MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 3485 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 52 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 1838 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 35 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(__disjvr_0HAT0, __disjvr_1HAT0, deltaHAT0, delta_newHAT0, deltaextHAT0, deltaext_newHAT0, deltextHAT0, wntHAT0, wntextHAT0) -> l2(__disjvr_0HATpost, __disjvr_1HATpost, deltaHATpost, delta_newHATpost, deltaextHATpost, deltaext_newHATpost, deltextHATpost, wntHATpost, wntextHATpost) :|: wntextHAT0 = wntextHATpost && wntHAT0 = wntHATpost && deltextHAT0 = deltextHATpost && deltaext_newHAT0 = deltaext_newHATpost && deltaextHAT0 = deltaextHATpost && delta_newHAT0 = delta_newHATpost && deltaHAT0 = deltaHATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && __disjvr_0HATpost = __disjvr_0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x1 = x10 && x = x9 && x11 = x3 && x13 = x5 l0(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x28 = x19 l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x39 = x48 && x37 = x46 && x36 = x45 && x47 = x39 && x49 = x41 l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = x56 && -1 + 2 * x56 <= x58 + x62 && x58 + x62 <= -1 + 2 * x56 l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l0(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x84 = x74 && 2 * x74 <= x76 + x80 && x76 + x80 <= 2 * x74 l4(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l0(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x92 = x101 && x91 = x100 && x90 = x99 && x102 = -1 + x92 && 1 + x94 + x98 <= -1 + 2 * x92 l4(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l0(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x110 && 1 + 2 * x110 <= x112 + x116 l1(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l4(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x140 = x130 && -1 + 2 * x130 <= 2 + x133 && 2 + x133 <= -1 + 2 * x130 l1(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x158 = x148 && 2 * x148 <= 2 + x151 && 2 + x151 <= 2 * x148 l1(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x166 = x175 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x176 = -1 + x166 && 3 + x169 <= -1 + 2 * x166 l1(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 && x194 = 1 + x184 && 1 + 2 * x184 <= 2 + x187 l5(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l1(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 && x200 <= 3 && 0 <= x200 && x206 <= 3 && 0 <= x206 && x204 <= 3 && 0 <= x202 && x205 <= 3 && 0 <= x205 l6(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x219 = x228 && x218 = x227 && x217 = x226 && x216 = x225 Start term: l6(__disjvr_0HAT0, __disjvr_1HAT0, deltaHAT0, delta_newHAT0, deltaextHAT0, deltaext_newHAT0, deltextHAT0, wntHAT0, wntextHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__disjvr_0HAT0, __disjvr_1HAT0, deltaHAT0, delta_newHAT0, deltaextHAT0, deltaext_newHAT0, deltextHAT0, wntHAT0, wntextHAT0) -> l2(__disjvr_0HATpost, __disjvr_1HATpost, deltaHATpost, delta_newHATpost, deltaextHATpost, deltaext_newHATpost, deltextHATpost, wntHATpost, wntextHATpost) :|: wntextHAT0 = wntextHATpost && wntHAT0 = wntHATpost && deltextHAT0 = deltextHATpost && deltaext_newHAT0 = deltaext_newHATpost && deltaextHAT0 = deltaextHATpost && delta_newHAT0 = delta_newHATpost && deltaHAT0 = deltaHATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && __disjvr_0HATpost = __disjvr_0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x1 = x10 && x = x9 && x11 = x3 && x13 = x5 l0(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x28 = x19 l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x39 = x48 && x37 = x46 && x36 = x45 && x47 = x39 && x49 = x41 l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = x56 && -1 + 2 * x56 <= x58 + x62 && x58 + x62 <= -1 + 2 * x56 l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l0(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x84 = x74 && 2 * x74 <= x76 + x80 && x76 + x80 <= 2 * x74 l4(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l0(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x92 = x101 && x91 = x100 && x90 = x99 && x102 = -1 + x92 && 1 + x94 + x98 <= -1 + 2 * x92 l4(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l0(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x110 && 1 + 2 * x110 <= x112 + x116 l1(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l4(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x140 = x130 && -1 + 2 * x130 <= 2 + x133 && 2 + x133 <= -1 + 2 * x130 l1(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x158 = x148 && 2 * x148 <= 2 + x151 && 2 + x151 <= 2 * x148 l1(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x166 = x175 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x176 = -1 + x166 && 3 + x169 <= -1 + 2 * x166 l1(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 && x194 = 1 + x184 && 1 + 2 * x184 <= 2 + x187 l5(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l1(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 && x200 <= 3 && 0 <= x200 && x206 <= 3 && 0 <= x206 && x204 <= 3 && 0 <= x202 && x205 <= 3 && 0 <= x205 l6(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x219 = x228 && x218 = x227 && x217 = x226 && x216 = x225 Start term: l6(__disjvr_0HAT0, __disjvr_1HAT0, deltaHAT0, delta_newHAT0, deltaextHAT0, deltaext_newHAT0, deltextHAT0, wntHAT0, wntextHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__disjvr_0HAT0, __disjvr_1HAT0, deltaHAT0, delta_newHAT0, deltaextHAT0, deltaext_newHAT0, deltextHAT0, wntHAT0, wntextHAT0) -> l2(__disjvr_0HATpost, __disjvr_1HATpost, deltaHATpost, delta_newHATpost, deltaextHATpost, deltaext_newHATpost, deltextHATpost, wntHATpost, wntextHATpost) :|: wntextHAT0 = wntextHATpost && wntHAT0 = wntHATpost && deltextHAT0 = deltextHATpost && deltaext_newHAT0 = deltaext_newHATpost && deltaextHAT0 = deltaextHATpost && delta_newHAT0 = delta_newHATpost && deltaHAT0 = deltaHATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && __disjvr_0HATpost = __disjvr_0HAT0 (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x1 = x10 && x = x9 && x11 = x3 && x13 = x5 (3) l0(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x28 = x19 (4) l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x39 = x48 && x37 = x46 && x36 = x45 && x47 = x39 && x49 = x41 (5) l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = x56 && -1 + 2 * x56 <= x58 + x62 && x58 + x62 <= -1 + 2 * x56 (6) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l0(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x84 = x74 && 2 * x74 <= x76 + x80 && x76 + x80 <= 2 * x74 (7) l4(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l0(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x92 = x101 && x91 = x100 && x90 = x99 && x102 = -1 + x92 && 1 + x94 + x98 <= -1 + 2 * x92 (8) l4(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l0(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x110 && 1 + 2 * x110 <= x112 + x116 (9) l1(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l4(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x140 = x130 && -1 + 2 * x130 <= 2 + x133 && 2 + x133 <= -1 + 2 * x130 (10) l1(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x158 = x148 && 2 * x148 <= 2 + x151 && 2 + x151 <= 2 * x148 (11) l1(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x166 = x175 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x176 = -1 + x166 && 3 + x169 <= -1 + 2 * x166 (12) l1(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 && x194 = 1 + x184 && 1 + 2 * x184 <= 2 + x187 (13) l5(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l1(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 && x200 <= 3 && 0 <= x200 && x206 <= 3 && 0 <= x206 && x204 <= 3 && 0 <= x202 && x205 <= 3 && 0 <= x205 (14) l6(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x219 = x228 && x218 = x227 && x217 = x226 && x216 = x225 Arcs: (1) -> (2) (2) -> (9), (10), (11), (12) (3) -> (4) (4) -> (9), (10), (11), (12) (5) -> (1), (3) (6) -> (1), (3) (7) -> (1), (3) (8) -> (1), (3) (9) -> (5), (6), (7), (8) (10) -> (5), (6), (7), (8) (11) -> (5), (6), (7), (8) (12) -> (5), (6), (7), (8) (13) -> (9), (10), (11), (12) (14) -> (13) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(__disjvr_0HAT0, __disjvr_1HAT0, deltaHAT0, delta_newHAT0, deltaextHAT0, deltaext_newHAT0, deltextHAT0, wntHAT0, wntextHAT0) -> l2(__disjvr_0HATpost, __disjvr_1HATpost, deltaHATpost, delta_newHATpost, deltaextHATpost, deltaext_newHATpost, deltextHATpost, wntHATpost, wntextHATpost) :|: wntextHAT0 = wntextHATpost && wntHAT0 = wntHATpost && deltextHAT0 = deltextHATpost && deltaext_newHAT0 = deltaext_newHATpost && deltaextHAT0 = deltaextHATpost && delta_newHAT0 = delta_newHATpost && deltaHAT0 = deltaHATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && __disjvr_0HATpost = __disjvr_0HAT0 (2) l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l0(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = x56 && -1 + 2 * x56 <= x58 + x62 && x58 + x62 <= -1 + 2 * x56 (3) l1(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l4(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x140 = x130 && -1 + 2 * x130 <= 2 + x133 && 2 + x133 <= -1 + 2 * x130 (4) l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x39 = x48 && x37 = x46 && x36 = x45 && x47 = x39 && x49 = x41 (5) l0(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 && x28 = x19 (6) l4(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l0(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x110 && 1 + 2 * x110 <= x112 + x116 (7) l4(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l0(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x92 = x101 && x91 = x100 && x90 = x99 && x102 = -1 + x92 && 1 + x94 + x98 <= -1 + 2 * x92 (8) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l0(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x80 = x89 && x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x74 = x83 && x73 = x82 && x72 = x81 && x84 = x74 && 2 * x74 <= x76 + x80 && x76 + x80 <= 2 * x74 (9) l1(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l4(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 && x194 = 1 + x184 && 1 + 2 * x184 <= 2 + x187 (10) l1(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x166 = x175 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x176 = -1 + x166 && 3 + x169 <= -1 + 2 * x166 (11) l1(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x158 = x148 && 2 * x148 <= 2 + x151 && 2 + x151 <= 2 * x148 (12) l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x3 = x12 && x1 = x10 && x = x9 && x11 = x3 && x13 = x5 Arcs: (1) -> (12) (2) -> (1), (5) (3) -> (2), (6), (7), (8) (4) -> (3), (9), (10), (11) (5) -> (4) (6) -> (1), (5) (7) -> (1), (5) (8) -> (1), (5) (9) -> (2), (6), (7), (8) (10) -> (2), (6), (7), (8) (11) -> (2), (6), (7), (8) (12) -> (3), (9), (10), (11) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l4(x72:0, x73:0, x74:0, x75:0, x76:0, x77:0, x78:0, x79:0, x80:0) -> l0(x72:0, x73:0, x74:0, x74:0, x76:0, x77:0, x78:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 l1(x180:0, x181:0, x182:0, x183:0, x184:0, x185:0, x186:0, x187:0, x188:0) -> l4(x180:0, x181:0, x182:0, x183:0, x184:0, 1 + x184:0, x186:0, x187:0, x188:0) :|: 2 + x187:0 >= 1 + 2 * x184:0 l1(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0) -> l4(x126:0, x127:0, x128:0, x129:0, x130:0, x130:0, x132:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l4(x90:0, x100:0, x101:0, x93:0, x103:0, x104:0, x105:0, x106:0, x107:0) -> l0(x90:0, x100:0, x101:0, -1 + x101:0, x103:0, x104:0, x105:0, x106:0, x107:0) :|: 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 l4(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0) -> l0(x108:0, x109:0, x110:0, 1 + x110:0, x112:0, x113:0, x114:0, x115:0, x116:0) :|: x112:0 + x116:0 >= 1 + 2 * x110:0 l0(__disjvr_0HAT0:0, __disjvr_1HAT0:0, deltaHAT0:0, delta_newHAT0:0, deltaextHAT0:0, deltaext_newHAT0:0, deltextHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(__disjvr_0HAT0:0, __disjvr_1HAT0:0, delta_newHAT0:0, delta_newHAT0:0, deltaext_newHAT0:0, deltaext_newHAT0:0, deltextHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE l1(x144:0, x145:0, x146:0, x147:0, x148:0, x149:0, x150:0, x151:0, x152:0) -> l4(x144:0, x145:0, x146:0, x147:0, x148:0, x148:0, x150:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l4(x54:0, x55:0, x56:0, x57:0, x58:0, x59:0, x60:0, x61:0, x62:0) -> l0(x54:0, x55:0, x56:0, x56:0, x58:0, x59:0, x60:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 l1(x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0, x170:0) -> l4(x162:0, x163:0, x164:0, x165:0, x166:0, -1 + x166:0, x168:0, x169:0, x170:0) :|: 3 + x169:0 <= -1 + 2 * x166:0 ---------------------------------------- (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) -> l4(x3, x5, x6, x8, x9) l1(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l1(x3, x5, x8, x9) l0(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x4, x6, x8, x9) ---------------------------------------- (8) Obligation: Rules: l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 l1(x182:0, x184:0, x187:0, x188:0) -> l4(x182:0, x184:0, 1 + x184:0, x187:0, x188:0) :|: 2 + x187:0 >= 1 + 2 * x184:0 l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(-1 + x101:0, x104:0, x106:0, x107:0) :|: 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(1 + x110:0, x113:0, x115:0, x116:0) :|: x112:0 + x116:0 >= 1 + 2 * x110:0 l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 l1(x164:0, x166:0, x169:0, x170:0) -> l4(x164:0, x166:0, -1 + x166:0, x169:0, x170:0) :|: 3 + x169:0 <= -1 + 2 * x166:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(VARIABLE, INTEGER, VARIABLE, VARIABLE, VARIABLE) l0(VARIABLE, VARIABLE, VARIABLE, VARIABLE) l1(VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 l1(x182:0, x184:0, x187:0, x188:0) -> l4(x182:0, x184:0, c, x187:0, x188:0) :|: c = 1 + x184:0 && 2 + x187:0 >= 1 + 2 * x184:0 l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(c1, x104:0, x106:0, x107:0) :|: c1 = -1 + x101:0 && 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(c2, x113:0, x115:0, x116:0) :|: c2 = 1 + x110:0 && x112:0 + x116:0 >= 1 + 2 * x110:0 l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 l1(x164:0, x166:0, x169:0, x170:0) -> l4(x164:0, x166:0, c3, x169:0, x170:0) :|: c3 = -1 + x166:0 && 3 + x169:0 <= -1 + 2 * x166:0 Found the following polynomial interpretation: [l4(x, x1, x2, x3, x4)] = 9 - 12*x2 - 4*x2*x3 + 4*x2^2 + 6*x3 + x3^2 [l0(x5, x6, x7, x8)] = 9 - 12*x6 - 4*x6*x7 + 4*x6^2 + 6*x7 + x7^2 [l1(x9, x10, x11, x12)] = 9 - 12*x10 - 4*x10*x11 + 4*x10^2 + 6*x11 + x11^2 The following rules are decreasing: l1(x182:0, x184:0, x187:0, x188:0) -> l4(x182:0, x184:0, c, x187:0, x188:0) :|: c = 1 + x184:0 && 2 + x187:0 >= 1 + 2 * x184:0 The following rules are bounded: l1(x182:0, x184:0, x187:0, x188:0) -> l4(x182:0, x184:0, c, x187:0, x188:0) :|: c = 1 + x184:0 && 2 + x187:0 >= 1 + 2 * x184:0 l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l1(x164:0, x166:0, x169:0, x170:0) -> l4(x164:0, x166:0, c3, x169:0, x170:0) :|: c3 = -1 + x166:0 && 3 + x169:0 <= -1 + 2 * x166:0 - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(c1, x104:0, x106:0, x107:0) :|: c1 = -1 + x101:0 && 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(c2, x113:0, x115:0, x116:0) :|: c2 = 1 + x110:0 && x112:0 + x116:0 >= 1 + 2 * x110:0 l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 l1(x164:0, x166:0, x169:0, x170:0) -> l4(x164:0, x166:0, c3, x169:0, x170:0) :|: c3 = -1 + x166:0 && 3 + x169:0 <= -1 + 2 * x166:0 Found the following polynomial interpretation: [l4(x, x1, x2, x3, x4)] = -1 + 2*x2 - x3 [l0(x5, x6, x7, x8)] = -1 + 2*x6 - x7 [l1(x9, x10, x11, x12)] = -1 + 2*x10 - x11 The following rules are decreasing: l1(x164:0, x166:0, x169:0, x170:0) -> l4(x164:0, x166:0, c3, x169:0, x170:0) :|: c3 = -1 + x166:0 && 3 + x169:0 <= -1 + 2 * x166:0 The following rules are bounded: l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l1(x164:0, x166:0, x169:0, x170:0) -> l4(x164:0, x166:0, c3, x169:0, x170:0) :|: c3 = -1 + x166:0 && 3 + x169:0 <= -1 + 2 * x166:0 - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(c1, x104:0, x106:0, x107:0) :|: c1 = -1 + x101:0 && 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(c2, x113:0, x115:0, x116:0) :|: c2 = 1 + x110:0 && x112:0 + x116:0 >= 1 + 2 * x110:0 l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 ---------------------------------------- (10) Obligation: Rules: l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(-1 + x101:0, x104:0, x106:0, x107:0) :|: 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(1 + x110:0, x113:0, x115:0, x116:0) :|: x112:0 + x116:0 >= 1 + 2 * x110:0 l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 (2) l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 (3) l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(-1 + x101:0, x104:0, x106:0, x107:0) :|: 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 (4) l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(1 + x110:0, x113:0, x115:0, x116:0) :|: x112:0 + x116:0 >= 1 + 2 * x110:0 (5) l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE (6) l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 (7) l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 Arcs: (1) -> (5) (2) -> (1), (3), (4), (7) (3) -> (5) (4) -> (5) (5) -> (2), (6) (6) -> (1), (3), (4), (7) (7) -> (5) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l4(x74:0, x76:0, x77:0, x79:0, x80:0) -> l0(x74:0, x77:0, x79:0, x80:0) :|: x76:0 + x80:0 = 2 * x74:0 (2) l1(x128:0, x130:0, x133:0, x134:0) -> l4(x128:0, x130:0, x130:0, x133:0, x134:0) :|: 2 + x133:0 = -1 + 2 * x130:0 (3) l0(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) -> l1(delta_newHAT0:0, deltaext_newHAT0:0, wntHAT0:0, wntextHAT0:0) :|: TRUE (4) l4(x56:0, x58:0, x59:0, x61:0, x62:0) -> l0(x56:0, x59:0, x61:0, x62:0) :|: x58:0 + x62:0 = -1 + 2 * x56:0 (5) l4(x110:0, x112:0, x113:0, x115:0, x116:0) -> l0(1 + x110:0, x113:0, x115:0, x116:0) :|: x112:0 + x116:0 >= 1 + 2 * x110:0 (6) l4(x101:0, x103:0, x104:0, x106:0, x107:0) -> l0(-1 + x101:0, x104:0, x106:0, x107:0) :|: 1 + x103:0 + x107:0 <= -1 + 2 * x101:0 (7) l1(x146:0, x148:0, x151:0, x152:0) -> l4(x146:0, x148:0, x148:0, x151:0, x152:0) :|: 2 + x151:0 = 2 * x148:0 Arcs: (1) -> (3) (2) -> (1), (4), (5), (6) (3) -> (2), (7) (4) -> (3) (5) -> (3) (6) -> (3) (7) -> (1), (4), (5), (6) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l4(x74:0:0, x76:0:0, x77:0:0, x79:0:0, x80:0:0) -> l1(x74:0:0, x77:0:0, x79:0:0, x80:0:0) :|: x76:0:0 + x80:0:0 = 2 * x74:0:0 l1(x128:0:0, x130:0:0, x133:0:0, x134:0:0) -> l4(x128:0:0, x130:0:0, x130:0:0, x133:0:0, x134:0:0) :|: 2 + x133:0:0 = -1 + 2 * x130:0:0 l4(x110:0:0, x112:0:0, x113:0:0, x115:0:0, x116:0:0) -> l1(1 + x110:0:0, x113:0:0, x115:0:0, x116:0:0) :|: x112:0:0 + x116:0:0 >= 1 + 2 * x110:0:0 l4(x101:0:0, x103:0:0, x104:0:0, x106:0:0, x107:0:0) -> l1(-1 + x101:0:0, x104:0:0, x106:0:0, x107:0:0) :|: 1 + x103:0:0 + x107:0:0 <= -1 + 2 * x101:0:0 l4(x56:0:0, x58:0:0, x59:0:0, x61:0:0, x62:0:0) -> l1(x56:0:0, x59:0:0, x61:0:0, x62:0:0) :|: x58:0:0 + x62:0:0 = -1 + 2 * x56:0:0 l1(x146:0:0, x148:0:0, x151:0:0, x152:0:0) -> l4(x146:0:0, x148:0:0, x148:0:0, x151:0:0, x152:0:0) :|: 2 + x151:0:0 = 2 * x148:0:0