NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1536 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 23 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, 0 ms] (14) NO ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, cnt_20HAT0, cnt_25HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, p2_8HAT0, p_7HAT0, tmp_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, cnt_20HATpost, cnt_25HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, p2_8HATpost, p_7HATpost, tmp_9HATpost, x_5HATpost, y_6HATpost) :|: lt_11HAT1 = cnt_20HAT0 && lt_12HAT1 = cnt_25HAT0 && -1 * lt_11HAT1 + lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_25HAT0 = cnt_25HATpost && lt_10HAT0 = lt_10HATpost && p2_8HAT0 = p2_8HATpost && p_7HAT0 = p_7HATpost && tmp_9HAT0 = tmp_9HATpost && x_5HAT0 = x_5HATpost && y_6HAT0 = y_6HATpost 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 = x2 && x25 = x3 && 0 <= -1 - x24 + x25 && x17 = x17 && x18 = x18 && x21 = x21 && x21 <= 0 && 0 <= x21 && x = x12 && x1 = x13 && x2 = x14 && x3 = x15 && x4 = x16 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 l2(x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) :|: x37 = x49 && x36 = x48 && x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) -> l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x52 && x75 = x53 && 0 <= -1 - x74 + x75 && x67 = x67 && x68 = x68 && x71 = x71 && x50 = x62 && x51 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x60 = x72 && x61 = x73 l4(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x86 = x98 && x85 = x97 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x80 = x92 && x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x89 = x77 l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x124 = x102 && x116 = x116 && x100 = x112 && x101 = x113 && x102 = x114 && x103 = x115 && x105 = x117 && x106 = x118 && x107 = x119 && x108 = x120 && x109 = x121 && x110 = x122 && x111 = x123 l3(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l0(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) :|: x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 && x130 = x142 && x129 = x141 && x128 = x140 && x127 = x139 && x126 = x138 && x125 = x137 l6(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) -> l0(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172) :|: x158 = x170 && x155 = x167 && x154 = x166 && x153 = x165 && x152 = x164 && x151 = x163 && x150 = x162 && x149 = x161 && x168 = x172 && x169 = x171 && x171 = x171 && x172 = x172 l7(x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184) -> l6(x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196) :|: x184 = x196 && x183 = x195 && x182 = x194 && x181 = x193 && x180 = x192 && x179 = x191 && x178 = x190 && x177 = x189 && x176 = x188 && x175 = x187 && x174 = x186 && x173 = x185 Start term: l7(Result_4HAT0, __disjvr_0HAT0, cnt_20HAT0, cnt_25HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, p2_8HAT0, p_7HAT0, tmp_9HAT0, 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_20HAT0, cnt_25HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, p2_8HAT0, p_7HAT0, tmp_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, cnt_20HATpost, cnt_25HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, p2_8HATpost, p_7HATpost, tmp_9HATpost, x_5HATpost, y_6HATpost) :|: lt_11HAT1 = cnt_20HAT0 && lt_12HAT1 = cnt_25HAT0 && -1 * lt_11HAT1 + lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_25HAT0 = cnt_25HATpost && lt_10HAT0 = lt_10HATpost && p2_8HAT0 = p2_8HATpost && p_7HAT0 = p_7HATpost && tmp_9HAT0 = tmp_9HATpost && x_5HAT0 = x_5HATpost && y_6HAT0 = y_6HATpost 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 = x2 && x25 = x3 && 0 <= -1 - x24 + x25 && x17 = x17 && x18 = x18 && x21 = x21 && x21 <= 0 && 0 <= x21 && x = x12 && x1 = x13 && x2 = x14 && x3 = x15 && x4 = x16 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 l2(x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) :|: x37 = x49 && x36 = x48 && x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) -> l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x52 && x75 = x53 && 0 <= -1 - x74 + x75 && x67 = x67 && x68 = x68 && x71 = x71 && x50 = x62 && x51 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x60 = x72 && x61 = x73 l4(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x86 = x98 && x85 = x97 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x80 = x92 && x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x89 = x77 l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x124 = x102 && x116 = x116 && x100 = x112 && x101 = x113 && x102 = x114 && x103 = x115 && x105 = x117 && x106 = x118 && x107 = x119 && x108 = x120 && x109 = x121 && x110 = x122 && x111 = x123 l3(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l0(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) :|: x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 && x130 = x142 && x129 = x141 && x128 = x140 && x127 = x139 && x126 = x138 && x125 = x137 l6(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) -> l0(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172) :|: x158 = x170 && x155 = x167 && x154 = x166 && x153 = x165 && x152 = x164 && x151 = x163 && x150 = x162 && x149 = x161 && x168 = x172 && x169 = x171 && x171 = x171 && x172 = x172 l7(x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184) -> l6(x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196) :|: x184 = x196 && x183 = x195 && x182 = x194 && x181 = x193 && x180 = x192 && x179 = x191 && x178 = x190 && x177 = x189 && x176 = x188 && x175 = x187 && x174 = x186 && x173 = x185 Start term: l7(Result_4HAT0, __disjvr_0HAT0, cnt_20HAT0, cnt_25HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, p2_8HAT0, p_7HAT0, tmp_9HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, cnt_20HAT0, cnt_25HAT0, lt_10HAT0, lt_11HAT0, lt_12HAT0, p2_8HAT0, p_7HAT0, tmp_9HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, cnt_20HATpost, cnt_25HATpost, lt_10HATpost, lt_11HATpost, lt_12HATpost, p2_8HATpost, p_7HATpost, tmp_9HATpost, x_5HATpost, y_6HATpost) :|: lt_11HAT1 = cnt_20HAT0 && lt_12HAT1 = cnt_25HAT0 && -1 * lt_11HAT1 + lt_12HAT1 <= 0 && lt_11HATpost = lt_11HATpost && lt_12HATpost = lt_12HATpost && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && cnt_20HAT0 = cnt_20HATpost && cnt_25HAT0 = cnt_25HATpost && lt_10HAT0 = lt_10HATpost && p2_8HAT0 = p2_8HATpost && p_7HAT0 = p_7HATpost && tmp_9HAT0 = tmp_9HATpost && x_5HAT0 = x_5HATpost && y_6HAT0 = y_6HATpost (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 = x2 && x25 = x3 && 0 <= -1 - x24 + x25 && x17 = x17 && x18 = x18 && x21 = x21 && x21 <= 0 && 0 <= x21 && x = x12 && x1 = x13 && x2 = x14 && x3 = x15 && x4 = x16 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 (3) l2(x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) :|: x37 = x49 && x36 = x48 && x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 (4) l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) -> l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x52 && x75 = x53 && 0 <= -1 - x74 + x75 && x67 = x67 && x68 = x68 && x71 = x71 && x50 = x62 && x51 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x60 = x72 && x61 = x73 (5) l4(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x86 = x98 && x85 = x97 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x80 = x92 && x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x89 = x77 (6) l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x124 = x102 && x116 = x116 && x100 = x112 && x101 = x113 && x102 = x114 && x103 = x115 && x105 = x117 && x106 = x118 && x107 = x119 && x108 = x120 && x109 = x121 && x110 = x122 && x111 = x123 (7) l3(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l0(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) :|: x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 && x130 = x142 && x129 = x141 && x128 = x140 && x127 = x139 && x126 = x138 && x125 = x137 (8) l6(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) -> l0(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172) :|: x158 = x170 && x155 = x167 && x154 = x166 && x153 = x165 && x152 = x164 && x151 = x163 && x150 = x162 && x149 = x161 && x168 = x172 && x169 = x171 && x171 = x171 && x172 = x172 (9) l7(x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184) -> l6(x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196) :|: x184 = x196 && x183 = x195 && x182 = x194 && x181 = x193 && x180 = x192 && x179 = x191 && x178 = x190 && x177 = x189 && x176 = x188 && x175 = x187 && x174 = x186 && x173 = x185 Arcs: (2) -> (3) (3) -> (1), (2), (4) (4) -> (5) (5) -> (6) (6) -> (7) (7) -> (1), (2), (4) (8) -> (1), (2), (4) (9) -> (8) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) 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 = x2 && x25 = x3 && 0 <= -1 - x24 + x25 && x17 = x17 && x18 = x18 && x21 = x21 && x21 <= 0 && 0 <= x21 && x = x12 && x1 = x13 && x2 = x14 && x3 = x15 && x4 = x16 && x7 = x19 && x8 = x20 && x10 = x22 && x11 = x23 (2) l3(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136) -> l0(x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) :|: x136 = x148 && x135 = x147 && x134 = x146 && x133 = x145 && x132 = x144 && x131 = x143 && x130 = x142 && x129 = x141 && x128 = x140 && x127 = x139 && x126 = x138 && x125 = x137 (3) l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111) -> l3(x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123) :|: x124 = x102 && x116 = x116 && x100 = x112 && x101 = x113 && x102 = x114 && x103 = x115 && x105 = x117 && x106 = x118 && x107 = x119 && x108 = x120 && x109 = x121 && x110 = x122 && x111 = x123 (4) l4(x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x87 = x99 && x86 = x98 && x85 = x97 && x84 = x96 && x83 = x95 && x82 = x94 && x81 = x93 && x80 = x92 && x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x89 = x77 (5) l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61) -> l4(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73) :|: x74 = x52 && x75 = x53 && 0 <= -1 - x74 + x75 && x67 = x67 && x68 = x68 && x71 = x71 && x50 = x62 && x51 = x63 && x52 = x64 && x53 = x65 && x54 = x66 && x57 = x69 && x58 = x70 && x60 = x72 && x61 = x73 (6) l2(x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37) -> l0(x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) :|: x37 = x49 && x36 = x48 && x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 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: l0(x112:0, x113:0, x114:0, x115:0, x54:0, x55:0, x56:0, x119:0, x120:0, x59:0, x122:0, x123:0) -> l0(x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x118:0, x119:0, x120:0, x121:0, x122:0, x123:0) :|: 0 <= -1 - x114:0 + x115:0 l0(x12:0, x13:0, x14:0, x15:0, x16:0, x5:0, x6:0, x19:0, x20:0, x9:0, x10:0, x11:0) -> l0(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0, x21:0, x10:0, x11:0) :|: x21:0 < 1 && 0 <= -1 - x14:0 + x15:0 && x21:0 > -1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> l0(x3, x4) ---------------------------------------- (8) Obligation: Rules: l0(x114:0, x115:0) -> l0(x114:0, x115:0) :|: 0 <= -1 - x114:0 + x115:0 l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x21:0 < 1 && 0 <= -1 - x14:0 + x15:0 && x21:0 > -1 ---------------------------------------- (9) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l0(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l0(x114:0, x115:0) -> l0(x114:0, x115:0) :|: 0 <= -1 - x114:0 + x115:0 l0(x14:0, x15:0) -> l0(x14:0, x15:0) :|: x21:0 < 1 && 0 <= -1 - x14:0 + x15:0 && x21:0 > -1 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: l0(x14:0:0, x15:0:0) -> l0(x14:0:0, x15:0:0) :|: x21:0:0 < 1 && 0 <= -1 - x14:0:0 + x15:0:0 && x21:0:0 > -1 l0(x114:0:0, x115:0:0) -> l0(x114:0:0, x115:0:0) :|: 0 <= -1 - x114:0:0 + x115:0:0 ---------------------------------------- (13) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x14:0:0, x15:0:0) -> f(1, x14:0:0, x15:0:0) :|: pc = 1 && (x21:0:0 < 1 && 0 <= -1 - x14:0:0 + x15:0:0 && x21:0:0 > -1) f(pc, x114:0:0, x115:0:0) -> f(1, x114:0:0, x115:0:0) :|: pc = 1 && 0 <= -1 - x114:0:0 + x115:0:0 Witness term starting non-terminating reduction: f(1, -7, -6) ---------------------------------------- (14) NO