MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 3657 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 109 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && -1 * x5 + x6 <= 0 && -1 * x5 + x6 <= 0 l3(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x22 = x15 l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x35 = x35 l1(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && 0 <= x53 && x53 <= 0 && x53 = x53 && x48 <= x47 && x47 <= x48 && -1 * x47 + x48 <= 0 && -1 * x47 + x48 <= 0 l5(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 l1(x70, x71, x72, x73, x74, x75, x76) -> l7(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x81 = x81 && x76 <= x75 && x75 <= x76 && -1 * x75 + x76 <= 0 && -1 * x75 + x76 <= 0 l7(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x93 = x86 l8(x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x110 = 1 + x103 l6(x112, x113, x114, x115, x116, x117, x118) -> l1(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119 l1(x126, x127, x128, x129, x130, x131, x132) -> l9(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 0 <= x137 && x137 <= 0 && x137 = x137 && 0 <= -1 - x131 + x132 l9(x140, x141, x142, x143, x144, x145, x146) -> l1(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 l1(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 && x165 = x165 && 0 <= -1 - x159 + x160 l11(x168, x169, x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = x171 l12(x182, x183, x184, x185, x186, x187, x188) -> l10(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && x194 = 1 + x187 l10(x196, x197, x198, x199, x200, x201, x202) -> l1(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 l13(x210, x211, x212, x213, x214, x215, x216) -> l0(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 Start term: l13(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (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_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && -1 * x5 + x6 <= 0 && -1 * x5 + x6 <= 0 l3(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x22 = x15 l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x35 = x35 l1(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && 0 <= x53 && x53 <= 0 && x53 = x53 && x48 <= x47 && x47 <= x48 && -1 * x47 + x48 <= 0 && -1 * x47 + x48 <= 0 l5(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 l1(x70, x71, x72, x73, x74, x75, x76) -> l7(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x81 = x81 && x76 <= x75 && x75 <= x76 && -1 * x75 + x76 <= 0 && -1 * x75 + x76 <= 0 l7(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x93 = x86 l8(x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x110 = 1 + x103 l6(x112, x113, x114, x115, x116, x117, x118) -> l1(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119 l1(x126, x127, x128, x129, x130, x131, x132) -> l9(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 0 <= x137 && x137 <= 0 && x137 = x137 && 0 <= -1 - x131 + x132 l9(x140, x141, x142, x143, x144, x145, x146) -> l1(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 l1(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 && x165 = x165 && 0 <= -1 - x159 + x160 l11(x168, x169, x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = x171 l12(x182, x183, x184, x185, x186, x187, x188) -> l10(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && x194 = 1 + x187 l10(x196, x197, x198, x199, x200, x201, x202) -> l1(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 l13(x210, x211, x212, x213, x214, x215, x216) -> l0(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 Start term: l13(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost (2) l1(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x5 = x12 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && -1 * x5 + x6 <= 0 && -1 * x5 + x6 <= 0 (3) l3(x14, x15, x16, x17, x18, x19, x20) -> l4(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x19 = x26 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x22 = x15 (4) l4(x28, x29, x30, x31, x32, x33, x34) -> l2(x35, x36, x37, x38, x39, x40, x41) :|: x34 = x41 && x33 = x40 && x32 = x39 && x31 = x38 && x30 = x37 && x29 = x36 && x35 = x35 (5) l1(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && 0 <= x53 && x53 <= 0 && x53 = x53 && x48 <= x47 && x47 <= x48 && -1 * x47 + x48 <= 0 && -1 * x47 + x48 <= 0 (6) l5(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 (7) l1(x70, x71, x72, x73, x74, x75, x76) -> l7(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x81 = x81 && x76 <= x75 && x75 <= x76 && -1 * x75 + x76 <= 0 && -1 * x75 + x76 <= 0 (8) l7(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x93 = x86 (9) l8(x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x110 = 1 + x103 (10) l6(x112, x113, x114, x115, x116, x117, x118) -> l1(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119 (11) l1(x126, x127, x128, x129, x130, x131, x132) -> l9(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 0 <= x137 && x137 <= 0 && x137 = x137 && 0 <= -1 - x131 + x132 (12) l9(x140, x141, x142, x143, x144, x145, x146) -> l1(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 (13) l1(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 && x165 = x165 && 0 <= -1 - x159 + x160 (14) l11(x168, x169, x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = x171 (15) l12(x182, x183, x184, x185, x186, x187, x188) -> l10(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && x194 = 1 + x187 (16) l10(x196, x197, x198, x199, x200, x201, x202) -> l1(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 (17) l13(x210, x211, x212, x213, x214, x215, x216) -> l0(x217, x218, x219, x220, x221, x222, x223) :|: x216 = x223 && x215 = x222 && x214 = x221 && x213 = x220 && x212 = x219 && x211 = x218 && x210 = x217 Arcs: (1) -> (2), (5), (7), (11), (13) (2) -> (3) (3) -> (4) (5) -> (6) (6) -> (2), (5), (7), (11), (13) (7) -> (8) (8) -> (9) (9) -> (10) (10) -> (2), (5), (7), (11), (13) (11) -> (12) (12) -> (2), (5), (7), (11), (13) (13) -> (14) (14) -> (15) (15) -> (16) (16) -> (2), (5), (7), (11), (13) (17) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x42, x43, x44, x45, x46, x47, x48) -> l5(x49, x50, x51, x52, x53, x54, x55) :|: x48 = x55 && x47 = x54 && x45 = x52 && x44 = x51 && x43 = x50 && x42 = x49 && 0 <= x53 && x53 <= 0 && x53 = x53 && x48 <= x47 && x47 <= x48 && -1 * x47 + x48 <= 0 && -1 * x47 + x48 <= 0 (2) l6(x112, x113, x114, x115, x116, x117, x118) -> l1(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x113 = x120 && x112 = x119 (3) l8(x98, x99, x100, x101, x102, x103, x104) -> l6(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && x110 = 1 + x103 (4) l7(x84, x85, x86, x87, x88, x89, x90) -> l8(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x93 = x86 (5) l1(x70, x71, x72, x73, x74, x75, x76) -> l7(x77, x78, x79, x80, x81, x82, x83) :|: x76 = x83 && x75 = x82 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x81 = x81 && x76 <= x75 && x75 <= x76 && -1 * x75 + x76 <= 0 && -1 * x75 + x76 <= 0 (6) l9(x140, x141, x142, x143, x144, x145, x146) -> l1(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 (7) l1(x126, x127, x128, x129, x130, x131, x132) -> l9(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 0 <= x137 && x137 <= 0 && x137 = x137 && 0 <= -1 - x131 + x132 (8) l10(x196, x197, x198, x199, x200, x201, x202) -> l1(x203, x204, x205, x206, x207, x208, x209) :|: x202 = x209 && x201 = x208 && x200 = x207 && x199 = x206 && x198 = x205 && x197 = x204 && x196 = x203 (9) l12(x182, x183, x184, x185, x186, x187, x188) -> l10(x189, x190, x191, x192, x193, x194, x195) :|: x188 = x195 && x186 = x193 && x185 = x192 && x184 = x191 && x183 = x190 && x182 = x189 && x194 = 1 + x187 (10) l11(x168, x169, x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 && x178 = x171 (11) l1(x154, x155, x156, x157, x158, x159, x160) -> l11(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 && x165 = x165 && 0 <= -1 - x159 + x160 (12) l5(x56, x57, x58, x59, x60, x61, x62) -> l1(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x58 = x65 && x57 = x64 && x56 = x63 Arcs: (1) -> (12) (2) -> (1), (5), (7), (11) (3) -> (2) (4) -> (3) (5) -> (4) (6) -> (1), (5), (7), (11) (7) -> (6) (8) -> (1), (5), (7), (11) (9) -> (8) (10) -> (9) (11) -> (10) (12) -> (1), (5), (7), (11) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x42:0, x43:0, x44:0, x45:0, x46:0, x47:0, x47:0) -> l1(x42:0, x43:0, x44:0, x45:0, x53:0, x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 l1(x126:0, x127:0, x128:0, x129:0, x130:0, x131:0, x132:0) -> l1(x126:0, x127:0, x128:0, x129:0, x137:0, x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 l1(x154:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0) -> l1(x154:0, x155:0, x156:0, x157:0, x165:0, 1 + x159:0, x160:0) :|: 0 <= -1 - x159:0 + x160:0 l1(x105:0, x106:0, x107:0, x108:0, x74:0, x111:0, x111:0) -> l1(x105:0, x106:0, x107:0, x108:0, x109:0, 1 + x111:0, x111:0) :|: 0 >= -1 * x111:0 + x111:0 ---------------------------------------- (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) -> l1(x6, x7) ---------------------------------------- (8) Obligation: Rules: l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 l1(x159:0, x160:0) -> l1(1 + x159:0, x160:0) :|: 0 <= -1 - x159:0 + x160:0 l1(x111:0, x111:0) -> l1(1 + x111:0, x111:0) :|: 0 >= -1 * x111:0 + x111:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(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 - PolynomialOrderProcessor Rules: l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 l1(x159:0, x160:0) -> l1(c, x160:0) :|: c = 1 + x159:0 && 0 <= -1 - x159:0 + x160:0 l1(x111:0, x111:0) -> l1(c1, x111:0) :|: c1 = 1 + x111:0 && 0 >= -1 * x111:0 + x111:0 Found the following polynomial interpretation: [l1(x, x1)] = -x + x1 The following rules are decreasing: l1(x159:0, x160:0) -> l1(c, x160:0) :|: c = 1 + x159:0 && 0 <= -1 - x159:0 + x160:0 l1(x111:0, x111:0) -> l1(c1, x111:0) :|: c1 = 1 + x111:0 && 0 >= -1 * x111:0 + x111:0 The following rules are bounded: l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 l1(x159:0, x160:0) -> l1(c, x160:0) :|: c = 1 + x159:0 && 0 <= -1 - x159:0 + x160:0 l1(x111:0, x111:0) -> l1(c1, x111:0) :|: c1 = 1 + x111:0 && 0 >= -1 * x111:0 + x111:0 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 ---------------------------------------- (10) Obligation: Rules: l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 (2) l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 Arcs: (1) -> (1) (2) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) l1(x131:0, x132:0) -> l1(x131:0, x132:0) :|: x137:0 < 1 && x137:0 > -1 && 0 <= -1 - x131:0 + x132:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: l1(x131:0:0, x132:0:0) -> l1(x131:0:0, x132:0:0) :|: x137:0:0 < 1 && x137:0:0 > -1 && 0 <= -1 - x131:0:0 + x132:0:0 ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l1(x47:0, x47:0) -> l1(x47:0, x47:0) :|: 0 >= -1 * x47:0 + x47:0 && x53:0 > -1 && x53:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l1(x47:0:0, x47:0:0) -> l1(x47:0:0, x47:0:0) :|: 0 >= -1 * x47:0:0 + x47:0:0 && x53:0:0 > -1 && x53:0:0 < 1