NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1140 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 7 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, 8 ms] (14) NO ---------------------------------------- (0) Obligation: Rules: l0(lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) -> l1(lt_15HATpost, lt_19HATpost, nd_12HATpost, p_14HATpost, rt_11HATpost, rv_18HATpost, st_17HATpost, x_13HATpost, y_16HATpost) :|: y_16HAT0 = y_16HATpost && x_13HAT0 = x_13HATpost && st_17HAT0 = st_17HATpost && rv_18HAT0 = rv_18HATpost && rt_11HAT0 = rt_11HATpost && nd_12HAT0 = nd_12HATpost && lt_19HAT0 = lt_19HATpost && lt_15HAT0 = lt_15HATpost && p_14HATpost = x_13HAT0 l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x2 = x11 && x1 = x10 && x13 = x6 && x9 = x9 && x8 <= x l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: 1 + x18 <= x26 && x27 = x27 && x36 = x36 && x32 = x36 && x29 = x29 && 0 <= x32 && x32 <= 0 && x19 = x28 && x21 = x30 && x22 = x31 && x24 = x33 && x25 = x34 && x26 = x35 l3(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l1(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 l1(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l5(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: 1 + x55 <= x63 && x64 = x64 && x73 = x73 && x69 = x73 && x66 = x66 && x56 = x65 && x58 = x67 && x59 = x68 && x61 = x70 && x62 = x71 && x63 = x72 l5(x74, x75, x76, x77, x78, x79, x80, x81, x82) -> l6(x83, x84, x85, x86, x87, x88, x89, x90, x91) :|: x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && 1 <= x79 l5(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l6(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && 1 + x97 <= 0 l6(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l4(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x120 = x120 l4(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 l7(x146, x147, x148, x149, x150, x151, x152, x153, x154) -> l0(x155, x156, x157, x158, x159, x160, x161, x162, x163) :|: x154 = x163 && x153 = x162 && x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 Start term: l7(lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) -> l1(lt_15HATpost, lt_19HATpost, nd_12HATpost, p_14HATpost, rt_11HATpost, rv_18HATpost, st_17HATpost, x_13HATpost, y_16HATpost) :|: y_16HAT0 = y_16HATpost && x_13HAT0 = x_13HATpost && st_17HAT0 = st_17HATpost && rv_18HAT0 = rv_18HATpost && rt_11HAT0 = rt_11HATpost && nd_12HAT0 = nd_12HATpost && lt_19HAT0 = lt_19HATpost && lt_15HAT0 = lt_15HATpost && p_14HATpost = x_13HAT0 l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x2 = x11 && x1 = x10 && x13 = x6 && x9 = x9 && x8 <= x l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: 1 + x18 <= x26 && x27 = x27 && x36 = x36 && x32 = x36 && x29 = x29 && 0 <= x32 && x32 <= 0 && x19 = x28 && x21 = x30 && x22 = x31 && x24 = x33 && x25 = x34 && x26 = x35 l3(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l1(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 l1(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l5(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: 1 + x55 <= x63 && x64 = x64 && x73 = x73 && x69 = x73 && x66 = x66 && x56 = x65 && x58 = x67 && x59 = x68 && x61 = x70 && x62 = x71 && x63 = x72 l5(x74, x75, x76, x77, x78, x79, x80, x81, x82) -> l6(x83, x84, x85, x86, x87, x88, x89, x90, x91) :|: x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && 1 <= x79 l5(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l6(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && 1 + x97 <= 0 l6(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l4(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x120 = x120 l4(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 l7(x146, x147, x148, x149, x150, x151, x152, x153, x154) -> l0(x155, x156, x157, x158, x159, x160, x161, x162, x163) :|: x154 = x163 && x153 = x162 && x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 Start term: l7(lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) -> l1(lt_15HATpost, lt_19HATpost, nd_12HATpost, p_14HATpost, rt_11HATpost, rv_18HATpost, st_17HATpost, x_13HATpost, y_16HATpost) :|: y_16HAT0 = y_16HATpost && x_13HAT0 = x_13HATpost && st_17HAT0 = st_17HATpost && rv_18HAT0 = rv_18HATpost && rt_11HAT0 = rt_11HATpost && nd_12HAT0 = nd_12HATpost && lt_19HAT0 = lt_19HATpost && lt_15HAT0 = lt_15HATpost && p_14HATpost = x_13HAT0 (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x2 = x11 && x1 = x10 && x13 = x6 && x9 = x9 && x8 <= x (3) l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: 1 + x18 <= x26 && x27 = x27 && x36 = x36 && x32 = x36 && x29 = x29 && 0 <= x32 && x32 <= 0 && x19 = x28 && x21 = x30 && x22 = x31 && x24 = x33 && x25 = x34 && x26 = x35 (4) l3(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l1(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 (5) l1(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l5(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: 1 + x55 <= x63 && x64 = x64 && x73 = x73 && x69 = x73 && x66 = x66 && x56 = x65 && x58 = x67 && x59 = x68 && x61 = x70 && x62 = x71 && x63 = x72 (6) l5(x74, x75, x76, x77, x78, x79, x80, x81, x82) -> l6(x83, x84, x85, x86, x87, x88, x89, x90, x91) :|: x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && 1 <= x79 (7) l5(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l6(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && 1 + x97 <= 0 (8) l6(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l4(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x120 = x120 (9) l4(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 (10) l7(x146, x147, x148, x149, x150, x151, x152, x153, x154) -> l0(x155, x156, x157, x158, x159, x160, x161, x162, x163) :|: x154 = x163 && x153 = x162 && x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 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(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: 1 + x18 <= x26 && x27 = x27 && x36 = x36 && x32 = x36 && x29 = x29 && 0 <= x32 && x32 <= 0 && x19 = x28 && x21 = x30 && x22 = x31 && x24 = x33 && x25 = x34 && x26 = x35 (2) l4(x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l1(x137, x138, x139, x140, x141, x142, x143, x144, x145) :|: x136 = x145 && x135 = x144 && x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 (3) l6(x110, x111, x112, x113, x114, x115, x116, x117, x118) -> l4(x119, x120, x121, x122, x123, x124, x125, x126, x127) :|: x118 = x127 && x117 = x126 && x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x120 = x120 (4) l5(x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l6(x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x100 = x109 && x99 = x108 && x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && 1 + x97 <= 0 (5) l5(x74, x75, x76, x77, x78, x79, x80, x81, x82) -> l6(x83, x84, x85, x86, x87, x88, x89, x90, x91) :|: x82 = x91 && x81 = x90 && x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && 1 <= x79 (6) l1(x55, x56, x57, x58, x59, x60, x61, x62, x63) -> l5(x64, x65, x66, x67, x68, x69, x70, x71, x72) :|: 1 + x55 <= x63 && x64 = x64 && x73 = x73 && x69 = x73 && x66 = x66 && x56 = x65 && x58 = x67 && x59 = x68 && x61 = x70 && x62 = x71 && x63 = x72 (7) l3(x37, x38, x39, x40, x41, x42, x43, x44, x45) -> l1(x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x45 = x54 && x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 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(x18:0, x19:0, x20:0, x21:0, x22:0, x23:0, x24:0, x25:0, x26:0) -> l1(x27:0, x19:0, x29:0, x21:0, x22:0, x32:0, x24:0, x25:0, x26:0) :|: x32:0 > -1 && x26:0 >= 1 + x18:0 && x32:0 < 1 l1(x55:0, x56:0, x57:0, x122:0, x123:0, x60:0, x125:0, x126:0, x127:0) -> l1(x119:0, x120:0, x121:0, x122:0, x123:0, x124:0, x125:0, x126:0, x127:0) :|: x124:0 > 0 && x127:0 >= 1 + x55:0 l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x9, x10, x11, x3, x4, x12, x6, x7, x8) :|: x12 < 0 && x8 >= 1 + x ---------------------------------------- (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(x1, x9) ---------------------------------------- (8) Obligation: Rules: l1(x18:0, x26:0) -> l1(x27:0, x26:0) :|: x32:0 > -1 && x26:0 >= 1 + x18:0 && x32:0 < 1 l1(x55:0, x127:0) -> l1(x119:0, x127:0) :|: x124:0 > 0 && x127:0 >= 1 + x55:0 l1(x, x8) -> l1(x9, x8) :|: x12 < 0 && x8 >= 1 + x ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l1(VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l1(x18:0, x26:0) -> l1(x27:0, x26:0) :|: x32:0 > -1 && x26:0 >= 1 + x18:0 && x32:0 < 1 l1(x55:0, x127:0) -> l1(x119:0, x127:0) :|: x124:0 > 0 && x127:0 >= 1 + x55:0 l1(x, x8) -> l1(x9, x8) :|: x12 < 0 && x8 >= 1 + x ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l1(x55:0:0, x127:0:0) -> l1(x119:0:0, x127:0:0) :|: x124:0:0 > 0 && x127:0:0 >= 1 + x55:0:0 l1(x:0, x8:0) -> l1(x9:0, x8:0) :|: x12:0 < 0 && x8:0 >= 1 + x:0 l1(x18:0:0, x26:0:0) -> l1(x27:0:0, x26:0:0) :|: x32:0:0 > -1 && x26:0:0 >= 1 + x18:0:0 && x32:0:0 < 1 ---------------------------------------- (13) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x55:0:0, x127:0:0) -> f(1, x119:0:0, x127:0:0) :|: pc = 1 && (x124:0:0 > 0 && x127:0:0 >= 1 + x55:0:0) f(pc, x:0, x8:0) -> f(1, x9:0, x8:0) :|: pc = 1 && (x12:0 < 0 && x8:0 >= 1 + x:0) f(pc, x18:0:0, x26:0:0) -> f(1, x27:0:0, x26:0:0) :|: pc = 1 && (x32:0:0 > -1 && x26:0:0 >= 1 + x18:0:0 && x32:0:0 < 1) Witness term starting non-terminating reduction: f(1, -1, 6) ---------------------------------------- (14) NO