MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 8012 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 57 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 194 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (16) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_8HAT0 = tmp_8HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && 0 <= x12 && x12 <= 0 && x12 = x12 && 0 <= -1 - x6 + x7 l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x28 = x28 && 0 <= -1 - x22 + x23 l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x41 = x33 l6(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x62 = 1 + x54 l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l2(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 l2(x80, x81, x82, x83, x84, x85, x86, x87) -> l1(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88 && x93 = 1 + x85 && -1 * x86 + x87 <= 0 l1(x96, x97, x98, x99, x100, x101, x102, x103) -> l7(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && 0 <= -1 - x101 + x102 l1(x112, x113, x114, x115, x116, x117, x118, x119) -> l8(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x120 = x120 && -1 * x117 + x118 <= 0 l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l3(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 && 0 <= x140 && x140 <= 0 && x140 = x140 && 0 <= -1 - x134 + x135 l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l9(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x156 = x156 && 0 <= -1 - x150 + x151 l9(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x170 = x162 l10(x176, x177, x178, x179, x180, x181, x182, x183) -> l2(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 && x190 = 1 + x182 l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l1(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 && x205 = 1 + x197 && -1 * x198 + x199 <= 0 l3(x208, x209, x210, x211, x212, x213, x214, x215) -> l11(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 && 0 <= x220 && x220 <= 0 && x220 = x220 && 0 <= -1 - x214 + x215 l11(x224, x225, x226, x227, x228, x229, x230, x231) -> l3(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l3(x240, x241, x242, x243, x244, x245, x246, x247) -> l12(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 && x252 = x252 && 0 <= -1 - x246 + x247 l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && x267 = x259 l13(x272, x273, x274, x275, x276, x277, x278, x279) -> l2(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && x286 = 1 + x278 l14(x288, x289, x290, x291, x292, x293, x294, x295) -> l0(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 Start term: l14(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_8HAT0 = tmp_8HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && 0 <= x12 && x12 <= 0 && x12 = x12 && 0 <= -1 - x6 + x7 l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x28 = x28 && 0 <= -1 - x22 + x23 l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x41 = x33 l6(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x62 = 1 + x54 l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l2(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 l2(x80, x81, x82, x83, x84, x85, x86, x87) -> l1(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88 && x93 = 1 + x85 && -1 * x86 + x87 <= 0 l1(x96, x97, x98, x99, x100, x101, x102, x103) -> l7(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && 0 <= -1 - x101 + x102 l1(x112, x113, x114, x115, x116, x117, x118, x119) -> l8(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x120 = x120 && -1 * x117 + x118 <= 0 l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l3(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 && 0 <= x140 && x140 <= 0 && x140 = x140 && 0 <= -1 - x134 + x135 l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l9(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x156 = x156 && 0 <= -1 - x150 + x151 l9(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x170 = x162 l10(x176, x177, x178, x179, x180, x181, x182, x183) -> l2(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 && x190 = 1 + x182 l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l1(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 && x205 = 1 + x197 && -1 * x198 + x199 <= 0 l3(x208, x209, x210, x211, x212, x213, x214, x215) -> l11(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 && 0 <= x220 && x220 <= 0 && x220 = x220 && 0 <= -1 - x214 + x215 l11(x224, x225, x226, x227, x228, x229, x230, x231) -> l3(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l3(x240, x241, x242, x243, x244, x245, x246, x247) -> l12(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 && x252 = x252 && 0 <= -1 - x246 + x247 l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && x267 = x259 l13(x272, x273, x274, x275, x276, x277, x278, x279) -> l2(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && x286 = 1 + x278 l14(x288, x289, x290, x291, x292, x293, x294, x295) -> l0(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 Start term: l14(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_8HAT0 = tmp_8HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost (2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && 0 <= x12 && x12 <= 0 && x12 = x12 && 0 <= -1 - x6 + x7 (3) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x28 = x28 && 0 <= -1 - x22 + x23 (4) l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x41 = x33 (5) l6(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x62 = 1 + x54 (6) l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l2(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 (7) l2(x80, x81, x82, x83, x84, x85, x86, x87) -> l1(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88 && x93 = 1 + x85 && -1 * x86 + x87 <= 0 (8) l1(x96, x97, x98, x99, x100, x101, x102, x103) -> l7(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && 0 <= -1 - x101 + x102 (9) l1(x112, x113, x114, x115, x116, x117, x118, x119) -> l8(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x115 = x123 && x114 = x122 && x113 = x121 && x120 = x120 && -1 * x117 + x118 <= 0 (10) l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l3(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 && 0 <= x140 && x140 <= 0 && x140 = x140 && 0 <= -1 - x134 + x135 (11) l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l9(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x156 = x156 && 0 <= -1 - x150 + x151 (12) l9(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x170 = x162 (13) l10(x176, x177, x178, x179, x180, x181, x182, x183) -> l2(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 && x190 = 1 + x182 (14) l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l1(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 && x205 = 1 + x197 && -1 * x198 + x199 <= 0 (15) l3(x208, x209, x210, x211, x212, x213, x214, x215) -> l11(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 && 0 <= x220 && x220 <= 0 && x220 = x220 && 0 <= -1 - x214 + x215 (16) l11(x224, x225, x226, x227, x228, x229, x230, x231) -> l3(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 (17) l3(x240, x241, x242, x243, x244, x245, x246, x247) -> l12(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 && x252 = x252 && 0 <= -1 - x246 + x247 (18) l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && x267 = x259 (19) l13(x272, x273, x274, x275, x276, x277, x278, x279) -> l2(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && x286 = 1 + x278 (20) l14(x288, x289, x290, x291, x292, x293, x294, x295) -> l0(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 Arcs: (1) -> (8), (9) (2) -> (15), (17) (3) -> (4) (4) -> (5) (5) -> (6) (6) -> (2), (3), (7) (7) -> (8), (9) (8) -> (10), (11), (14) (10) -> (15), (17) (11) -> (12) (12) -> (13) (13) -> (2), (3), (7) (14) -> (8), (9) (15) -> (16) (16) -> (15), (17) (17) -> (18) (18) -> (19) (19) -> (2), (3), (7) (20) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x96, x97, x98, x99, x100, x101, x102, x103) -> l7(x104, x105, x106, x107, x108, x109, x110, x111) :|: x103 = x111 && x102 = x110 && x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && 0 <= -1 - x101 + x102 (2) l7(x192, x193, x194, x195, x196, x197, x198, x199) -> l1(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x196 = x204 && x195 = x203 && x194 = x202 && x193 = x201 && x192 = x200 && x205 = 1 + x197 && -1 * x198 + x199 <= 0 (3) l2(x80, x81, x82, x83, x84, x85, x86, x87) -> l1(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x84 = x92 && x83 = x91 && x82 = x90 && x81 = x89 && x80 = x88 && x93 = 1 + x85 && -1 * x86 + x87 <= 0 (4) l4(x64, x65, x66, x67, x68, x69, x70, x71) -> l2(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 (5) l6(x48, x49, x50, x51, x52, x53, x54, x55) -> l4(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 && x62 = 1 + x54 (6) l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x34 = x42 && x33 = x41 && x32 = x40 && x41 = x33 (7) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l5(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x19 = x27 && x18 = x26 && x17 = x25 && x16 = x24 && x28 = x28 && 0 <= -1 - x22 + x23 (8) l13(x272, x273, x274, x275, x276, x277, x278, x279) -> l2(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && x286 = 1 + x278 (9) l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && x267 = x259 (10) l3(x240, x241, x242, x243, x244, x245, x246, x247) -> l12(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 && x252 = x252 && 0 <= -1 - x246 + x247 (11) l11(x224, x225, x226, x227, x228, x229, x230, x231) -> l3(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 (12) l3(x208, x209, x210, x211, x212, x213, x214, x215) -> l11(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 && 0 <= x220 && x220 <= 0 && x220 = x220 && 0 <= -1 - x214 + x215 (13) l7(x128, x129, x130, x131, x132, x133, x134, x135) -> l3(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 && 0 <= x140 && x140 <= 0 && x140 = x140 && 0 <= -1 - x134 + x135 (14) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && 0 <= x12 && x12 <= 0 && x12 = x12 && 0 <= -1 - x6 + x7 (15) l10(x176, x177, x178, x179, x180, x181, x182, x183) -> l2(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x181 = x189 && x180 = x188 && x179 = x187 && x178 = x186 && x177 = x185 && x176 = x184 && x190 = 1 + x182 (16) l9(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x167 = x175 && x166 = x174 && x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x170 = x162 (17) l7(x144, x145, x146, x147, x148, x149, x150, x151) -> l9(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x147 = x155 && x146 = x154 && x145 = x153 && x144 = x152 && x156 = x156 && 0 <= -1 - x150 + x151 Arcs: (1) -> (2), (13), (17) (2) -> (1) (3) -> (1) (4) -> (3), (7), (14) (5) -> (4) (6) -> (5) (7) -> (6) (8) -> (3), (7), (14) (9) -> (8) (10) -> (9) (11) -> (10), (12) (12) -> (11) (13) -> (10), (12) (14) -> (10), (12) (15) -> (3), (7), (14) (16) -> (15) (17) -> (16) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x104:0, x105:0, x106:0, x107:0, x100:0, x101:0, x102:0, x103:0) -> l3(x104:0, x105:0, x106:0, x107:0, x140:0, x101:0, x102:0, x103:0) :|: 0 <= -1 - x102:0 + x103:0 && 0 <= -1 - x101:0 + x102:0 && x140:0 > -1 && x140:0 < 1 l1(x, x1, x2, x3, x4, x5, x6, x7) -> l2(x, x1, x2, x3, x8, x5, 1 + x6, x7) :|: 0 <= -1 - x5 + x6 && 0 <= -1 - x6 + x7 l1(x9, x10, x11, x12, x13, x14, x15, x16) -> l1(x9, x10, x11, x12, x13, 1 + x14, x15, x16) :|: 0 <= -1 - x14 + x15 && 0 >= -1 * x15 + x16 l3(x208:0, x209:0, x210:0, x211:0, x212:0, x213:0, x214:0, x215:0) -> l3(x208:0, x209:0, x210:0, x211:0, x220:0, x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 l2(x16:0, x17:0, x18:0, x19:0, x20:0, x21:0, x22:0, x23:0) -> l2(x16:0, x17:0, x18:0, x19:0, x28:0, x21:0, 1 + x22:0, x23:0) :|: 0 <= -1 - x22:0 + x23:0 l2(x80:0, x81:0, x82:0, x83:0, x84:0, x85:0, x86:0, x87:0) -> l1(x80:0, x81:0, x82:0, x83:0, x84:0, 1 + x85:0, x86:0, x87:0) :|: 0 >= -1 * x86:0 + x87:0 l2(x8:0, x1:0, x10:0, x11:0, x4:0, x13:0, x14:0, x15:0) -> l3(x8:0, x1:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x240:0, x241:0, x242:0, x243:0, x244:0, x245:0, x246:0, x247:0) -> l2(x240:0, x241:0, x242:0, x243:0, x252:0, x245:0, 1 + x246:0, x247:0) :|: 0 <= -1 - x246:0 + x247:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x6, x7, x8) l3(x1, x2, x3, x4, x5, x6, x7, x8) -> l3(x6, x7, x8) l2(x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x6, x7, x8) ---------------------------------------- (8) Obligation: Rules: l1(x101:0, x102:0, x103:0) -> l3(x101:0, x102:0, x103:0) :|: 0 <= -1 - x102:0 + x103:0 && 0 <= -1 - x101:0 + x102:0 && x140:0 > -1 && x140:0 < 1 l1(x5, x6, x7) -> l2(x5, 1 + x6, x7) :|: 0 <= -1 - x5 + x6 && 0 <= -1 - x6 + x7 l1(x14, x15, x16) -> l1(1 + x14, x15, x16) :|: 0 <= -1 - x14 + x15 && 0 >= -1 * x15 + x16 l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 l2(x21:0, x22:0, x23:0) -> l2(x21:0, 1 + x22:0, x23:0) :|: 0 <= -1 - x22:0 + x23:0 l2(x85:0, x86:0, x87:0) -> l1(1 + x85:0, x86:0, x87:0) :|: 0 >= -1 * x86:0 + x87:0 l2(x13:0, x14:0, x15:0) -> l3(x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x245:0, x246:0, x247:0) -> l2(x245:0, 1 + x246:0, x247:0) :|: 0 <= -1 - x246:0 + x247:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(INTEGER, INTEGER, INTEGER) l3(VARIABLE, INTEGER, INTEGER) l2(VARIABLE, INTEGER, INTEGER) 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: l1(x101:0, x102:0, x103:0) -> l3(x101:0, x102:0, x103:0) :|: 0 <= -1 - x102:0 + x103:0 && 0 <= -1 - x101:0 + x102:0 && x140:0 > -1 && x140:0 < 1 l1(x5, x6, x7) -> l2(x5, c, x7) :|: c = 1 + x6 && (0 <= -1 - x5 + x6 && 0 <= -1 - x6 + x7) l1(x14, x15, x16) -> l1(c1, x15, x16) :|: c1 = 1 + x14 && (0 <= -1 - x14 + x15 && 0 >= -1 * x15 + x16) l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 l2(x21:0, x22:0, x23:0) -> l2(x21:0, c2, x23:0) :|: c2 = 1 + x22:0 && 0 <= -1 - x22:0 + x23:0 l2(x85:0, x86:0, x87:0) -> l1(c3, x86:0, x87:0) :|: c3 = 1 + x85:0 && 0 >= -1 * x86:0 + x87:0 l2(x13:0, x14:0, x15:0) -> l3(x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x245:0, x246:0, x247:0) -> l2(x245:0, c4, x247:0) :|: c4 = 1 + x246:0 && 0 <= -1 - x246:0 + x247:0 Interpretation: [ l1 ] = -2*l1_2 + 2*l1_3 + -1 [ l3 ] = 0 [ l2 ] = 0 The following rules are decreasing: l1(x101:0, x102:0, x103:0) -> l3(x101:0, x102:0, x103:0) :|: 0 <= -1 - x102:0 + x103:0 && 0 <= -1 - x101:0 + x102:0 && x140:0 > -1 && x140:0 < 1 l1(x5, x6, x7) -> l2(x5, c, x7) :|: c = 1 + x6 && (0 <= -1 - x5 + x6 && 0 <= -1 - x6 + x7) l2(x85:0, x86:0, x87:0) -> l1(c3, x86:0, x87:0) :|: c3 = 1 + x85:0 && 0 >= -1 * x86:0 + x87:0 The following rules are bounded: l1(x101:0, x102:0, x103:0) -> l3(x101:0, x102:0, x103:0) :|: 0 <= -1 - x102:0 + x103:0 && 0 <= -1 - x101:0 + x102:0 && x140:0 > -1 && x140:0 < 1 l1(x5, x6, x7) -> l2(x5, c, x7) :|: c = 1 + x6 && (0 <= -1 - x5 + x6 && 0 <= -1 - x6 + x7) l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 l2(x85:0, x86:0, x87:0) -> l1(c3, x86:0, x87:0) :|: c3 = 1 + x85:0 && 0 >= -1 * x86:0 + x87:0 l2(x13:0, x14:0, x15:0) -> l3(x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x245:0, x246:0, x247:0) -> l2(x245:0, c4, x247:0) :|: c4 = 1 + x246:0 && 0 <= -1 - x246:0 + x247:0 - IntTRS - RankingReductionPairProof - IntTRS - RankingReductionPairProof Rules: l1(x14, x15, x16) -> l1(c1, x15, x16) :|: c1 = 1 + x14 && (0 <= -1 - x14 + x15 && 0 >= -1 * x15 + x16) l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 l2(x21:0, x22:0, x23:0) -> l2(x21:0, c2, x23:0) :|: c2 = 1 + x22:0 && 0 <= -1 - x22:0 + x23:0 l2(x13:0, x14:0, x15:0) -> l3(x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x245:0, x246:0, x247:0) -> l2(x245:0, c4, x247:0) :|: c4 = 1 + x246:0 && 0 <= -1 - x246:0 + x247:0 Interpretation: [ l1 ] = -1*l1_1 + l1_2 [ l3 ] = -2*l3_2 + 2*l3_3 [ l2 ] = -2*l2_2 + 2*l2_3 + 1 The following rules are decreasing: l1(x14, x15, x16) -> l1(c1, x15, x16) :|: c1 = 1 + x14 && (0 <= -1 - x14 + x15 && 0 >= -1 * x15 + x16) l2(x21:0, x22:0, x23:0) -> l2(x21:0, c2, x23:0) :|: c2 = 1 + x22:0 && 0 <= -1 - x22:0 + x23:0 l2(x13:0, x14:0, x15:0) -> l3(x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x245:0, x246:0, x247:0) -> l2(x245:0, c4, x247:0) :|: c4 = 1 + x246:0 && 0 <= -1 - x246:0 + x247:0 The following rules are bounded: l1(x14, x15, x16) -> l1(c1, x15, x16) :|: c1 = 1 + x14 && (0 <= -1 - x14 + x15 && 0 >= -1 * x15 + x16) l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 l2(x21:0, x22:0, x23:0) -> l2(x21:0, c2, x23:0) :|: c2 = 1 + x22:0 && 0 <= -1 - x22:0 + x23:0 l2(x13:0, x14:0, x15:0) -> l3(x13:0, x14:0, x15:0) :|: x12:0 < 1 && x12:0 > -1 && 0 <= -1 - x14:0 + x15:0 l3(x245:0, x246:0, x247:0) -> l2(x245:0, c4, x247:0) :|: c4 = 1 + x246:0 && 0 <= -1 - x246:0 + x247:0 - IntTRS - RankingReductionPairProof - IntTRS - RankingReductionPairProof - IntTRS Rules: l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 ---------------------------------------- (10) Obligation: Rules: l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l3(x213:0, x214:0, x215:0) -> l3(x213:0, x214:0, x215:0) :|: x220:0 < 1 && x220:0 > -1 && 0 <= -1 - x214:0 + x215:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l3(x213:0:0, x214:0:0, x215:0:0) -> l3(x213:0:0, x214:0:0, x215:0:0) :|: x220:0:0 < 1 && x220:0:0 > -1 && 0 <= -1 - x214:0:0 + x215:0:0 ---------------------------------------- (15) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3) -> l3(x2, x3) ---------------------------------------- (16) Obligation: Rules: l3(x214:0:0, x215:0:0) -> l3(x214:0:0, x215:0:0) :|: x220:0:0 < 1 && x220:0:0 > -1 && 0 <= -1 - x214:0:0 + x215:0:0