1 - x1:0 + x7:0 l1(x18:0:0, x24:0:0) -> l1(x18:0:0, x24:0:0) :|: x30:0:0 < 1 && 0 <= -1 - x18:0:0 + x24:0:0 && x30:0:0 > -1 ---------------------------------------- (13) IntTRSNonPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x108:0:0, x114:0:0) -> f(1, x108:0:0, x114:0:0) :|: pc = 1 && (x112:0:0 < 0 && 0 <= -1 - x108:0:0 + x114:0:0) f(pc, x1:0, x7:0) -> f(1, x1:0, x7:0) :|: pc = 1 && (x10:0 > 0 && 0 <= -1 - x1:0 + x7:0) f(pc, x18:0:0, x24:0:0) -> f(1, x18:0:0, x24:0:0) :|: pc = 1 && (x30:0:0 < 1 && 0 <= -1 - x18:0:0 + x24:0:0 && x30:0:0 > -1) Proved unsatisfiability of the following formula, indicating that the system is never left after entering: ((((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and (((run1_3 * 1)) < 0 and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))))) or ((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and (((run1_3 * 1)) > 0 and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))))) or ((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((((run1_3 * 1)) < ((1 * 1)) and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))) and ((run1_3 * 1)) > ((1 * -1)))))) and (!(((run2_0 * 1)) = ((1 * 1)) and (((run2_3 * 1)) < 0 and 0 <= ((1 * -1) + (run2_1 * -1) + (run2_2 * 1)))) and !(((run2_0 * 1)) = ((1 * 1)) and (((run2_3 * 1)) > 0 and 0 <= ((1 * -1) + (run2_1 * -1) + (run2_2 * 1)))) and !(((run2_0 * 1)) = ((1 * 1)) and ((((run2_3 * 1)) < ((1 * 1)) and 0 <= ((1 * -1) + (run2_1 * -1) + (run2_2 * 1))) and ((run2_3 * 1)) > ((1 * -1)))))) Proved satisfiability of the following formula, indicating that the system is entered at least once: (((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and (((run1_3 * 1)) < 0 and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))))) or ((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and (((run1_3 * 1)) > 0 and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))))) or ((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1)) and run2_2 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((((run1_3 * 1)) < ((1 * 1)) and 0 <= ((1 * -1) + (run1_1 * -1) + (run1_2 * 1))) and ((run1_3 * 1)) > ((1 * -1)))))) ---------------------------------------- (14) NO