YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 15.1 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 24 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 17 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 0 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 0 ms] (25) IRSwT (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (27) IRSwT (28) TempFilterProof [SOUND, 6 ms] (29) IntTRS (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Rules: l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: x1HATpost = oldX3HATpost && x0HATpost = oldX2HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = -1 + x7 && x10 = x6 && x7 = x5 && x6 = x4 l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 + x19 <= 0 && x19 = x17 && x18 = x16 l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 0 <= x31 && x31 = x29 && x30 = x28 l4(x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x47 = x44 && x46 = -1 + x42 && x44 = x44 && x43 = x41 && x42 = x40 l5(x48, x49, x50, x51, x52, x53) -> l3(x54, x55, x56, x57, x58, x59) :|: x51 = x57 && x50 = x56 && x59 = 7 && x58 = x54 && 1 + x54 <= 0 && x55 = x53 && x54 = x52 l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x63 = x69 && x71 = x68 && x70 = x66 && 0 <= x66 && x68 = x68 && x67 = x65 && x66 = x64 l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x83 = x80 && x82 = 7 && x80 = x80 && x79 = x77 && x78 = x76 l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x95 = x93 && x94 = x92 && x93 = x93 && x92 = x92 && x91 = x89 && x90 = x88 l9(x96, x97, x98, x99, x100, x101) -> l10(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x107 = x104 && x106 = 1 + x102 && x104 = x104 && x103 = x101 && x102 = x100 l10(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x111 = x117 && x110 = x116 && x119 = x115 && x118 = x114 && 64 <= x114 && x115 = x113 && x114 = x112 l10(x120, x121, x122, x123, x124, x125) -> l9(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = x127 && x130 = x126 && x126 <= 63 && x127 = x125 && x126 = x124 l11(x132, x133, x134, x135, x136, x137) -> l10(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = 0 && x142 = 0 && x139 = x137 && x138 = x136 l12(x144, x145, x146, x147, x148, x149) -> l11(x150, x151, x152, x153, x154, x155) :|: x155 = x153 && x154 = x152 && x153 = x153 && x152 = x152 && x151 = x149 && x150 = x148 l12(x156, x157, x158, x159, x160, x161) -> l6(x162, x163, x164, x165, x166, x167) :|: x167 = x165 && x166 = x164 && x165 = x165 && x164 = x164 && x163 = x161 && x162 = x160 l12(x168, x169, x170, x171, x172, x173) -> l1(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x172 = x178 && x171 = x177 && x170 = x176 && x169 = x175 && x168 = x174 l12(x180, x181, x182, x183, x184, x185) -> l0(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x183 = x189 && x182 = x188 && x181 = x187 && x180 = x186 l12(x192, x193, x194, x195, x196, x197) -> l2(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x195 = x201 && x194 = x200 && x193 = x199 && x192 = x198 l12(x204, x205, x206, x207, x208, x209) -> l3(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x207 = x213 && x206 = x212 && x205 = x211 && x204 = x210 l12(x216, x217, x218, x219, x220, x221) -> l4(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x219 = x225 && x218 = x224 && x217 = x223 && x216 = x222 l12(x228, x229, x230, x231, x232, x233) -> l5(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x232 = x238 && x231 = x237 && x230 = x236 && x229 = x235 && x228 = x234 l12(x240, x241, x242, x243, x244, x245) -> l6(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x243 = x249 && x242 = x248 && x241 = x247 && x240 = x246 l12(x252, x253, x254, x255, x256, x257) -> l8(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x254 = x260 && x253 = x259 && x252 = x258 l12(x264, x265, x266, x267, x268, x269) -> l7(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x267 = x273 && x266 = x272 && x265 = x271 && x264 = x270 l12(x276, x277, x278, x279, x280, x281) -> l9(x282, x283, x284, x285, x286, x287) :|: x281 = x287 && x280 = x286 && x279 = x285 && x278 = x284 && x277 = x283 && x276 = x282 l12(x288, x289, x290, x291, x292, x293) -> l10(x294, x295, x296, x297, x298, x299) :|: x293 = x299 && x292 = x298 && x291 = x297 && x290 = x296 && x289 = x295 && x288 = x294 l12(x300, x301, x302, x303, x304, x305) -> l11(x306, x307, x308, x309, x310, x311) :|: x305 = x311 && x304 = x310 && x303 = x309 && x302 = x308 && x301 = x307 && x300 = x306 l13(x312, x313, x314, x315, x316, x317) -> l12(x318, x319, x320, x321, x322, x323) :|: x317 = x323 && x316 = x322 && x315 = x321 && x314 = x320 && x313 = x319 && x312 = x318 Start term: l13(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: x1HATpost = oldX3HATpost && x0HATpost = oldX2HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = -1 + x7 && x10 = x6 && x7 = x5 && x6 = x4 l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 + x19 <= 0 && x19 = x17 && x18 = x16 l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 0 <= x31 && x31 = x29 && x30 = x28 l4(x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x47 = x44 && x46 = -1 + x42 && x44 = x44 && x43 = x41 && x42 = x40 l5(x48, x49, x50, x51, x52, x53) -> l3(x54, x55, x56, x57, x58, x59) :|: x51 = x57 && x50 = x56 && x59 = 7 && x58 = x54 && 1 + x54 <= 0 && x55 = x53 && x54 = x52 l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x63 = x69 && x71 = x68 && x70 = x66 && 0 <= x66 && x68 = x68 && x67 = x65 && x66 = x64 l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x83 = x80 && x82 = 7 && x80 = x80 && x79 = x77 && x78 = x76 l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x95 = x93 && x94 = x92 && x93 = x93 && x92 = x92 && x91 = x89 && x90 = x88 l9(x96, x97, x98, x99, x100, x101) -> l10(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x107 = x104 && x106 = 1 + x102 && x104 = x104 && x103 = x101 && x102 = x100 l10(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x111 = x117 && x110 = x116 && x119 = x115 && x118 = x114 && 64 <= x114 && x115 = x113 && x114 = x112 l10(x120, x121, x122, x123, x124, x125) -> l9(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = x127 && x130 = x126 && x126 <= 63 && x127 = x125 && x126 = x124 l11(x132, x133, x134, x135, x136, x137) -> l10(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = 0 && x142 = 0 && x139 = x137 && x138 = x136 l12(x144, x145, x146, x147, x148, x149) -> l11(x150, x151, x152, x153, x154, x155) :|: x155 = x153 && x154 = x152 && x153 = x153 && x152 = x152 && x151 = x149 && x150 = x148 l12(x156, x157, x158, x159, x160, x161) -> l6(x162, x163, x164, x165, x166, x167) :|: x167 = x165 && x166 = x164 && x165 = x165 && x164 = x164 && x163 = x161 && x162 = x160 l12(x168, x169, x170, x171, x172, x173) -> l1(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x172 = x178 && x171 = x177 && x170 = x176 && x169 = x175 && x168 = x174 l12(x180, x181, x182, x183, x184, x185) -> l0(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x183 = x189 && x182 = x188 && x181 = x187 && x180 = x186 l12(x192, x193, x194, x195, x196, x197) -> l2(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x195 = x201 && x194 = x200 && x193 = x199 && x192 = x198 l12(x204, x205, x206, x207, x208, x209) -> l3(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x207 = x213 && x206 = x212 && x205 = x211 && x204 = x210 l12(x216, x217, x218, x219, x220, x221) -> l4(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x219 = x225 && x218 = x224 && x217 = x223 && x216 = x222 l12(x228, x229, x230, x231, x232, x233) -> l5(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x232 = x238 && x231 = x237 && x230 = x236 && x229 = x235 && x228 = x234 l12(x240, x241, x242, x243, x244, x245) -> l6(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x243 = x249 && x242 = x248 && x241 = x247 && x240 = x246 l12(x252, x253, x254, x255, x256, x257) -> l8(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x254 = x260 && x253 = x259 && x252 = x258 l12(x264, x265, x266, x267, x268, x269) -> l7(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x267 = x273 && x266 = x272 && x265 = x271 && x264 = x270 l12(x276, x277, x278, x279, x280, x281) -> l9(x282, x283, x284, x285, x286, x287) :|: x281 = x287 && x280 = x286 && x279 = x285 && x278 = x284 && x277 = x283 && x276 = x282 l12(x288, x289, x290, x291, x292, x293) -> l10(x294, x295, x296, x297, x298, x299) :|: x293 = x299 && x292 = x298 && x291 = x297 && x290 = x296 && x289 = x295 && x288 = x294 l12(x300, x301, x302, x303, x304, x305) -> l11(x306, x307, x308, x309, x310, x311) :|: x305 = x311 && x304 = x310 && x303 = x309 && x302 = x308 && x301 = x307 && x300 = x306 l13(x312, x313, x314, x315, x316, x317) -> l12(x318, x319, x320, x321, x322, x323) :|: x317 = x323 && x316 = x322 && x315 = x321 && x314 = x320 && x313 = x319 && x312 = x318 Start term: l13(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: x1HATpost = oldX3HATpost && x0HATpost = oldX2HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = -1 + x7 && x10 = x6 && x7 = x5 && x6 = x4 (3) l3(x12, x13, x14, x15, x16, x17) -> l0(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 + x19 <= 0 && x19 = x17 && x18 = x16 (4) l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 0 <= x31 && x31 = x29 && x30 = x28 (5) l4(x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x47 = x44 && x46 = -1 + x42 && x44 = x44 && x43 = x41 && x42 = x40 (6) l5(x48, x49, x50, x51, x52, x53) -> l3(x54, x55, x56, x57, x58, x59) :|: x51 = x57 && x50 = x56 && x59 = 7 && x58 = x54 && 1 + x54 <= 0 && x55 = x53 && x54 = x52 (7) l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x63 = x69 && x71 = x68 && x70 = x66 && 0 <= x66 && x68 = x68 && x67 = x65 && x66 = x64 (8) l6(x72, x73, x74, x75, x76, x77) -> l5(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x83 = x80 && x82 = 7 && x80 = x80 && x79 = x77 && x78 = x76 (9) l7(x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95) :|: x95 = x93 && x94 = x92 && x93 = x93 && x92 = x92 && x91 = x89 && x90 = x88 (10) l9(x96, x97, x98, x99, x100, x101) -> l10(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x107 = x104 && x106 = 1 + x102 && x104 = x104 && x103 = x101 && x102 = x100 (11) l10(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x111 = x117 && x110 = x116 && x119 = x115 && x118 = x114 && 64 <= x114 && x115 = x113 && x114 = x112 (12) l10(x120, x121, x122, x123, x124, x125) -> l9(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = x127 && x130 = x126 && x126 <= 63 && x127 = x125 && x126 = x124 (13) l11(x132, x133, x134, x135, x136, x137) -> l10(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = 0 && x142 = 0 && x139 = x137 && x138 = x136 (14) l12(x144, x145, x146, x147, x148, x149) -> l11(x150, x151, x152, x153, x154, x155) :|: x155 = x153 && x154 = x152 && x153 = x153 && x152 = x152 && x151 = x149 && x150 = x148 (15) l12(x156, x157, x158, x159, x160, x161) -> l6(x162, x163, x164, x165, x166, x167) :|: x167 = x165 && x166 = x164 && x165 = x165 && x164 = x164 && x163 = x161 && x162 = x160 (16) l12(x168, x169, x170, x171, x172, x173) -> l1(x174, x175, x176, x177, x178, x179) :|: x173 = x179 && x172 = x178 && x171 = x177 && x170 = x176 && x169 = x175 && x168 = x174 (17) l12(x180, x181, x182, x183, x184, x185) -> l0(x186, x187, x188, x189, x190, x191) :|: x185 = x191 && x184 = x190 && x183 = x189 && x182 = x188 && x181 = x187 && x180 = x186 (18) l12(x192, x193, x194, x195, x196, x197) -> l2(x198, x199, x200, x201, x202, x203) :|: x197 = x203 && x196 = x202 && x195 = x201 && x194 = x200 && x193 = x199 && x192 = x198 (19) l12(x204, x205, x206, x207, x208, x209) -> l3(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x207 = x213 && x206 = x212 && x205 = x211 && x204 = x210 (20) l12(x216, x217, x218, x219, x220, x221) -> l4(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x219 = x225 && x218 = x224 && x217 = x223 && x216 = x222 (21) l12(x228, x229, x230, x231, x232, x233) -> l5(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x232 = x238 && x231 = x237 && x230 = x236 && x229 = x235 && x228 = x234 (22) l12(x240, x241, x242, x243, x244, x245) -> l6(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x243 = x249 && x242 = x248 && x241 = x247 && x240 = x246 (23) l12(x252, x253, x254, x255, x256, x257) -> l8(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x254 = x260 && x253 = x259 && x252 = x258 (24) l12(x264, x265, x266, x267, x268, x269) -> l7(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x267 = x273 && x266 = x272 && x265 = x271 && x264 = x270 (25) l12(x276, x277, x278, x279, x280, x281) -> l9(x282, x283, x284, x285, x286, x287) :|: x281 = x287 && x280 = x286 && x279 = x285 && x278 = x284 && x277 = x283 && x276 = x282 (26) l12(x288, x289, x290, x291, x292, x293) -> l10(x294, x295, x296, x297, x298, x299) :|: x293 = x299 && x292 = x298 && x291 = x297 && x290 = x296 && x289 = x295 && x288 = x294 (27) l12(x300, x301, x302, x303, x304, x305) -> l11(x306, x307, x308, x309, x310, x311) :|: x305 = x311 && x304 = x310 && x303 = x309 && x302 = x308 && x301 = x307 && x300 = x306 (28) l13(x312, x313, x314, x315, x316, x317) -> l12(x318, x319, x320, x321, x322, x323) :|: x317 = x323 && x316 = x322 && x315 = x321 && x314 = x320 && x313 = x319 && x312 = x318 Arcs: (2) -> (3), (4) (3) -> (1) (4) -> (2) (5) -> (6), (7) (6) -> (4) (7) -> (5) (8) -> (7) (10) -> (11), (12) (11) -> (9) (12) -> (10) (13) -> (12) (14) -> (13) (15) -> (8) (17) -> (1) (18) -> (2) (19) -> (3), (4) (20) -> (5) (21) -> (6), (7) (22) -> (8) (24) -> (9) (25) -> (10) (26) -> (11), (12) (27) -> (13) (28) -> (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l9(x96, x97, x98, x99, x100, x101) -> l10(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x107 = x104 && x106 = 1 + x102 && x104 = x104 && x103 = x101 && x102 = x100 (2) l10(x120, x121, x122, x123, x124, x125) -> l9(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = x127 && x130 = x126 && x126 <= 63 && x127 = x125 && x126 = x124 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l9(x96:0, x97:0, x98:0, x105:0, x100:0, x101:0) -> l9(1 + x100:0, x104:0, x104:0, x105:0, 1 + x100:0, x104:0) :|: x100:0 < 63 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l9(x1, x2, x3, x4, x5, x6) -> l9(x5) ---------------------------------------- (9) Obligation: Rules: l9(x100:0) -> l9(1 + x100:0) :|: x100:0 < 63 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l9(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l9(x100:0) -> l9(c) :|: c = 1 + x100:0 && x100:0 < 63 ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l9 ] = -1*l9_1 The following rules are decreasing: l9(x100:0) -> l9(c) :|: c = 1 + x100:0 && x100:0 < 63 The following rules are bounded: l9(x100:0) -> l9(c) :|: c = 1 + x100:0 && x100:0 < 63 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) l4(x36, x37, x38, x39, x40, x41) -> l5(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x47 = x44 && x46 = -1 + x42 && x44 = x44 && x43 = x41 && x42 = x40 (2) l5(x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71) :|: x63 = x69 && x71 = x68 && x70 = x66 && 0 <= x66 && x68 = x68 && x67 = x65 && x66 = x64 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: l4(x36:0, x37:0, x38:0, x39:0, x40:0, x41:0) -> l4(-1 + x40:0, x44:0, x68:0, x39:0, -1 + x40:0, x68:0) :|: x40:0 > 0 ---------------------------------------- (17) 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) -> l4(x5) ---------------------------------------- (18) Obligation: Rules: l4(x40:0) -> l4(-1 + x40:0) :|: x40:0 > 0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l4(x40:0) -> l4(c) :|: c = -1 + x40:0 && x40:0 > 0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l4 ] = l4_1 The following rules are decreasing: l4(x40:0) -> l4(c) :|: c = -1 + x40:0 && x40:0 > 0 The following rules are bounded: l4(x40:0) -> l4(c) :|: c = -1 + x40:0 && x40:0 > 0 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = -1 + x7 && x10 = x6 && x7 = x5 && x6 = x4 (2) l3(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 0 <= x31 && x31 = x29 && x30 = x28 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: l2(x:0, x1:0, x2:0, x33:0, x10:0, x5:0) -> l2(x10:0, -1 + x5:0, x2:0, x33:0, x10:0, -1 + x5:0) :|: x5:0 > 0 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4, x5, x6) -> l2(x6) ---------------------------------------- (27) Obligation: Rules: l2(x5:0) -> l2(-1 + x5:0) :|: x5:0 > 0 ---------------------------------------- (28) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: l2(x5:0) -> l2(c) :|: c = -1 + x5:0 && x5:0 > 0 ---------------------------------------- (30) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l2(x)] = x The following rules are decreasing: l2(x5:0) -> l2(c) :|: c = -1 + x5:0 && x5:0 > 0 The following rules are bounded: l2(x5:0) -> l2(c) :|: c = -1 + x5:0 && x5:0 > 0 ---------------------------------------- (31) YES