MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 5687 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 71 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 266 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 4 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (16) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_8HAT0 = tmp_8HATpost && Result_4HAT0 = Result_4HATpost l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x = x5 && 0 <= x6 && x6 <= 0 && x6 = x6 && 0 <= -1 - x3 + x4 l2(x10, x11, x12, x13, x14) -> l5(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && x16 = x16 && 0 <= -1 - x13 + x14 l5(x20, x21, x22, x23, x24) -> l6(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 && 1 + x21 <= 0 l5(x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && 1 <= x31 l6(x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 l4(x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l2(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x61 = x66 && x60 = x65 && x67 = 1 + x62 && -1 * x63 + x64 <= 0 l1(x70, x71, x72, x73, x74) -> l7(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 && 0 <= -1 - x72 + x73 l1(x80, x81, x82, x83, x84) -> l8(x85, x86, x87, x88, x89) :|: x84 = x89 && x83 = x88 && x82 = x87 && x81 = x86 && x85 = x85 && -1 * x82 + x83 <= 0 l7(x90, x91, x92, x93, x94) -> l3(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x90 = x95 && 0 <= x96 && x96 <= 0 && x96 = x96 && 0 <= -1 - x93 + x94 l7(x100, x101, x102, x103, x104) -> l9(x105, x106, x107, x108, x109) :|: x104 = x109 && x103 = x108 && x102 = x107 && x100 = x105 && x106 = x106 && 0 <= -1 - x103 + x104 l9(x110, x111, x112, x113, x114) -> l10(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 && 1 + x111 <= 0 l9(x120, x121, x122, x123, x124) -> l10(x125, x126, x127, x128, x129) :|: x124 = x129 && x123 = x128 && x122 = x127 && x121 = x126 && x120 = x125 && 1 <= x121 l10(x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139) :|: x134 = x139 && x132 = x137 && x131 = x136 && x130 = x135 && x138 = 1 + x133 l7(x140, x141, x142, x143, x144) -> l1(x145, x146, x147, x148, x149) :|: x144 = x149 && x143 = x148 && x141 = x146 && x140 = x145 && x147 = 1 + x142 && -1 * x143 + x144 <= 0 l3(x150, x151, x152, x153, x154) -> l11(x155, x156, x157, x158, x159) :|: x154 = x159 && x153 = x158 && x152 = x157 && x150 = x155 && 0 <= x156 && x156 <= 0 && x156 = x156 && 0 <= -1 - x153 + x154 l11(x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169) :|: x164 = x169 && x163 = x168 && x162 = x167 && x161 = x166 && x160 = x165 l3(x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179) :|: x174 = x179 && x173 = x178 && x172 = x177 && x170 = x175 && x176 = x176 && 0 <= -1 - x173 + x174 l12(x180, x181, x182, x183, x184) -> l13(x185, x186, x187, x188, x189) :|: x184 = x189 && x183 = x188 && x182 = x187 && x181 = x186 && x180 = x185 && 1 + x181 <= 0 l12(x190, x191, x192, x193, x194) -> l13(x195, x196, x197, x198, x199) :|: x194 = x199 && x193 = x198 && x192 = x197 && x191 = x196 && x190 = x195 && 1 <= x191 l13(x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209) :|: x204 = x209 && x202 = x207 && x201 = x206 && x200 = x205 && x208 = 1 + x203 l14(x210, x211, x212, x213, x214) -> l0(x215, x216, x217, x218, x219) :|: x214 = x219 && x213 = x218 && x212 = x217 && x211 = x216 && x210 = x215 Start term: l14(Result_4HAT0, 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, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_8HAT0 = tmp_8HATpost && Result_4HAT0 = Result_4HATpost l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x = x5 && 0 <= x6 && x6 <= 0 && x6 = x6 && 0 <= -1 - x3 + x4 l2(x10, x11, x12, x13, x14) -> l5(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && x16 = x16 && 0 <= -1 - x13 + x14 l5(x20, x21, x22, x23, x24) -> l6(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 && 1 + x21 <= 0 l5(x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && 1 <= x31 l6(x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 l4(x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l2(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x61 = x66 && x60 = x65 && x67 = 1 + x62 && -1 * x63 + x64 <= 0 l1(x70, x71, x72, x73, x74) -> l7(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 && 0 <= -1 - x72 + x73 l1(x80, x81, x82, x83, x84) -> l8(x85, x86, x87, x88, x89) :|: x84 = x89 && x83 = x88 && x82 = x87 && x81 = x86 && x85 = x85 && -1 * x82 + x83 <= 0 l7(x90, x91, x92, x93, x94) -> l3(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x90 = x95 && 0 <= x96 && x96 <= 0 && x96 = x96 && 0 <= -1 - x93 + x94 l7(x100, x101, x102, x103, x104) -> l9(x105, x106, x107, x108, x109) :|: x104 = x109 && x103 = x108 && x102 = x107 && x100 = x105 && x106 = x106 && 0 <= -1 - x103 + x104 l9(x110, x111, x112, x113, x114) -> l10(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 && 1 + x111 <= 0 l9(x120, x121, x122, x123, x124) -> l10(x125, x126, x127, x128, x129) :|: x124 = x129 && x123 = x128 && x122 = x127 && x121 = x126 && x120 = x125 && 1 <= x121 l10(x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139) :|: x134 = x139 && x132 = x137 && x131 = x136 && x130 = x135 && x138 = 1 + x133 l7(x140, x141, x142, x143, x144) -> l1(x145, x146, x147, x148, x149) :|: x144 = x149 && x143 = x148 && x141 = x146 && x140 = x145 && x147 = 1 + x142 && -1 * x143 + x144 <= 0 l3(x150, x151, x152, x153, x154) -> l11(x155, x156, x157, x158, x159) :|: x154 = x159 && x153 = x158 && x152 = x157 && x150 = x155 && 0 <= x156 && x156 <= 0 && x156 = x156 && 0 <= -1 - x153 + x154 l11(x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169) :|: x164 = x169 && x163 = x168 && x162 = x167 && x161 = x166 && x160 = x165 l3(x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179) :|: x174 = x179 && x173 = x178 && x172 = x177 && x170 = x175 && x176 = x176 && 0 <= -1 - x173 + x174 l12(x180, x181, x182, x183, x184) -> l13(x185, x186, x187, x188, x189) :|: x184 = x189 && x183 = x188 && x182 = x187 && x181 = x186 && x180 = x185 && 1 + x181 <= 0 l12(x190, x191, x192, x193, x194) -> l13(x195, x196, x197, x198, x199) :|: x194 = x199 && x193 = x198 && x192 = x197 && x191 = x196 && x190 = x195 && 1 <= x191 l13(x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209) :|: x204 = x209 && x202 = x207 && x201 = x206 && x200 = x205 && x208 = 1 + x203 l14(x210, x211, x212, x213, x214) -> l0(x215, x216, x217, x218, x219) :|: x214 = x219 && x213 = x218 && x212 = x217 && x211 = x216 && x210 = x215 Start term: l14(Result_4HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, tmp_8HAT0, x_5HAT0, y_6HAT0, z_7HAT0) -> l1(Result_4HATpost, tmp_8HATpost, x_5HATpost, y_6HATpost, z_7HATpost) :|: z_7HAT0 = z_7HATpost && y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_8HAT0 = tmp_8HATpost && Result_4HAT0 = Result_4HATpost (2) l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x = x5 && 0 <= x6 && x6 <= 0 && x6 = x6 && 0 <= -1 - x3 + x4 (3) l2(x10, x11, x12, x13, x14) -> l5(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && x16 = x16 && 0 <= -1 - x13 + x14 (4) l5(x20, x21, x22, x23, x24) -> l6(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 && 1 + x21 <= 0 (5) l5(x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && 1 <= x31 (6) l6(x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 (7) l4(x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (8) l2(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x61 = x66 && x60 = x65 && x67 = 1 + x62 && -1 * x63 + x64 <= 0 (9) l1(x70, x71, x72, x73, x74) -> l7(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 && 0 <= -1 - x72 + x73 (10) l1(x80, x81, x82, x83, x84) -> l8(x85, x86, x87, x88, x89) :|: x84 = x89 && x83 = x88 && x82 = x87 && x81 = x86 && x85 = x85 && -1 * x82 + x83 <= 0 (11) l7(x90, x91, x92, x93, x94) -> l3(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x90 = x95 && 0 <= x96 && x96 <= 0 && x96 = x96 && 0 <= -1 - x93 + x94 (12) l7(x100, x101, x102, x103, x104) -> l9(x105, x106, x107, x108, x109) :|: x104 = x109 && x103 = x108 && x102 = x107 && x100 = x105 && x106 = x106 && 0 <= -1 - x103 + x104 (13) l9(x110, x111, x112, x113, x114) -> l10(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 && 1 + x111 <= 0 (14) l9(x120, x121, x122, x123, x124) -> l10(x125, x126, x127, x128, x129) :|: x124 = x129 && x123 = x128 && x122 = x127 && x121 = x126 && x120 = x125 && 1 <= x121 (15) l10(x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139) :|: x134 = x139 && x132 = x137 && x131 = x136 && x130 = x135 && x138 = 1 + x133 (16) l7(x140, x141, x142, x143, x144) -> l1(x145, x146, x147, x148, x149) :|: x144 = x149 && x143 = x148 && x141 = x146 && x140 = x145 && x147 = 1 + x142 && -1 * x143 + x144 <= 0 (17) l3(x150, x151, x152, x153, x154) -> l11(x155, x156, x157, x158, x159) :|: x154 = x159 && x153 = x158 && x152 = x157 && x150 = x155 && 0 <= x156 && x156 <= 0 && x156 = x156 && 0 <= -1 - x153 + x154 (18) l11(x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169) :|: x164 = x169 && x163 = x168 && x162 = x167 && x161 = x166 && x160 = x165 (19) l3(x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179) :|: x174 = x179 && x173 = x178 && x172 = x177 && x170 = x175 && x176 = x176 && 0 <= -1 - x173 + x174 (20) l12(x180, x181, x182, x183, x184) -> l13(x185, x186, x187, x188, x189) :|: x184 = x189 && x183 = x188 && x182 = x187 && x181 = x186 && x180 = x185 && 1 + x181 <= 0 (21) l12(x190, x191, x192, x193, x194) -> l13(x195, x196, x197, x198, x199) :|: x194 = x199 && x193 = x198 && x192 = x197 && x191 = x196 && x190 = x195 && 1 <= x191 (22) l13(x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209) :|: x204 = x209 && x202 = x207 && x201 = x206 && x200 = x205 && x208 = 1 + x203 (23) l14(x210, x211, x212, x213, x214) -> l0(x215, x216, x217, x218, x219) :|: x214 = x219 && x213 = x218 && x212 = x217 && x211 = x216 && x210 = x215 Arcs: (1) -> (9), (10) (2) -> (17), (19) (3) -> (4), (5) (4) -> (6) (5) -> (6) (6) -> (7) (7) -> (2), (3), (8) (8) -> (9), (10) (9) -> (11), (12), (16) (11) -> (17), (19) (12) -> (13), (14) (13) -> (15) (14) -> (15) (15) -> (2), (3), (8) (16) -> (9), (10) (17) -> (18) (18) -> (17), (19) (19) -> (20), (21) (20) -> (22) (21) -> (22) (22) -> (2), (3), (8) (23) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x70, x71, x72, x73, x74) -> l7(x75, x76, x77, x78, x79) :|: x74 = x79 && x73 = x78 && x72 = x77 && x71 = x76 && x70 = x75 && 0 <= -1 - x72 + x73 (2) l7(x140, x141, x142, x143, x144) -> l1(x145, x146, x147, x148, x149) :|: x144 = x149 && x143 = x148 && x141 = x146 && x140 = x145 && x147 = 1 + x142 && -1 * x143 + x144 <= 0 (3) l2(x60, x61, x62, x63, x64) -> l1(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x61 = x66 && x60 = x65 && x67 = 1 + x62 && -1 * x63 + x64 <= 0 (4) l4(x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (5) l6(x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49) :|: x44 = x49 && x42 = x47 && x41 = x46 && x40 = x45 && x48 = 1 + x43 (6) l5(x30, x31, x32, x33, x34) -> l6(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && 1 <= x31 (7) l5(x20, x21, x22, x23, x24) -> l6(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x22 = x27 && x21 = x26 && x20 = x25 && 1 + x21 <= 0 (8) l2(x10, x11, x12, x13, x14) -> l5(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x10 = x15 && x16 = x16 && 0 <= -1 - x13 + x14 (9) l13(x200, x201, x202, x203, x204) -> l2(x205, x206, x207, x208, x209) :|: x204 = x209 && x202 = x207 && x201 = x206 && x200 = x205 && x208 = 1 + x203 (10) l12(x190, x191, x192, x193, x194) -> l13(x195, x196, x197, x198, x199) :|: x194 = x199 && x193 = x198 && x192 = x197 && x191 = x196 && x190 = x195 && 1 <= x191 (11) l12(x180, x181, x182, x183, x184) -> l13(x185, x186, x187, x188, x189) :|: x184 = x189 && x183 = x188 && x182 = x187 && x181 = x186 && x180 = x185 && 1 + x181 <= 0 (12) l3(x170, x171, x172, x173, x174) -> l12(x175, x176, x177, x178, x179) :|: x174 = x179 && x173 = x178 && x172 = x177 && x170 = x175 && x176 = x176 && 0 <= -1 - x173 + x174 (13) l11(x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169) :|: x164 = x169 && x163 = x168 && x162 = x167 && x161 = x166 && x160 = x165 (14) l3(x150, x151, x152, x153, x154) -> l11(x155, x156, x157, x158, x159) :|: x154 = x159 && x153 = x158 && x152 = x157 && x150 = x155 && 0 <= x156 && x156 <= 0 && x156 = x156 && 0 <= -1 - x153 + x154 (15) l7(x90, x91, x92, x93, x94) -> l3(x95, x96, x97, x98, x99) :|: x94 = x99 && x93 = x98 && x92 = x97 && x90 = x95 && 0 <= x96 && x96 <= 0 && x96 = x96 && 0 <= -1 - x93 + x94 (16) l2(x, x1, x2, x3, x4) -> l3(x5, x6, x7, x8, x9) :|: x4 = x9 && x3 = x8 && x2 = x7 && x = x5 && 0 <= x6 && x6 <= 0 && x6 = x6 && 0 <= -1 - x3 + x4 (17) l10(x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139) :|: x134 = x139 && x132 = x137 && x131 = x136 && x130 = x135 && x138 = 1 + x133 (18) l9(x120, x121, x122, x123, x124) -> l10(x125, x126, x127, x128, x129) :|: x124 = x129 && x123 = x128 && x122 = x127 && x121 = x126 && x120 = x125 && 1 <= x121 (19) l9(x110, x111, x112, x113, x114) -> l10(x115, x116, x117, x118, x119) :|: x114 = x119 && x113 = x118 && x112 = x117 && x111 = x116 && x110 = x115 && 1 + x111 <= 0 (20) l7(x100, x101, x102, x103, x104) -> l9(x105, x106, x107, x108, x109) :|: x104 = x109 && x103 = x108 && x102 = x107 && x100 = x105 && x106 = x106 && 0 <= -1 - x103 + x104 Arcs: (1) -> (2), (15), (20) (2) -> (1) (3) -> (1) (4) -> (3), (8), (16) (5) -> (4) (6) -> (5) (7) -> (5) (8) -> (6), (7) (9) -> (3), (8), (16) (10) -> (9) (11) -> (9) (12) -> (10), (11) (13) -> (12), (14) (14) -> (13) (15) -> (12), (14) (16) -> (12), (14) (17) -> (3), (8), (16) (18) -> (17) (19) -> (17) (20) -> (18), (19) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l3(x170:0, x171:0, x172:0, x173:0, x174:0) -> l2(x170:0, x176:0, x172:0, 1 + x173:0, x174:0) :|: 0 <= -1 - x173:0 + x174:0 && x176:0 > 0 l1(x105:0, x71:0, x107:0, x108:0, x109:0) -> l2(x105:0, x106:0, x107:0, 1 + x108:0, x109:0) :|: 0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0 l2(x10:0, x11:0, x12:0, x13:0, x14:0) -> l2(x10:0, x16:0, x12:0, 1 + x13:0, x14:0) :|: 0 <= -1 - x13:0 + x14:0 && x16:0 < 0 l1(x, x1, x2, x3, x4) -> l2(x, x5, x2, 1 + x3, x4) :|: 0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3 l2(x5:0, x1:0, x2:0, x3:0, x4:0) -> l3(x5:0, x6:0, x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x150:0, x151:0, x152:0, x153:0, x154:0) -> l3(x150:0, x156:0, x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x6, x7, x8, x9, x10) -> l2(x6, x11, x8, 1 + x9, x10) :|: 0 <= -1 - x9 + x10 && x11 < 0 l1(x12, x13, x14, x15, x16) -> l3(x12, x17, x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 l2(x18, x19, x20, x21, x22) -> l2(x18, x23, x20, 1 + x21, x22) :|: 0 <= -1 - x21 + x22 && x23 > 0 l1(x145:0, x146:0, x72:0, x148:0, x149:0) -> l1(x145:0, x146:0, 1 + x72:0, x148:0, x149:0) :|: 0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0 l2(x60:0, x61:0, x62:0, x63:0, x64:0) -> l1(x60:0, x61:0, 1 + x62:0, x63:0, x64:0) :|: 0 >= -1 * x63:0 + x64:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3, x4, x5) -> l3(x3, x4, x5) l1(x1, x2, x3, x4, x5) -> l1(x3, x4, x5) l2(x1, x2, x3, x4, x5) -> l2(x3, x4, x5) ---------------------------------------- (8) Obligation: Rules: l3(x172:0, x173:0, x174:0) -> l2(x172:0, 1 + x173:0, x174:0) :|: 0 <= -1 - x173:0 + x174:0 && x176:0 > 0 l1(x107:0, x108:0, x109:0) -> l2(x107:0, 1 + x108:0, x109:0) :|: 0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0 l2(x12:0, x13:0, x14:0) -> l2(x12:0, 1 + x13:0, x14:0) :|: 0 <= -1 - x13:0 + x14:0 && x16:0 < 0 l1(x2, x3, x4) -> l2(x2, 1 + x3, x4) :|: 0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3 l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, 1 + x9, x10) :|: 0 <= -1 - x9 + x10 && x11 < 0 l1(x14, x15, x16) -> l3(x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 l2(x20, x21, x22) -> l2(x20, 1 + x21, x22) :|: 0 <= -1 - x21 + x22 && x23 > 0 l1(x72:0, x148:0, x149:0) -> l1(1 + x72:0, x148:0, x149:0) :|: 0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0 l2(x62:0, x63:0, x64:0) -> l1(1 + x62:0, x63:0, x64:0) :|: 0 >= -1 * x63:0 + x64:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l3(VARIABLE, INTEGER, INTEGER) l2(VARIABLE, INTEGER, INTEGER) l1(INTEGER, 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: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l1(x107:0, x108:0, x109:0) -> l2(x107:0, c1, x109:0) :|: c1 = 1 + x108:0 && (0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l1(x2, x3, x4) -> l2(x2, c3, x4) :|: c3 = 1 + x3 && (0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l1(x14, x15, x16) -> l3(x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l1(x72:0, x148:0, x149:0) -> l1(c6, x148:0, x149:0) :|: c6 = 1 + x72:0 && (0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0) l2(x62:0, x63:0, x64:0) -> l1(c7, x63:0, x64:0) :|: c7 = 1 + x62:0 && 0 >= -1 * x63:0 + x64:0 Found the following polynomial interpretation: [l3(x, x1, x2)] = 0 [l2(x3, x4, x5)] = 0 [l1(x6, x7, x8)] = -1 - x7 + x8 The following rules are decreasing: l2(x62:0, x63:0, x64:0) -> l1(c7, x63:0, x64:0) :|: c7 = 1 + x62:0 && 0 >= -1 * x63:0 + x64:0 The following rules are bounded: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l1(x107:0, x108:0, x109:0) -> l2(x107:0, c1, x109:0) :|: c1 = 1 + x108:0 && (0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l1(x2, x3, x4) -> l2(x2, c3, x4) :|: c3 = 1 + x3 && (0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l1(x14, x15, x16) -> l3(x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l2(x62:0, x63:0, x64:0) -> l1(c7, x63:0, x64:0) :|: c7 = 1 + x62:0 && 0 >= -1 * x63:0 + x64:0 - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l1(x107:0, x108:0, x109:0) -> l2(x107:0, c1, x109:0) :|: c1 = 1 + x108:0 && (0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l1(x2, x3, x4) -> l2(x2, c3, x4) :|: c3 = 1 + x3 && (0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l1(x14, x15, x16) -> l3(x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l1(x72:0, x148:0, x149:0) -> l1(c6, x148:0, x149:0) :|: c6 = 1 + x72:0 && (0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0) Found the following polynomial interpretation: [l3(x, x1, x2)] = 0 [l2(x3, x4, x5)] = 0 [l1(x6, x7, x8)] = 1 The following rules are decreasing: l1(x107:0, x108:0, x109:0) -> l2(x107:0, c1, x109:0) :|: c1 = 1 + x108:0 && (0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0) l1(x2, x3, x4) -> l2(x2, c3, x4) :|: c3 = 1 + x3 && (0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3) l1(x14, x15, x16) -> l3(x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 The following rules are bounded: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l1(x107:0, x108:0, x109:0) -> l2(x107:0, c1, x109:0) :|: c1 = 1 + x108:0 && (0 <= -1 - x108:0 + x109:0 && x106:0 > 0 && 0 <= -1 - x107:0 + x108:0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l1(x2, x3, x4) -> l2(x2, c3, x4) :|: c3 = 1 + x3 && (0 <= -1 - x3 + x4 && x5 < 0 && 0 <= -1 - x2 + x3) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l1(x14, x15, x16) -> l3(x14, x15, x16) :|: 0 <= -1 - x15 + x16 && 0 <= -1 - x14 + x15 && x17 > -1 && x17 < 1 l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l1(x72:0, x148:0, x149:0) -> l1(c6, x148:0, x149:0) :|: c6 = 1 + x72:0 && (0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof Rules: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l1(x72:0, x148:0, x149:0) -> l1(c6, x148:0, x149:0) :|: c6 = 1 + x72:0 && (0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0) Interpretation: [ l3 ] = -2*l3_2 + 2*l3_3 + -1 [ l2 ] = 2*l2_3 + -2*l2_2 [ l1 ] = -1*l1_1 + l1_2 The following rules are decreasing: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l1(x72:0, x148:0, x149:0) -> l1(c6, x148:0, x149:0) :|: c6 = 1 + x72:0 && (0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0) The following rules are bounded: l3(x172:0, x173:0, x174:0) -> l2(x172:0, c, x174:0) :|: c = 1 + x173:0 && (0 <= -1 - x173:0 + x174:0 && x176:0 > 0) l2(x12:0, x13:0, x14:0) -> l2(x12:0, c2, x14:0) :|: c2 = 1 + x13:0 && (0 <= -1 - x13:0 + x14:0 && x16:0 < 0) l2(x2:0, x3:0, x4:0) -> l3(x2:0, x3:0, x4:0) :|: x6:0 < 1 && x6:0 > -1 && 0 <= -1 - x3:0 + x4:0 l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 l3(x8, x9, x10) -> l2(x8, c4, x10) :|: c4 = 1 + x9 && (0 <= -1 - x9 + x10 && x11 < 0) l2(x20, x21, x22) -> l2(x20, c5, x22) :|: c5 = 1 + x21 && (0 <= -1 - x21 + x22 && x23 > 0) l1(x72:0, x148:0, x149:0) -> l1(c6, x148:0, x149:0) :|: c6 = 1 + x72:0 && (0 <= -1 - x72:0 + x148:0 && 0 >= -1 * x148:0 + x149:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof - IntTRS Rules: l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 ---------------------------------------- (10) Obligation: Rules: l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l3(x152:0, x153:0, x154:0) -> l3(x152:0, x153:0, x154:0) :|: x156:0 < 1 && x156:0 > -1 && 0 <= -1 - x153:0 + x154:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l3(x152:0:0, x153:0:0, x154:0:0) -> l3(x152:0:0, x153:0:0, x154:0:0) :|: x156:0:0 < 1 && x156:0:0 > -1 && 0 <= -1 - x153:0:0 + x154:0:0 ---------------------------------------- (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(x153:0:0, x154:0:0) -> l3(x153:0:0, x154:0:0) :|: x156:0:0 < 1 && x156:0:0 > -1 && 0 <= -1 - x153:0:0 + x154:0:0