YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 4087 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 104 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 105 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 27 ms] (12) IntTRS (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (14) IntTRS (15) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Rules: l0(__const_10HAT0, __const_285HAT0, __const_35HAT0, acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(__const_10HATpost, __const_285HATpost, __const_35HATpost, acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost && __const_35HAT0 = __const_35HATpost && __const_285HAT0 = __const_285HATpost && __const_10HAT0 = __const_10HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l0(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x6 <= x4 l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x37 = 1 + x26 && 1 + x26 <= x28 l1(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x62 = 1 + x51 l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = -1 + x92 l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x136 <= x141 l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x156 = x167 && x155 = x166 && x154 = x165 && x174 = 1 + x163 && x168 = x168 && 1 + x163 <= x158 l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l8(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 && x206 <= x205 l5(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x222 = x233 && x221 = x232 && x220 = x231 && x240 = 1 && x234 = x234 && 1 + x227 <= x228 l9(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 && x260 = 0 && x257 = x258 && x258 = x258 && x263 = x243 && x259 = x244 && x261 = x242 l10(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 Start term: l10(__const_10HAT0, __const_285HAT0, __const_35HAT0, acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__const_10HAT0, __const_285HAT0, __const_35HAT0, acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(__const_10HATpost, __const_285HATpost, __const_35HATpost, acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost && __const_35HAT0 = __const_35HATpost && __const_285HAT0 = __const_285HATpost && __const_10HAT0 = __const_10HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l0(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x6 <= x4 l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x37 = 1 + x26 && 1 + x26 <= x28 l1(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x62 = 1 + x51 l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = -1 + x92 l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x136 <= x141 l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x156 = x167 && x155 = x166 && x154 = x165 && x174 = 1 + x163 && x168 = x168 && 1 + x163 <= x158 l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l8(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 && x206 <= x205 l5(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x222 = x233 && x221 = x232 && x220 = x231 && x240 = 1 && x234 = x234 && 1 + x227 <= x228 l9(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 && x260 = 0 && x257 = x258 && x258 = x258 && x263 = x243 && x259 = x244 && x261 = x242 l10(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 Start term: l10(__const_10HAT0, __const_285HAT0, __const_35HAT0, acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_10HAT0, __const_285HAT0, __const_35HAT0, acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(__const_10HATpost, __const_285HATpost, __const_35HATpost, acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost && __const_35HAT0 = __const_35HATpost && __const_285HAT0 = __const_285HATpost && __const_10HAT0 = __const_10HATpost (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l0(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x6 <= x4 (3) l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x37 = 1 + x26 && 1 + x26 <= x28 (4) l1(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x62 = 1 + x51 (5) l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 (6) l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = -1 + x92 (7) l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 (8) l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x136 <= x141 (9) l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x156 = x167 && x155 = x166 && x154 = x165 && x174 = 1 + x163 && x168 = x168 && 1 + x163 <= x158 (10) l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 (11) l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l8(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x200 = x211 && x199 = x210 && x198 = x209 && x206 <= x205 (12) l5(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x222 = x233 && x221 = x232 && x220 = x231 && x240 = 1 && x234 = x234 && 1 + x227 <= x228 (13) l9(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x251 = x262 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 && x260 = 0 && x257 = x258 && x258 = x258 && x263 = x243 && x259 = x244 && x261 = x242 (14) l10(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 Arcs: (1) -> (4) (2) -> (1) (3) -> (1) (4) -> (7) (5) -> (2), (3) (6) -> (4) (7) -> (11), (12) (8) -> (5), (6) (9) -> (10) (10) -> (8), (9) (12) -> (10) (13) -> (7) (14) -> (13) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(__const_10HAT0, __const_285HAT0, __const_35HAT0, acc12HAT0, acc_length11HAT0, coef_len210HAT0, coef_len6HAT0, i8HAT0, in_len4HAT0, j9HAT0, scale7HAT0) -> l1(__const_10HATpost, __const_285HATpost, __const_35HATpost, acc12HATpost, acc_length11HATpost, coef_len210HATpost, coef_len6HATpost, i8HATpost, in_len4HATpost, j9HATpost, scale7HATpost) :|: scale7HAT0 = scale7HATpost && j9HAT0 = j9HATpost && in_len4HAT0 = in_len4HATpost && i8HAT0 = i8HATpost && coef_len6HAT0 = coef_len6HATpost && coef_len210HAT0 = coef_len210HATpost && acc_length11HAT0 = acc_length11HATpost && acc12HAT0 = acc12HATpost && __const_35HAT0 = __const_35HATpost && __const_285HAT0 = __const_285HATpost && __const_10HAT0 = __const_10HATpost (2) l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l0(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x30 = x41 && x29 = x40 && x28 = x39 && x27 = x38 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x37 = 1 + x26 && 1 + x26 <= x28 (3) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l0(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x6 <= x4 (4) l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 (5) l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l4(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x136 <= x141 (6) l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l6(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 (7) l5(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x222 = x233 && x221 = x232 && x220 = x231 && x240 = 1 && x234 = x234 && 1 + x227 <= x228 (8) l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 (9) l1(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x50 = x61 && x49 = x60 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x62 = 1 + x51 (10) l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && x103 = -1 + x92 (11) l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l7(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x156 = x167 && x155 = x166 && x154 = x165 && x174 = 1 + x163 && x168 = x168 && 1 + x163 <= x158 Arcs: (1) -> (9) (2) -> (1) (3) -> (1) (4) -> (2), (3) (5) -> (4), (10) (6) -> (5), (11) (7) -> (6) (8) -> (7) (9) -> (8) (10) -> (9) (11) -> (6) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l7(__const_10HATpost:0, __const_285HATpost:0, __const_35HATpost:0, acc12HATpost:0, x147:0, coef_len210HATpost:0, coef_len6HATpost:0, i8HATpost:0, in_len4HATpost:0, j9HATpost:0, scale7HATpost:0) -> l7(__const_10HATpost:0, __const_285HATpost:0, __const_35HATpost:0, x234:0, 1 + x147:0, coef_len210HATpost:0, coef_len6HATpost:0, 1 + i8HATpost:0, in_len4HATpost:0, 1, scale7HATpost:0) :|: x147:0 <= j9HATpost:0 && coef_len6HATpost:0 >= 1 + x147:0 && in_len4HATpost:0 >= 1 + (1 + i8HATpost:0) l7(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l7(x, x1, x2, x11, -1 + x4, x5, x6, 1 + x7, x8, 1, x10) :|: x8 >= 1 + (1 + x7) && x4 <= x9 l7(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> l7(x12, x13, x14, x23, x16, x17, x18, 1 + x19, x20, 1, x22) :|: x21 >= x16 && x18 <= x16 && x20 >= 1 + (1 + x19) l7(x165:0, x166:0, x167:0, x179:0, x169:0, x170:0, x171:0, x172:0, x173:0, x185:0, x175:0) -> l7(x165:0, x166:0, x167:0, x168:0, x169:0, x170:0, x171:0, x172:0, x173:0, 1 + x185:0, x175:0) :|: x169:0 >= 1 + x185:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l7(x5, x7, x8, x9, x10) ---------------------------------------- (8) Obligation: Rules: l7(x147:0, coef_len6HATpost:0, i8HATpost:0, in_len4HATpost:0, j9HATpost:0) -> l7(1 + x147:0, coef_len6HATpost:0, 1 + i8HATpost:0, in_len4HATpost:0, 1) :|: x147:0 <= j9HATpost:0 && coef_len6HATpost:0 >= 1 + x147:0 && in_len4HATpost:0 >= 1 + (1 + i8HATpost:0) l7(x4, x6, x7, x8, x9) -> l7(-1 + x4, x6, 1 + x7, x8, 1) :|: x8 >= 1 + (1 + x7) && x4 <= x9 l7(x16, x18, x19, x20, x21) -> l7(x16, x18, 1 + x19, x20, 1) :|: x21 >= x16 && x18 <= x16 && x20 >= 1 + (1 + x19) l7(x169:0, x171:0, x172:0, x173:0, x185:0) -> l7(x169:0, x171:0, x172:0, x173:0, 1 + x185:0) :|: x169:0 >= 1 + x185:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l7(INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l7(x147:0, coef_len6HATpost:0, i8HATpost:0, in_len4HATpost:0, j9HATpost:0) -> l7(c, coef_len6HATpost:0, c1, in_len4HATpost:0, c2) :|: c2 = 1 && (c1 = 1 + i8HATpost:0 && c = 1 + x147:0) && (x147:0 <= j9HATpost:0 && coef_len6HATpost:0 >= 1 + x147:0 && in_len4HATpost:0 >= 1 + (1 + i8HATpost:0)) l7(x4, x6, x7, x8, x9) -> l7(c3, x6, c4, x8, c5) :|: c5 = 1 && (c4 = 1 + x7 && c3 = -1 + x4) && (x8 >= 1 + (1 + x7) && x4 <= x9) l7(x16, x18, x19, x20, x21) -> l7(x16, x18, c6, x20, c7) :|: c7 = 1 && c6 = 1 + x19 && (x21 >= x16 && x18 <= x16 && x20 >= 1 + (1 + x19)) l7(x169:0, x171:0, x172:0, x173:0, x185:0) -> l7(x169:0, x171:0, x172:0, x173:0, c8) :|: c8 = 1 + x185:0 && x169:0 >= 1 + x185:0 ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l7(x, x1, x2, x3, x4)] = -2 + x - x1 - x2 + x3 The following rules are decreasing: l7(x4, x6, x7, x8, x9) -> l7(c3, x6, c4, x8, c5) :|: c5 = 1 && (c4 = 1 + x7 && c3 = -1 + x4) && (x8 >= 1 + (1 + x7) && x4 <= x9) l7(x16, x18, x19, x20, x21) -> l7(x16, x18, c6, x20, c7) :|: c7 = 1 && c6 = 1 + x19 && (x21 >= x16 && x18 <= x16 && x20 >= 1 + (1 + x19)) The following rules are bounded: l7(x16, x18, x19, x20, x21) -> l7(x16, x18, c6, x20, c7) :|: c7 = 1 && c6 = 1 + x19 && (x21 >= x16 && x18 <= x16 && x20 >= 1 + (1 + x19)) ---------------------------------------- (12) Obligation: Rules: l7(x147:0, coef_len6HATpost:0, i8HATpost:0, in_len4HATpost:0, j9HATpost:0) -> l7(c, coef_len6HATpost:0, c1, in_len4HATpost:0, c2) :|: c2 = 1 && (c1 = 1 + i8HATpost:0 && c = 1 + x147:0) && (x147:0 <= j9HATpost:0 && coef_len6HATpost:0 >= 1 + x147:0 && in_len4HATpost:0 >= 1 + (1 + i8HATpost:0)) l7(x4, x6, x7, x8, x9) -> l7(c3, x6, c4, x8, c5) :|: c5 = 1 && (c4 = 1 + x7 && c3 = -1 + x4) && (x8 >= 1 + (1 + x7) && x4 <= x9) l7(x169:0, x171:0, x172:0, x173:0, x185:0) -> l7(x169:0, x171:0, x172:0, x173:0, c8) :|: c8 = 1 + x185:0 && x169:0 >= 1 + x185:0 ---------------------------------------- (13) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l7(x, x1, x2, x3, x4)] = -1 - x2 + x3 The following rules are decreasing: l7(x147:0, coef_len6HATpost:0, i8HATpost:0, in_len4HATpost:0, j9HATpost:0) -> l7(c, coef_len6HATpost:0, c1, in_len4HATpost:0, c2) :|: c2 = 1 && (c1 = 1 + i8HATpost:0 && c = 1 + x147:0) && (x147:0 <= j9HATpost:0 && coef_len6HATpost:0 >= 1 + x147:0 && in_len4HATpost:0 >= 1 + (1 + i8HATpost:0)) l7(x4, x6, x7, x8, x9) -> l7(c3, x6, c4, x8, c5) :|: c5 = 1 && (c4 = 1 + x7 && c3 = -1 + x4) && (x8 >= 1 + (1 + x7) && x4 <= x9) The following rules are bounded: l7(x147:0, coef_len6HATpost:0, i8HATpost:0, in_len4HATpost:0, j9HATpost:0) -> l7(c, coef_len6HATpost:0, c1, in_len4HATpost:0, c2) :|: c2 = 1 && (c1 = 1 + i8HATpost:0 && c = 1 + x147:0) && (x147:0 <= j9HATpost:0 && coef_len6HATpost:0 >= 1 + x147:0 && in_len4HATpost:0 >= 1 + (1 + i8HATpost:0)) l7(x4, x6, x7, x8, x9) -> l7(c3, x6, c4, x8, c5) :|: c5 = 1 && (c4 = 1 + x7 && c3 = -1 + x4) && (x8 >= 1 + (1 + x7) && x4 <= x9) ---------------------------------------- (14) Obligation: Rules: l7(x169:0, x171:0, x172:0, x173:0, x185:0) -> l7(x169:0, x171:0, x172:0, x173:0, c8) :|: c8 = 1 + x185:0 && x169:0 >= 1 + x185:0 ---------------------------------------- (15) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l7(x, x1, x2, x3, x4)] = x - x4 The following rules are decreasing: l7(x169:0, x171:0, x172:0, x173:0, x185:0) -> l7(x169:0, x171:0, x172:0, x173:0, c8) :|: c8 = 1 + x185:0 && x169:0 >= 1 + x185:0 The following rules are bounded: l7(x169:0, x171:0, x172:0, x173:0, x185:0) -> l7(x169:0, x171:0, x172:0, x173:0, c8) :|: c8 = 1 + x185:0 && x169:0 >= 1 + x185:0 ---------------------------------------- (16) YES