MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1959 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 9 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTChainingProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 94 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IRSwTChainingProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IRSwTTerminationDigraphProof [EQUIVALENT, 218 ms] (18) IRSwT (19) IntTRSCompressionProof [EQUIVALENT, 11 ms] (20) IRSwT (21) TempFilterProof [SOUND, 7349 ms] (22) IRSwT (23) IRSwTTerminationDigraphProof [EQUIVALENT, 84 ms] (24) IRSwT (25) IntTRSCompressionProof [EQUIVALENT, 0 ms] (26) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(NHAT0, choiceHAT0, iHAT0, posHAT0, seqHAT0, walkerHAT0, zHAT0) -> l1(NHATpost, choiceHATpost, iHATpost, posHATpost, seqHATpost, walkerHATpost, zHATpost) :|: zHAT0 = zHATpost && walkerHAT0 = walkerHATpost && seqHAT0 = seqHATpost && posHAT0 = posHATpost && iHAT0 = iHATpost && choiceHAT0 = choiceHATpost && NHAT0 = NHATpost l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x12 = 1 + x5 && 1 <= x1 l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x26 = -1 + x19 && x15 <= 0 l4(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x29 = x36 && x40 = 1 && 2 <= x35 && x35 <= 2 && x35 = x35 && x38 = 0 && 0 <= x41 && x41 = x41 && x37 = x39 && x39 = 1 l5(x42, x43, x44, x45, x46, x47, x48) -> l2(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x45 = x52 && x43 = x50 && x42 = x49 && 0 <= x55 && x55 = x55 && x51 = x53 && x53 = 1 + x46 && x44 <= 0 l5(x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x57 = x64 && x56 = x63 && x65 = -1 + x58 && x57 <= 0 && 1 <= x58 l6(x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = -1 + x76 && 1 <= x76 l6(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x90 <= 0 l7(x98, x99, x100, x101, x102, x103, x104) -> l0(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 + x103 <= 1 l7(x112, x113, x114, x115, x116, x117, x118) -> l6(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 <= 1 && 0 <= x120 && x120 = x120 && 1 <= x117 l8(x126, x127, x128, x129, x130, x131, x132) -> l0(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 1 + x126 <= x131 l8(x140, x141, x142, x143, x144, x145, x146) -> l7(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x145 <= x140 l3(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 l9(x168, x169, x170, x171, x172, x173, x174) -> l4(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 Start term: l9(NHAT0, choiceHAT0, iHAT0, posHAT0, seqHAT0, walkerHAT0, zHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(NHAT0, choiceHAT0, iHAT0, posHAT0, seqHAT0, walkerHAT0, zHAT0) -> l1(NHATpost, choiceHATpost, iHATpost, posHATpost, seqHATpost, walkerHATpost, zHATpost) :|: zHAT0 = zHATpost && walkerHAT0 = walkerHATpost && seqHAT0 = seqHATpost && posHAT0 = posHATpost && iHAT0 = iHATpost && choiceHAT0 = choiceHATpost && NHAT0 = NHATpost l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x12 = 1 + x5 && 1 <= x1 l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x26 = -1 + x19 && x15 <= 0 l4(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x29 = x36 && x40 = 1 && 2 <= x35 && x35 <= 2 && x35 = x35 && x38 = 0 && 0 <= x41 && x41 = x41 && x37 = x39 && x39 = 1 l5(x42, x43, x44, x45, x46, x47, x48) -> l2(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x45 = x52 && x43 = x50 && x42 = x49 && 0 <= x55 && x55 = x55 && x51 = x53 && x53 = 1 + x46 && x44 <= 0 l5(x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x57 = x64 && x56 = x63 && x65 = -1 + x58 && x57 <= 0 && 1 <= x58 l6(x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = -1 + x76 && 1 <= x76 l6(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x90 <= 0 l7(x98, x99, x100, x101, x102, x103, x104) -> l0(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 + x103 <= 1 l7(x112, x113, x114, x115, x116, x117, x118) -> l6(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 <= 1 && 0 <= x120 && x120 = x120 && 1 <= x117 l8(x126, x127, x128, x129, x130, x131, x132) -> l0(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 1 + x126 <= x131 l8(x140, x141, x142, x143, x144, x145, x146) -> l7(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x145 <= x140 l3(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 l9(x168, x169, x170, x171, x172, x173, x174) -> l4(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 Start term: l9(NHAT0, choiceHAT0, iHAT0, posHAT0, seqHAT0, walkerHAT0, zHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(NHAT0, choiceHAT0, iHAT0, posHAT0, seqHAT0, walkerHAT0, zHAT0) -> l1(NHATpost, choiceHATpost, iHATpost, posHATpost, seqHATpost, walkerHATpost, zHATpost) :|: zHAT0 = zHATpost && walkerHAT0 = walkerHATpost && seqHAT0 = seqHATpost && posHAT0 = posHATpost && iHAT0 = iHATpost && choiceHAT0 = choiceHATpost && NHAT0 = NHATpost (2) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x12 = 1 + x5 && 1 <= x1 (3) l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x26 = -1 + x19 && x15 <= 0 (4) l4(x28, x29, x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39, x40, x41) :|: x29 = x36 && x40 = 1 && 2 <= x35 && x35 <= 2 && x35 = x35 && x38 = 0 && 0 <= x41 && x41 = x41 && x37 = x39 && x39 = 1 (5) l5(x42, x43, x44, x45, x46, x47, x48) -> l2(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x45 = x52 && x43 = x50 && x42 = x49 && 0 <= x55 && x55 = x55 && x51 = x53 && x53 = 1 + x46 && x44 <= 0 (6) l5(x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x57 = x64 && x56 = x63 && x65 = -1 + x58 && x57 <= 0 && 1 <= x58 (7) l6(x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = -1 + x76 && 1 <= x76 (8) l6(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x90 <= 0 (9) l7(x98, x99, x100, x101, x102, x103, x104) -> l0(x105, x106, x107, x108, x109, x110, x111) :|: x104 = x111 && x103 = x110 && x102 = x109 && x101 = x108 && x100 = x107 && x99 = x106 && x98 = x105 && 1 + x103 <= 1 (10) l7(x112, x113, x114, x115, x116, x117, x118) -> l6(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 <= 1 && 0 <= x120 && x120 = x120 && 1 <= x117 (11) l8(x126, x127, x128, x129, x130, x131, x132) -> l0(x133, x134, x135, x136, x137, x138, x139) :|: x132 = x139 && x131 = x138 && x130 = x137 && x129 = x136 && x128 = x135 && x127 = x134 && x126 = x133 && 1 + x126 <= x131 (12) l8(x140, x141, x142, x143, x144, x145, x146) -> l7(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x145 <= x140 (13) l3(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 (14) l9(x168, x169, x170, x171, x172, x173, x174) -> l4(x175, x176, x177, x178, x179, x180, x181) :|: x174 = x181 && x173 = x180 && x172 = x179 && x171 = x178 && x170 = x177 && x169 = x176 && x168 = x175 Arcs: (2) -> (13) (3) -> (13) (4) -> (13) (5) -> (2), (3) (6) -> (3) (7) -> (2), (3) (8) -> (5), (6) (9) -> (1) (10) -> (7), (8) (11) -> (1) (12) -> (9), (10) (13) -> (11), (12) (14) -> (4) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l2(x, x1, x2, x3, x4, x5, x6) -> l3(x7, x8, x9, x10, x11, x12, x13) :|: x6 = x13 && x4 = x11 && x3 = x10 && x2 = x9 && x1 = x8 && x = x7 && x12 = 1 + x5 && 1 <= x1 (2) l5(x42, x43, x44, x45, x46, x47, x48) -> l2(x49, x50, x51, x52, x53, x54, x55) :|: x47 = x54 && x45 = x52 && x43 = x50 && x42 = x49 && 0 <= x55 && x55 = x55 && x51 = x53 && x53 = 1 + x46 && x44 <= 0 (3) l6(x84, x85, x86, x87, x88, x89, x90) -> l5(x91, x92, x93, x94, x95, x96, x97) :|: x90 = x97 && x89 = x96 && x88 = x95 && x87 = x94 && x86 = x93 && x85 = x92 && x84 = x91 && x90 <= 0 (4) l7(x112, x113, x114, x115, x116, x117, x118) -> l6(x119, x120, x121, x122, x123, x124, x125) :|: x118 = x125 && x117 = x124 && x116 = x123 && x115 = x122 && x114 = x121 && x112 = x119 && x120 <= 1 && 0 <= x120 && x120 = x120 && 1 <= x117 (5) l8(x140, x141, x142, x143, x144, x145, x146) -> l7(x147, x148, x149, x150, x151, x152, x153) :|: x146 = x153 && x145 = x152 && x144 = x151 && x143 = x150 && x142 = x149 && x141 = x148 && x140 = x147 && x145 <= x140 (6) l3(x154, x155, x156, x157, x158, x159, x160) -> l8(x161, x162, x163, x164, x165, x166, x167) :|: x160 = x167 && x159 = x166 && x158 = x165 && x157 = x164 && x156 = x163 && x155 = x162 && x154 = x161 (7) l2(x14, x15, x16, x17, x18, x19, x20) -> l3(x21, x22, x23, x24, x25, x26, x27) :|: x20 = x27 && x18 = x25 && x17 = x24 && x16 = x23 && x15 = x22 && x14 = x21 && x26 = -1 + x19 && x15 <= 0 (8) l6(x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83) :|: x75 = x82 && x74 = x81 && x73 = x80 && x72 = x79 && x71 = x78 && x70 = x77 && x83 = -1 + x76 && 1 <= x76 (9) l5(x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69) :|: x62 = x69 && x61 = x68 && x60 = x67 && x59 = x66 && x57 = x64 && x56 = x63 && x65 = -1 + x58 && x57 <= 0 && 1 <= x58 Arcs: (1) -> (6) (2) -> (1), (7) (3) -> (2), (9) (4) -> (3), (8) (5) -> (4) (6) -> (5) (7) -> (6) (8) -> (1), (7) (9) -> (7) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l8(x119:0, x141:0, x121:0, x122:0, x123:0, x124:0, x125:0) -> l2(x119:0, x120:0, 1 + x123:0, x122:0, 1 + x123:0, x124:0, x55:0) :|: x124:0 > 0 && x124:0 <= x119:0 && x125:0 < 1 && x121:0 < 1 && x120:0 > -1 && x55:0 > -1 && x120:0 < 2 l2(x14:0, x15:0, x163:0, x164:0, x165:0, x19:0, x167:0) -> l8(x14:0, x15:0, x163:0, x164:0, x165:0, -1 + x19:0, x167:0) :|: x15:0 < 1 l2(x, x1, x2, x3, x4, x5, x6) -> l8(x, x1, x2, x3, x4, 1 + x5, x6) :|: x1 > 0 l8(x7, x8, x9, x10, x11, x12, x13) -> l2(x7, x14, x9, x10, x11, x12, -1 + x13) :|: x12 > 0 && x12 <= x7 && x13 > 0 && x14 < 2 && x14 > -1 l8(x15, x16, x17, x18, x19, x20, x21) -> l2(x15, x22, -1 + x17, x18, x19, x20, x21) :|: x20 > 0 && x20 <= x15 && x21 < 1 && x17 > 0 && x22 > -1 && x22 < 2 && x22 < 1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l8(x1, x2, x3, x4, x5, x6, x7) -> l8(x1, x3, x5, x6, x7) l2(x1, x2, x3, x4, x5, x6, x7) -> l2(x1, x2, x3, x5, x6, x7) ---------------------------------------- (8) Obligation: Rules: l8(x119:0, x121:0, x123:0, x124:0, x125:0) -> l2(x119:0, x120:0, 1 + x123:0, 1 + x123:0, x124:0, x55:0) :|: x124:0 > 0 && x124:0 <= x119:0 && x125:0 < 1 && x121:0 < 1 && x120:0 > -1 && x55:0 > -1 && x120:0 < 2 l2(x14:0, x15:0, x163:0, x165:0, x19:0, x167:0) -> l8(x14:0, x163:0, x165:0, -1 + x19:0, x167:0) :|: x15:0 < 1 l2(x, x1, x2, x4, x5, x6) -> l8(x, x2, x4, 1 + x5, x6) :|: x1 > 0 l8(x7, x9, x11, x12, x13) -> l2(x7, x14, x9, x11, x12, -1 + x13) :|: x12 > 0 && x12 <= x7 && x13 > 0 && x14 < 2 && x14 > -1 l8(x15, x17, x19, x20, x21) -> l2(x15, x22, -1 + x17, x19, x20, x21) :|: x20 > 0 && x20 <= x15 && x21 < 1 && x17 > 0 && x22 > -1 && x22 < 2 && x22 < 1 ---------------------------------------- (9) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (10) Obligation: Rules: l2(x14:0, x15:0, x163:0, x165:0, x19:0, x167:0) -> l8(x14:0, x163:0, x165:0, -1 + x19:0, x167:0) :|: x15:0 < 1 l8(x32, x33, x34, x35, x36) -> l8(x32, 1 + x34, 1 + x34, -1 + x35, x38) :|: TRUE && x35 >= 1 && x35 + -1 * x32 <= 0 && x36 <= 0 && x33 <= 0 && x37 >= 0 && x38 >= 0 && x37 <= 0 l2(x, x1, x2, x4, x5, x6) -> l8(x, x2, x4, 1 + x5, x6) :|: x1 > 0 l8(x45, x46, x47, x48, x49) -> l8(x45, 1 + x47, 1 + x47, 1 + x48, x51) :|: TRUE && x48 >= 1 && x48 + -1 * x45 <= 0 && x49 <= 0 && x46 <= 0 && x51 >= 0 && x50 <= 1 && x50 >= 1 l8(x7, x9, x11, x12, x13) -> l2(x7, x14, x9, x11, x12, -1 + x13) :|: x12 > 0 && x12 <= x7 && x13 > 0 && x14 < 2 && x14 > -1 l8(x15, x17, x19, x20, x21) -> l2(x15, x22, -1 + x17, x19, x20, x21) :|: x20 > 0 && x20 <= x15 && x21 < 1 && x17 > 0 && x22 > -1 && x22 < 2 && x22 < 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x14:0, x15:0, x163:0, x165:0, x19:0, x167:0) -> l8(x14:0, x163:0, x165:0, -1 + x19:0, x167:0) :|: x15:0 < 1 (2) l8(x32, x33, x34, x35, x36) -> l8(x32, 1 + x34, 1 + x34, -1 + x35, x38) :|: TRUE && x35 >= 1 && x35 + -1 * x32 <= 0 && x36 <= 0 && x33 <= 0 && x37 >= 0 && x38 >= 0 && x37 <= 0 (3) l2(x, x1, x2, x4, x5, x6) -> l8(x, x2, x4, 1 + x5, x6) :|: x1 > 0 (4) l8(x45, x46, x47, x48, x49) -> l8(x45, 1 + x47, 1 + x47, 1 + x48, x51) :|: TRUE && x48 >= 1 && x48 + -1 * x45 <= 0 && x49 <= 0 && x46 <= 0 && x51 >= 0 && x50 <= 1 && x50 >= 1 (5) l8(x7, x9, x11, x12, x13) -> l2(x7, x14, x9, x11, x12, -1 + x13) :|: x12 > 0 && x12 <= x7 && x13 > 0 && x14 < 2 && x14 > -1 (6) l8(x15, x17, x19, x20, x21) -> l2(x15, x22, -1 + x17, x19, x20, x21) :|: x20 > 0 && x20 <= x15 && x21 < 1 && x17 > 0 && x22 > -1 && x22 < 2 && x22 < 1 Arcs: (1) -> (2), (4), (5), (6) (2) -> (2), (4), (5), (6) (3) -> (2), (4), (5), (6) (4) -> (2), (4), (5), (6) (5) -> (1), (3) (6) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x14:0, x15:0, x163:0, x165:0, x19:0, x167:0) -> l8(x14:0, x163:0, x165:0, -1 + x19:0, x167:0) :|: x15:0 < 1 (2) l8(x15, x17, x19, x20, x21) -> l2(x15, x22, -1 + x17, x19, x20, x21) :|: x20 > 0 && x20 <= x15 && x21 < 1 && x17 > 0 && x22 > -1 && x22 < 2 && x22 < 1 (3) l8(x7, x9, x11, x12, x13) -> l2(x7, x14, x9, x11, x12, -1 + x13) :|: x12 > 0 && x12 <= x7 && x13 > 0 && x14 < 2 && x14 > -1 (4) l8(x32, x33, x34, x35, x36) -> l8(x32, 1 + x34, 1 + x34, -1 + x35, x38) :|: TRUE && x35 >= 1 && x35 + -1 * x32 <= 0 && x36 <= 0 && x33 <= 0 && x37 >= 0 && x38 >= 0 && x37 <= 0 (5) l8(x45, x46, x47, x48, x49) -> l8(x45, 1 + x47, 1 + x47, 1 + x48, x51) :|: TRUE && x48 >= 1 && x48 + -1 * x45 <= 0 && x49 <= 0 && x46 <= 0 && x51 >= 0 && x50 <= 1 && x50 >= 1 (6) l2(x, x1, x2, x4, x5, x6) -> l8(x, x2, x4, 1 + x5, x6) :|: x1 > 0 Arcs: (1) -> (2), (3), (4), (5) (2) -> (1) (3) -> (1), (6) (4) -> (2), (3), (4), (5) (5) -> (2), (3), (4), (5) (6) -> (2), (3), (4), (5) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l8(x32:0, x33:0, x34:0, x35:0, x36:0) -> l8(x32:0, 1 + x34:0, 1 + x34:0, -1 + x35:0, x38:0) :|: x38:0 > -1 && x37:0 < 1 && x37:0 > -1 && x33:0 < 1 && x36:0 < 1 && x35:0 > 0 && x35:0 + -1 * x32:0 <= 0 l2(x:0, x1:0, x2:0, x4:0, x5:0, x6:0) -> l8(x:0, x2:0, x4:0, 1 + x5:0, x6:0) :|: x1:0 > 0 l8(x45:0, x46:0, x47:0, x48:0, x49:0) -> l8(x45:0, 1 + x47:0, 1 + x47:0, 1 + x48:0, x51:0) :|: x50:0 < 2 && x50:0 > 0 && x51:0 > -1 && x46:0 < 1 && x49:0 < 1 && x48:0 > 0 && x48:0 + -1 * x45:0 <= 0 l2(x14:0:0, x15:0:0, x163:0:0, x165:0:0, x19:0:0, x167:0:0) -> l8(x14:0:0, x163:0:0, x165:0:0, -1 + x19:0:0, x167:0:0) :|: x15:0:0 < 1 l8(x7:0, x9:0, x11:0, x12:0, x13:0) -> l2(x7:0, x14:0, x9:0, x11:0, x12:0, -1 + x13:0) :|: x14:0 < 2 && x14:0 > -1 && x13:0 > 0 && x7:0 >= x12:0 && x12:0 > 0 l8(x15:0, x17:0, x19:0, x20:0, x21:0) -> l2(x15:0, x22:0, -1 + x17:0, x19:0, x20:0, x21:0) :|: x22:0 < 2 && x22:0 < 1 && x22:0 > -1 && x17:0 > 0 && x21:0 < 1 && x20:0 <= x15:0 && x20:0 > 0 ---------------------------------------- (15) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (16) Obligation: Rules: l8(x, x1, x2, x3, x4) -> l8(x, 2 + x2, 2 + x2, -2 + x3, x12) :|: TRUE && x5 >= 0 && x6 <= 0 && x6 >= 0 && x1 <= 0 && x4 <= 0 && x3 + -1 * x <= 0 && x12 >= 0 && x13 <= 0 && x13 >= 0 && x2 <= -1 && x5 <= 0 && x3 >= 2 l2(x:0, x1:0, x2:0, x4:0, x5:0, x6:0) -> l8(x:0, x2:0, x4:0, 1 + x5:0, x6:0) :|: x1:0 > 0 l8(x45:0, x46:0, x47:0, x48:0, x49:0) -> l8(x45:0, 1 + x47:0, 1 + x47:0, 1 + x48:0, x51:0) :|: x50:0 < 2 && x50:0 > 0 && x51:0 > -1 && x46:0 < 1 && x49:0 < 1 && x48:0 > 0 && x48:0 + -1 * x45:0 <= 0 l8(x27, x28, x29, x30, x31) -> l8(x27, 2 + x29, 2 + x29, x30, x39) :|: TRUE && x32 >= 0 && x33 <= 0 && x33 >= 0 && x28 <= 0 && x31 <= 0 && x30 + -1 * x27 <= 0 && x40 <= 1 && x40 >= 1 && x39 >= 0 && x29 <= -1 && x32 <= 0 && x30 >= 2 l2(x14:0:0, x15:0:0, x163:0:0, x165:0:0, x19:0:0, x167:0:0) -> l8(x14:0:0, x163:0:0, x165:0:0, -1 + x19:0:0, x167:0:0) :|: x15:0:0 < 1 l8(x7:0, x9:0, x11:0, x12:0, x13:0) -> l2(x7:0, x14:0, x9:0, x11:0, x12:0, -1 + x13:0) :|: x14:0 < 2 && x14:0 > -1 && x13:0 > 0 && x7:0 >= x12:0 && x12:0 > 0 l8(x54, x55, x56, x57, x58) -> l2(x54, x66, 1 + x56, 1 + x56, -1 + x57, -1 + x59) :|: TRUE && x60 <= 0 && x60 >= 0 && x55 <= 0 && x58 <= 0 && x57 + -1 * x54 <= 0 && x66 <= 1 && x66 >= 0 && x59 >= 1 && x57 >= 2 l8(x15:0, x17:0, x19:0, x20:0, x21:0) -> l2(x15:0, x22:0, -1 + x17:0, x19:0, x20:0, x21:0) :|: x22:0 < 2 && x22:0 < 1 && x22:0 > -1 && x17:0 > 0 && x21:0 < 1 && x20:0 <= x15:0 && x20:0 > 0 l8(x67, x68, x69, x70, x71) -> l2(x67, x79, x69, 1 + x69, -1 + x70, x72) :|: TRUE && x72 >= 0 && x73 <= 0 && x73 >= 0 && x68 <= 0 && x71 <= 0 && x70 + -1 * x67 <= 0 && x79 <= 0 && x79 >= 0 && x69 >= 0 && x72 <= 0 && x70 >= 2 ---------------------------------------- (17) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l8(x, x1, x2, x3, x4) -> l8(x, 2 + x2, 2 + x2, -2 + x3, x12) :|: TRUE && x5 >= 0 && x6 <= 0 && x6 >= 0 && x1 <= 0 && x4 <= 0 && x3 + -1 * x <= 0 && x12 >= 0 && x13 <= 0 && x13 >= 0 && x2 <= -1 && x5 <= 0 && x3 >= 2 (2) l2(x:0, x1:0, x2:0, x4:0, x5:0, x6:0) -> l8(x:0, x2:0, x4:0, 1 + x5:0, x6:0) :|: x1:0 > 0 (3) l8(x45:0, x46:0, x47:0, x48:0, x49:0) -> l8(x45:0, 1 + x47:0, 1 + x47:0, 1 + x48:0, x51:0) :|: x50:0 < 2 && x50:0 > 0 && x51:0 > -1 && x46:0 < 1 && x49:0 < 1 && x48:0 > 0 && x48:0 + -1 * x45:0 <= 0 (4) l8(x27, x28, x29, x30, x31) -> l8(x27, 2 + x29, 2 + x29, x30, x39) :|: TRUE && x32 >= 0 && x33 <= 0 && x33 >= 0 && x28 <= 0 && x31 <= 0 && x30 + -1 * x27 <= 0 && x40 <= 1 && x40 >= 1 && x39 >= 0 && x29 <= -1 && x32 <= 0 && x30 >= 2 (5) l2(x14:0:0, x15:0:0, x163:0:0, x165:0:0, x19:0:0, x167:0:0) -> l8(x14:0:0, x163:0:0, x165:0:0, -1 + x19:0:0, x167:0:0) :|: x15:0:0 < 1 (6) l8(x7:0, x9:0, x11:0, x12:0, x13:0) -> l2(x7:0, x14:0, x9:0, x11:0, x12:0, -1 + x13:0) :|: x14:0 < 2 && x14:0 > -1 && x13:0 > 0 && x7:0 >= x12:0 && x12:0 > 0 (7) l8(x54, x55, x56, x57, x58) -> l2(x54, x66, 1 + x56, 1 + x56, -1 + x57, -1 + x59) :|: TRUE && x60 <= 0 && x60 >= 0 && x55 <= 0 && x58 <= 0 && x57 + -1 * x54 <= 0 && x66 <= 1 && x66 >= 0 && x59 >= 1 && x57 >= 2 (8) l8(x15:0, x17:0, x19:0, x20:0, x21:0) -> l2(x15:0, x22:0, -1 + x17:0, x19:0, x20:0, x21:0) :|: x22:0 < 2 && x22:0 < 1 && x22:0 > -1 && x17:0 > 0 && x21:0 < 1 && x20:0 <= x15:0 && x20:0 > 0 (9) l8(x67, x68, x69, x70, x71) -> l2(x67, x79, x69, 1 + x69, -1 + x70, x72) :|: TRUE && x72 >= 0 && x73 <= 0 && x73 >= 0 && x68 <= 0 && x71 <= 0 && x70 + -1 * x67 <= 0 && x79 <= 0 && x79 >= 0 && x69 >= 0 && x72 <= 0 && x70 >= 2 Arcs: (1) -> (1), (3), (4), (6), (7), (8), (9) (2) -> (1), (3), (4), (6), (7), (8), (9) (3) -> (1), (3), (4), (6), (7), (8), (9) (4) -> (1), (3), (4), (6), (7), (8), (9) (5) -> (1), (3), (4), (6), (7), (8), (9) (6) -> (2), (5) (7) -> (2), (5) (8) -> (5) (9) -> (5) This digraph is fully evaluated! ---------------------------------------- (18) Obligation: Termination digraph: Nodes: (1) l8(x, x1, x2, x3, x4) -> l8(x, 2 + x2, 2 + x2, -2 + x3, x12) :|: TRUE && x5 >= 0 && x6 <= 0 && x6 >= 0 && x1 <= 0 && x4 <= 0 && x3 + -1 * x <= 0 && x12 >= 0 && x13 <= 0 && x13 >= 0 && x2 <= -1 && x5 <= 0 && x3 >= 2 (2) l2(x:0, x1:0, x2:0, x4:0, x5:0, x6:0) -> l8(x:0, x2:0, x4:0, 1 + x5:0, x6:0) :|: x1:0 > 0 (3) l8(x7:0, x9:0, x11:0, x12:0, x13:0) -> l2(x7:0, x14:0, x9:0, x11:0, x12:0, -1 + x13:0) :|: x14:0 < 2 && x14:0 > -1 && x13:0 > 0 && x7:0 >= x12:0 && x12:0 > 0 (4) l8(x45:0, x46:0, x47:0, x48:0, x49:0) -> l8(x45:0, 1 + x47:0, 1 + x47:0, 1 + x48:0, x51:0) :|: x50:0 < 2 && x50:0 > 0 && x51:0 > -1 && x46:0 < 1 && x49:0 < 1 && x48:0 > 0 && x48:0 + -1 * x45:0 <= 0 (5) l8(x27, x28, x29, x30, x31) -> l8(x27, 2 + x29, 2 + x29, x30, x39) :|: TRUE && x32 >= 0 && x33 <= 0 && x33 >= 0 && x28 <= 0 && x31 <= 0 && x30 + -1 * x27 <= 0 && x40 <= 1 && x40 >= 1 && x39 >= 0 && x29 <= -1 && x32 <= 0 && x30 >= 2 (6) l2(x14:0:0, x15:0:0, x163:0:0, x165:0:0, x19:0:0, x167:0:0) -> l8(x14:0:0, x163:0:0, x165:0:0, -1 + x19:0:0, x167:0:0) :|: x15:0:0 < 1 (7) l8(x67, x68, x69, x70, x71) -> l2(x67, x79, x69, 1 + x69, -1 + x70, x72) :|: TRUE && x72 >= 0 && x73 <= 0 && x73 >= 0 && x68 <= 0 && x71 <= 0 && x70 + -1 * x67 <= 0 && x79 <= 0 && x79 >= 0 && x69 >= 0 && x72 <= 0 && x70 >= 2 (8) l8(x15:0, x17:0, x19:0, x20:0, x21:0) -> l2(x15:0, x22:0, -1 + x17:0, x19:0, x20:0, x21:0) :|: x22:0 < 2 && x22:0 < 1 && x22:0 > -1 && x17:0 > 0 && x21:0 < 1 && x20:0 <= x15:0 && x20:0 > 0 (9) l8(x54, x55, x56, x57, x58) -> l2(x54, x66, 1 + x56, 1 + x56, -1 + x57, -1 + x59) :|: TRUE && x60 <= 0 && x60 >= 0 && x55 <= 0 && x58 <= 0 && x57 + -1 * x54 <= 0 && x66 <= 1 && x66 >= 0 && x59 >= 1 && x57 >= 2 Arcs: (1) -> (1), (3), (4), (5), (7), (8), (9) (2) -> (1), (3), (4), (5), (7), (8), (9) (3) -> (2), (6) (4) -> (1), (3), (4), (5), (7), (8), (9) (5) -> (1), (3), (4), (5), (7), (8), (9) (6) -> (1), (3), (4), (5), (7), (8), (9) (7) -> (6) (8) -> (6) (9) -> (2), (6) This digraph is fully evaluated! ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: l8(x15:0:0, x17:0:0, x19:0:0, x20:0:0, x21:0:0) -> l2(x15:0:0, x22:0:0, -1 + x17:0:0, x19:0:0, x20:0:0, x21:0:0) :|: x20:0:0 <= x15:0:0 && x20:0:0 > 0 && x21:0:0 < 1 && x17:0:0 > 0 && x22:0:0 > -1 && x22:0:0 < 1 && x22:0:0 < 2 l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, 1 + x56:0, 1 + x56:0, -1 + x57:0, -1 + x59:0) :|: x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1 l2(x:0:0, x1:0:0, x2:0:0, x4:0:0, x5:0:0, x6:0:0) -> l8(x:0:0, x2:0:0, x4:0:0, 1 + x5:0:0, x6:0:0) :|: x1:0:0 > 0 l2(x14:0:0:0, x15:0:0:0, x163:0:0:0, x165:0:0:0, x19:0:0:0, x167:0:0:0) -> l8(x14:0:0:0, x163:0:0:0, x165:0:0:0, -1 + x19:0:0:0, x167:0:0:0) :|: x15:0:0:0 < 1 l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, 1 + x69:0, -1 + x70:0, x72:0) :|: x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1 l8(x27:0, x28:0, x29:0, x30:0, x31:0) -> l8(x27:0, 2 + x29:0, 2 + x29:0, x30:0, x39:0) :|: x32:0 < 1 && x30:0 > 1 && x29:0 < 0 && x39:0 > -1 && x40:0 > 0 && x40:0 < 2 && x30:0 + -1 * x27:0 <= 0 && x31:0 < 1 && x28:0 < 1 && x33:0 > -1 && x32:0 > -1 && x33:0 < 1 l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, 1 + x47:0:0, 1 + x47:0:0, 1 + x48:0:0, x51:0:0) :|: x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2 l8(x7:0:0, x9:0:0, x11:0:0, x12:0:0, x13:0:0) -> l2(x7:0:0, x14:0:0, x9:0:0, x11:0:0, x12:0:0, -1 + x13:0:0) :|: x7:0:0 >= x12:0:0 && x12:0:0 > 0 && x13:0:0 > 0 && x14:0:0 > -1 && x14:0:0 < 2 l8(x:0, x1:0, x2:0, x3:0, x4:0) -> l8(x:0, 2 + x2:0, 2 + x2:0, -2 + x3:0, x12:0) :|: x5:0 < 1 && x3:0 > 1 && x2:0 < 0 && x13:0 > -1 && x13:0 < 1 && x12:0 > -1 && x3:0 + -1 * x:0 <= 0 && x4:0 < 1 && x1:0 < 1 && x6:0 > -1 && x5:0 > -1 && x6:0 < 1 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l8(VARIABLE, VARIABLE, VARIABLE, INTEGER, VARIABLE) l2(VARIABLE, INTEGER, VARIABLE, VARIABLE, VARIABLE, VARIABLE) 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: l8(x15:0:0, x17:0:0, x19:0:0, x20:0:0, x21:0:0) -> l2(x15:0:0, x22:0:0, c, x19:0:0, x20:0:0, x21:0:0) :|: c = -1 + x17:0:0 && (x20:0:0 <= x15:0:0 && x20:0:0 > 0 && x21:0:0 < 1 && x17:0:0 > 0 && x22:0:0 > -1 && x22:0:0 < 1 && x22:0:0 < 2) l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, c1, c2, c3, c4) :|: c4 = -1 + x59:0 && (c3 = -1 + x57:0 && (c2 = 1 + x56:0 && c1 = 1 + x56:0)) && (x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1) l2(x:0:0, x1:0:0, x2:0:0, x4:0:0, x5:0:0, x6:0:0) -> l8(x:0:0, x2:0:0, x4:0:0, c5, x6:0:0) :|: c5 = 1 + x5:0:0 && x1:0:0 > 0 l2(x14:0:0:0, x15:0:0:0, x163:0:0:0, x165:0:0:0, x19:0:0:0, x167:0:0:0) -> l8(x14:0:0:0, x163:0:0:0, x165:0:0:0, c6, x167:0:0:0) :|: c6 = -1 + x19:0:0:0 && x15:0:0:0 < 1 l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, c7, c8, x72:0) :|: c8 = -1 + x70:0 && c7 = 1 + x69:0 && (x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1) l8(x27:0, x28:0, x29:0, x30:0, x31:0) -> l8(x27:0, c9, c10, x30:0, x39:0) :|: c10 = 2 + x29:0 && c9 = 2 + x29:0 && (x32:0 < 1 && x30:0 > 1 && x29:0 < 0 && x39:0 > -1 && x40:0 > 0 && x40:0 < 2 && x30:0 + -1 * x27:0 <= 0 && x31:0 < 1 && x28:0 < 1 && x33:0 > -1 && x32:0 > -1 && x33:0 < 1) l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, c11, c12, c13, x51:0:0) :|: c13 = 1 + x48:0:0 && (c12 = 1 + x47:0:0 && c11 = 1 + x47:0:0) && (x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2) l8(x7:0:0, x9:0:0, x11:0:0, x12:0:0, x13:0:0) -> l2(x7:0:0, x14:0:0, x9:0:0, x11:0:0, x12:0:0, c14) :|: c14 = -1 + x13:0:0 && (x7:0:0 >= x12:0:0 && x12:0:0 > 0 && x13:0:0 > 0 && x14:0:0 > -1 && x14:0:0 < 2) l8(x:0, x1:0, x2:0, x3:0, x4:0) -> l8(x:0, c15, c16, c17, x12:0) :|: c17 = -2 + x3:0 && (c16 = 2 + x2:0 && c15 = 2 + x2:0) && (x5:0 < 1 && x3:0 > 1 && x2:0 < 0 && x13:0 > -1 && x13:0 < 1 && x12:0 > -1 && x3:0 + -1 * x:0 <= 0 && x4:0 < 1 && x1:0 < 1 && x6:0 > -1 && x5:0 > -1 && x6:0 < 1) Found the following polynomial interpretation: [l8(x, x1, x2, x3, x4)] = -3 + x - x2 [l2(x5, x6, x7, x8, x9, x10)] = -3 + x5 - x8 The following rules are decreasing: l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, c1, c2, c3, c4) :|: c4 = -1 + x59:0 && (c3 = -1 + x57:0 && (c2 = 1 + x56:0 && c1 = 1 + x56:0)) && (x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1) l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, c7, c8, x72:0) :|: c8 = -1 + x70:0 && c7 = 1 + x69:0 && (x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1) l8(x27:0, x28:0, x29:0, x30:0, x31:0) -> l8(x27:0, c9, c10, x30:0, x39:0) :|: c10 = 2 + x29:0 && c9 = 2 + x29:0 && (x32:0 < 1 && x30:0 > 1 && x29:0 < 0 && x39:0 > -1 && x40:0 > 0 && x40:0 < 2 && x30:0 + -1 * x27:0 <= 0 && x31:0 < 1 && x28:0 < 1 && x33:0 > -1 && x32:0 > -1 && x33:0 < 1) l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, c11, c12, c13, x51:0:0) :|: c13 = 1 + x48:0:0 && (c12 = 1 + x47:0:0 && c11 = 1 + x47:0:0) && (x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2) l8(x:0, x1:0, x2:0, x3:0, x4:0) -> l8(x:0, c15, c16, c17, x12:0) :|: c17 = -2 + x3:0 && (c16 = 2 + x2:0 && c15 = 2 + x2:0) && (x5:0 < 1 && x3:0 > 1 && x2:0 < 0 && x13:0 > -1 && x13:0 < 1 && x12:0 > -1 && x3:0 + -1 * x:0 <= 0 && x4:0 < 1 && x1:0 < 1 && x6:0 > -1 && x5:0 > -1 && x6:0 < 1) The following rules are bounded: l8(x27:0, x28:0, x29:0, x30:0, x31:0) -> l8(x27:0, c9, c10, x30:0, x39:0) :|: c10 = 2 + x29:0 && c9 = 2 + x29:0 && (x32:0 < 1 && x30:0 > 1 && x29:0 < 0 && x39:0 > -1 && x40:0 > 0 && x40:0 < 2 && x30:0 + -1 * x27:0 <= 0 && x31:0 < 1 && x28:0 < 1 && x33:0 > -1 && x32:0 > -1 && x33:0 < 1) l8(x:0, x1:0, x2:0, x3:0, x4:0) -> l8(x:0, c15, c16, c17, x12:0) :|: c17 = -2 + x3:0 && (c16 = 2 + x2:0 && c15 = 2 + x2:0) && (x5:0 < 1 && x3:0 > 1 && x2:0 < 0 && x13:0 > -1 && x13:0 < 1 && x12:0 > -1 && x3:0 + -1 * x:0 <= 0 && x4:0 < 1 && x1:0 < 1 && x6:0 > -1 && x5:0 > -1 && x6:0 < 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l8(x15:0:0, x17:0:0, x19:0:0, x20:0:0, x21:0:0) -> l2(x15:0:0, x22:0:0, c, x19:0:0, x20:0:0, x21:0:0) :|: c = -1 + x17:0:0 && (x20:0:0 <= x15:0:0 && x20:0:0 > 0 && x21:0:0 < 1 && x17:0:0 > 0 && x22:0:0 > -1 && x22:0:0 < 1 && x22:0:0 < 2) l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, c1, c2, c3, c4) :|: c4 = -1 + x59:0 && (c3 = -1 + x57:0 && (c2 = 1 + x56:0 && c1 = 1 + x56:0)) && (x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1) l2(x:0:0, x1:0:0, x2:0:0, x4:0:0, x5:0:0, x6:0:0) -> l8(x:0:0, x2:0:0, x4:0:0, c5, x6:0:0) :|: c5 = 1 + x5:0:0 && x1:0:0 > 0 l2(x14:0:0:0, x15:0:0:0, x163:0:0:0, x165:0:0:0, x19:0:0:0, x167:0:0:0) -> l8(x14:0:0:0, x163:0:0:0, x165:0:0:0, c6, x167:0:0:0) :|: c6 = -1 + x19:0:0:0 && x15:0:0:0 < 1 l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, c7, c8, x72:0) :|: c8 = -1 + x70:0 && c7 = 1 + x69:0 && (x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1) l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, c11, c12, c13, x51:0:0) :|: c13 = 1 + x48:0:0 && (c12 = 1 + x47:0:0 && c11 = 1 + x47:0:0) && (x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2) l8(x7:0:0, x9:0:0, x11:0:0, x12:0:0, x13:0:0) -> l2(x7:0:0, x14:0:0, x9:0:0, x11:0:0, x12:0:0, c14) :|: c14 = -1 + x13:0:0 && (x7:0:0 >= x12:0:0 && x12:0:0 > 0 && x13:0:0 > 0 && x14:0:0 > -1 && x14:0:0 < 2) ---------------------------------------- (22) Obligation: Rules: l8(x15:0:0, x17:0:0, x19:0:0, x20:0:0, x21:0:0) -> l2(x15:0:0, x22:0:0, -1 + x17:0:0, x19:0:0, x20:0:0, x21:0:0) :|: x20:0:0 <= x15:0:0 && x20:0:0 > 0 && x21:0:0 < 1 && x17:0:0 > 0 && x22:0:0 > -1 && x22:0:0 < 1 && x22:0:0 < 2 l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, 1 + x56:0, 1 + x56:0, -1 + x57:0, -1 + x59:0) :|: x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1 l2(x:0:0, x1:0:0, x2:0:0, x4:0:0, x5:0:0, x6:0:0) -> l8(x:0:0, x2:0:0, x4:0:0, 1 + x5:0:0, x6:0:0) :|: x1:0:0 > 0 l2(x14:0:0:0, x15:0:0:0, x163:0:0:0, x165:0:0:0, x19:0:0:0, x167:0:0:0) -> l8(x14:0:0:0, x163:0:0:0, x165:0:0:0, -1 + x19:0:0:0, x167:0:0:0) :|: x15:0:0:0 < 1 l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, 1 + x69:0, -1 + x70:0, x72:0) :|: x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1 l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, 1 + x47:0:0, 1 + x47:0:0, 1 + x48:0:0, x51:0:0) :|: x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2 l8(x7:0:0, x9:0:0, x11:0:0, x12:0:0, x13:0:0) -> l2(x7:0:0, x14:0:0, x9:0:0, x11:0:0, x12:0:0, -1 + x13:0:0) :|: x7:0:0 >= x12:0:0 && x12:0:0 > 0 && x13:0:0 > 0 && x14:0:0 > -1 && x14:0:0 < 2 ---------------------------------------- (23) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l8(x15:0:0, x17:0:0, x19:0:0, x20:0:0, x21:0:0) -> l2(x15:0:0, x22:0:0, -1 + x17:0:0, x19:0:0, x20:0:0, x21:0:0) :|: x20:0:0 <= x15:0:0 && x20:0:0 > 0 && x21:0:0 < 1 && x17:0:0 > 0 && x22:0:0 > -1 && x22:0:0 < 1 && x22:0:0 < 2 (2) l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, 1 + x56:0, 1 + x56:0, -1 + x57:0, -1 + x59:0) :|: x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1 (3) l2(x:0:0, x1:0:0, x2:0:0, x4:0:0, x5:0:0, x6:0:0) -> l8(x:0:0, x2:0:0, x4:0:0, 1 + x5:0:0, x6:0:0) :|: x1:0:0 > 0 (4) l2(x14:0:0:0, x15:0:0:0, x163:0:0:0, x165:0:0:0, x19:0:0:0, x167:0:0:0) -> l8(x14:0:0:0, x163:0:0:0, x165:0:0:0, -1 + x19:0:0:0, x167:0:0:0) :|: x15:0:0:0 < 1 (5) l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, 1 + x69:0, -1 + x70:0, x72:0) :|: x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1 (6) l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, 1 + x47:0:0, 1 + x47:0:0, 1 + x48:0:0, x51:0:0) :|: x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2 (7) l8(x7:0:0, x9:0:0, x11:0:0, x12:0:0, x13:0:0) -> l2(x7:0:0, x14:0:0, x9:0:0, x11:0:0, x12:0:0, -1 + x13:0:0) :|: x7:0:0 >= x12:0:0 && x12:0:0 > 0 && x13:0:0 > 0 && x14:0:0 > -1 && x14:0:0 < 2 Arcs: (1) -> (4) (2) -> (3), (4) (3) -> (1), (2), (5), (6), (7) (4) -> (1), (2), (5), (6), (7) (5) -> (4) (6) -> (1), (2), (5), (6), (7) (7) -> (3), (4) This digraph is fully evaluated! ---------------------------------------- (24) Obligation: Termination digraph: Nodes: (1) l8(x15:0:0, x17:0:0, x19:0:0, x20:0:0, x21:0:0) -> l2(x15:0:0, x22:0:0, -1 + x17:0:0, x19:0:0, x20:0:0, x21:0:0) :|: x20:0:0 <= x15:0:0 && x20:0:0 > 0 && x21:0:0 < 1 && x17:0:0 > 0 && x22:0:0 > -1 && x22:0:0 < 1 && x22:0:0 < 2 (2) l2(x:0:0, x1:0:0, x2:0:0, x4:0:0, x5:0:0, x6:0:0) -> l8(x:0:0, x2:0:0, x4:0:0, 1 + x5:0:0, x6:0:0) :|: x1:0:0 > 0 (3) l8(x54:0, x55:0, x56:0, x57:0, x58:0) -> l2(x54:0, x66:0, 1 + x56:0, 1 + x56:0, -1 + x57:0, -1 + x59:0) :|: x59:0 > 0 && x57:0 > 1 && x66:0 > -1 && x66:0 < 2 && x57:0 + -1 * x54:0 <= 0 && x58:0 < 1 && x55:0 < 1 && x60:0 < 1 && x60:0 > -1 (4) l2(x14:0:0:0, x15:0:0:0, x163:0:0:0, x165:0:0:0, x19:0:0:0, x167:0:0:0) -> l8(x14:0:0:0, x163:0:0:0, x165:0:0:0, -1 + x19:0:0:0, x167:0:0:0) :|: x15:0:0:0 < 1 (5) l8(x7:0:0, x9:0:0, x11:0:0, x12:0:0, x13:0:0) -> l2(x7:0:0, x14:0:0, x9:0:0, x11:0:0, x12:0:0, -1 + x13:0:0) :|: x7:0:0 >= x12:0:0 && x12:0:0 > 0 && x13:0:0 > 0 && x14:0:0 > -1 && x14:0:0 < 2 (6) l8(x67:0, x68:0, x69:0, x70:0, x71:0) -> l2(x67:0, x79:0, x69:0, 1 + x69:0, -1 + x70:0, x72:0) :|: x72:0 < 1 && x70:0 > 1 && x69:0 > -1 && x79:0 > -1 && x79:0 < 1 && x70:0 + -1 * x67:0 <= 0 && x71:0 < 1 && x68:0 < 1 && x73:0 > -1 && x72:0 > -1 && x73:0 < 1 (7) l8(x45:0:0, x46:0:0, x47:0:0, x48:0:0, x49:0:0) -> l8(x45:0:0, 1 + x47:0:0, 1 + x47:0:0, 1 + x48:0:0, x51:0:0) :|: x48:0:0 > 0 && x48:0:0 + -1 * x45:0:0 <= 0 && x49:0:0 < 1 && x46:0:0 < 1 && x51:0:0 > -1 && x50:0:0 > 0 && x50:0:0 < 2 Arcs: (1) -> (4) (2) -> (1), (3), (5), (6), (7) (3) -> (2), (4) (4) -> (1), (3), (5), (6), (7) (5) -> (2), (4) (6) -> (4) (7) -> (1), (3), (5), (6), (7) This digraph is fully evaluated! ---------------------------------------- (25) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (26) Obligation: Rules: l2(x:0:0:0, x1:0:0:0, x2:0:0:0, x4:0:0:0, x5:0:0:0, x6:0:0:0) -> l8(x:0:0:0, x2:0:0:0, x4:0:0:0, 1 + x5:0:0:0, x6:0:0:0) :|: x1:0:0:0 > 0 l2(x14:0:0:0:0, x15:0:0:0:0, x163:0:0:0:0, x165:0:0:0:0, x19:0:0:0:0, x167:0:0:0:0) -> l8(x14:0:0:0:0, x163:0:0:0:0, x165:0:0:0:0, -1 + x19:0:0:0:0, x167:0:0:0:0) :|: x15:0:0:0:0 < 1 l8(x45:0:0:0, x46:0:0:0, x47:0:0:0, x48:0:0:0, x49:0:0:0) -> l8(x45:0:0:0, 1 + x47:0:0:0, 1 + x47:0:0:0, 1 + x48:0:0:0, x51:0:0:0) :|: x50:0:0:0 > 0 && x50:0:0:0 < 2 && x51:0:0:0 > -1 && x46:0:0:0 < 1 && x49:0:0:0 < 1 && x48:0:0:0 + -1 * x45:0:0:0 <= 0 && x48:0:0:0 > 0 l8(x15:0:0:0, x17:0:0:0, x19:0:0:0, x20:0:0:0, x21:0:0:0) -> l2(x15:0:0:0, x22:0:0:0, -1 + x17:0:0:0, x19:0:0:0, x20:0:0:0, x21:0:0:0) :|: x22:0:0:0 < 1 && x22:0:0:0 < 2 && x22:0:0:0 > -1 && x17:0:0:0 > 0 && x21:0:0:0 < 1 && x20:0:0:0 > 0 && x20:0:0:0 <= x15:0:0:0 l8(x54:0:0, x55:0:0, x56:0:0, x57:0:0, x58:0:0) -> l2(x54:0:0, x66:0:0, 1 + x56:0:0, 1 + x56:0:0, -1 + x57:0:0, -1 + x59:0:0) :|: x60:0:0 < 1 && x60:0:0 > -1 && x55:0:0 < 1 && x58:0:0 < 1 && x57:0:0 + -1 * x54:0:0 <= 0 && x66:0:0 < 2 && x66:0:0 > -1 && x57:0:0 > 1 && x59:0:0 > 0 l8(x67:0:0, x68:0:0, x69:0:0, x70:0:0, x71:0:0) -> l2(x67:0:0, x79:0:0, x69:0:0, 1 + x69:0:0, -1 + x70:0:0, x72:0:0) :|: x72:0:0 > -1 && x73:0:0 < 1 && x73:0:0 > -1 && x68:0:0 < 1 && x71:0:0 < 1 && x70:0:0 + -1 * x67:0:0 <= 0 && x79:0:0 < 1 && x79:0:0 > -1 && x69:0:0 > -1 && x70:0:0 > 1 && x72:0:0 < 1 l8(x7:0:0:0, x9:0:0:0, x11:0:0:0, x12:0:0:0, x13:0:0:0) -> l2(x7:0:0:0, x14:0:0:0, x9:0:0:0, x11:0:0:0, x12:0:0:0, -1 + x13:0:0:0) :|: x14:0:0:0 > -1 && x14:0:0:0 < 2 && x13:0:0:0 > 0 && x12:0:0:0 > 0 && x7:0:0:0 >= x12:0:0:0