NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1211 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 54 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(__disjvr_0HAT0, lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) -> l1(__disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && p_14HATpost = x_13HAT0 l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x4 = x14 && x3 = x13 && x2 = x12 && x = x10 && x15 = x7 && x11 = x11 && x9 <= x1 l1(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: 1 + x21 <= x29 && x31 = x31 && x40 = x40 && x36 = x40 && x33 = x33 && 0 <= x36 && x36 <= 0 && x20 = x30 && x22 = x32 && x24 = x34 && x25 = x35 && x27 = x37 && x28 = x38 && x29 = x39 l3(x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l1(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60) :|: x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 l1(x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) -> l5(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: 1 + x62 <= x70 && x72 = x72 && x81 = x81 && x77 = x81 && x74 = x74 && x61 = x71 && x63 = x73 && x65 = x75 && x66 = x76 && x68 = x78 && x69 = x79 && x70 = x80 l5(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91) -> l6(x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x92 = x82 l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l4(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) :|: x111 = x121 && x110 = x120 && x109 = x119 && x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x103 = x113 && x102 = x112 && x114 = x114 l4(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l1(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 l7(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151) -> l0(x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x151 = x161 && x150 = x160 && x149 = x159 && x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 Start term: l7(__disjvr_0HAT0, 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(__disjvr_0HAT0, lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) -> l1(__disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && p_14HATpost = x_13HAT0 l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x4 = x14 && x3 = x13 && x2 = x12 && x = x10 && x15 = x7 && x11 = x11 && x9 <= x1 l1(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: 1 + x21 <= x29 && x31 = x31 && x40 = x40 && x36 = x40 && x33 = x33 && 0 <= x36 && x36 <= 0 && x20 = x30 && x22 = x32 && x24 = x34 && x25 = x35 && x27 = x37 && x28 = x38 && x29 = x39 l3(x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l1(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60) :|: x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 l1(x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) -> l5(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: 1 + x62 <= x70 && x72 = x72 && x81 = x81 && x77 = x81 && x74 = x74 && x61 = x71 && x63 = x73 && x65 = x75 && x66 = x76 && x68 = x78 && x69 = x79 && x70 = x80 l5(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91) -> l6(x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x92 = x82 l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l4(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) :|: x111 = x121 && x110 = x120 && x109 = x119 && x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x103 = x113 && x102 = x112 && x114 = x114 l4(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l1(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 l7(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151) -> l0(x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x151 = x161 && x150 = x160 && x149 = x159 && x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 Start term: l7(__disjvr_0HAT0, 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(__disjvr_0HAT0, lt_15HAT0, lt_19HAT0, nd_12HAT0, p_14HAT0, rt_11HAT0, rv_18HAT0, st_17HAT0, x_13HAT0, y_16HAT0) -> l1(__disjvr_0HATpost, 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 && __disjvr_0HAT0 = __disjvr_0HATpost && p_14HATpost = x_13HAT0 (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x4 = x14 && x3 = x13 && x2 = x12 && x = x10 && x15 = x7 && x11 = x11 && x9 <= x1 (3) l1(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: 1 + x21 <= x29 && x31 = x31 && x40 = x40 && x36 = x40 && x33 = x33 && 0 <= x36 && x36 <= 0 && x20 = x30 && x22 = x32 && x24 = x34 && x25 = x35 && x27 = x37 && x28 = x38 && x29 = x39 (4) l3(x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l1(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60) :|: x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 (5) l1(x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) -> l5(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: 1 + x62 <= x70 && x72 = x72 && x81 = x81 && x77 = x81 && x74 = x74 && x61 = x71 && x63 = x73 && x65 = x75 && x66 = x76 && x68 = x78 && x69 = x79 && x70 = x80 (6) l5(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91) -> l6(x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x92 = x82 (7) l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l4(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) :|: x111 = x121 && x110 = x120 && x109 = x119 && x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x103 = x113 && x102 = x112 && x114 = x114 (8) l4(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l1(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 (9) l7(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151) -> l0(x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x151 = x161 && x150 = x160 && x149 = x159 && x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 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(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: 1 + x21 <= x29 && x31 = x31 && x40 = x40 && x36 = x40 && x33 = x33 && 0 <= x36 && x36 <= 0 && x20 = x30 && x22 = x32 && x24 = x34 && x25 = x35 && x27 = x37 && x28 = x38 && x29 = x39 (2) l4(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l1(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x131 = x141 && x130 = x140 && x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 (3) l6(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l4(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) :|: x111 = x121 && x110 = x120 && x109 = x119 && x108 = x118 && x107 = x117 && x106 = x116 && x105 = x115 && x103 = x113 && x102 = x112 && x114 = x114 (4) l5(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91) -> l6(x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x91 = x101 && x90 = x100 && x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x92 = x82 (5) l1(x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) -> l5(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: 1 + x62 <= x70 && x72 = x72 && x81 = x81 && x77 = x81 && x74 = x74 && x61 = x71 && x63 = x73 && x65 = x75 && x66 = x76 && x68 = x78 && x69 = x79 && x70 = x80 (6) l3(x41, x42, x43, x44, x45, x46, x47, x48, x49, x50) -> l1(x51, x52, x53, x54, x55, x56, x57, x58, x59, x60) :|: x50 = x60 && x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 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(x20:0, x21:0, x22:0, x23:0, x24:0, x25:0, x26:0, x27:0, x28:0, x29:0) -> l1(x20:0, x31:0, x22:0, x33:0, x24:0, x25:0, x36:0, x27:0, x28:0, x29:0) :|: x36:0 > -1 && x29:0 >= 1 + x21:0 && x36:0 < 1 l1(x112:0, x62:0, x63:0, x64:0, x116:0, x117:0, x67:0, x119:0, x100:0, x101:0) -> l1(x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x118:0, x119:0, x100:0, x101:0) :|: x101:0 >= 1 + x62:0 ---------------------------------------- (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(x2, x10) ---------------------------------------- (8) Obligation: Rules: l1(x21:0, x29:0) -> l1(x31:0, x29:0) :|: x36:0 > -1 && x29:0 >= 1 + x21:0 && x36:0 < 1 l1(x62:0, x101:0) -> l1(x113:0, x101:0) :|: x101:0 >= 1 + x62:0 ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l1(VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l1(x21:0, x29:0) -> l1(x31:0, x29:0) :|: x36:0 > -1 && x29:0 >= 1 + x21:0 && x36:0 < 1 l1(x62:0, x101:0) -> l1(x113:0, x101:0) :|: x101:0 >= 1 + x62:0 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l1(x62:0:0, x101:0:0) -> l1(x113:0:0, x101:0:0) :|: x101:0:0 >= 1 + x62:0:0 l1(x21:0:0, x29:0:0) -> l1(x31:0:0, x29:0:0) :|: x36:0:0 > -1 && x29:0:0 >= 1 + x21:0:0 && x36:0:0 < 1 ---------------------------------------- (13) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x62:0:0, x101:0:0) -> f(1, x113:0:0, x101:0:0) :|: pc = 1 && x101:0:0 >= 1 + x62:0:0 f(pc, x21:0:0, x29:0:0) -> f(1, x31:0:0, x29:0:0) :|: pc = 1 && (x36:0:0 > -1 && x29:0:0 >= 1 + x21:0:0 && x36:0:0 < 1) Witness term starting non-terminating reduction: f(1, -1, 2) ---------------------------------------- (14) NO