MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 15.5 s] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 140 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 4995 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 130 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(KHAT0, NHAT0, nextHAT0, posHAT0, xxHAT0, yyHAT0, zHAT0) -> l1(KHATpost, NHATpost, nextHATpost, posHATpost, xxHATpost, yyHATpost, zHATpost) :|: zHAT0 = zHATpost && yyHAT0 = yyHATpost && xxHAT0 = xxHATpost && posHAT0 = posHATpost && nextHAT0 = nextHATpost && NHAT0 = NHATpost && KHATpost = -1 + KHAT0 l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x5 = x12 && x4 = x11 && x1 = x8 && x = x7 && x10 = 0 && 0 <= x13 && x13 = x13 && x9 = 1 + x2 && 3 <= x3 l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x16 = x23 && x15 = x22 && x14 = x21 && x24 = 1 + x17 && x19 <= 0 && x17 <= 2 l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && 2 <= x31 l4(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x44 = x51 && x43 = x50 && x42 = x49 && x52 = 1 + x45 && 1 <= x47 && x45 <= 1 l3(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x61 <= x60 && x60 <= x61 l3(x70, x71, x72, x73, x74, x75, x76) -> l0(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && 1 + x75 <= x74 l3(x84, x85, x86, x87, x88, x89, x90) -> l0(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 + x88 <= x89 l5(x98, x99, x100, x101, x102, x103, x104) -> l4(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 <= x101 l5(x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x114 = x121 && x113 = x120 && x112 = x119 && x122 = 1 + x115 && x117 <= 0 && x115 <= 0 l6(x126, x127, x128, x129, x130, x131, x132) -> l3(x133, x134, x135, x136, x137, x138, x139) :|: x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && x139 = -1 + x132 && 1 <= x132 l6(x140, x141, x142, x143, x144, x145, x146) -> l5(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x146 <= 0 l7(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x159 = x166 && x158 = x165 && x155 = x162 && x154 = x161 && x164 = 0 && 0 <= x167 && x167 = x167 && x163 = 1 + x156 && 3 <= x157 l7(x168, x169, x170, x171, x172, x173, x174) -> l8(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = 1 + x171 && x172 <= 0 && x171 <= 2 l9(x182, x183, x184, x185, x186, x187, x188) -> l7(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 2 <= x185 l9(x196, x197, x198, x199, x200, x201, x202) -> l8(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x198 = x205 && x197 = x204 && x196 = x203 && x206 = 1 + x199 && 1 <= x200 && x199 <= 1 l8(x210, x211, x212, x213, x214, x215, x216) -> l6(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x222 <= 1 && 0 <= x222 && x222 = x222 l1(x224, x225, x226, x227, x228, x229, x230) -> l10(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231 l11(x238, x239, x240, x241, x242, x243, x244) -> l9(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 1 <= x241 l11(x252, x253, x254, x255, x256, x257, x258) -> l8(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x254 = x261 && x253 = x260 && x252 = x259 && x262 = 1 + x255 && x256 <= 0 && x255 <= 0 l12(x266, x267, x268, x269, x270, x271, x272) -> l8(x273, x274, x275, x276, x277, x278, x279) :|: x271 = x278 && x270 = x277 && x269 = x276 && x268 = x275 && x267 = x274 && x266 = x273 && x279 = -1 + x272 && 1 <= x272 l12(x280, x281, x282, x283, x284, x285, x286) -> l11(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x286 <= 0 l10(x294, x295, x296, x297, x298, x299, x300) -> l13(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x296 = x303 && x295 = x302 && x294 = x301 && x294 <= 0 l10(x308, x309, x310, x311, x312, x313, x314) -> l12(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315 && x319 <= 1 && 0 <= x319 && x319 = x319 && 1 <= x308 l14(x322, x323, x324, x325, x326, x327, x328) -> l1(x329, x330, x331, x332, x333, x334, x335) :|: x334 = 0 && x333 = 0 && x329 = x330 && 1 <= x330 && x330 = x330 && x331 = 1 && x332 = 0 && 0 <= x335 && x335 = x335 l15(x336, x337, x338, x339, x340, x341, x342) -> l14(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x338 = x345 && x337 = x344 && x336 = x343 Start term: l15(KHAT0, NHAT0, nextHAT0, posHAT0, xxHAT0, yyHAT0, zHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(KHAT0, NHAT0, nextHAT0, posHAT0, xxHAT0, yyHAT0, zHAT0) -> l1(KHATpost, NHATpost, nextHATpost, posHATpost, xxHATpost, yyHATpost, zHATpost) :|: zHAT0 = zHATpost && yyHAT0 = yyHATpost && xxHAT0 = xxHATpost && posHAT0 = posHATpost && nextHAT0 = nextHATpost && NHAT0 = NHATpost && KHATpost = -1 + KHAT0 l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x5 = x12 && x4 = x11 && x1 = x8 && x = x7 && x10 = 0 && 0 <= x13 && x13 = x13 && x9 = 1 + x2 && 3 <= x3 l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x16 = x23 && x15 = x22 && x14 = x21 && x24 = 1 + x17 && x19 <= 0 && x17 <= 2 l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && 2 <= x31 l4(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x44 = x51 && x43 = x50 && x42 = x49 && x52 = 1 + x45 && 1 <= x47 && x45 <= 1 l3(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x61 <= x60 && x60 <= x61 l3(x70, x71, x72, x73, x74, x75, x76) -> l0(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && 1 + x75 <= x74 l3(x84, x85, x86, x87, x88, x89, x90) -> l0(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 + x88 <= x89 l5(x98, x99, x100, x101, x102, x103, x104) -> l4(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 <= x101 l5(x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x114 = x121 && x113 = x120 && x112 = x119 && x122 = 1 + x115 && x117 <= 0 && x115 <= 0 l6(x126, x127, x128, x129, x130, x131, x132) -> l3(x133, x134, x135, x136, x137, x138, x139) :|: x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && x139 = -1 + x132 && 1 <= x132 l6(x140, x141, x142, x143, x144, x145, x146) -> l5(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x146 <= 0 l7(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x159 = x166 && x158 = x165 && x155 = x162 && x154 = x161 && x164 = 0 && 0 <= x167 && x167 = x167 && x163 = 1 + x156 && 3 <= x157 l7(x168, x169, x170, x171, x172, x173, x174) -> l8(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = 1 + x171 && x172 <= 0 && x171 <= 2 l9(x182, x183, x184, x185, x186, x187, x188) -> l7(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 2 <= x185 l9(x196, x197, x198, x199, x200, x201, x202) -> l8(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x198 = x205 && x197 = x204 && x196 = x203 && x206 = 1 + x199 && 1 <= x200 && x199 <= 1 l8(x210, x211, x212, x213, x214, x215, x216) -> l6(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x222 <= 1 && 0 <= x222 && x222 = x222 l1(x224, x225, x226, x227, x228, x229, x230) -> l10(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231 l11(x238, x239, x240, x241, x242, x243, x244) -> l9(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 1 <= x241 l11(x252, x253, x254, x255, x256, x257, x258) -> l8(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x254 = x261 && x253 = x260 && x252 = x259 && x262 = 1 + x255 && x256 <= 0 && x255 <= 0 l12(x266, x267, x268, x269, x270, x271, x272) -> l8(x273, x274, x275, x276, x277, x278, x279) :|: x271 = x278 && x270 = x277 && x269 = x276 && x268 = x275 && x267 = x274 && x266 = x273 && x279 = -1 + x272 && 1 <= x272 l12(x280, x281, x282, x283, x284, x285, x286) -> l11(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x286 <= 0 l10(x294, x295, x296, x297, x298, x299, x300) -> l13(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x296 = x303 && x295 = x302 && x294 = x301 && x294 <= 0 l10(x308, x309, x310, x311, x312, x313, x314) -> l12(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315 && x319 <= 1 && 0 <= x319 && x319 = x319 && 1 <= x308 l14(x322, x323, x324, x325, x326, x327, x328) -> l1(x329, x330, x331, x332, x333, x334, x335) :|: x334 = 0 && x333 = 0 && x329 = x330 && 1 <= x330 && x330 = x330 && x331 = 1 && x332 = 0 && 0 <= x335 && x335 = x335 l15(x336, x337, x338, x339, x340, x341, x342) -> l14(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x338 = x345 && x337 = x344 && x336 = x343 Start term: l15(KHAT0, NHAT0, nextHAT0, posHAT0, xxHAT0, yyHAT0, zHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(KHAT0, NHAT0, nextHAT0, posHAT0, xxHAT0, yyHAT0, zHAT0) -> l1(KHATpost, NHATpost, nextHATpost, posHATpost, xxHATpost, yyHATpost, zHATpost) :|: zHAT0 = zHATpost && yyHAT0 = yyHATpost && xxHAT0 = xxHATpost && posHAT0 = posHATpost && nextHAT0 = nextHATpost && NHAT0 = NHATpost && KHATpost = -1 + KHAT0 (2) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x5 = x12 && x4 = x11 && x1 = x8 && x = x7 && x10 = 0 && 0 <= x13 && x13 = x13 && x9 = 1 + x2 && 3 <= x3 (3) l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x16 = x23 && x15 = x22 && x14 = x21 && x24 = 1 + x17 && x19 <= 0 && x17 <= 2 (4) l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && 2 <= x31 (5) l4(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x44 = x51 && x43 = x50 && x42 = x49 && x52 = 1 + x45 && 1 <= x47 && x45 <= 1 (6) l3(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x61 <= x60 && x60 <= x61 (7) l3(x70, x71, x72, x73, x74, x75, x76) -> l0(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && 1 + x75 <= x74 (8) l3(x84, x85, x86, x87, x88, x89, x90) -> l0(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 + x88 <= x89 (9) l5(x98, x99, x100, x101, x102, x103, x104) -> l4(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 <= x101 (10) l5(x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x114 = x121 && x113 = x120 && x112 = x119 && x122 = 1 + x115 && x117 <= 0 && x115 <= 0 (11) l6(x126, x127, x128, x129, x130, x131, x132) -> l3(x133, x134, x135, x136, x137, x138, x139) :|: x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && x139 = -1 + x132 && 1 <= x132 (12) l6(x140, x141, x142, x143, x144, x145, x146) -> l5(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x146 <= 0 (13) l7(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x159 = x166 && x158 = x165 && x155 = x162 && x154 = x161 && x164 = 0 && 0 <= x167 && x167 = x167 && x163 = 1 + x156 && 3 <= x157 (14) l7(x168, x169, x170, x171, x172, x173, x174) -> l8(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = 1 + x171 && x172 <= 0 && x171 <= 2 (15) l9(x182, x183, x184, x185, x186, x187, x188) -> l7(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 2 <= x185 (16) l9(x196, x197, x198, x199, x200, x201, x202) -> l8(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x198 = x205 && x197 = x204 && x196 = x203 && x206 = 1 + x199 && 1 <= x200 && x199 <= 1 (17) l8(x210, x211, x212, x213, x214, x215, x216) -> l6(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x222 <= 1 && 0 <= x222 && x222 = x222 (18) l1(x224, x225, x226, x227, x228, x229, x230) -> l10(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231 (19) l11(x238, x239, x240, x241, x242, x243, x244) -> l9(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 1 <= x241 (20) l11(x252, x253, x254, x255, x256, x257, x258) -> l8(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x254 = x261 && x253 = x260 && x252 = x259 && x262 = 1 + x255 && x256 <= 0 && x255 <= 0 (21) l12(x266, x267, x268, x269, x270, x271, x272) -> l8(x273, x274, x275, x276, x277, x278, x279) :|: x271 = x278 && x270 = x277 && x269 = x276 && x268 = x275 && x267 = x274 && x266 = x273 && x279 = -1 + x272 && 1 <= x272 (22) l12(x280, x281, x282, x283, x284, x285, x286) -> l11(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x286 <= 0 (23) l10(x294, x295, x296, x297, x298, x299, x300) -> l13(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x298 = x305 && x297 = x304 && x296 = x303 && x295 = x302 && x294 = x301 && x294 <= 0 (24) l10(x308, x309, x310, x311, x312, x313, x314) -> l12(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315 && x319 <= 1 && 0 <= x319 && x319 = x319 && 1 <= x308 (25) l14(x322, x323, x324, x325, x326, x327, x328) -> l1(x329, x330, x331, x332, x333, x334, x335) :|: x334 = 0 && x333 = 0 && x329 = x330 && 1 <= x330 && x330 = x330 && x331 = 1 && x332 = 0 && 0 <= x335 && x335 = x335 (26) l15(x336, x337, x338, x339, x340, x341, x342) -> l14(x343, x344, x345, x346, x347, x348, x349) :|: x342 = x349 && x341 = x348 && x340 = x347 && x339 = x346 && x338 = x345 && x337 = x344 && x336 = x343 Arcs: (1) -> (18) (2) -> (6), (7), (8) (3) -> (6), (7), (8) (4) -> (2), (3) (5) -> (6), (7), (8) (6) -> (18) (7) -> (1) (8) -> (1) (9) -> (4), (5) (10) -> (6), (7), (8) (11) -> (6), (7), (8) (12) -> (9), (10) (13) -> (17) (14) -> (17) (15) -> (13), (14) (16) -> (17) (17) -> (11), (12) (18) -> (23), (24) (19) -> (15), (16) (20) -> (17) (21) -> (17) (22) -> (19), (20) (24) -> (21), (22) (25) -> (18) (26) -> (25) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(KHAT0, NHAT0, nextHAT0, posHAT0, xxHAT0, yyHAT0, zHAT0) -> l1(KHATpost, NHATpost, nextHATpost, posHATpost, xxHATpost, yyHATpost, zHATpost) :|: zHAT0 = zHATpost && yyHAT0 = yyHATpost && xxHAT0 = xxHATpost && posHAT0 = posHATpost && nextHAT0 = nextHATpost && NHAT0 = NHATpost && KHATpost = -1 + KHAT0 (2) l3(x84, x85, x86, x87, x88, x89, x90) -> l0(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && 1 + x88 <= x89 (3) l3(x70, x71, x72, x73, x74, x75, x76) -> l0(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && 1 + x75 <= x74 (4) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x5 = x12 && x4 = x11 && x1 = x8 && x = x7 && x10 = 0 && 0 <= x13 && x13 = x13 && x9 = 1 + x2 && 3 <= x3 (5) l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x28 = x35 && 2 <= x31 (6) l5(x98, x99, x100, x101, x102, x103, x104) -> l4(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 <= x101 (7) l6(x140, x141, x142, x143, x144, x145, x146) -> l5(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x146 <= 0 (8) l8(x210, x211, x212, x213, x214, x215, x216) -> l6(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 && x222 <= 1 && 0 <= x222 && x222 = x222 (9) l12(x266, x267, x268, x269, x270, x271, x272) -> l8(x273, x274, x275, x276, x277, x278, x279) :|: x271 = x278 && x270 = x277 && x269 = x276 && x268 = x275 && x267 = x274 && x266 = x273 && x279 = -1 + x272 && 1 <= x272 (10) l11(x252, x253, x254, x255, x256, x257, x258) -> l8(x259, x260, x261, x262, x263, x264, x265) :|: x258 = x265 && x257 = x264 && x256 = x263 && x254 = x261 && x253 = x260 && x252 = x259 && x262 = 1 + x255 && x256 <= 0 && x255 <= 0 (11) l9(x196, x197, x198, x199, x200, x201, x202) -> l8(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x198 = x205 && x197 = x204 && x196 = x203 && x206 = 1 + x199 && 1 <= x200 && x199 <= 1 (12) l7(x168, x169, x170, x171, x172, x173, x174) -> l8(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = 1 + x171 && x172 <= 0 && x171 <= 2 (13) l7(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x159 = x166 && x158 = x165 && x155 = x162 && x154 = x161 && x164 = 0 && 0 <= x167 && x167 = x167 && x163 = 1 + x156 && 3 <= x157 (14) l9(x182, x183, x184, x185, x186, x187, x188) -> l7(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x187 = x194 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && 2 <= x185 (15) l11(x238, x239, x240, x241, x242, x243, x244) -> l9(x245, x246, x247, x248, x249, x250, x251) :|: x244 = x251 && x243 = x250 && x242 = x249 && x241 = x248 && x240 = x247 && x239 = x246 && x238 = x245 && 1 <= x241 (16) l12(x280, x281, x282, x283, x284, x285, x286) -> l11(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x293 && x285 = x292 && x284 = x291 && x283 = x290 && x282 = x289 && x281 = x288 && x280 = x287 && x286 <= 0 (17) l10(x308, x309, x310, x311, x312, x313, x314) -> l12(x315, x316, x317, x318, x319, x320, x321) :|: x314 = x321 && x313 = x320 && x311 = x318 && x310 = x317 && x309 = x316 && x308 = x315 && x319 <= 1 && 0 <= x319 && x319 = x319 && 1 <= x308 (18) l1(x224, x225, x226, x227, x228, x229, x230) -> l10(x231, x232, x233, x234, x235, x236, x237) :|: x230 = x237 && x229 = x236 && x228 = x235 && x227 = x234 && x226 = x233 && x225 = x232 && x224 = x231 (19) l3(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 && x61 <= x60 && x60 <= x61 (20) l6(x126, x127, x128, x129, x130, x131, x132) -> l3(x133, x134, x135, x136, x137, x138, x139) :|: x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && x139 = -1 + x132 && 1 <= x132 (21) l5(x112, x113, x114, x115, x116, x117, x118) -> l3(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x114 = x121 && x113 = x120 && x112 = x119 && x122 = 1 + x115 && x117 <= 0 && x115 <= 0 (22) l4(x42, x43, x44, x45, x46, x47, x48) -> l3(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x46 = x53 && x44 = x51 && x43 = x50 && x42 = x49 && x52 = 1 + x45 && 1 <= x47 && x45 <= 1 (23) l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x16 = x23 && x15 = x22 && x14 = x21 && x24 = 1 + x17 && x19 <= 0 && x17 <= 2 Arcs: (1) -> (18) (2) -> (1) (3) -> (1) (4) -> (2), (3), (19) (5) -> (4), (23) (6) -> (5), (22) (7) -> (6), (21) (8) -> (7), (20) (9) -> (8) (10) -> (8) (11) -> (8) (12) -> (8) (13) -> (8) (14) -> (12), (13) (15) -> (11), (14) (16) -> (10), (15) (17) -> (9), (16) (18) -> (17) (19) -> (18) (20) -> (2), (3), (19) (21) -> (2), (3), (19) (22) -> (2), (3), (19) (23) -> (2), (3), (19) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l10(x203:0, x204:0, x205:0, x248:0, x312:0, x208:0, x209:0) -> l8(x203:0, x204:0, x205:0, 1 + x248:0, x207:0, x208:0, x209:0) :|: x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2 l8(x105:0, x106:0, x107:0, x108:0, x109:0, x215:0, x111:0) -> l3(x105:0, x106:0, x107:0, 1 + x108:0, x109:0, x110:0, x111:0) :|: x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2 l8(x, x1, x2, x3, x4, x5, x6) -> l3(x, x1, x2, 1 + x3, x4, x7, x6) :|: x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1 l3(x84:0, NHATpost:0, nextHATpost:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(-1 + x84:0, NHATpost:0, nextHATpost:0, posHATpost:0, x235:0, x236:0, x237:0) :|: x236:0 >= 1 + x235:0 l8(x8, x9, x10, x11, x12, x13, x14) -> l3(x8, x9, x10, 1 + x11, x12, x15, x14) :|: x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2 l10(x16, x17, x18, x19, x20, x21, x22) -> l8(x16, x17, x18, x19, x23, x21, -1 + x22) :|: x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1 l3(x24, x25, x26, x27, x28, x29, x30) -> l10(-1 + x24, x25, x26, x27, x28, x29, x30) :|: x28 >= 1 + x29 l10(x31, x32, x33, x34, x35, x36, x37) -> l8(x31, x32, 1 + x33, 0, x38, x36, x39) :|: x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1 l10(x40, x41, x42, x43, x44, x45, x46) -> l8(x40, x41, x42, 1 + x43, x47, x45, x46) :|: x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1 l3(x48, x49, x50, x51, x52, x52, x53) -> l10(x48, x49, x50, x51, x52, x52, x53) :|: TRUE l10(x54, x55, x56, x57, x58, x59, x60) -> l8(x54, x55, x56, 1 + x57, x61, x59, x60) :|: x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1 l8(x62, x63, x64, x65, x66, x67, x68) -> l3(x62, x63, x64, x65, x66, x69, -1 + x68) :|: x69 > -1 && x69 < 2 && x68 > 0 l8(x70, x71, x72, x73, x74, x75, x76) -> l3(x70, x71, 1 + x72, 0, x74, x77, x78) :|: x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l10(x1, x2, x3, x4, x5, x6, x7) -> l10(x1, x4, x7) l8(x1, x2, x3, x4, x5, x6, x7) -> l8(x1, x4, x5, x7) l3(x1, x2, x3, x4, x5, x6, x7) -> l3(x1, x4, x5, x6, x7) ---------------------------------------- (8) Obligation: Rules: l10(x203:0, x248:0, x209:0) -> l8(x203:0, 1 + x248:0, x207:0, x209:0) :|: x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2 l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, 1 + x108:0, x109:0, x110:0, x111:0) :|: x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2 l8(x, x3, x4, x6) -> l3(x, 1 + x3, x4, x7, x6) :|: x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1 l3(x84:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(-1 + x84:0, posHATpost:0, x237:0) :|: x236:0 >= 1 + x235:0 l8(x8, x11, x12, x14) -> l3(x8, 1 + x11, x12, x15, x14) :|: x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2 l10(x16, x19, x22) -> l8(x16, x19, x23, -1 + x22) :|: x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1 l3(x24, x27, x28, x29, x30) -> l10(-1 + x24, x27, x30) :|: x28 >= 1 + x29 l10(x31, x34, x37) -> l8(x31, 0, x38, x39) :|: x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1 l10(x40, x43, x46) -> l8(x40, 1 + x43, x47, x46) :|: x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1 l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE l10(x54, x57, x60) -> l8(x54, 1 + x57, x61, x60) :|: x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1 l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, -1 + x68) :|: x69 > -1 && x69 < 2 && x68 > 0 l8(x70, x73, x74, x76) -> l3(x70, 0, x74, x77, x78) :|: x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l10(VARIABLE, VARIABLE, VARIABLE) l8(VARIABLE, VARIABLE, VARIABLE, INTEGER) l3(VARIABLE, 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: l10(x203:0, x248:0, x209:0) -> l8(x203:0, c, x207:0, x209:0) :|: c = 1 + x248:0 && (x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2) l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l3(x84:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(c3, posHATpost:0, x237:0) :|: c3 = -1 + x84:0 && x236:0 >= 1 + x235:0 l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l10(x16, x19, x22) -> l8(x16, x19, x23, c5) :|: c5 = -1 + x22 && (x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1) l3(x24, x27, x28, x29, x30) -> l10(c6, x27, x30) :|: c6 = -1 + x24 && x28 >= 1 + x29 l10(x31, x34, x37) -> l8(x31, c7, x38, x39) :|: c7 = 0 && (x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1) l10(x40, x43, x46) -> l8(x40, c8, x47, x46) :|: c8 = 1 + x43 && (x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1) l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE l10(x54, x57, x60) -> l8(x54, c9, x61, x60) :|: c9 = 1 + x57 && (x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) Found the following polynomial interpretation: [l10(x, x1, x2)] = -1 + x [l8(x3, x4, x5, x6)] = -1 + x3 [l3(x7, x8, x9, x10, x11)] = -1 + x7 The following rules are decreasing: l3(x84:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(c3, posHATpost:0, x237:0) :|: c3 = -1 + x84:0 && x236:0 >= 1 + x235:0 l3(x24, x27, x28, x29, x30) -> l10(c6, x27, x30) :|: c6 = -1 + x24 && x28 >= 1 + x29 The following rules are bounded: l10(x203:0, x248:0, x209:0) -> l8(x203:0, c, x207:0, x209:0) :|: c = 1 + x248:0 && (x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2) l10(x16, x19, x22) -> l8(x16, x19, x23, c5) :|: c5 = -1 + x22 && (x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1) l10(x31, x34, x37) -> l8(x31, c7, x38, x39) :|: c7 = 0 && (x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1) l10(x40, x43, x46) -> l8(x40, c8, x47, x46) :|: c8 = 1 + x43 && (x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1) l10(x54, x57, x60) -> l8(x54, c9, x61, x60) :|: c9 = 1 + x57 && (x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS Rules: l10(x203:0, x248:0, x209:0) -> l8(x203:0, c, x207:0, x209:0) :|: c = 1 + x248:0 && (x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2) l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l10(x16, x19, x22) -> l8(x16, x19, x23, c5) :|: c5 = -1 + x22 && (x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1) l10(x31, x34, x37) -> l8(x31, c7, x38, x39) :|: c7 = 0 && (x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1) l10(x40, x43, x46) -> l8(x40, c8, x47, x46) :|: c8 = 1 + x43 && (x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1) l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE l10(x54, x57, x60) -> l8(x54, c9, x61, x60) :|: c9 = 1 + x57 && (x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l3(x84:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(c3, posHATpost:0, x237:0) :|: c3 = -1 + x84:0 && x236:0 >= 1 + x235:0 l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l3(x24, x27, x28, x29, x30) -> l10(c6, x27, x30) :|: c6 = -1 + x24 && x28 >= 1 + x29 l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) Found the following polynomial interpretation: [l8(x, x1, x2, x3)] = 1 [l3(x4, x5, x6, x7, x8)] = 1 [l10(x9, x10, x11)] = 0 The following rules are decreasing: l3(x84:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(c3, posHATpost:0, x237:0) :|: c3 = -1 + x84:0 && x236:0 >= 1 + x235:0 l3(x24, x27, x28, x29, x30) -> l10(c6, x27, x30) :|: c6 = -1 + x24 && x28 >= 1 + x29 l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE The following rules are bounded: l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l3(x84:0, posHATpost:0, x235:0, x236:0, x237:0) -> l10(c3, posHATpost:0, x237:0) :|: c3 = -1 + x84:0 && x236:0 >= 1 + x235:0 l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l3(x24, x27, x28, x29, x30) -> l10(c6, x27, x30) :|: c6 = -1 + x24 && x28 >= 1 + x29 l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) Found the following polynomial interpretation: [l8(x, x1, x2, x3)] = 0 [l3(x4, x5, x6, x7, x8)] = -x7 The following rules are decreasing: l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) The following rules are bounded: l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, c1, x109:0, x110:0, x111:0) :|: c1 = 1 + x108:0 && (x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2) l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof Rules: l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) Interpretation: [ l8 ] = 1 [ l3 ] = 0 The following rules are decreasing: l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) The following rules are bounded: l8(x, x3, x4, x6) -> l3(x, c2, x4, x7, x6) :|: c2 = 1 + x3 && (x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1) l8(x8, x11, x12, x14) -> l3(x8, c4, x12, x15, x14) :|: c4 = 1 + x11 && (x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, c10) :|: c10 = -1 + x68 && (x69 > -1 && x69 < 2 && x68 > 0) l8(x70, x73, x74, x76) -> l3(x70, c11, x74, x77, x78) :|: c11 = 0 && (x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1) ---------------------------------------- (10) Obligation: Rules: l10(x203:0, x248:0, x209:0) -> l8(x203:0, 1 + x248:0, x207:0, x209:0) :|: x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2 l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, 1 + x108:0, x109:0, x110:0, x111:0) :|: x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2 l8(x, x3, x4, x6) -> l3(x, 1 + x3, x4, x7, x6) :|: x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1 l8(x8, x11, x12, x14) -> l3(x8, 1 + x11, x12, x15, x14) :|: x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2 l10(x16, x19, x22) -> l8(x16, x19, x23, -1 + x22) :|: x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1 l10(x31, x34, x37) -> l8(x31, 0, x38, x39) :|: x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1 l10(x40, x43, x46) -> l8(x40, 1 + x43, x47, x46) :|: x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1 l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE l10(x54, x57, x60) -> l8(x54, 1 + x57, x61, x60) :|: x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1 l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, -1 + x68) :|: x69 > -1 && x69 < 2 && x68 > 0 l8(x70, x73, x74, x76) -> l3(x70, 0, x74, x77, x78) :|: x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l10(x203:0, x248:0, x209:0) -> l8(x203:0, 1 + x248:0, x207:0, x209:0) :|: x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2 (2) l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, 1 + x108:0, x109:0, x110:0, x111:0) :|: x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2 (3) l8(x, x3, x4, x6) -> l3(x, 1 + x3, x4, x7, x6) :|: x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1 (4) l8(x8, x11, x12, x14) -> l3(x8, 1 + x11, x12, x15, x14) :|: x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2 (5) l10(x16, x19, x22) -> l8(x16, x19, x23, -1 + x22) :|: x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1 (6) l10(x31, x34, x37) -> l8(x31, 0, x38, x39) :|: x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1 (7) l10(x40, x43, x46) -> l8(x40, 1 + x43, x47, x46) :|: x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1 (8) l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE (9) l10(x54, x57, x60) -> l8(x54, 1 + x57, x61, x60) :|: x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1 (10) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, -1 + x68) :|: x69 > -1 && x69 < 2 && x68 > 0 (11) l8(x70, x73, x74, x76) -> l3(x70, 0, x74, x77, x78) :|: x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1 Arcs: (1) -> (3) (2) -> (8) (3) -> (8) (4) -> (8) (5) -> (2), (3), (4), (10), (11) (6) -> (4), (10) (7) -> (11) (8) -> (1), (5), (6), (7), (9) (9) -> (2), (4) (10) -> (8) (11) -> (8) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l10(x203:0, x248:0, x209:0) -> l8(x203:0, 1 + x248:0, x207:0, x209:0) :|: x209:0 < 1 && x203:0 > 0 && x248:0 > 0 && x248:0 < 2 && x207:0 > 0 && x207:0 < 2 (2) l3(x48, x51, x52, x52, x53) -> l10(x48, x51, x53) :|: TRUE (3) l8(x70, x73, x74, x76) -> l3(x70, 0, x74, x77, x78) :|: x76 < 1 && x77 > -1 && x77 < 2 && x73 > 2 && x78 > -1 (4) l10(x40, x43, x46) -> l8(x40, 1 + x43, x47, x46) :|: x46 < 1 && x40 > 0 && x47 > -1 && x47 < 2 && x43 < 3 && x43 > 1 && x47 < 1 (5) l8(x62, x65, x66, x68) -> l3(x62, x65, x66, x69, -1 + x68) :|: x69 > -1 && x69 < 2 && x68 > 0 (6) l8(x8, x11, x12, x14) -> l3(x8, 1 + x11, x12, x15, x14) :|: x14 < 1 && x15 > -1 && x11 < 1 && x15 < 1 && x15 < 2 (7) l10(x31, x34, x37) -> l8(x31, 0, x38, x39) :|: x37 < 1 && x31 > 0 && x38 > -1 && x38 < 2 && x34 > 2 && x39 > -1 (8) l8(x, x3, x4, x6) -> l3(x, 1 + x3, x4, x7, x6) :|: x6 < 1 && x7 > -1 && x7 < 2 && x3 < 3 && x3 > 1 && x7 < 1 (9) l8(x105:0, x108:0, x109:0, x111:0) -> l3(x105:0, 1 + x108:0, x109:0, x110:0, x111:0) :|: x110:0 < 2 && x111:0 < 1 && x108:0 > 0 && x110:0 > 0 && x108:0 < 2 (10) l10(x54, x57, x60) -> l8(x54, 1 + x57, x61, x60) :|: x60 < 1 && x54 > 0 && x57 < 1 && x61 > -1 && x61 < 2 && x61 < 1 (11) l10(x16, x19, x22) -> l8(x16, x19, x23, -1 + x22) :|: x22 > 0 && x16 > 0 && x23 < 2 && x23 > -1 Arcs: (1) -> (8) (2) -> (1), (4), (7), (10), (11) (3) -> (2) (4) -> (3) (5) -> (2) (6) -> (2) (7) -> (5), (6) (8) -> (2) (9) -> (2) (10) -> (6), (9) (11) -> (3), (5), (6), (8), (9) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l3(x48:0, x51:0, x52:0, x52:0, x53:0) -> l8(x48:0, 1 + x51:0, x207:0:0, x53:0) :|: x207:0:0 > 0 && x207:0:0 < 2 && x51:0 < 2 && x51:0 > 0 && x48:0 > 0 && x53:0 < 1 l3(x, x1, x2, x2, x3) -> l8(x, 1 + x1, x4, x3) :|: x1 > 1 && x4 < 1 && x1 < 3 && x4 < 2 && x4 > -1 && x > 0 && x3 < 1 l3(x5, x6, x7, x7, x8) -> l8(x5, 1 + x6, x9, x8) :|: x9 < 2 && x9 < 1 && x9 > -1 && x6 < 1 && x5 > 0 && x8 < 1 l8(x8:0, x11:0, x12:0, x14:0) -> l3(x8:0, 1 + x11:0, x12:0, x15:0, x14:0) :|: x15:0 < 1 && x15:0 < 2 && x11:0 < 1 && x15:0 > -1 && x14:0 < 1 l3(x10, x11, x12, x12, x13) -> l8(x10, 0, x14, x15) :|: x11 > 2 && x15 > -1 && x14 < 2 && x14 > -1 && x10 > 0 && x13 < 1 l8(x70:0, x73:0, x74:0, x76:0) -> l3(x70:0, 0, x74:0, x77:0, x78:0) :|: x73:0 > 2 && x78:0 > -1 && x77:0 < 2 && x77:0 > -1 && x76:0 < 1 l8(x:0, x3:0, x4:0, x6:0) -> l3(x:0, 1 + x3:0, x4:0, x7:0, x6:0) :|: x3:0 > 1 && x7:0 < 1 && x3:0 < 3 && x7:0 < 2 && x7:0 > -1 && x6:0 < 1 l8(x105:0:0, x108:0:0, x109:0:0, x111:0:0) -> l3(x105:0:0, 1 + x108:0:0, x109:0:0, x110:0:0, x111:0:0) :|: x110:0:0 > 0 && x108:0:0 < 2 && x108:0:0 > 0 && x111:0:0 < 1 && x110:0:0 < 2 l3(x16, x17, x18, x18, x19) -> l8(x16, x17, x20, -1 + x19) :|: x20 < 2 && x20 > -1 && x16 > 0 && x19 > 0 l8(x62:0, x65:0, x66:0, x68:0) -> l3(x62:0, x65:0, x66:0, x69:0, -1 + x68:0) :|: x69:0 > -1 && x69:0 < 2 && x68:0 > 0