NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1306 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 71 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, 10 ms] (14) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_16HATpost, cnt_21HATpost, lt_10HATpost, lt_8HATpost, lt_9HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: tmp_7HAT0 = tmp_7HATpost && lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_10HAT0 = lt_10HATpost && cnt_21HAT0 = cnt_21HATpost && cnt_16HAT0 = cnt_16HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x1 && x19 = x2 && x19 - x18 <= 0 && x14 = x14 && x12 = x12 && x9 = x9 && x1 = x10 && x2 = x11 && x4 = x13 && x6 = x15 && x7 = x16 && x8 = x17 l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l3(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x38 = x21 && x39 = x22 && 0 <= -1 + x39 - x38 && x34 = x34 && x32 = x32 && x35 = x35 && x35 <= 0 && 0 <= x35 && x20 = x29 && x21 = x30 && x22 = x31 && x24 = x33 && x27 = x36 && x28 = x37 l3(x40, x41, x42, x43, x44, x45, x46, x47, x48) -> l1(x49, x50, x51, x52, x53, x54, x55, x56, x57) :|: x48 = x57 && x47 = x56 && x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 l1(x58, x59, x60, x61, x62, x63, x64, x65, x66) -> l5(x67, x68, x69, x70, x71, x72, x73, x74, x75) :|: x76 = x59 && x77 = x60 && 0 <= -1 + x77 - x76 && x72 = x72 && x70 = x70 && x73 = x73 && x58 = x67 && x59 = x68 && x60 = x69 && x62 = x71 && x65 = x74 && x66 = x75 l5(x78, x79, x80, x81, x82, x83, x84, x85, x86) -> l6(x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x86 = x95 && x85 = x94 && x84 = x93 && x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && 1 + x84 <= 0 l5(x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111, x112, x113) :|: x104 = x113 && x103 = x112 && x102 = x111 && x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && 1 <= x102 l6(x114, x115, x116, x117, x118, x119, x120, x121, x122) -> l4(x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x132 = x115 && x127 = x127 && x114 = x123 && x115 = x124 && x116 = x125 && x117 = x126 && x119 = x128 && x120 = x129 && x121 = x130 && x122 = x131 l4(x133, x134, x135, x136, x137, x138, x139, x140, x141) -> l1(x142, x143, x144, x145, x146, x147, x148, x149, x150) :|: x141 = x150 && x140 = x149 && x139 = x148 && x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 l7(x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l0(x160, x161, x162, x163, x164, x165, x166, x167, x168) :|: x159 = x168 && x158 = x167 && x157 = x166 && x156 = x165 && x155 = x164 && x154 = x163 && x153 = x162 && x152 = x161 && x151 = x160 Start term: l7(Result_4HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, 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, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_16HATpost, cnt_21HATpost, lt_10HATpost, lt_8HATpost, lt_9HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: tmp_7HAT0 = tmp_7HATpost && lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_10HAT0 = lt_10HATpost && cnt_21HAT0 = cnt_21HATpost && cnt_16HAT0 = cnt_16HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x1 && x19 = x2 && x19 - x18 <= 0 && x14 = x14 && x12 = x12 && x9 = x9 && x1 = x10 && x2 = x11 && x4 = x13 && x6 = x15 && x7 = x16 && x8 = x17 l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l3(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x38 = x21 && x39 = x22 && 0 <= -1 + x39 - x38 && x34 = x34 && x32 = x32 && x35 = x35 && x35 <= 0 && 0 <= x35 && x20 = x29 && x21 = x30 && x22 = x31 && x24 = x33 && x27 = x36 && x28 = x37 l3(x40, x41, x42, x43, x44, x45, x46, x47, x48) -> l1(x49, x50, x51, x52, x53, x54, x55, x56, x57) :|: x48 = x57 && x47 = x56 && x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 l1(x58, x59, x60, x61, x62, x63, x64, x65, x66) -> l5(x67, x68, x69, x70, x71, x72, x73, x74, x75) :|: x76 = x59 && x77 = x60 && 0 <= -1 + x77 - x76 && x72 = x72 && x70 = x70 && x73 = x73 && x58 = x67 && x59 = x68 && x60 = x69 && x62 = x71 && x65 = x74 && x66 = x75 l5(x78, x79, x80, x81, x82, x83, x84, x85, x86) -> l6(x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x86 = x95 && x85 = x94 && x84 = x93 && x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && 1 + x84 <= 0 l5(x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111, x112, x113) :|: x104 = x113 && x103 = x112 && x102 = x111 && x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && 1 <= x102 l6(x114, x115, x116, x117, x118, x119, x120, x121, x122) -> l4(x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x132 = x115 && x127 = x127 && x114 = x123 && x115 = x124 && x116 = x125 && x117 = x126 && x119 = x128 && x120 = x129 && x121 = x130 && x122 = x131 l4(x133, x134, x135, x136, x137, x138, x139, x140, x141) -> l1(x142, x143, x144, x145, x146, x147, x148, x149, x150) :|: x141 = x150 && x140 = x149 && x139 = x148 && x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 l7(x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l0(x160, x161, x162, x163, x164, x165, x166, x167, x168) :|: x159 = x168 && x158 = x167 && x157 = x166 && x156 = x165 && x155 = x164 && x154 = x163 && x153 = x162 && x152 = x161 && x151 = x160 Start term: l7(Result_4HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, cnt_16HATpost, cnt_21HATpost, lt_10HATpost, lt_8HATpost, lt_9HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: tmp_7HAT0 = tmp_7HATpost && lt_9HAT0 = lt_9HATpost && lt_8HAT0 = lt_8HATpost && lt_10HAT0 = lt_10HATpost && cnt_21HAT0 = cnt_21HATpost && cnt_16HAT0 = cnt_16HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x18 = x1 && x19 = x2 && x19 - x18 <= 0 && x14 = x14 && x12 = x12 && x9 = x9 && x1 = x10 && x2 = x11 && x4 = x13 && x6 = x15 && x7 = x16 && x8 = x17 (3) l1(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l3(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x38 = x21 && x39 = x22 && 0 <= -1 + x39 - x38 && x34 = x34 && x32 = x32 && x35 = x35 && x35 <= 0 && 0 <= x35 && x20 = x29 && x21 = x30 && x22 = x31 && x24 = x33 && x27 = x36 && x28 = x37 (4) l3(x40, x41, x42, x43, x44, x45, x46, x47, x48) -> l1(x49, x50, x51, x52, x53, x54, x55, x56, x57) :|: x48 = x57 && x47 = x56 && x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 (5) l1(x58, x59, x60, x61, x62, x63, x64, x65, x66) -> l5(x67, x68, x69, x70, x71, x72, x73, x74, x75) :|: x76 = x59 && x77 = x60 && 0 <= -1 + x77 - x76 && x72 = x72 && x70 = x70 && x73 = x73 && x58 = x67 && x59 = x68 && x60 = x69 && x62 = x71 && x65 = x74 && x66 = x75 (6) l5(x78, x79, x80, x81, x82, x83, x84, x85, x86) -> l6(x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x86 = x95 && x85 = x94 && x84 = x93 && x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && 1 + x84 <= 0 (7) l5(x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111, x112, x113) :|: x104 = x113 && x103 = x112 && x102 = x111 && x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && 1 <= x102 (8) l6(x114, x115, x116, x117, x118, x119, x120, x121, x122) -> l4(x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x132 = x115 && x127 = x127 && x114 = x123 && x115 = x124 && x116 = x125 && x117 = x126 && x119 = x128 && x120 = x129 && x121 = x130 && x122 = x131 (9) l4(x133, x134, x135, x136, x137, x138, x139, x140, x141) -> l1(x142, x143, x144, x145, x146, x147, x148, x149, x150) :|: x141 = x150 && x140 = x149 && x139 = x148 && x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 (10) l7(x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l0(x160, x161, x162, x163, x164, x165, x166, x167, x168) :|: x159 = x168 && x158 = x167 && x157 = x166 && x156 = x165 && x155 = x164 && x154 = x163 && x153 = x162 && x152 = x161 && x151 = x160 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(x20, x21, x22, x23, x24, x25, x26, x27, x28) -> l3(x29, x30, x31, x32, x33, x34, x35, x36, x37) :|: x38 = x21 && x39 = x22 && 0 <= -1 + x39 - x38 && x34 = x34 && x32 = x32 && x35 = x35 && x35 <= 0 && 0 <= x35 && x20 = x29 && x21 = x30 && x22 = x31 && x24 = x33 && x27 = x36 && x28 = x37 (2) l4(x133, x134, x135, x136, x137, x138, x139, x140, x141) -> l1(x142, x143, x144, x145, x146, x147, x148, x149, x150) :|: x141 = x150 && x140 = x149 && x139 = x148 && x138 = x147 && x137 = x146 && x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 (3) l6(x114, x115, x116, x117, x118, x119, x120, x121, x122) -> l4(x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x132 = x115 && x127 = x127 && x114 = x123 && x115 = x124 && x116 = x125 && x117 = x126 && x119 = x128 && x120 = x129 && x121 = x130 && x122 = x131 (4) l5(x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111, x112, x113) :|: x104 = x113 && x103 = x112 && x102 = x111 && x101 = x110 && x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && 1 <= x102 (5) l5(x78, x79, x80, x81, x82, x83, x84, x85, x86) -> l6(x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x86 = x95 && x85 = x94 && x84 = x93 && x83 = x92 && x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && 1 + x84 <= 0 (6) l1(x58, x59, x60, x61, x62, x63, x64, x65, x66) -> l5(x67, x68, x69, x70, x71, x72, x73, x74, x75) :|: x76 = x59 && x77 = x60 && 0 <= -1 + x77 - x76 && x72 = x72 && x70 = x70 && x73 = x73 && x58 = x67 && x59 = x68 && x60 = x69 && x62 = x71 && x65 = x74 && x66 = x75 (7) l3(x40, x41, x42, x43, x44, x45, x46, x47, x48) -> l1(x49, x50, x51, x52, x53, x54, x55, x56, x57) :|: x48 = x57 && x47 = x56 && x46 = x55 && x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 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(x105:0, x106:0, x107:0, x61:0, x109:0, x63:0, x64:0, x112:0, x113:0) -> l1(x105:0, x106:0, x107:0, x108:0, x127:0, x110:0, x111:0, x112:0, x113:0) :|: x111:0 > 0 && 0 <= -1 + x107:0 - x106:0 l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x, x1, x2, x9, x10, x11, x12, x7, x8) :|: x12 < 0 && 0 <= -1 + x2 - x1 l1(x20:0, x21:0, x22:0, x23:0, x24:0, x25:0, x26:0, x27:0, x28:0) -> l1(x20:0, x21:0, x22:0, x32:0, x24:0, x34:0, x35:0, x27:0, x28:0) :|: x35:0 < 1 && 0 <= -1 + x22:0 - x21:0 && x35:0 > -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(x2, x3) ---------------------------------------- (8) Obligation: Rules: l1(x106:0, x107:0) -> l1(x106:0, x107:0) :|: x111:0 > 0 && 0 <= -1 + x107:0 - x106:0 l1(x1, x2) -> l1(x1, x2) :|: x12 < 0 && 0 <= -1 + x2 - x1 l1(x21:0, x22:0) -> l1(x21:0, x22:0) :|: x35:0 < 1 && 0 <= -1 + x22:0 - x21:0 && x35:0 > -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(x106:0, x107:0) -> l1(x106:0, x107:0) :|: x111:0 > 0 && 0 <= -1 + x107:0 - x106:0 l1(x1, x2) -> l1(x1, x2) :|: x12 < 0 && 0 <= -1 + x2 - x1 l1(x21:0, x22:0) -> l1(x21:0, x22:0) :|: x35:0 < 1 && 0 <= -1 + x22:0 - x21:0 && x35:0 > -1 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l1(x106:0:0, x107:0:0) -> l1(x106:0:0, x107:0:0) :|: x111:0:0 > 0 && 0 <= -1 + x107:0:0 - x106:0:0 l1(x21:0:0, x22:0:0) -> l1(x21:0:0, x22:0:0) :|: x35:0:0 < 1 && 0 <= -1 + x22:0:0 - x21:0:0 && x35:0:0 > -1 l1(x1:0, x2:0) -> l1(x1:0, x2:0) :|: x12:0 < 0 && 0 <= -1 + x2:0 - x1:0 ---------------------------------------- (13) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x106:0:0, x107:0:0) -> f(1, x106:0:0, x107:0:0) :|: pc = 1 && (x111:0:0 > 0 && 0 <= -1 + x107:0:0 - x106:0:0) f(pc, x21:0:0, x22:0:0) -> f(1, x21:0:0, x22:0:0) :|: pc = 1 && (x35:0:0 < 1 && 0 <= -1 + x22:0:0 - x21:0:0 && x35:0:0 > -1) f(pc, x1:0, x2:0) -> f(1, x1:0, x2:0) :|: pc = 1 && (x12:0 < 0 && 0 <= -1 + x2:0 - x1:0) Witness term starting non-terminating reduction: f(1, 0, 1) ---------------------------------------- (14) NO