NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 973 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 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) IntTRSPeriodicNontermProof [COMPLETE, 6 ms] (14) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x2 && -1 * x18 + x8 <= 0 && x12 = x12 && x9 = x9 && x1 = x10 && x2 = x11 && x4 = x13 && x5 = x14 && x6 = x15 && x7 = x16 && x8 = x17 l1(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l3(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x37 = x21 && 0 <= -1 - x37 + x27 && x31 = x31 && x34 = x34 && x34 <= 0 && 0 <= x34 && x19 = x28 && x20 = x29 && x21 = x30 && x23 = x32 && x24 = x33 && x26 = x35 && x27 = x36 l3(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l1(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 l1(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x58 && 0 <= -1 - x74 + x64 && x68 = x68 && x71 = x71 && x56 = x65 && x57 = x66 && x58 = x67 && x60 = x69 && x61 = x70 && x63 = x72 && x64 = x73 l5(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l6(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x85 = x76 l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x111 = x95 && x106 = x106 && x93 = x102 && x94 = x103 && x95 = x104 && x96 = x105 && x98 = x107 && x99 = x108 && x100 = x109 && x101 = x110 l4(x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l1(x121, x122, x123, x124, x125, x126, x127, x128, x129) :|: x120 = x129 && x119 = x128 && x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 l7(x130, x131, x132, x133, x134, x135, x136, x137, x138) -> l0(x139, x140, x141, x142, x143, x144, x145, x146, x147) :|: x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 Start term: l7(Result_4HAT0, __disjvr_0HAT0, 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, __disjvr_0HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x2 && -1 * x18 + x8 <= 0 && x12 = x12 && x9 = x9 && x1 = x10 && x2 = x11 && x4 = x13 && x5 = x14 && x6 = x15 && x7 = x16 && x8 = x17 l1(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l3(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x37 = x21 && 0 <= -1 - x37 + x27 && x31 = x31 && x34 = x34 && x34 <= 0 && 0 <= x34 && x19 = x28 && x20 = x29 && x21 = x30 && x23 = x32 && x24 = x33 && x26 = x35 && x27 = x36 l3(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l1(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 l1(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x58 && 0 <= -1 - x74 + x64 && x68 = x68 && x71 = x71 && x56 = x65 && x57 = x66 && x58 = x67 && x60 = x69 && x61 = x70 && x63 = x72 && x64 = x73 l5(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l6(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x85 = x76 l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x111 = x95 && x106 = x106 && x93 = x102 && x94 = x103 && x95 = x104 && x96 = x105 && x98 = x107 && x99 = x108 && x100 = x109 && x101 = x110 l4(x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l1(x121, x122, x123, x124, x125, x126, x127, x128, x129) :|: x120 = x129 && x119 = x128 && x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 l7(x130, x131, x132, x133, x134, x135, x136, x137, x138) -> l0(x139, x140, x141, x142, x143, x144, x145, x146, x147) :|: x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 Start term: l7(Result_4HAT0, __disjvr_0HAT0, 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, __disjvr_0HAT0, cnt_16HAT0, lt_10HAT0, lt_9HAT0, p_7HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && p_7HATpost = x_5HATpost && x_5HATpost = x_5HATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x2 && -1 * x18 + x8 <= 0 && x12 = x12 && x9 = x9 && x1 = x10 && x2 = x11 && x4 = x13 && x5 = x14 && x6 = x15 && x7 = x16 && x8 = x17 (3) l1(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l3(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x37 = x21 && 0 <= -1 - x37 + x27 && x31 = x31 && x34 = x34 && x34 <= 0 && 0 <= x34 && x19 = x28 && x20 = x29 && x21 = x30 && x23 = x32 && x24 = x33 && x26 = x35 && x27 = x36 (4) l3(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l1(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 (5) l1(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x58 && 0 <= -1 - x74 + x64 && x68 = x68 && x71 = x71 && x56 = x65 && x57 = x66 && x58 = x67 && x60 = x69 && x61 = x70 && x63 = x72 && x64 = x73 (6) l5(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l6(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x85 = x76 (7) l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x111 = x95 && x106 = x106 && x93 = x102 && x94 = x103 && x95 = x104 && x96 = x105 && x98 = x107 && x99 = x108 && x100 = x109 && x101 = x110 (8) l4(x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l1(x121, x122, x123, x124, x125, x126, x127, x128, x129) :|: x120 = x129 && x119 = x128 && x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 (9) l7(x130, x131, x132, x133, x134, x135, x136, x137, x138) -> l0(x139, x140, x141, x142, x143, x144, x145, x146, x147) :|: x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 Arcs: (1) -> (2), (3), (5) (3) -> (4) (4) -> (2), (3), (5) (5) -> (6) (6) -> (7) (7) -> (8) (8) -> (2), (3), (5) (9) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l3(x28, x29, x30, x31, x32, x33, x34, x35, x36) :|: x37 = x21 && 0 <= -1 - x37 + x27 && x31 = x31 && x34 = x34 && x34 <= 0 && 0 <= x34 && x19 = x28 && x20 = x29 && x21 = x30 && x23 = x32 && x24 = x33 && x26 = x35 && x27 = x36 (2) l4(x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l1(x121, x122, x123, x124, x125, x126, x127, x128, x129) :|: x120 = x129 && x119 = x128 && x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 (3) l6(x93, x94, x95, x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107, x108, x109, x110) :|: x111 = x95 && x106 = x106 && x93 = x102 && x94 = x103 && x95 = x104 && x96 = x105 && x98 = x107 && x99 = x108 && x100 = x109 && x101 = x110 (4) l5(x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l6(x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x85 = x76 (5) l1(x56, x57, x58, x59, x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x58 && 0 <= -1 - x74 + x64 && x68 = x68 && x71 = x71 && x56 = x65 && x57 = x66 && x58 = x67 && x60 = x69 && x61 = x70 && x63 = x72 && x64 = x73 (6) l3(x38, x39, x40, x41, x42, x43, x44, x45, x46) -> l1(x47, x48, x49, x50, x51, x52, x53, x54, x55) :|: x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 Arcs: (1) -> (6) (2) -> (1), (5) (3) -> (2) (4) -> (3) (5) -> (4) (6) -> (1), (5) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x102:0, x103:0, x104:0, x59:0, x60:0, x107:0, x62:0, x109:0, x110:0) -> l1(x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0, x110:0) :|: 0 <= -1 - x104:0 + x110:0 l1(x19:0, x20:0, x21:0, x22:0, x23:0, x24:0, x25:0, x26:0, x27:0) -> l1(x19:0, x20:0, x21:0, x31:0, x23:0, x24:0, x34:0, x26:0, x27:0) :|: x34:0 < 1 && 0 <= -1 - x21:0 + x27:0 && x34:0 > -1 ---------------------------------------- (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, x9) -> l1(x3, x9) ---------------------------------------- (8) Obligation: Rules: l1(x104:0, x110:0) -> l1(x104:0, x110:0) :|: 0 <= -1 - x104:0 + x110:0 l1(x21:0, x27:0) -> l1(x21:0, x27:0) :|: x34:0 < 1 && 0 <= -1 - x21:0 + x27:0 && x34:0 > -1 ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l1(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l1(x104:0, x110:0) -> l1(x104:0, x110:0) :|: 0 <= -1 - x104:0 + x110:0 l1(x21:0, x27:0) -> l1(x21:0, x27:0) :|: x34:0 < 1 && 0 <= -1 - x21:0 + x27:0 && x34:0 > -1 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l1(x104:0:0, x110:0:0) -> l1(x104:0:0, x110:0:0) :|: 0 <= -1 - x104:0:0 + x110:0:0 l1(x21:0:0, x27:0:0) -> l1(x21:0:0, x27:0:0) :|: x34:0:0 < 1 && 0 <= -1 - x21:0:0 + x27:0:0 && x34:0:0 > -1 ---------------------------------------- (13) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x104:0:0, x110:0:0) -> f(1, x104:0:0, x110:0:0) :|: pc = 1 && 0 <= -1 - x104:0:0 + x110:0:0 f(pc, x21:0:0, x27:0:0) -> f(1, x21:0:0, x27:0:0) :|: pc = 1 && (x34:0:0 < 1 && 0 <= -1 - x21:0:0 + x27:0:0 && x34:0:0 > -1) Witness term starting non-terminating reduction: f(1, 2, 6) ---------------------------------------- (14) NO