YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 6233 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 45 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 16 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Rules: l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost) :|: x3HATpost = oldX7HATpost && x2HATpost = oldX6HATpost && x1HATpost = oldX5HATpost && x0HATpost = oldX4HATpost && oldX7HATpost = oldX7HATpost && oldX6HATpost = oldX6HATpost && oldX5HATpost = oldX5HATpost && oldX4HATpost = oldX4HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l1(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x23 = x19 && x22 = x18 && x21 = x17 && x20 = x16 && x19 = x19 && x18 = x18 && x17 = x17 && x16 = x16 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8 l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l3(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x37 && x46 = x38 && x45 = x39 && x44 = -1 + x36 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32 l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x62 && x70 = x63 && x69 = x61 && x68 = -1 + x60 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56 l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l0(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x87 && x94 = x86 && x93 = x85 && x92 = x84 && 1 <= x84 && x84 <= 1 && x87 = x83 && x86 = x82 && x85 = x81 && x84 = x80 l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l0(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x100 = x112 && x119 = x111 && x118 = x110 && x117 = x109 && x116 = x108 && x108 <= 0 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104 l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 2 <= x132 && 1 <= x132 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128 l4(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l2(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x158 && x165 = x157 && x164 = x156 && 1 + x156 <= 1 && 1 <= x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152 l3(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176 l5(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x203 = x215 && x202 = x214 && x201 = x213 && x200 = x212 && x199 = x211 && x198 = x210 && x197 = x209 && x196 = x208 && x195 = x207 && x194 = x206 && x193 = x205 && x192 = x204 l5(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l0(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x239 && x226 = x238 && x225 = x237 && x224 = x236 && x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x219 = x231 && x218 = x230 && x217 = x229 && x216 = x228 l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l2(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x263 && x250 = x262 && x249 = x261 && x248 = x260 && x247 = x259 && x246 = x258 && x245 = x257 && x244 = x256 && x243 = x255 && x242 = x254 && x241 = x253 && x240 = x252 l5(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l4(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x275 = x287 && x274 = x286 && x273 = x285 && x272 = x284 && x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x267 = x279 && x266 = x278 && x265 = x277 && x264 = x276 l5(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x299 = x311 && x298 = x310 && x297 = x309 && x296 = x308 && x295 = x307 && x294 = x306 && x293 = x305 && x292 = x304 && x291 = x303 && x290 = x302 && x289 = x301 && x288 = x300 l6(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l5(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x323 = x335 && x322 = x334 && x321 = x333 && x320 = x332 && x319 = x331 && x318 = x330 && x317 = x329 && x316 = x328 && x315 = x327 && x314 = x326 && x313 = x325 && x312 = x324 Start term: l6(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) ---------------------------------------- (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, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost) :|: x3HATpost = oldX7HATpost && x2HATpost = oldX6HATpost && x1HATpost = oldX5HATpost && x0HATpost = oldX4HATpost && oldX7HATpost = oldX7HATpost && oldX6HATpost = oldX6HATpost && oldX5HATpost = oldX5HATpost && oldX4HATpost = oldX4HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l1(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x23 = x19 && x22 = x18 && x21 = x17 && x20 = x16 && x19 = x19 && x18 = x18 && x17 = x17 && x16 = x16 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8 l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l3(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x37 && x46 = x38 && x45 = x39 && x44 = -1 + x36 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32 l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x62 && x70 = x63 && x69 = x61 && x68 = -1 + x60 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56 l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l0(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x87 && x94 = x86 && x93 = x85 && x92 = x84 && 1 <= x84 && x84 <= 1 && x87 = x83 && x86 = x82 && x85 = x81 && x84 = x80 l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l0(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x100 = x112 && x119 = x111 && x118 = x110 && x117 = x109 && x116 = x108 && x108 <= 0 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104 l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 2 <= x132 && 1 <= x132 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128 l4(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l2(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x158 && x165 = x157 && x164 = x156 && 1 + x156 <= 1 && 1 <= x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152 l3(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176 l5(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x203 = x215 && x202 = x214 && x201 = x213 && x200 = x212 && x199 = x211 && x198 = x210 && x197 = x209 && x196 = x208 && x195 = x207 && x194 = x206 && x193 = x205 && x192 = x204 l5(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l0(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x239 && x226 = x238 && x225 = x237 && x224 = x236 && x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x219 = x231 && x218 = x230 && x217 = x229 && x216 = x228 l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l2(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x263 && x250 = x262 && x249 = x261 && x248 = x260 && x247 = x259 && x246 = x258 && x245 = x257 && x244 = x256 && x243 = x255 && x242 = x254 && x241 = x253 && x240 = x252 l5(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l4(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x275 = x287 && x274 = x286 && x273 = x285 && x272 = x284 && x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x267 = x279 && x266 = x278 && x265 = x277 && x264 = x276 l5(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x299 = x311 && x298 = x310 && x297 = x309 && x296 = x308 && x295 = x307 && x294 = x306 && x293 = x305 && x292 = x304 && x291 = x303 && x290 = x302 && x289 = x301 && x288 = x300 l6(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l5(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x323 = x335 && x322 = x334 && x321 = x333 && x320 = x332 && x319 = x331 && x318 = x330 && x317 = x329 && x316 = x328 && x315 = x327 && x314 = x326 && x313 = x325 && x312 = x324 Start term: l6(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost) :|: x3HATpost = oldX7HATpost && x2HATpost = oldX6HATpost && x1HATpost = oldX5HATpost && x0HATpost = oldX4HATpost && oldX7HATpost = oldX7HATpost && oldX6HATpost = oldX6HATpost && oldX5HATpost = oldX5HATpost && oldX4HATpost = oldX4HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l1(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x23 = x19 && x22 = x18 && x21 = x17 && x20 = x16 && x19 = x19 && x18 = x18 && x17 = x17 && x16 = x16 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8 (3) l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l3(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x37 && x46 = x38 && x45 = x39 && x44 = -1 + x36 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32 (4) l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x62 && x70 = x63 && x69 = x61 && x68 = -1 + x60 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56 (5) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l0(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x87 && x94 = x86 && x93 = x85 && x92 = x84 && 1 <= x84 && x84 <= 1 && x87 = x83 && x86 = x82 && x85 = x81 && x84 = x80 (6) l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l0(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x100 = x112 && x119 = x111 && x118 = x110 && x117 = x109 && x116 = x108 && x108 <= 0 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104 (7) l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 2 <= x132 && 1 <= x132 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128 (8) l4(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l2(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x158 && x165 = x157 && x164 = x156 && 1 + x156 <= 1 && 1 <= x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152 (9) l3(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176 (10) l5(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x203 = x215 && x202 = x214 && x201 = x213 && x200 = x212 && x199 = x211 && x198 = x210 && x197 = x209 && x196 = x208 && x195 = x207 && x194 = x206 && x193 = x205 && x192 = x204 (11) l5(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l0(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x239 && x226 = x238 && x225 = x237 && x224 = x236 && x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x219 = x231 && x218 = x230 && x217 = x229 && x216 = x228 (12) l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l2(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x263 && x250 = x262 && x249 = x261 && x248 = x260 && x247 = x259 && x246 = x258 && x245 = x257 && x244 = x256 && x243 = x255 && x242 = x254 && x241 = x253 && x240 = x252 (13) l5(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l4(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x275 = x287 && x274 = x286 && x273 = x285 && x272 = x284 && x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x267 = x279 && x266 = x278 && x265 = x277 && x264 = x276 (14) l5(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l3(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x299 = x311 && x298 = x310 && x297 = x309 && x296 = x308 && x295 = x307 && x294 = x306 && x293 = x305 && x292 = x304 && x291 = x303 && x290 = x302 && x289 = x301 && x288 = x300 (15) l6(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l5(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x323 = x335 && x322 = x334 && x321 = x333 && x320 = x332 && x319 = x331 && x318 = x330 && x317 = x329 && x316 = x328 && x315 = x327 && x314 = x326 && x313 = x325 && x312 = x324 Arcs: (3) -> (9) (4) -> (9) (5) -> (1) (6) -> (1) (7) -> (2), (3), (4) (9) -> (5), (6), (7) (11) -> (1) (12) -> (2), (3), (4) (13) -> (5), (6), (7) (14) -> (9) (15) -> (10), (11), (12), (13), (14) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l3(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x37 && x46 = x38 && x45 = x39 && x44 = -1 + x36 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32 (2) l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 2 <= x132 && 1 <= x132 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128 (3) l3(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176 (4) l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x62 && x70 = x63 && x69 = x61 && x68 = -1 + x60 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56 Arcs: (1) -> (3) (2) -> (1), (4) (3) -> (2) (4) -> (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l4(x120:0, x121:0, x122:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0, x129:0, x130:0, x131:0) -> l4(-1 + x128:0, x131:0, x130:0, x129:0, x124:0, x125:0, x126:0, x127:0, -1 + x128:0, x131:0, x130:0, x129:0) :|: x128:0 > 1 l4(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l4(-1 + x8, x9, x11, x10, x4, x5, x6, x7, -1 + x8, x9, x11, x10) :|: x8 > 1 ---------------------------------------- (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, x10, x11, x12) -> l4(x9) ---------------------------------------- (8) Obligation: Rules: l4(x128:0) -> l4(-1 + x128:0) :|: x128:0 > 1 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l4(x128:0) -> l4(c) :|: c = -1 + x128:0 && x128:0 > 1 ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l4(x)] = x The following rules are decreasing: l4(x128:0) -> l4(c) :|: c = -1 + x128:0 && x128:0 > 1 The following rules are bounded: l4(x128:0) -> l4(c) :|: c = -1 + x128:0 && x128:0 > 1 ---------------------------------------- (12) YES