NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1129 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 60 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, 1 ms] (14) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x2 && x21 = x3 && x21 - x20 <= 0 && x16 = x16 && x14 = x14 && x10 = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x5 = x15 && x7 = x17 && x8 = x18 && x9 = x19 l1(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x24 && x43 = x25 && 0 <= -1 + x43 - x42 && x38 = x38 && x36 = x36 && x39 = x39 && x39 <= 0 && 0 <= x39 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x27 = x37 && x30 = x40 && x31 = x41 l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l1(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 l1(x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) -> l5(x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) :|: x84 = x66 && x85 = x67 && 0 <= -1 + x85 - x84 && x80 = x80 && x78 = x78 && x81 = x81 && x64 = x74 && x65 = x75 && x66 = x76 && x67 = x77 && x69 = x79 && x72 = x82 && x73 = x83 l5(x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) -> l6(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105) :|: x95 = x105 && x94 = x104 && x93 = x103 && x92 = x102 && x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x97 = x87 l6(x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l4(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x126 = x108 && x121 = x121 && x106 = x116 && x107 = x117 && x108 = x118 && x109 = x119 && x110 = x120 && x112 = x122 && x113 = x123 && x114 = x124 && x115 = x125 l4(x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146) :|: x136 = x146 && x135 = x145 && x134 = x144 && x133 = x143 && x132 = x142 && x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 l7(x147, x148, x149, x150, x151, x152, x153, x154, x155, x156) -> l0(x157, x158, x159, x160, x161, x162, x163, x164, x165, x166) :|: x156 = x166 && x155 = x165 && x154 = x164 && x153 = x163 && x152 = x162 && x151 = x161 && x150 = x160 && x149 = x159 && x148 = x158 && x147 = x157 Start term: l7(Result_4HAT0, __disjvr_0HAT0, 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, __disjvr_0HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x2 && x21 = x3 && x21 - x20 <= 0 && x16 = x16 && x14 = x14 && x10 = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x5 = x15 && x7 = x17 && x8 = x18 && x9 = x19 l1(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x24 && x43 = x25 && 0 <= -1 + x43 - x42 && x38 = x38 && x36 = x36 && x39 = x39 && x39 <= 0 && 0 <= x39 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x27 = x37 && x30 = x40 && x31 = x41 l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l1(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 l1(x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) -> l5(x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) :|: x84 = x66 && x85 = x67 && 0 <= -1 + x85 - x84 && x80 = x80 && x78 = x78 && x81 = x81 && x64 = x74 && x65 = x75 && x66 = x76 && x67 = x77 && x69 = x79 && x72 = x82 && x73 = x83 l5(x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) -> l6(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105) :|: x95 = x105 && x94 = x104 && x93 = x103 && x92 = x102 && x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x97 = x87 l6(x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l4(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x126 = x108 && x121 = x121 && x106 = x116 && x107 = x117 && x108 = x118 && x109 = x119 && x110 = x120 && x112 = x122 && x113 = x123 && x114 = x124 && x115 = x125 l4(x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146) :|: x136 = x146 && x135 = x145 && x134 = x144 && x133 = x143 && x132 = x142 && x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 l7(x147, x148, x149, x150, x151, x152, x153, x154, x155, x156) -> l0(x157, x158, x159, x160, x161, x162, x163, x164, x165, x166) :|: x156 = x166 && x155 = x165 && x154 = x164 && x153 = x163 && x152 = x162 && x151 = x161 && x150 = x160 && x149 = x159 && x148 = x158 && x147 = x157 Start term: l7(Result_4HAT0, __disjvr_0HAT0, 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, __disjvr_0HAT0, cnt_16HAT0, cnt_21HAT0, lt_10HAT0, lt_8HAT0, lt_9HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && x_5HATpost = x_5HATpost && y_6HATpost = y_6HATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x20 = x2 && x21 = x3 && x21 - x20 <= 0 && x16 = x16 && x14 = x14 && x10 = x10 && x1 = x11 && x2 = x12 && x3 = x13 && x5 = x15 && x7 = x17 && x8 = x18 && x9 = x19 (3) l1(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x24 && x43 = x25 && 0 <= -1 + x43 - x42 && x38 = x38 && x36 = x36 && x39 = x39 && x39 <= 0 && 0 <= x39 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x27 = x37 && x30 = x40 && x31 = x41 (4) l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l1(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 (5) l1(x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) -> l5(x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) :|: x84 = x66 && x85 = x67 && 0 <= -1 + x85 - x84 && x80 = x80 && x78 = x78 && x81 = x81 && x64 = x74 && x65 = x75 && x66 = x76 && x67 = x77 && x69 = x79 && x72 = x82 && x73 = x83 (6) l5(x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) -> l6(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105) :|: x95 = x105 && x94 = x104 && x93 = x103 && x92 = x102 && x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x97 = x87 (7) l6(x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l4(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x126 = x108 && x121 = x121 && x106 = x116 && x107 = x117 && x108 = x118 && x109 = x119 && x110 = x120 && x112 = x122 && x113 = x123 && x114 = x124 && x115 = x125 (8) l4(x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146) :|: x136 = x146 && x135 = x145 && x134 = x144 && x133 = x143 && x132 = x142 && x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 (9) l7(x147, x148, x149, x150, x151, x152, x153, x154, x155, x156) -> l0(x157, x158, x159, x160, x161, x162, x163, x164, x165, x166) :|: x156 = x166 && x155 = x165 && x154 = x164 && x153 = x163 && x152 = x162 && x151 = x161 && x150 = x160 && x149 = x159 && x148 = x158 && x147 = x157 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(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31) -> l3(x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) :|: x42 = x24 && x43 = x25 && 0 <= -1 + x43 - x42 && x38 = x38 && x36 = x36 && x39 = x39 && x39 <= 0 && 0 <= x39 && x22 = x32 && x23 = x33 && x24 = x34 && x25 = x35 && x27 = x37 && x30 = x40 && x31 = x41 (2) l4(x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146) :|: x136 = x146 && x135 = x145 && x134 = x144 && x133 = x143 && x132 = x142 && x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 (3) l6(x106, x107, x108, x109, x110, x111, x112, x113, x114, x115) -> l4(x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x126 = x108 && x121 = x121 && x106 = x116 && x107 = x117 && x108 = x118 && x109 = x119 && x110 = x120 && x112 = x122 && x113 = x123 && x114 = x124 && x115 = x125 (4) l5(x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) -> l6(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105) :|: x95 = x105 && x94 = x104 && x93 = x103 && x92 = x102 && x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x97 = x87 (5) l1(x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) -> l5(x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) :|: x84 = x66 && x85 = x67 && 0 <= -1 + x85 - x84 && x80 = x80 && x78 = x78 && x81 = x81 && x64 = x74 && x65 = x75 && x66 = x76 && x67 = x77 && x69 = x79 && x72 = x82 && x73 = x83 (6) l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l1(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x63 && x52 = x62 && x51 = x61 && x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 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(x116:0, x117:0, x118:0, x119:0, x68:0, x101:0, x70:0, x71:0, x104:0, x105:0) -> l1(x116:0, x117:0, x118:0, x119:0, x100:0, x121:0, x102:0, x103:0, x104:0, x105:0) :|: 0 <= -1 + x119:0 - x118:0 l1(x22:0, x23:0, x24:0, x25:0, x26:0, x27:0, x28:0, x29:0, x30:0, x31:0) -> l1(x22:0, x23:0, x24:0, x25:0, x36:0, x27:0, x38:0, x39:0, x30:0, x31:0) :|: x39:0 < 1 && 0 <= -1 + x25:0 - x24:0 && x39:0 > -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, x10) -> l1(x3, x4) ---------------------------------------- (8) Obligation: Rules: l1(x118:0, x119:0) -> l1(x118:0, x119:0) :|: 0 <= -1 + x119:0 - x118:0 l1(x24:0, x25:0) -> l1(x24:0, x25:0) :|: x39:0 < 1 && 0 <= -1 + x25:0 - x24:0 && x39:0 > -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(x118:0, x119:0) -> l1(x118:0, x119:0) :|: 0 <= -1 + x119:0 - x118:0 l1(x24:0, x25:0) -> l1(x24:0, x25:0) :|: x39:0 < 1 && 0 <= -1 + x25:0 - x24:0 && x39:0 > -1 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l1(x24:0:0, x25:0:0) -> l1(x24:0:0, x25:0:0) :|: x39:0:0 < 1 && 0 <= -1 + x25:0:0 - x24:0:0 && x39:0:0 > -1 l1(x118:0:0, x119:0:0) -> l1(x118:0:0, x119:0:0) :|: 0 <= -1 + x119:0:0 - x118:0:0 ---------------------------------------- (13) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x24:0:0, x25:0:0) -> f(1, x24:0:0, x25:0:0) :|: pc = 1 && (x39:0:0 < 1 && 0 <= -1 + x25:0:0 - x24:0:0 && x39:0:0 > -1) f(pc, x118:0:0, x119:0:0) -> f(1, x118:0:0, x119:0:0) :|: pc = 1 && 0 <= -1 + x119:0:0 - x118:0:0 Witness term starting non-terminating reduction: f(1, -8, -5) ---------------------------------------- (14) NO