YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 2659 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 3 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 36 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 15 ms] (12) YES ---------------------------------------- (0) Obligation: Rules: l0(head_16HAT0, head_21HAT0, head_SLAM_f_18HAT0, i_19HAT0, i_86HAT0, length_17HAT0, nondet_12HAT0, rcd_50HAT0, rcd_80HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, tail_14HAT0, temp0_15HAT0, temp0_20HAT0, temp_26HAT0, tmp_23HAT0) -> l1(head_16HATpost, head_21HATpost, head_SLAM_f_18HATpost, i_19HATpost, i_86HATpost, length_17HATpost, nondet_12HATpost, rcd_50HATpost, rcd_80HATpost, result_11HATpost, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost, result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost, tail_14HATpost, temp0_15HATpost, temp0_20HATpost, temp_26HATpost, tmp_23HATpost) :|: nondet_12HAT1 = nondet_12HAT1 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = nondet_12HAT1 && nondet_12HATpost = nondet_12HATpost && length_17HATpost = result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_SLAM_f_18HATpost = tail_14HAT0 && head_21HATpost = head_SLAM_f_18HATpost && i_19HATpost = 0 && 0 <= i_19HATpost && i_19HATpost <= 0 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost <= length_17HATpost && length_17HATpost <= result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && tail_14HAT0 <= head_SLAM_f_18HATpost && head_SLAM_f_18HATpost <= tail_14HAT0 && tail_14HAT0 <= head_21HATpost && head_21HATpost <= tail_14HAT0 && head_SLAM_f_18HATpost <= head_21HATpost && head_21HATpost <= head_SLAM_f_18HATpost && head_16HAT0 = head_16HATpost && i_86HAT0 = i_86HATpost && rcd_50HAT0 = rcd_50HATpost && rcd_80HAT0 = rcd_80HATpost && result_11HAT0 = result_11HATpost && result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0 = result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost && tail_14HAT0 = tail_14HATpost && temp0_15HAT0 = temp0_15HATpost && temp0_20HAT0 = temp0_20HATpost && temp_26HAT0 = temp_26HATpost && tmp_23HAT0 = tmp_23HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x28 = x28 && x5 <= x3 && x34 = x1 && x35 = x34 && x22 = x22 && x19 = x19 && x20 = x20 && x31 = x31 && x18 = x18 && x27 = x27 && x33 = x33 && x32 = x32 && x17 = x35 && x36 = x36 && x26 = x13 && 1 <= x28 && x28 <= 1 && 1 <= x28 && x28 <= 1 && x4 = x21 && x6 = x23 && x7 = x24 && x8 = x25 && x12 = x29 && x13 = x30 l2(x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x51 = x68 && x50 = x67 && x46 = x63 && x45 = x62 && x43 = x60 && x42 = x59 && x41 = x58 && x37 = x54 && 2 <= x42 && 1 <= x42 && x70 <= x64 && x64 <= x70 && x70 <= x55 && x55 <= x70 && x64 <= x55 && x55 <= x64 && x56 <= x66 && x66 <= x56 && x42 <= x65 && x65 <= x42 && x57 <= 2 && 2 <= x57 && x57 = 1 + x40 && x55 = x70 && x69 = x69 && x70 = x52 && 1 + x40 <= x42 && x61 = x61 && x64 = x64 && x56 = x56 && x66 = x66 && x65 = x65 l4(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) :|: 0 <= x74 && x99 = x99 && x76 <= x74 && x105 = x72 && x106 = x105 && x93 = x93 && x90 = x90 && x91 = x91 && x102 = x102 && x89 = x89 && x98 = x98 && x104 = x104 && x103 = x103 && x88 = x106 && x107 = x107 && x97 = x84 && 1 <= x99 && 2 <= x99 && x99 <= x91 && x75 = x92 && x77 = x94 && x78 = x95 && x79 = x96 && x83 = x100 && x84 = x101 l4(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124) -> l5(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x122 = x139 && x121 = x138 && x120 = x137 && x119 = x136 && x118 = x135 && x117 = x134 && x115 = x132 && x114 = x131 && x113 = x130 && x110 = x127 && x108 = x125 && 1 + x129 <= x113 && -1 + x128 <= x129 && x129 <= -1 + x128 && 1 + x129 <= x128 && x128 <= 1 + x129 && x128 = 1 + x111 && x126 = x141 && x140 = x140 && x141 = x123 && 1 + x111 <= x113 && x129 = x129 && x133 = x133 && 0 <= x111 l5(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158) -> l4(x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x158 = x175 && x157 = x174 && x156 = x173 && x155 = x172 && x154 = x171 && x153 = x170 && x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x142 = x159 l1(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192) -> l3(x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x204 = x204 && x181 <= x179 && x210 = x177 && x211 = x210 && x198 = x198 && x195 = x195 && x196 = x196 && x207 = x207 && x194 = x194 && x203 = x203 && x209 = x209 && x208 = x208 && x193 = x211 && x212 = x212 && x202 = x189 && x204 <= 0 && x180 = x197 && x182 = x199 && x183 = x200 && x184 = x201 && x188 = x205 && x189 = x206 l1(x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l2(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246) :|: x227 = x244 && x226 = x243 && x222 = x239 && x221 = x238 && x220 = x237 && x219 = x236 && x218 = x235 && x217 = x234 && x213 = x230 && 1 <= x218 && x246 <= x240 && x240 <= x246 && x246 <= x231 && x231 <= x246 && x240 <= x231 && x231 <= x240 && x232 <= x242 && x242 <= x232 && x218 <= x241 && x241 <= x218 && x233 <= 1 && 1 <= x233 && x233 = 1 + x216 && x231 = x246 && x245 = x245 && x246 = x228 && 1 + x216 <= x218 && x240 = x240 && x232 = x232 && x242 = x242 && x241 = x241 l6(x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l0(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280) :|: x263 = x280 && x262 = x279 && x261 = x278 && x260 = x277 && x259 = x276 && x258 = x275 && x257 = x274 && x256 = x273 && x255 = x272 && x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 Start term: l6(head_16HAT0, head_21HAT0, head_SLAM_f_18HAT0, i_19HAT0, i_86HAT0, length_17HAT0, nondet_12HAT0, rcd_50HAT0, rcd_80HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, tail_14HAT0, temp0_15HAT0, temp0_20HAT0, temp_26HAT0, tmp_23HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(head_16HAT0, head_21HAT0, head_SLAM_f_18HAT0, i_19HAT0, i_86HAT0, length_17HAT0, nondet_12HAT0, rcd_50HAT0, rcd_80HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, tail_14HAT0, temp0_15HAT0, temp0_20HAT0, temp_26HAT0, tmp_23HAT0) -> l1(head_16HATpost, head_21HATpost, head_SLAM_f_18HATpost, i_19HATpost, i_86HATpost, length_17HATpost, nondet_12HATpost, rcd_50HATpost, rcd_80HATpost, result_11HATpost, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost, result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost, tail_14HATpost, temp0_15HATpost, temp0_20HATpost, temp_26HATpost, tmp_23HATpost) :|: nondet_12HAT1 = nondet_12HAT1 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = nondet_12HAT1 && nondet_12HATpost = nondet_12HATpost && length_17HATpost = result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_SLAM_f_18HATpost = tail_14HAT0 && head_21HATpost = head_SLAM_f_18HATpost && i_19HATpost = 0 && 0 <= i_19HATpost && i_19HATpost <= 0 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost <= length_17HATpost && length_17HATpost <= result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && tail_14HAT0 <= head_SLAM_f_18HATpost && head_SLAM_f_18HATpost <= tail_14HAT0 && tail_14HAT0 <= head_21HATpost && head_21HATpost <= tail_14HAT0 && head_SLAM_f_18HATpost <= head_21HATpost && head_21HATpost <= head_SLAM_f_18HATpost && head_16HAT0 = head_16HATpost && i_86HAT0 = i_86HATpost && rcd_50HAT0 = rcd_50HATpost && rcd_80HAT0 = rcd_80HATpost && result_11HAT0 = result_11HATpost && result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0 = result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost && tail_14HAT0 = tail_14HATpost && temp0_15HAT0 = temp0_15HATpost && temp0_20HAT0 = temp0_20HATpost && temp_26HAT0 = temp_26HATpost && tmp_23HAT0 = tmp_23HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x28 = x28 && x5 <= x3 && x34 = x1 && x35 = x34 && x22 = x22 && x19 = x19 && x20 = x20 && x31 = x31 && x18 = x18 && x27 = x27 && x33 = x33 && x32 = x32 && x17 = x35 && x36 = x36 && x26 = x13 && 1 <= x28 && x28 <= 1 && 1 <= x28 && x28 <= 1 && x4 = x21 && x6 = x23 && x7 = x24 && x8 = x25 && x12 = x29 && x13 = x30 l2(x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x51 = x68 && x50 = x67 && x46 = x63 && x45 = x62 && x43 = x60 && x42 = x59 && x41 = x58 && x37 = x54 && 2 <= x42 && 1 <= x42 && x70 <= x64 && x64 <= x70 && x70 <= x55 && x55 <= x70 && x64 <= x55 && x55 <= x64 && x56 <= x66 && x66 <= x56 && x42 <= x65 && x65 <= x42 && x57 <= 2 && 2 <= x57 && x57 = 1 + x40 && x55 = x70 && x69 = x69 && x70 = x52 && 1 + x40 <= x42 && x61 = x61 && x64 = x64 && x56 = x56 && x66 = x66 && x65 = x65 l4(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) :|: 0 <= x74 && x99 = x99 && x76 <= x74 && x105 = x72 && x106 = x105 && x93 = x93 && x90 = x90 && x91 = x91 && x102 = x102 && x89 = x89 && x98 = x98 && x104 = x104 && x103 = x103 && x88 = x106 && x107 = x107 && x97 = x84 && 1 <= x99 && 2 <= x99 && x99 <= x91 && x75 = x92 && x77 = x94 && x78 = x95 && x79 = x96 && x83 = x100 && x84 = x101 l4(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124) -> l5(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x122 = x139 && x121 = x138 && x120 = x137 && x119 = x136 && x118 = x135 && x117 = x134 && x115 = x132 && x114 = x131 && x113 = x130 && x110 = x127 && x108 = x125 && 1 + x129 <= x113 && -1 + x128 <= x129 && x129 <= -1 + x128 && 1 + x129 <= x128 && x128 <= 1 + x129 && x128 = 1 + x111 && x126 = x141 && x140 = x140 && x141 = x123 && 1 + x111 <= x113 && x129 = x129 && x133 = x133 && 0 <= x111 l5(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158) -> l4(x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x158 = x175 && x157 = x174 && x156 = x173 && x155 = x172 && x154 = x171 && x153 = x170 && x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x142 = x159 l1(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192) -> l3(x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x204 = x204 && x181 <= x179 && x210 = x177 && x211 = x210 && x198 = x198 && x195 = x195 && x196 = x196 && x207 = x207 && x194 = x194 && x203 = x203 && x209 = x209 && x208 = x208 && x193 = x211 && x212 = x212 && x202 = x189 && x204 <= 0 && x180 = x197 && x182 = x199 && x183 = x200 && x184 = x201 && x188 = x205 && x189 = x206 l1(x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l2(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246) :|: x227 = x244 && x226 = x243 && x222 = x239 && x221 = x238 && x220 = x237 && x219 = x236 && x218 = x235 && x217 = x234 && x213 = x230 && 1 <= x218 && x246 <= x240 && x240 <= x246 && x246 <= x231 && x231 <= x246 && x240 <= x231 && x231 <= x240 && x232 <= x242 && x242 <= x232 && x218 <= x241 && x241 <= x218 && x233 <= 1 && 1 <= x233 && x233 = 1 + x216 && x231 = x246 && x245 = x245 && x246 = x228 && 1 + x216 <= x218 && x240 = x240 && x232 = x232 && x242 = x242 && x241 = x241 l6(x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l0(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280) :|: x263 = x280 && x262 = x279 && x261 = x278 && x260 = x277 && x259 = x276 && x258 = x275 && x257 = x274 && x256 = x273 && x255 = x272 && x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 Start term: l6(head_16HAT0, head_21HAT0, head_SLAM_f_18HAT0, i_19HAT0, i_86HAT0, length_17HAT0, nondet_12HAT0, rcd_50HAT0, rcd_80HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, tail_14HAT0, temp0_15HAT0, temp0_20HAT0, temp_26HAT0, tmp_23HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(head_16HAT0, head_21HAT0, head_SLAM_f_18HAT0, i_19HAT0, i_86HAT0, length_17HAT0, nondet_12HAT0, rcd_50HAT0, rcd_80HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, tail_14HAT0, temp0_15HAT0, temp0_20HAT0, temp_26HAT0, tmp_23HAT0) -> l1(head_16HATpost, head_21HATpost, head_SLAM_f_18HATpost, i_19HATpost, i_86HATpost, length_17HATpost, nondet_12HATpost, rcd_50HATpost, rcd_80HATpost, result_11HATpost, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost, result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost, tail_14HATpost, temp0_15HATpost, temp0_20HATpost, temp_26HATpost, tmp_23HATpost) :|: nondet_12HAT1 = nondet_12HAT1 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = nondet_12HAT1 && nondet_12HATpost = nondet_12HATpost && length_17HATpost = result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_SLAM_f_18HATpost = tail_14HAT0 && head_21HATpost = head_SLAM_f_18HATpost && i_19HATpost = 0 && 0 <= i_19HATpost && i_19HATpost <= 0 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost <= length_17HATpost && length_17HATpost <= result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && tail_14HAT0 <= head_SLAM_f_18HATpost && head_SLAM_f_18HATpost <= tail_14HAT0 && tail_14HAT0 <= head_21HATpost && head_21HATpost <= tail_14HAT0 && head_SLAM_f_18HATpost <= head_21HATpost && head_21HATpost <= head_SLAM_f_18HATpost && head_16HAT0 = head_16HATpost && i_86HAT0 = i_86HATpost && rcd_50HAT0 = rcd_50HATpost && rcd_80HAT0 = rcd_80HATpost && result_11HAT0 = result_11HATpost && result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HAT0 = result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_22HATpost && tail_14HAT0 = tail_14HATpost && temp0_15HAT0 = temp0_15HATpost && temp0_20HAT0 = temp0_20HATpost && temp_26HAT0 = temp_26HATpost && tmp_23HAT0 = tmp_23HATpost (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16) -> l3(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) :|: x28 = x28 && x5 <= x3 && x34 = x1 && x35 = x34 && x22 = x22 && x19 = x19 && x20 = x20 && x31 = x31 && x18 = x18 && x27 = x27 && x33 = x33 && x32 = x32 && x17 = x35 && x36 = x36 && x26 = x13 && 1 <= x28 && x28 <= 1 && 1 <= x28 && x28 <= 1 && x4 = x21 && x6 = x23 && x7 = x24 && x8 = x25 && x12 = x29 && x13 = x30 (3) l2(x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l4(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70) :|: x51 = x68 && x50 = x67 && x46 = x63 && x45 = x62 && x43 = x60 && x42 = x59 && x41 = x58 && x37 = x54 && 2 <= x42 && 1 <= x42 && x70 <= x64 && x64 <= x70 && x70 <= x55 && x55 <= x70 && x64 <= x55 && x55 <= x64 && x56 <= x66 && x66 <= x56 && x42 <= x65 && x65 <= x42 && x57 <= 2 && 2 <= x57 && x57 = 1 + x40 && x55 = x70 && x69 = x69 && x70 = x52 && 1 + x40 <= x42 && x61 = x61 && x64 = x64 && x56 = x56 && x66 = x66 && x65 = x65 (4) l4(x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) -> l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) :|: 0 <= x74 && x99 = x99 && x76 <= x74 && x105 = x72 && x106 = x105 && x93 = x93 && x90 = x90 && x91 = x91 && x102 = x102 && x89 = x89 && x98 = x98 && x104 = x104 && x103 = x103 && x88 = x106 && x107 = x107 && x97 = x84 && 1 <= x99 && 2 <= x99 && x99 <= x91 && x75 = x92 && x77 = x94 && x78 = x95 && x79 = x96 && x83 = x100 && x84 = x101 (5) l4(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124) -> l5(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x122 = x139 && x121 = x138 && x120 = x137 && x119 = x136 && x118 = x135 && x117 = x134 && x115 = x132 && x114 = x131 && x113 = x130 && x110 = x127 && x108 = x125 && 1 + x129 <= x113 && -1 + x128 <= x129 && x129 <= -1 + x128 && 1 + x129 <= x128 && x128 <= 1 + x129 && x128 = 1 + x111 && x126 = x141 && x140 = x140 && x141 = x123 && 1 + x111 <= x113 && x129 = x129 && x133 = x133 && 0 <= x111 (6) l5(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158) -> l4(x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x158 = x175 && x157 = x174 && x156 = x173 && x155 = x172 && x154 = x171 && x153 = x170 && x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x142 = x159 (7) l1(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192) -> l3(x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x204 = x204 && x181 <= x179 && x210 = x177 && x211 = x210 && x198 = x198 && x195 = x195 && x196 = x196 && x207 = x207 && x194 = x194 && x203 = x203 && x209 = x209 && x208 = x208 && x193 = x211 && x212 = x212 && x202 = x189 && x204 <= 0 && x180 = x197 && x182 = x199 && x183 = x200 && x184 = x201 && x188 = x205 && x189 = x206 (8) l1(x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l2(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246) :|: x227 = x244 && x226 = x243 && x222 = x239 && x221 = x238 && x220 = x237 && x219 = x236 && x218 = x235 && x217 = x234 && x213 = x230 && 1 <= x218 && x246 <= x240 && x240 <= x246 && x246 <= x231 && x231 <= x246 && x240 <= x231 && x231 <= x240 && x232 <= x242 && x242 <= x232 && x218 <= x241 && x241 <= x218 && x233 <= 1 && 1 <= x233 && x233 = 1 + x216 && x231 = x246 && x245 = x245 && x246 = x228 && 1 + x216 <= x218 && x240 = x240 && x232 = x232 && x242 = x242 && x241 = x241 (9) l6(x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l0(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280) :|: x263 = x280 && x262 = x279 && x261 = x278 && x260 = x277 && x259 = x276 && x258 = x275 && x257 = x274 && x256 = x273 && x255 = x272 && x254 = x271 && x253 = x270 && x252 = x269 && x251 = x268 && x250 = x267 && x249 = x266 && x248 = x265 && x247 = x264 Arcs: (1) -> (7), (8) (3) -> (4), (5) (5) -> (6) (6) -> (4), (5) (8) -> (2), (3) (9) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l4(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124) -> l5(x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: x122 = x139 && x121 = x138 && x120 = x137 && x119 = x136 && x118 = x135 && x117 = x134 && x115 = x132 && x114 = x131 && x113 = x130 && x110 = x127 && x108 = x125 && 1 + x129 <= x113 && -1 + x128 <= x129 && x129 <= -1 + x128 && 1 + x129 <= x128 && x128 <= 1 + x129 && x128 = 1 + x111 && x126 = x141 && x140 = x140 && x141 = x123 && 1 + x111 <= x113 && x129 = x129 && x133 = x133 && 0 <= x111 (2) l5(x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158) -> l4(x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x158 = x175 && x157 = x174 && x156 = x173 && x155 = x172 && x154 = x171 && x153 = x170 && x152 = x169 && x151 = x168 && x150 = x167 && x149 = x166 && x148 = x165 && x147 = x164 && x146 = x163 && x145 = x162 && x144 = x161 && x143 = x160 && x142 = x159 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l4(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x118:0, x119:0, x120:0, x121:0, x122:0, x123:0, x124:0) -> l4(x108:0, x123:0, x110:0, 1 + x111:0, -1 + (1 + x111:0), x113:0, x114:0, x115:0, x133:0, x117:0, x118:0, x119:0, x120:0, x121:0, x122:0, x140:0, x123:0) :|: x113:0 >= 1 + x111:0 && x111:0 > -1 && 1 + x111:0 = 1 + (-1 + (1 + x111:0)) && x113:0 >= 1 + (-1 + (1 + x111:0)) ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> l4(x4, x6) ---------------------------------------- (8) Obligation: Rules: l4(x111:0, x113:0) -> l4(1 + x111:0, x113:0) :|: x113:0 >= 1 + x111:0 && x111:0 > -1 && 1 + x111:0 = 1 + (-1 + (1 + x111:0)) && x113:0 >= 1 + (-1 + (1 + x111:0)) ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l4(x111:0, x113:0) -> l4(c, x113:0) :|: c = 1 + x111:0 && (x113:0 >= 1 + x111:0 && x111:0 > -1 && 1 + x111:0 = 1 + (-1 + (1 + x111:0)) && x113:0 >= 1 + (-1 + (1 + x111:0))) ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l4(x, x1)] = -x + x1 The following rules are decreasing: l4(x111:0, x113:0) -> l4(c, x113:0) :|: c = 1 + x111:0 && (x113:0 >= 1 + x111:0 && x111:0 > -1 && 1 + x111:0 = 1 + (-1 + (1 + x111:0)) && x113:0 >= 1 + (-1 + (1 + x111:0))) The following rules are bounded: l4(x111:0, x113:0) -> l4(c, x113:0) :|: c = 1 + x111:0 && (x113:0 >= 1 + x111:0 && x111:0 > -1 && 1 + x111:0 = 1 + (-1 + (1 + x111:0)) && x113:0 >= 1 + (-1 + (1 + x111:0))) ---------------------------------------- (12) YES