YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 2364 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 37 ms] (10) IntTRS (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Rules: l0(head_15HAT0, head_19HAT0, i_17HAT0, i_83HAT0, length_16HAT0, nondet_12HAT0, rcd_47HAT0, rcd_77HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, temp0_14HAT0, temp0_18HAT0, temp_24HAT0, tmp_21HAT0) -> l1(head_15HATpost, head_19HATpost, i_17HATpost, i_83HATpost, length_16HATpost, nondet_12HATpost, rcd_47HATpost, rcd_77HATpost, result_11HATpost, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HATpost, result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost, temp0_14HATpost, temp0_18HATpost, temp_24HATpost, tmp_21HATpost) :|: nondet_12HAT1 = nondet_12HAT1 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = nondet_12HAT1 && nondet_12HATpost = nondet_12HATpost && length_16HATpost = result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_19HATpost = 0 && i_17HATpost = 0 && 0 <= i_17HATpost && i_17HATpost <= 0 && 0 <= head_19HATpost && head_19HATpost <= 0 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost <= length_16HATpost && length_16HATpost <= result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_15HAT0 = head_15HATpost && i_83HAT0 = i_83HATpost && rcd_47HAT0 = rcd_47HATpost && rcd_77HAT0 = rcd_77HATpost && result_11HAT0 = result_11HATpost && result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0 = result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HATpost && temp0_14HAT0 = temp0_14HATpost && temp0_18HAT0 = temp0_18HATpost && temp_24HAT0 = temp_24HATpost && tmp_21HAT0 = tmp_21HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x25 = x25 && x4 <= x2 && x30 = x1 && x31 = x30 && x19 = x19 && x17 = x17 && x27 = x27 && x16 = x16 && x24 = x24 && x29 = x29 && x28 = x28 && x15 = x31 && x32 = x32 && x23 = x11 && 1 <= x25 && x25 <= 1 && 1 <= x25 && x25 <= 1 && x3 = x18 && x5 = x20 && x6 = x21 && x7 = x22 && x11 = x26 l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) -> l4(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) :|: x45 = x60 && x44 = x59 && x41 = x56 && x40 = x55 && x38 = x53 && x37 = x52 && x36 = x51 && x33 = x48 && 2 <= x37 && 1 <= x37 && x62 <= x57 && x57 <= x62 && x62 <= x49 && x49 <= x62 && x57 <= x49 && x49 <= x57 && x37 <= x58 && x58 <= x37 && x50 <= 2 && 2 <= x50 && x50 = 1 + x35 && x49 = x62 && x61 = x61 && x62 = x46 && 1 + x35 <= x37 && x54 = x54 && x57 = x57 && x58 = x58 l4(x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77) -> l3(x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: 0 <= x65 && x88 = x88 && x67 <= x65 && x93 = x64 && x94 = x93 && x82 = x82 && x80 = x80 && x90 = x90 && x79 = x79 && x87 = x87 && x92 = x92 && x91 = x91 && x78 = x94 && x95 = x95 && x86 = x74 && 1 <= x88 && 2 <= x88 && x88 <= x80 && x66 = x81 && x68 = x83 && x69 = x84 && x70 = x85 && x74 = x89 l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110) -> l5(x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x108 = x123 && x107 = x122 && x106 = x121 && x105 = x120 && x104 = x119 && x102 = x117 && x101 = x116 && x100 = x115 && x96 = x111 && 1 + x114 <= x100 && -1 + x113 <= x114 && x114 <= -1 + x113 && 1 + x114 <= x113 && x113 <= 1 + x114 && x113 = 1 + x98 && x112 = x125 && x124 = x124 && x125 = x109 && 1 + x98 <= x100 && x114 = x114 && x118 = x118 && 0 <= x98 l5(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140) -> l4(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) :|: x140 = x155 && x139 = x154 && x138 = x153 && x137 = x152 && x136 = x151 && x135 = x150 && x134 = x149 && x133 = x148 && x132 = x147 && x131 = x146 && x130 = x145 && x129 = x144 && x128 = x143 && x127 = x142 && x126 = x141 l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l3(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185) :|: x181 = x181 && x160 <= x158 && x186 = x157 && x187 = x186 && x175 = x175 && x173 = x173 && x183 = x183 && x172 = x172 && x180 = x180 && x185 = x185 && x184 = x184 && x171 = x187 && x188 = x188 && x179 = x167 && x181 <= 0 && x159 = x174 && x161 = x176 && x162 = x177 && x163 = x178 && x167 = x182 l1(x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l2(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218) :|: x201 = x216 && x200 = x215 && x197 = x212 && x196 = x211 && x195 = x210 && x194 = x209 && x193 = x208 && x192 = x207 && x189 = x204 && 1 <= x193 && x218 <= x213 && x213 <= x218 && x218 <= x205 && x205 <= x218 && x213 <= x205 && x205 <= x213 && x193 <= x214 && x214 <= x193 && x206 <= 1 && 1 <= x206 && x206 = 1 + x191 && x205 = x218 && x217 = x217 && x218 = x202 && 1 + x191 <= x193 && x213 = x213 && x214 = x214 l6(x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248) :|: x233 = x248 && x232 = x247 && x231 = x246 && x230 = x245 && x229 = x244 && x228 = x243 && x227 = x242 && x226 = x241 && x225 = x240 && x224 = x239 && x223 = x238 && x222 = x237 && x221 = x236 && x220 = x235 && x219 = x234 Start term: l6(head_15HAT0, head_19HAT0, i_17HAT0, i_83HAT0, length_16HAT0, nondet_12HAT0, rcd_47HAT0, rcd_77HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, temp0_14HAT0, temp0_18HAT0, temp_24HAT0, tmp_21HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(head_15HAT0, head_19HAT0, i_17HAT0, i_83HAT0, length_16HAT0, nondet_12HAT0, rcd_47HAT0, rcd_77HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, temp0_14HAT0, temp0_18HAT0, temp_24HAT0, tmp_21HAT0) -> l1(head_15HATpost, head_19HATpost, i_17HATpost, i_83HATpost, length_16HATpost, nondet_12HATpost, rcd_47HATpost, rcd_77HATpost, result_11HATpost, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HATpost, result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost, temp0_14HATpost, temp0_18HATpost, temp_24HATpost, tmp_21HATpost) :|: nondet_12HAT1 = nondet_12HAT1 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = nondet_12HAT1 && nondet_12HATpost = nondet_12HATpost && length_16HATpost = result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_19HATpost = 0 && i_17HATpost = 0 && 0 <= i_17HATpost && i_17HATpost <= 0 && 0 <= head_19HATpost && head_19HATpost <= 0 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost <= length_16HATpost && length_16HATpost <= result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_15HAT0 = head_15HATpost && i_83HAT0 = i_83HATpost && rcd_47HAT0 = rcd_47HATpost && rcd_77HAT0 = rcd_77HATpost && result_11HAT0 = result_11HATpost && result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0 = result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HATpost && temp0_14HAT0 = temp0_14HATpost && temp0_18HAT0 = temp0_18HATpost && temp_24HAT0 = temp_24HATpost && tmp_21HAT0 = tmp_21HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x25 = x25 && x4 <= x2 && x30 = x1 && x31 = x30 && x19 = x19 && x17 = x17 && x27 = x27 && x16 = x16 && x24 = x24 && x29 = x29 && x28 = x28 && x15 = x31 && x32 = x32 && x23 = x11 && 1 <= x25 && x25 <= 1 && 1 <= x25 && x25 <= 1 && x3 = x18 && x5 = x20 && x6 = x21 && x7 = x22 && x11 = x26 l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) -> l4(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) :|: x45 = x60 && x44 = x59 && x41 = x56 && x40 = x55 && x38 = x53 && x37 = x52 && x36 = x51 && x33 = x48 && 2 <= x37 && 1 <= x37 && x62 <= x57 && x57 <= x62 && x62 <= x49 && x49 <= x62 && x57 <= x49 && x49 <= x57 && x37 <= x58 && x58 <= x37 && x50 <= 2 && 2 <= x50 && x50 = 1 + x35 && x49 = x62 && x61 = x61 && x62 = x46 && 1 + x35 <= x37 && x54 = x54 && x57 = x57 && x58 = x58 l4(x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77) -> l3(x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: 0 <= x65 && x88 = x88 && x67 <= x65 && x93 = x64 && x94 = x93 && x82 = x82 && x80 = x80 && x90 = x90 && x79 = x79 && x87 = x87 && x92 = x92 && x91 = x91 && x78 = x94 && x95 = x95 && x86 = x74 && 1 <= x88 && 2 <= x88 && x88 <= x80 && x66 = x81 && x68 = x83 && x69 = x84 && x70 = x85 && x74 = x89 l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110) -> l5(x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x108 = x123 && x107 = x122 && x106 = x121 && x105 = x120 && x104 = x119 && x102 = x117 && x101 = x116 && x100 = x115 && x96 = x111 && 1 + x114 <= x100 && -1 + x113 <= x114 && x114 <= -1 + x113 && 1 + x114 <= x113 && x113 <= 1 + x114 && x113 = 1 + x98 && x112 = x125 && x124 = x124 && x125 = x109 && 1 + x98 <= x100 && x114 = x114 && x118 = x118 && 0 <= x98 l5(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140) -> l4(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) :|: x140 = x155 && x139 = x154 && x138 = x153 && x137 = x152 && x136 = x151 && x135 = x150 && x134 = x149 && x133 = x148 && x132 = x147 && x131 = x146 && x130 = x145 && x129 = x144 && x128 = x143 && x127 = x142 && x126 = x141 l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l3(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185) :|: x181 = x181 && x160 <= x158 && x186 = x157 && x187 = x186 && x175 = x175 && x173 = x173 && x183 = x183 && x172 = x172 && x180 = x180 && x185 = x185 && x184 = x184 && x171 = x187 && x188 = x188 && x179 = x167 && x181 <= 0 && x159 = x174 && x161 = x176 && x162 = x177 && x163 = x178 && x167 = x182 l1(x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l2(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218) :|: x201 = x216 && x200 = x215 && x197 = x212 && x196 = x211 && x195 = x210 && x194 = x209 && x193 = x208 && x192 = x207 && x189 = x204 && 1 <= x193 && x218 <= x213 && x213 <= x218 && x218 <= x205 && x205 <= x218 && x213 <= x205 && x205 <= x213 && x193 <= x214 && x214 <= x193 && x206 <= 1 && 1 <= x206 && x206 = 1 + x191 && x205 = x218 && x217 = x217 && x218 = x202 && 1 + x191 <= x193 && x213 = x213 && x214 = x214 l6(x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248) :|: x233 = x248 && x232 = x247 && x231 = x246 && x230 = x245 && x229 = x244 && x228 = x243 && x227 = x242 && x226 = x241 && x225 = x240 && x224 = x239 && x223 = x238 && x222 = x237 && x221 = x236 && x220 = x235 && x219 = x234 Start term: l6(head_15HAT0, head_19HAT0, i_17HAT0, i_83HAT0, length_16HAT0, nondet_12HAT0, rcd_47HAT0, rcd_77HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, temp0_14HAT0, temp0_18HAT0, temp_24HAT0, tmp_21HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(head_15HAT0, head_19HAT0, i_17HAT0, i_83HAT0, length_16HAT0, nondet_12HAT0, rcd_47HAT0, rcd_77HAT0, result_11HAT0, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0, result_dot_nondet_sdv_special_RETURN_VALUE_13HAT0, temp0_14HAT0, temp0_18HAT0, temp_24HAT0, tmp_21HAT0) -> l1(head_15HATpost, head_19HATpost, i_17HATpost, i_83HATpost, length_16HATpost, nondet_12HATpost, rcd_47HATpost, rcd_77HATpost, result_11HATpost, result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HATpost, result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost, temp0_14HATpost, temp0_18HATpost, temp_24HATpost, tmp_21HATpost) :|: nondet_12HAT1 = nondet_12HAT1 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost = nondet_12HAT1 && nondet_12HATpost = nondet_12HATpost && length_16HATpost = result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_19HATpost = 0 && i_17HATpost = 0 && 0 <= i_17HATpost && i_17HATpost <= 0 && 0 <= head_19HATpost && head_19HATpost <= 0 && result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost <= length_16HATpost && length_16HATpost <= result_dot_nondet_sdv_special_RETURN_VALUE_13HATpost && head_15HAT0 = head_15HATpost && i_83HAT0 = i_83HATpost && rcd_47HAT0 = rcd_47HATpost && rcd_77HAT0 = rcd_77HATpost && result_11HAT0 = result_11HATpost && result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HAT0 = result_dot_SLAyer_malloc_sdv_special_RETURN_VALUE_20HATpost && temp0_14HAT0 = temp0_14HATpost && temp0_18HAT0 = temp0_18HATpost && temp_24HAT0 = temp_24HATpost && tmp_21HAT0 = tmp_21HATpost (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l3(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x25 = x25 && x4 <= x2 && x30 = x1 && x31 = x30 && x19 = x19 && x17 = x17 && x27 = x27 && x16 = x16 && x24 = x24 && x29 = x29 && x28 = x28 && x15 = x31 && x32 = x32 && x23 = x11 && 1 <= x25 && x25 <= 1 && 1 <= x25 && x25 <= 1 && x3 = x18 && x5 = x20 && x6 = x21 && x7 = x22 && x11 = x26 (3) l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) -> l4(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62) :|: x45 = x60 && x44 = x59 && x41 = x56 && x40 = x55 && x38 = x53 && x37 = x52 && x36 = x51 && x33 = x48 && 2 <= x37 && 1 <= x37 && x62 <= x57 && x57 <= x62 && x62 <= x49 && x49 <= x62 && x57 <= x49 && x49 <= x57 && x37 <= x58 && x58 <= x37 && x50 <= 2 && 2 <= x50 && x50 = 1 + x35 && x49 = x62 && x61 = x61 && x62 = x46 && 1 + x35 <= x37 && x54 = x54 && x57 = x57 && x58 = x58 (4) l4(x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77) -> l3(x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92) :|: 0 <= x65 && x88 = x88 && x67 <= x65 && x93 = x64 && x94 = x93 && x82 = x82 && x80 = x80 && x90 = x90 && x79 = x79 && x87 = x87 && x92 = x92 && x91 = x91 && x78 = x94 && x95 = x95 && x86 = x74 && 1 <= x88 && 2 <= x88 && x88 <= x80 && x66 = x81 && x68 = x83 && x69 = x84 && x70 = x85 && x74 = x89 (5) l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110) -> l5(x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x108 = x123 && x107 = x122 && x106 = x121 && x105 = x120 && x104 = x119 && x102 = x117 && x101 = x116 && x100 = x115 && x96 = x111 && 1 + x114 <= x100 && -1 + x113 <= x114 && x114 <= -1 + x113 && 1 + x114 <= x113 && x113 <= 1 + x114 && x113 = 1 + x98 && x112 = x125 && x124 = x124 && x125 = x109 && 1 + x98 <= x100 && x114 = x114 && x118 = x118 && 0 <= x98 (6) l5(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140) -> l4(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) :|: x140 = x155 && x139 = x154 && x138 = x153 && x137 = x152 && x136 = x151 && x135 = x150 && x134 = x149 && x133 = x148 && x132 = x147 && x131 = x146 && x130 = x145 && x129 = x144 && x128 = x143 && x127 = x142 && x126 = x141 (7) l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l3(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185) :|: x181 = x181 && x160 <= x158 && x186 = x157 && x187 = x186 && x175 = x175 && x173 = x173 && x183 = x183 && x172 = x172 && x180 = x180 && x185 = x185 && x184 = x184 && x171 = x187 && x188 = x188 && x179 = x167 && x181 <= 0 && x159 = x174 && x161 = x176 && x162 = x177 && x163 = x178 && x167 = x182 (8) l1(x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l2(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218) :|: x201 = x216 && x200 = x215 && x197 = x212 && x196 = x211 && x195 = x210 && x194 = x209 && x193 = x208 && x192 = x207 && x189 = x204 && 1 <= x193 && x218 <= x213 && x213 <= x218 && x218 <= x205 && x205 <= x218 && x213 <= x205 && x205 <= x213 && x193 <= x214 && x214 <= x193 && x206 <= 1 && 1 <= x206 && x206 = 1 + x191 && x205 = x218 && x217 = x217 && x218 = x202 && 1 + x191 <= x193 && x213 = x213 && x214 = x214 (9) l6(x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233) -> l0(x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248) :|: x233 = x248 && x232 = x247 && x231 = x246 && x230 = x245 && x229 = x244 && x228 = x243 && x227 = x242 && x226 = x241 && x225 = x240 && x224 = x239 && x223 = x238 && x222 = x237 && x221 = x236 && x220 = x235 && x219 = x234 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(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110) -> l5(x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x108 = x123 && x107 = x122 && x106 = x121 && x105 = x120 && x104 = x119 && x102 = x117 && x101 = x116 && x100 = x115 && x96 = x111 && 1 + x114 <= x100 && -1 + x113 <= x114 && x114 <= -1 + x113 && 1 + x114 <= x113 && x113 <= 1 + x114 && x113 = 1 + x98 && x112 = x125 && x124 = x124 && x125 = x109 && 1 + x98 <= x100 && x114 = x114 && x118 = x118 && 0 <= x98 (2) l5(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140) -> l4(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) :|: x140 = x155 && x139 = x154 && x138 = x153 && x137 = x152 && x136 = x151 && x135 = x150 && x134 = x149 && x133 = x148 && x132 = x147 && x131 = x146 && x130 = x145 && x129 = x144 && x128 = x143 && x127 = x142 && x126 = x141 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l4(x111:0, x97:0, x98:0, x99:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0, x110:0) -> l4(x111:0, x109:0, 1 + x98:0, -1 + (1 + x98:0), x100:0, x101:0, x102:0, x118:0, x104:0, x105:0, x106:0, x107:0, x108:0, x124:0, x109:0) :|: x100:0 >= 1 + x98:0 && x98:0 > -1 && 1 + x98:0 = 1 + (-1 + (1 + x98:0)) && x100:0 >= 1 + (-1 + (1 + x98:0)) ---------------------------------------- (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) -> l4(x3, x5) ---------------------------------------- (8) Obligation: Rules: l4(x98:0, x100:0) -> l4(1 + x98:0, x100:0) :|: x100:0 >= 1 + x98:0 && x98:0 > -1 && 1 + x98:0 = 1 + (-1 + (1 + x98:0)) && x100:0 >= 1 + (-1 + (1 + x98:0)) ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (10) Obligation: Rules: l4(x98:0, x100:0) -> l4(c, x100:0) :|: c = 1 + x98:0 && (x100:0 >= 1 + x98:0 && x98:0 > -1 && 1 + x98:0 = 1 + (-1 + (1 + x98:0)) && x100:0 >= 1 + (-1 + (1 + x98:0))) ---------------------------------------- (11) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l4(x, x1)] = -x + x1 The following rules are decreasing: l4(x98:0, x100:0) -> l4(c, x100:0) :|: c = 1 + x98:0 && (x100:0 >= 1 + x98:0 && x98:0 > -1 && 1 + x98:0 = 1 + (-1 + (1 + x98:0)) && x100:0 >= 1 + (-1 + (1 + x98:0))) The following rules are bounded: l4(x98:0, x100:0) -> l4(c, x100:0) :|: c = 1 + x98:0 && (x100:0 >= 1 + x98:0 && x98:0 > -1 && 1 + x98:0 = 1 + (-1 + (1 + x98:0)) && x100:0 >= 1 + (-1 + (1 + x98:0))) ---------------------------------------- (12) YES