MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 1817 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 29 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 142 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, statusHAT0) -> l1(DNameHATpost, IoCreateDeviceHATpost, PPBlockInitsHATpost, PPBunlockInitsHATpost, PdoHATpost, PdolenHATpost, conditionalHATpost, iHATpost, numHATpost, statusHATpost) :|: statusHAT0 = statusHATpost && numHAT0 = numHATpost && iHAT0 = iHATpost && conditionalHAT0 = conditionalHATpost && PdolenHAT0 = PdolenHATpost && PdoHAT0 = PdoHATpost && PPBunlockInitsHAT0 = PPBunlockInitsHATpost && PPBlockInitsHAT0 = PPBlockInitsHATpost && IoCreateDeviceHAT0 = IoCreateDeviceHATpost && DNameHAT0 = DNameHATpost && conditionalHAT0 <= 1 l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x18 = 1 + x8 && 2 <= x6 l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x20 = x30 && x37 = 1 + x27 && x39 = 1 && x31 = 0 && x26 <= 1 l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x45 = x55 && x43 = x53 && x42 = x52 && x40 = x50 && x56 = x56 && x54 = 0 && x51 = 0 && 2 <= x46 l1(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l4(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x62 = x72 && x61 = x71 && x60 = x70 && x73 = 1 && x78 = 0 l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l1(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x80 <= 0 l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x107 = x117 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x100 = x110 && x116 = x116 && x111 = 1 && 1 <= x100 l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l1(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 && x139 = 0 && x125 <= x127 l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l5(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x141 = x151 && x159 = 0 && x150 = x150 && 1 + x147 <= x145 && x152 = 1 l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l2(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x168 = x178 && x166 = x176 && x164 = x174 && x160 = x170 && x171 = 0 && x179 = 0 && x172 = 1 && x173 = 0 && x175 = x175 && x177 = x177 l7(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 Start term: l7(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, statusHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, statusHAT0) -> l1(DNameHATpost, IoCreateDeviceHATpost, PPBlockInitsHATpost, PPBunlockInitsHATpost, PdoHATpost, PdolenHATpost, conditionalHATpost, iHATpost, numHATpost, statusHATpost) :|: statusHAT0 = statusHATpost && numHAT0 = numHATpost && iHAT0 = iHATpost && conditionalHAT0 = conditionalHATpost && PdolenHAT0 = PdolenHATpost && PdoHAT0 = PdoHATpost && PPBunlockInitsHAT0 = PPBunlockInitsHATpost && PPBlockInitsHAT0 = PPBlockInitsHATpost && IoCreateDeviceHAT0 = IoCreateDeviceHATpost && DNameHAT0 = DNameHATpost && conditionalHAT0 <= 1 l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x18 = 1 + x8 && 2 <= x6 l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x20 = x30 && x37 = 1 + x27 && x39 = 1 && x31 = 0 && x26 <= 1 l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x45 = x55 && x43 = x53 && x42 = x52 && x40 = x50 && x56 = x56 && x54 = 0 && x51 = 0 && 2 <= x46 l1(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l4(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x62 = x72 && x61 = x71 && x60 = x70 && x73 = 1 && x78 = 0 l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l1(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x80 <= 0 l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x107 = x117 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x100 = x110 && x116 = x116 && x111 = 1 && 1 <= x100 l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l1(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 && x139 = 0 && x125 <= x127 l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l5(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x141 = x151 && x159 = 0 && x150 = x150 && 1 + x147 <= x145 && x152 = 1 l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l2(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x168 = x178 && x166 = x176 && x164 = x174 && x160 = x170 && x171 = 0 && x179 = 0 && x172 = 1 && x173 = 0 && x175 = x175 && x177 = x177 l7(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 Start term: l7(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, statusHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, statusHAT0) -> l1(DNameHATpost, IoCreateDeviceHATpost, PPBlockInitsHATpost, PPBunlockInitsHATpost, PdoHATpost, PdolenHATpost, conditionalHATpost, iHATpost, numHATpost, statusHATpost) :|: statusHAT0 = statusHATpost && numHAT0 = numHATpost && iHAT0 = iHATpost && conditionalHAT0 = conditionalHATpost && PdolenHAT0 = PdolenHATpost && PdoHAT0 = PdoHATpost && PPBunlockInitsHAT0 = PPBunlockInitsHATpost && PPBlockInitsHAT0 = PPBlockInitsHATpost && IoCreateDeviceHAT0 = IoCreateDeviceHATpost && DNameHAT0 = DNameHATpost && conditionalHAT0 <= 1 (2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x18 = 1 + x8 && 2 <= x6 (3) l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x20 = x30 && x37 = 1 + x27 && x39 = 1 && x31 = 0 && x26 <= 1 (4) l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x45 = x55 && x43 = x53 && x42 = x52 && x40 = x50 && x56 = x56 && x54 = 0 && x51 = 0 && 2 <= x46 (5) l1(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l4(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x62 = x72 && x61 = x71 && x60 = x70 && x73 = 1 && x78 = 0 (6) l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l1(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x80 <= 0 (7) l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x107 = x117 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x100 = x110 && x116 = x116 && x111 = 1 && 1 <= x100 (8) l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l1(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 && x139 = 0 && x125 <= x127 (9) l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l5(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x141 = x151 && x159 = 0 && x150 = x150 && 1 + x147 <= x145 && x152 = 1 (10) l6(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l2(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x168 = x178 && x166 = x176 && x164 = x174 && x160 = x170 && x171 = 0 && x179 = 0 && x172 = 1 && x173 = 0 && x175 = x175 && x177 = x177 (11) l7(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l6(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 Arcs: (1) -> (5) (2) -> (8), (9) (3) -> (8), (9) (4) -> (1), (2) (6) -> (5) (7) -> (3), (4) (8) -> (5) (9) -> (6), (7) (10) -> (8), (9) (11) -> (10) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l2(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x18 = 1 + x8 && 2 <= x6 (2) l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x45 = x55 && x43 = x53 && x42 = x52 && x40 = x50 && x56 = x56 && x54 = 0 && x51 = 0 && 2 <= x46 (3) l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l3(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x107 = x117 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x100 = x110 && x116 = x116 && x111 = 1 && 1 <= x100 (4) l2(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l5(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x148 = x158 && x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x141 = x151 && x159 = 0 && x150 = x150 && 1 + x147 <= x145 && x152 = 1 (5) l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x20 = x30 && x37 = 1 + x27 && x39 = 1 && x31 = 0 && x26 <= 1 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (5) (4) -> (3) (5) -> (4) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l5(x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) -> l5(x150:0, 0, 1, x103:0, 0, x105:0, x156:0, x107:0, 1 + x108:0, 0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 l5(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l5(x10, 0, 1, x3, x4, x5, x11, 1 + x7, x8, 0) :|: x11 < 2 && x5 >= 1 + (1 + x7) && x > 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l5(x1, x6, x8) ---------------------------------------- (8) Obligation: Rules: l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 l5(x, x5, x7) -> l5(x10, x5, 1 + x7) :|: x11 < 2 && x5 >= 1 + (1 + x7) && x > 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l5(VARIABLE, 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: l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 l5(x, x5, x7) -> l5(x10, x5, c) :|: c = 1 + x7 && (x11 < 2 && x5 >= 1 + (1 + x7) && x > 0) Found the following polynomial interpretation: [l5(x, x1, x2)] = x1 - x2 The following rules are decreasing: l5(x, x5, x7) -> l5(x10, x5, c) :|: c = 1 + x7 && (x11 < 2 && x5 >= 1 + (1 + x7) && x > 0) The following rules are bounded: l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 l5(x, x5, x7) -> l5(x10, x5, c) :|: c = 1 + x7 && (x11 < 2 && x5 >= 1 + (1 + x7) && x > 0) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 ---------------------------------------- (10) Obligation: Rules: l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l5(x100:0, x105:0, x107:0) -> l5(x150:0, x105:0, x107:0) :|: x116:0 > 1 && x100:0 > 0 && x105:0 >= 1 + x107:0 && x156:0 > 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l5(x100:0:0, x105:0:0, x107:0:0) -> l5(x150:0:0, x105:0:0, x107:0:0) :|: x105:0:0 >= 1 + x107:0:0 && x156:0:0 > 1 && x100:0:0 > 0 && x116:0:0 > 1