NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1002 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) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (12) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, cnt_33HAT0, cnt_54HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_65HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_33HATpost, cnt_54HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, lt_65HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_33HAT0 && lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && cnt_33HAT0 = cnt_33HATpost && cnt_54HAT0 = cnt_54HATpost && lt_10HAT0 = lt_10HATpost && lt_65HAT0 = lt_65HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x24 = x10 && x25 = x1 && 0 <= -1 + x25 && x16 = x16 && x17 = x17 && x26 = x1 && x15 = x15 && x21 = x8 && x = x12 && x1 = x13 && x2 = x14 && x6 = x18 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 l3(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38) -> l0(x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) :|: x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x48 = x46 && x50 = x50 && x47 = x47 && x49 = x49 && x46 = x46 l2(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) :|: x75 = x62 && x76 = x53 && x76 <= 0 && x67 = x67 && x68 = x68 && x63 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x59 = x71 && x60 = x72 && x61 = x73 && x62 = x74 l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88) -> l4(x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) :|: x101 = x88 && x102 = x79 && 0 <= -1 + x102 && x93 = x93 && x94 = x94 && x103 = -1 + x78 && x92 = x92 && x98 = x85 && x77 = x89 && x78 = x90 && x79 = x91 && x83 = x95 && x84 = x96 && x85 = x97 && x87 = x99 && x88 = x100 l4(x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l5(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x128 = x115 && x129 = x106 && 0 <= -1 + x129 && x120 = x120 && x121 = x121 && x130 = -1 + x110 && x119 = x119 && x125 = x112 && x104 = x116 && x105 = x117 && x106 = x118 && x110 = x122 && x111 = x123 && x112 = x124 && x114 = x126 && x115 = x127 l5(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154) :|: x142 = x154 && x141 = x153 && x140 = x152 && x139 = x151 && x138 = x150 && x137 = x149 && x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 l6(x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166) -> l3(x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178) :|: x166 = x178 && x165 = x177 && x164 = x176 && x163 = x175 && x162 = x174 && x161 = x173 && x160 = x172 && x159 = x171 && x158 = x170 && x157 = x169 && x156 = x168 && x155 = x167 Start term: l6(Result_4HAT0, cnt_33HAT0, cnt_54HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_65HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, cnt_33HAT0, cnt_54HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_65HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_33HATpost, cnt_54HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, lt_65HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_33HAT0 && lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && cnt_33HAT0 = cnt_33HATpost && cnt_54HAT0 = cnt_54HATpost && lt_10HAT0 = lt_10HATpost && lt_65HAT0 = lt_65HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x24 = x10 && x25 = x1 && 0 <= -1 + x25 && x16 = x16 && x17 = x17 && x26 = x1 && x15 = x15 && x21 = x8 && x = x12 && x1 = x13 && x2 = x14 && x6 = x18 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 l3(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38) -> l0(x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) :|: x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x48 = x46 && x50 = x50 && x47 = x47 && x49 = x49 && x46 = x46 l2(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) :|: x75 = x62 && x76 = x53 && x76 <= 0 && x67 = x67 && x68 = x68 && x63 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x59 = x71 && x60 = x72 && x61 = x73 && x62 = x74 l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88) -> l4(x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) :|: x101 = x88 && x102 = x79 && 0 <= -1 + x102 && x93 = x93 && x94 = x94 && x103 = -1 + x78 && x92 = x92 && x98 = x85 && x77 = x89 && x78 = x90 && x79 = x91 && x83 = x95 && x84 = x96 && x85 = x97 && x87 = x99 && x88 = x100 l4(x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l5(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x128 = x115 && x129 = x106 && 0 <= -1 + x129 && x120 = x120 && x121 = x121 && x130 = -1 + x110 && x119 = x119 && x125 = x112 && x104 = x116 && x105 = x117 && x106 = x118 && x110 = x122 && x111 = x123 && x112 = x124 && x114 = x126 && x115 = x127 l5(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154) :|: x142 = x154 && x141 = x153 && x140 = x152 && x139 = x151 && x138 = x150 && x137 = x149 && x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 l6(x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166) -> l3(x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178) :|: x166 = x178 && x165 = x177 && x164 = x176 && x163 = x175 && x162 = x174 && x161 = x173 && x160 = x172 && x159 = x171 && x158 = x170 && x157 = x169 && x156 = x168 && x155 = x167 Start term: l6(Result_4HAT0, cnt_33HAT0, cnt_54HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_65HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, cnt_33HAT0, cnt_54HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, lt_65HAT0, px_8HAT0, py_6HAT0, q_9HAT0, x_7HAT0, y_5HAT0) -> l1(Result_4HATpost, cnt_33HATpost, cnt_54HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, lt_65HATpost, px_8HATpost, py_6HATpost, q_9HATpost, x_7HATpost, y_5HATpost) :|: lt_11HAT1 = x_7HAT0 && lt_12HAT1 = cnt_33HAT0 && lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && cnt_33HAT0 = cnt_33HATpost && cnt_54HAT0 = cnt_54HATpost && lt_10HAT0 = lt_10HATpost && lt_65HAT0 = lt_65HATpost && px_8HAT0 = px_8HATpost && py_6HAT0 = py_6HATpost && q_9HAT0 = q_9HATpost && x_7HAT0 = x_7HATpost && y_5HAT0 = y_5HATpost (2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x24 = x10 && x25 = x1 && 0 <= -1 + x25 && x16 = x16 && x17 = x17 && x26 = x1 && x15 = x15 && x21 = x8 && x = x12 && x1 = x13 && x2 = x14 && x6 = x18 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 (3) l3(x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38) -> l0(x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) :|: x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x48 = x46 && x50 = x50 && x47 = x47 && x49 = x49 && x46 = x46 (4) l2(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) :|: x75 = x62 && x76 = x53 && x76 <= 0 && x67 = x67 && x68 = x68 && x63 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x59 = x71 && x60 = x72 && x61 = x73 && x62 = x74 (5) l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88) -> l4(x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) :|: x101 = x88 && x102 = x79 && 0 <= -1 + x102 && x93 = x93 && x94 = x94 && x103 = -1 + x78 && x92 = x92 && x98 = x85 && x77 = x89 && x78 = x90 && x79 = x91 && x83 = x95 && x84 = x96 && x85 = x97 && x87 = x99 && x88 = x100 (6) l4(x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l5(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x128 = x115 && x129 = x106 && 0 <= -1 + x129 && x120 = x120 && x121 = x121 && x130 = -1 + x110 && x119 = x119 && x125 = x112 && x104 = x116 && x105 = x117 && x106 = x118 && x110 = x122 && x111 = x123 && x112 = x124 && x114 = x126 && x115 = x127 (7) l5(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154) :|: x142 = x154 && x141 = x153 && x140 = x152 && x139 = x151 && x138 = x150 && x137 = x149 && x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 (8) l6(x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166) -> l3(x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178) :|: x166 = x178 && x165 = x177 && x164 = x176 && x163 = x175 && x162 = x174 && x161 = x173 && x160 = x172 && x159 = x171 && x158 = x170 && x157 = x169 && x156 = x168 && x155 = x167 Arcs: (2) -> (4), (5) (3) -> (1), (2) (5) -> (6) (6) -> (7) (7) -> (6) (8) -> (3) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l4(x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l5(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x128 = x115 && x129 = x106 && 0 <= -1 + x129 && x120 = x120 && x121 = x121 && x130 = -1 + x110 && x119 = x119 && x125 = x112 && x104 = x116 && x105 = x117 && x106 = x118 && x110 = x122 && x111 = x123 && x112 = x124 && x114 = x126 && x115 = x127 (2) l5(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154) :|: x142 = x154 && x141 = x153 && x140 = x152 && x139 = x151 && x138 = x150 && x137 = x149 && x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l4(x104:0, x105:0, x106:0, x107:0, x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> l4(x104:0, x105:0, x106:0, x119:0, x120:0, x121:0, x110:0, x111:0, x112:0, x112:0, x114:0, x115:0) :|: x106:0 > 0 ---------------------------------------- (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, x7, x8, x9, x10, x11, x12) -> l4(x3) ---------------------------------------- (8) Obligation: Rules: l4(x106:0) -> l4(x106:0) :|: x106:0 > 0 ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l4(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l4(x106:0) -> l4(x106:0) :|: x106:0 > 0 ---------------------------------------- (11) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x106:0) -> f(1, x106:0) :|: pc = 1 && x106:0 > 0 Witness term starting non-terminating reduction: f(1, 1) ---------------------------------------- (12) NO