MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 8937 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 84 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 1053 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 30 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 705 ms] (16) IRSwT (17) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (18) IRSwT (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] (20) IRSwT (21) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (22) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(loop_countHAT0, loop_maxHAT0, nPacketsOldHAT0, nPacketsHAT0, tmpHAT0, tmp___0HAT0) -> l1(loop_countHATpost, loop_maxHATpost, nPacketsOldHATpost, nPacketsHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nPacketsOldHAT0 = nPacketsOldHATpost && nPacketsHAT0 = nPacketsHATpost && loop_maxHAT0 = loop_maxHATpost && loop_countHAT0 = loop_countHATpost l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x14 = x20 && x15 = x21 && x13 = x19 && x12 = x18 l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 l4(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 l5(x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x50 = x56 && x51 = x57 && x49 = x55 && x48 = x54 && 1 + x48 <= x49 l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x62 = x68 && x63 = x69 && x61 = x67 && x60 = x66 && x61 <= x60 l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x74 = x80 && x75 = x81 && x73 = x79 && x72 = x78 l3(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x87 = x93 && x85 = x91 && x84 = x90 && 1 + x86 <= x87 l3(x96, x97, x98, x99, x100, x101) -> l8(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x99 = x105 && x97 = x103 && x96 = x102 && 1 + x99 <= x98 l3(x108, x109, x110, x111, x112, x113) -> l6(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x111 = x117 && x109 = x115 && x108 = x114 && x110 <= x111 && x111 <= x110 l9(x120, x121, x122, x123, x124, x125) -> l3(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x122 = x128 && x123 = x129 && x121 = x127 && x126 = 1 + x120 l10(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x134 = x140 && x135 = x141 && x133 = x139 && x132 = x138 && 0 <= x137 && x137 <= 0 l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x146 = x152 && x147 = x153 && x145 = x151 && x144 = x150 && 1 <= x149 l10(x156, x157, x158, x159, x160, x161) -> l9(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x160 = x166 && x158 = x164 && x159 = x165 && x157 = x163 && x156 = x162 && 1 + x161 <= 0 l11(x168, x169, x170, x171, x172, x173) -> l10(x174, x175, x176, x177, x178, x179) :|: x172 = x178 && x170 = x176 && x171 = x177 && x169 = x175 && x168 = x174 && x179 = x179 l12(x180, x181, x182, x183, x184, x185) -> l11(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186 && x189 = 1 + x183 l13(x192, x193, x194, x195, x196, x197) -> l11(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x194 = x200 && x195 = x201 && x193 = x199 && x192 = x198 && 0 <= x196 && x196 <= 0 l13(x204, x205, x206, x207, x208, x209) -> l12(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x206 = x212 && x207 = x213 && x205 = x211 && x204 = x210 && 1 <= x208 l13(x216, x217, x218, x219, x220, x221) -> l12(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x218 = x224 && x219 = x225 && x217 = x223 && x216 = x222 && 1 + x220 <= 0 l14(x228, x229, x230, x231, x232, x233) -> l13(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x230 = x236 && x231 = x237 && x229 = x235 && x228 = x234 && x238 = x238 l1(x240, x241, x242, x243, x244, x245) -> l14(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x242 = x248 && x243 = x249 && x241 = x247 && x240 = x246 l8(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x253 = x259 && x252 = x258 && x260 = x255 l15(x264, x265, x266, x267, x268, x269) -> l8(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x266 = x272 && x267 = x273 && x265 = x271 && x264 = x270 Start term: l15(loop_countHAT0, loop_maxHAT0, nPacketsOldHAT0, nPacketsHAT0, tmpHAT0, tmp___0HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(loop_countHAT0, loop_maxHAT0, nPacketsOldHAT0, nPacketsHAT0, tmpHAT0, tmp___0HAT0) -> l1(loop_countHATpost, loop_maxHATpost, nPacketsOldHATpost, nPacketsHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nPacketsOldHAT0 = nPacketsOldHATpost && nPacketsHAT0 = nPacketsHATpost && loop_maxHAT0 = loop_maxHATpost && loop_countHAT0 = loop_countHATpost l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x14 = x20 && x15 = x21 && x13 = x19 && x12 = x18 l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 l4(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 l5(x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x50 = x56 && x51 = x57 && x49 = x55 && x48 = x54 && 1 + x48 <= x49 l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x62 = x68 && x63 = x69 && x61 = x67 && x60 = x66 && x61 <= x60 l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x74 = x80 && x75 = x81 && x73 = x79 && x72 = x78 l3(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x87 = x93 && x85 = x91 && x84 = x90 && 1 + x86 <= x87 l3(x96, x97, x98, x99, x100, x101) -> l8(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x99 = x105 && x97 = x103 && x96 = x102 && 1 + x99 <= x98 l3(x108, x109, x110, x111, x112, x113) -> l6(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x111 = x117 && x109 = x115 && x108 = x114 && x110 <= x111 && x111 <= x110 l9(x120, x121, x122, x123, x124, x125) -> l3(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x122 = x128 && x123 = x129 && x121 = x127 && x126 = 1 + x120 l10(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x134 = x140 && x135 = x141 && x133 = x139 && x132 = x138 && 0 <= x137 && x137 <= 0 l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x146 = x152 && x147 = x153 && x145 = x151 && x144 = x150 && 1 <= x149 l10(x156, x157, x158, x159, x160, x161) -> l9(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x160 = x166 && x158 = x164 && x159 = x165 && x157 = x163 && x156 = x162 && 1 + x161 <= 0 l11(x168, x169, x170, x171, x172, x173) -> l10(x174, x175, x176, x177, x178, x179) :|: x172 = x178 && x170 = x176 && x171 = x177 && x169 = x175 && x168 = x174 && x179 = x179 l12(x180, x181, x182, x183, x184, x185) -> l11(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186 && x189 = 1 + x183 l13(x192, x193, x194, x195, x196, x197) -> l11(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x194 = x200 && x195 = x201 && x193 = x199 && x192 = x198 && 0 <= x196 && x196 <= 0 l13(x204, x205, x206, x207, x208, x209) -> l12(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x206 = x212 && x207 = x213 && x205 = x211 && x204 = x210 && 1 <= x208 l13(x216, x217, x218, x219, x220, x221) -> l12(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x218 = x224 && x219 = x225 && x217 = x223 && x216 = x222 && 1 + x220 <= 0 l14(x228, x229, x230, x231, x232, x233) -> l13(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x230 = x236 && x231 = x237 && x229 = x235 && x228 = x234 && x238 = x238 l1(x240, x241, x242, x243, x244, x245) -> l14(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x242 = x248 && x243 = x249 && x241 = x247 && x240 = x246 l8(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x253 = x259 && x252 = x258 && x260 = x255 l15(x264, x265, x266, x267, x268, x269) -> l8(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x266 = x272 && x267 = x273 && x265 = x271 && x264 = x270 Start term: l15(loop_countHAT0, loop_maxHAT0, nPacketsOldHAT0, nPacketsHAT0, tmpHAT0, tmp___0HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(loop_countHAT0, loop_maxHAT0, nPacketsOldHAT0, nPacketsHAT0, tmpHAT0, tmp___0HAT0) -> l1(loop_countHATpost, loop_maxHATpost, nPacketsOldHATpost, nPacketsHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nPacketsOldHAT0 = nPacketsOldHATpost && nPacketsHAT0 = nPacketsHATpost && loop_maxHAT0 = loop_maxHATpost && loop_countHAT0 = loop_countHATpost (2) l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 (3) l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x14 = x20 && x15 = x21 && x13 = x19 && x12 = x18 (4) l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 (5) l4(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 (6) l5(x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x50 = x56 && x51 = x57 && x49 = x55 && x48 = x54 && 1 + x48 <= x49 (7) l5(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x62 = x68 && x63 = x69 && x61 = x67 && x60 = x66 && x61 <= x60 (8) l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x74 = x80 && x75 = x81 && x73 = x79 && x72 = x78 (9) l3(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x87 = x93 && x85 = x91 && x84 = x90 && 1 + x86 <= x87 (10) l3(x96, x97, x98, x99, x100, x101) -> l8(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x99 = x105 && x97 = x103 && x96 = x102 && 1 + x99 <= x98 (11) l3(x108, x109, x110, x111, x112, x113) -> l6(x114, x115, x116, x117, x118, x119) :|: x113 = x119 && x112 = x118 && x110 = x116 && x111 = x117 && x109 = x115 && x108 = x114 && x110 <= x111 && x111 <= x110 (12) l9(x120, x121, x122, x123, x124, x125) -> l3(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x122 = x128 && x123 = x129 && x121 = x127 && x126 = 1 + x120 (13) l10(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x134 = x140 && x135 = x141 && x133 = x139 && x132 = x138 && 0 <= x137 && x137 <= 0 (14) l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x146 = x152 && x147 = x153 && x145 = x151 && x144 = x150 && 1 <= x149 (15) l10(x156, x157, x158, x159, x160, x161) -> l9(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x160 = x166 && x158 = x164 && x159 = x165 && x157 = x163 && x156 = x162 && 1 + x161 <= 0 (16) l11(x168, x169, x170, x171, x172, x173) -> l10(x174, x175, x176, x177, x178, x179) :|: x172 = x178 && x170 = x176 && x171 = x177 && x169 = x175 && x168 = x174 && x179 = x179 (17) l12(x180, x181, x182, x183, x184, x185) -> l11(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186 && x189 = 1 + x183 (18) l13(x192, x193, x194, x195, x196, x197) -> l11(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x194 = x200 && x195 = x201 && x193 = x199 && x192 = x198 && 0 <= x196 && x196 <= 0 (19) l13(x204, x205, x206, x207, x208, x209) -> l12(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x206 = x212 && x207 = x213 && x205 = x211 && x204 = x210 && 1 <= x208 (20) l13(x216, x217, x218, x219, x220, x221) -> l12(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x218 = x224 && x219 = x225 && x217 = x223 && x216 = x222 && 1 + x220 <= 0 (21) l14(x228, x229, x230, x231, x232, x233) -> l13(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x230 = x236 && x231 = x237 && x229 = x235 && x228 = x234 && x238 = x238 (22) l1(x240, x241, x242, x243, x244, x245) -> l14(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x242 = x248 && x243 = x249 && x241 = x247 && x240 = x246 (23) l8(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x253 = x259 && x252 = x258 && x260 = x255 (24) l15(x264, x265, x266, x267, x268, x269) -> l8(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x266 = x272 && x267 = x273 && x265 = x271 && x264 = x270 Arcs: (1) -> (22) (2) -> (1) (3) -> (9), (10), (11) (4) -> (2), (3) (5) -> (9), (10), (11) (6) -> (4), (5) (7) -> (8) (9) -> (23) (10) -> (23) (11) -> (8) (12) -> (9), (10), (11) (13) -> (9), (10), (11) (14) -> (12) (15) -> (12) (16) -> (13), (14), (15) (17) -> (16) (18) -> (16) (19) -> (17) (20) -> (17) (21) -> (18), (19), (20) (22) -> (21) (23) -> (6), (7) (24) -> (23) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(loop_countHAT0, loop_maxHAT0, nPacketsOldHAT0, nPacketsHAT0, tmpHAT0, tmp___0HAT0) -> l1(loop_countHATpost, loop_maxHATpost, nPacketsOldHATpost, nPacketsHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && nPacketsOldHAT0 = nPacketsOldHATpost && nPacketsHAT0 = nPacketsHATpost && loop_maxHAT0 = loop_maxHATpost && loop_countHAT0 = loop_countHATpost (2) l2(x, x1, x2, x3, x4, x5) -> l0(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x2 = x8 && x3 = x9 && x1 = x7 && x = x6 (3) l4(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x26 = x32 && x27 = x33 && x25 = x31 && x24 = x30 (4) l5(x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x50 = x56 && x51 = x57 && x49 = x55 && x48 = x54 && 1 + x48 <= x49 (5) l8(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x253 = x259 && x252 = x258 && x260 = x255 (6) l3(x96, x97, x98, x99, x100, x101) -> l8(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x98 = x104 && x99 = x105 && x97 = x103 && x96 = x102 && 1 + x99 <= x98 (7) l3(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x86 = x92 && x87 = x93 && x85 = x91 && x84 = x90 && 1 + x86 <= x87 (8) l10(x132, x133, x134, x135, x136, x137) -> l3(x138, x139, x140, x141, x142, x143) :|: x137 = x143 && x136 = x142 && x134 = x140 && x135 = x141 && x133 = x139 && x132 = x138 && 0 <= x137 && x137 <= 0 (9) l9(x120, x121, x122, x123, x124, x125) -> l3(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x122 = x128 && x123 = x129 && x121 = x127 && x126 = 1 + x120 (10) l10(x156, x157, x158, x159, x160, x161) -> l9(x162, x163, x164, x165, x166, x167) :|: x161 = x167 && x160 = x166 && x158 = x164 && x159 = x165 && x157 = x163 && x156 = x162 && 1 + x161 <= 0 (11) l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x149 = x155 && x148 = x154 && x146 = x152 && x147 = x153 && x145 = x151 && x144 = x150 && 1 <= x149 (12) l11(x168, x169, x170, x171, x172, x173) -> l10(x174, x175, x176, x177, x178, x179) :|: x172 = x178 && x170 = x176 && x171 = x177 && x169 = x175 && x168 = x174 && x179 = x179 (13) l13(x192, x193, x194, x195, x196, x197) -> l11(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x194 = x200 && x195 = x201 && x193 = x199 && x192 = x198 && 0 <= x196 && x196 <= 0 (14) l12(x180, x181, x182, x183, x184, x185) -> l11(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x182 = x188 && x181 = x187 && x180 = x186 && x189 = 1 + x183 (15) l13(x216, x217, x218, x219, x220, x221) -> l12(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x218 = x224 && x219 = x225 && x217 = x223 && x216 = x222 && 1 + x220 <= 0 (16) l13(x204, x205, x206, x207, x208, x209) -> l12(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x206 = x212 && x207 = x213 && x205 = x211 && x204 = x210 && 1 <= x208 (17) l14(x228, x229, x230, x231, x232, x233) -> l13(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x230 = x236 && x231 = x237 && x229 = x235 && x228 = x234 && x238 = x238 (18) l1(x240, x241, x242, x243, x244, x245) -> l14(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x242 = x248 && x243 = x249 && x241 = x247 && x240 = x246 (19) l4(x36, x37, x38, x39, x40, x41) -> l3(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x39 = x45 && x37 = x43 && x36 = x42 (20) l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x14 = x20 && x15 = x21 && x13 = x19 && x12 = x18 Arcs: (1) -> (18) (2) -> (1) (3) -> (2), (20) (4) -> (3), (19) (5) -> (4) (6) -> (5) (7) -> (5) (8) -> (6), (7) (9) -> (6), (7) (10) -> (9) (11) -> (9) (12) -> (8), (10), (11) (13) -> (12) (14) -> (12) (15) -> (14) (16) -> (14) (17) -> (13), (15), (16) (18) -> (17) (19) -> (6), (7) (20) -> (6), (7) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l3(x102:0, x103:0, x104:0, x105:0, x100:0, x101:0) -> l8(x102:0, x103:0, x104:0, x105:0, x100:0, x101:0) :|: x104:0 >= 1 + x105:0 l11(x162:0, x127:0, x128:0, x129:0, x130:0, x173:0) -> l3(1 + x162:0, x127:0, x128:0, x129:0, x130:0, x131:0) :|: x131:0 < 0 l8(loop_countHATpost:0, loop_maxHATpost:0, x254:0, nPacketsHATpost:0, tmpHATpost:0, tmp___0HATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, 1 + nPacketsHATpost:0, x190:0, tmp___0HATpost:0) :|: loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0 l11(x, x1, x2, x3, x4, x5) -> l3(x, x1, x2, x3, x4, x6) :|: x6 < 1 && x6 > -1 l8(x7, x8, x9, x10, x11, x12) -> l11(x7, x8, x10, x10, x13, x12) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 l8(x14, x15, x16, x17, x18, x19) -> l3(x14, x15, x17, x17, x18, x19) :|: x15 >= 1 + x14 l11(x20, x21, x22, x23, x24, x25) -> l3(1 + x20, x21, x22, x23, x24, x26) :|: x26 > 0 l3(x84:0, x85:0, x86:0, x87:0, x88:0, x89:0) -> l8(x84:0, x85:0, x86:0, x87:0, x88:0, x89:0) :|: x87:0 >= 1 + x86:0 l8(x27, x28, x29, x30, x31, x32) -> l11(x27, x28, x30, 1 + x30, x33, x32) :|: x28 >= 1 + x27 && x33 < 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3, x4, x5, x6) -> l3(x1, x2, x3, x4) l11(x1, x2, x3, x4, x5, x6) -> l11(x1, x2, x3, x4) l8(x1, x2, x3, x4, x5, x6) -> l8(x1, x2, x4) ---------------------------------------- (8) Obligation: Rules: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l11(x162:0, x127:0, x128:0, x129:0) -> l3(1 + x162:0, x127:0, x128:0, x129:0) :|: x131:0 < 0 l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, 1 + nPacketsHATpost:0) :|: loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0 l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 l8(x14, x15, x17) -> l3(x14, x15, x17, x17) :|: x15 >= 1 + x14 l11(x20, x21, x22, x23) -> l3(1 + x20, x21, x22, x23) :|: x26 > 0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 l8(x27, x28, x30) -> l11(x27, x28, x30, 1 + x30) :|: x28 >= 1 + x27 && x33 < 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l3(VARIABLE, VARIABLE, VARIABLE, VARIABLE) l8(VARIABLE, VARIABLE, VARIABLE) l11(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: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l11(x162:0, x127:0, x128:0, x129:0) -> l3(c, x127:0, x128:0, x129:0) :|: c = 1 + x162:0 && x131:0 < 0 l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, c1) :|: c1 = 1 + nPacketsHATpost:0 && (loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0) l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 l8(x14, x15, x17) -> l3(x14, x15, x17, x17) :|: x15 >= 1 + x14 l11(x20, x21, x22, x23) -> l3(c2, x21, x22, x23) :|: c2 = 1 + x20 && x26 > 0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 l8(x27, x28, x30) -> l11(x27, x28, x30, c3) :|: c3 = 1 + x30 && (x28 >= 1 + x27 && x33 < 0) Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = -1 - x + x1 [l8(x4, x5, x6)] = -1 - x4 + x5 [l11(x7, x8, x9, x10)] = -1 - x7 + x8 The following rules are decreasing: l11(x162:0, x127:0, x128:0, x129:0) -> l3(c, x127:0, x128:0, x129:0) :|: c = 1 + x162:0 && x131:0 < 0 l11(x20, x21, x22, x23) -> l3(c2, x21, x22, x23) :|: c2 = 1 + x20 && x26 > 0 The following rules are bounded: l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, c1) :|: c1 = 1 + nPacketsHATpost:0 && (loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0) l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 l8(x14, x15, x17) -> l3(x14, x15, x17, x17) :|: x15 >= 1 + x14 l8(x27, x28, x30) -> l11(x27, x28, x30, c3) :|: c3 = 1 + x30 && (x28 >= 1 + x27 && x33 < 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, c1) :|: c1 = 1 + nPacketsHATpost:0 && (loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0) l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 l8(x14, x15, x17) -> l3(x14, x15, x17, x17) :|: x15 >= 1 + x14 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 l8(x27, x28, x30) -> l11(x27, x28, x30, c3) :|: c3 = 1 + x30 && (x28 >= 1 + x27 && x33 < 0) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l11(x162:0, x127:0, x128:0, x129:0) -> l3(c, x127:0, x128:0, x129:0) :|: c = 1 + x162:0 && x131:0 < 0 l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l11(x20, x21, x22, x23) -> l3(c2, x21, x22, x23) :|: c2 = 1 + x20 && x26 > 0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = 0 [l8(x4, x5, x6)] = 0 [l11(x7, x8, x9, x10)] = 1 The following rules are decreasing: l11(x162:0, x127:0, x128:0, x129:0) -> l3(c, x127:0, x128:0, x129:0) :|: c = 1 + x162:0 && x131:0 < 0 l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l11(x20, x21, x22, x23) -> l3(c2, x21, x22, x23) :|: c2 = 1 + x20 && x26 > 0 The following rules are bounded: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l11(x162:0, x127:0, x128:0, x129:0) -> l3(c, x127:0, x128:0, x129:0) :|: c = 1 + x162:0 && x131:0 < 0 l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l11(x20, x21, x22, x23) -> l3(c2, x21, x22, x23) :|: c2 = 1 + x20 && x26 > 0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = 1 [l8(x4, x5, x6)] = 0 The following rules are decreasing: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 The following rules are bounded: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 ---------------------------------------- (10) Obligation: Rules: l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, 1 + nPacketsHATpost:0) :|: loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0 l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 l8(x14, x15, x17) -> l3(x14, x15, x17, x17) :|: x15 >= 1 + x14 l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 l8(x27, x28, x30) -> l11(x27, x28, x30, 1 + x30) :|: x28 >= 1 + x27 && x33 < 0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 (2) l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, 1 + nPacketsHATpost:0) :|: loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0 (3) l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 (4) l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 (5) l8(x14, x15, x17) -> l3(x14, x15, x17, x17) :|: x15 >= 1 + x14 (6) l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 (7) l8(x27, x28, x30) -> l11(x27, x28, x30, 1 + x30) :|: x28 >= 1 + x27 && x33 < 0 Arcs: (1) -> (2), (4), (5), (7) (2) -> (3) (3) -> (1), (6) (4) -> (3) (6) -> (2), (4), (5), (7) (7) -> (3) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l3(x102:0, x103:0, x104:0, x105:0) -> l8(x102:0, x103:0, x105:0) :|: x104:0 >= 1 + x105:0 (2) l11(x, x1, x2, x3) -> l3(x, x1, x2, x3) :|: x6 < 1 && x6 > -1 (3) l8(x27, x28, x30) -> l11(x27, x28, x30, 1 + x30) :|: x28 >= 1 + x27 && x33 < 0 (4) l8(x7, x8, x10) -> l11(x7, x8, x10, x10) :|: x8 >= 1 + x7 && x13 > -1 && x13 < 1 (5) l8(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0) -> l11(loop_countHATpost:0, loop_maxHATpost:0, nPacketsHATpost:0, 1 + nPacketsHATpost:0) :|: loop_maxHATpost:0 >= 1 + loop_countHATpost:0 && x190:0 > 0 (6) l3(x84:0, x85:0, x86:0, x87:0) -> l8(x84:0, x85:0, x87:0) :|: x87:0 >= 1 + x86:0 Arcs: (1) -> (3), (4), (5) (2) -> (1), (6) (3) -> (2) (4) -> (2) (5) -> (2) (6) -> (3), (4), (5) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l8(x7:0, x8:0, x10:0) -> l11(x7:0, x8:0, x10:0, x10:0) :|: x8:0 >= 1 + x7:0 && x13:0 > -1 && x13:0 < 1 l11(x:0, x1:0, x2:0, x3:0) -> l8(x:0, x1:0, x3:0) :|: x6:0 < 1 && x6:0 > -1 && x2:0 >= 1 + x3:0 l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, 1 + nPacketsHATpost:0:0) :|: loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0 l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, 1 + x30:0) :|: x28:0 >= 1 + x27:0 && x33:0 < 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l8(VARIABLE, VARIABLE, VARIABLE) l11(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 - RankingReductionPairProof Rules: l8(x7:0, x8:0, x10:0) -> l11(x7:0, x8:0, x10:0, x10:0) :|: x8:0 >= 1 + x7:0 && x13:0 > -1 && x13:0 < 1 l11(x:0, x1:0, x2:0, x3:0) -> l8(x:0, x1:0, x3:0) :|: x6:0 < 1 && x6:0 > -1 && x2:0 >= 1 + x3:0 l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, c) :|: c = 1 + nPacketsHATpost:0:0 && (loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0) l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, c1) :|: c1 = 1 + x30:0 && (x28:0 >= 1 + x27:0 && x33:0 < 0) Interpretation: [ l8 ] = 1 [ l11 ] = 1/2*l11_3 + -1/2*l11_4 + 3/2*l11_3^2 + -3*l11_3*l11_4 + 3/2*l11_4^2 The following rules are decreasing: l8(x7:0, x8:0, x10:0) -> l11(x7:0, x8:0, x10:0, x10:0) :|: x8:0 >= 1 + x7:0 && x13:0 > -1 && x13:0 < 1 l11(x:0, x1:0, x2:0, x3:0) -> l8(x:0, x1:0, x3:0) :|: x6:0 < 1 && x6:0 > -1 && x2:0 >= 1 + x3:0 The following rules are bounded: l8(x7:0, x8:0, x10:0) -> l11(x7:0, x8:0, x10:0, x10:0) :|: x8:0 >= 1 + x7:0 && x13:0 > -1 && x13:0 < 1 l11(x:0, x1:0, x2:0, x3:0) -> l8(x:0, x1:0, x3:0) :|: x6:0 < 1 && x6:0 > -1 && x2:0 >= 1 + x3:0 l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, c) :|: c = 1 + nPacketsHATpost:0:0 && (loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0) l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, c1) :|: c1 = 1 + x30:0 && (x28:0 >= 1 + x27:0 && x33:0 < 0) - IntTRS - RankingReductionPairProof - IntTRS Rules: l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, c) :|: c = 1 + nPacketsHATpost:0:0 && (loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0) l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, c1) :|: c1 = 1 + x30:0 && (x28:0 >= 1 + x27:0 && x33:0 < 0) ---------------------------------------- (16) Obligation: Rules: l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, 1 + nPacketsHATpost:0:0) :|: loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0 l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, 1 + x30:0) :|: x28:0 >= 1 + x27:0 && x33:0 < 0 ---------------------------------------- (17) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, 1 + nPacketsHATpost:0:0) :|: loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0 (2) l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 (3) l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, 1 + x30:0) :|: x28:0 >= 1 + x27:0 && x33:0 < 0 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (18) Obligation: Termination digraph: Nodes: (1) l8(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0) -> l11(loop_countHATpost:0:0, loop_maxHATpost:0:0, nPacketsHATpost:0:0, 1 + nPacketsHATpost:0:0) :|: loop_maxHATpost:0:0 >= 1 + loop_countHATpost:0:0 && x190:0:0 > 0 (2) l11(x, x1, x2, x3) -> l8(x, x1, x3) :|: x4 < 1 && x4 > -1 && x3 >= 1 + x2 (3) l8(x27:0, x28:0, x30:0) -> l11(x27:0, x28:0, x30:0, 1 + x30:0) :|: x28:0 >= 1 + x27:0 && x33:0 < 0 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: l8(x27:0:0, x28:0:0, x30:0:0) -> l8(x27:0:0, x28:0:0, 1 + x30:0:0) :|: x33:0:0 < 0 && x28:0:0 >= 1 + x27:0:0 && x4:0 > -1 && x4:0 < 1 l8(x, x1, x2) -> l8(x, x1, 1 + x2) :|: x3 > 0 && x1 >= 1 + x && x4 > -1 && x4 < 1 ---------------------------------------- (21) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l8(x1, x2, x3) -> l8(x1, x2) ---------------------------------------- (22) Obligation: Rules: l8(x27:0:0, x28:0:0) -> l8(x27:0:0, x28:0:0) :|: x33:0:0 < 0 && x28:0:0 >= 1 + x27:0:0 && x4:0 > -1 && x4:0 < 1 l8(x, x1) -> l8(x, x1) :|: x3 > 0 && x1 >= 1 + x && x4 > -1 && x4 < 1