MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 3424 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 120 ms] (11) IRSwT (12) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IRSwT (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 33 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Rules: l0(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, rho_1HAT0, statusHAT0) -> l1(DNameHATpost, IoCreateDeviceHATpost, PPBlockInitsHATpost, PPBunlockInitsHATpost, PdoHATpost, PdolenHATpost, conditionalHATpost, iHATpost, numHATpost, rho_1HATpost, statusHATpost) :|: statusHAT0 = statusHATpost && rho_1HAT0 = rho_1HATpost && 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, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x19 = 1 + x8 && 2 <= x6 l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x31 = x42 && x30 = x41 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x22 = x33 && x40 = 1 + x29 && x43 = 1 && x34 = 0 && x28 <= 1 l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x49 = x60 && x47 = x58 && x46 = x57 && x44 = x55 && x61 = x61 && x59 = 0 && x56 = 0 && 2 <= x50 l1(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l4(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x86 = -1 + x75 && 1 <= x75 l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 l1(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x112 = x123 && x111 = x122 && x110 = x121 && x124 = 1 && x129 = 0 && x119 <= 0 l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l1(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x132 <= 0 l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x171 = x171 && x166 = 1 && 1 <= x154 l2(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 && x197 = 0 && x181 <= x183 l2(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x219 = 0 && x209 = x209 && 1 + x205 <= x203 && x211 = 1 l7(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l2(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x229 = x240 && x228 = x239 && x226 = x237 && x224 = x235 && x220 = x231 && x232 = 0 && x241 = 0 && x233 = 1 && x234 = 0 && x236 = x236 && x238 = x238 l8(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l7(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x252 = x263 && x251 = x262 && x250 = x261 && x249 = x260 && x248 = x259 && x247 = x258 && x246 = x257 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 Start term: l8(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, rho_1HAT0, 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, rho_1HAT0, statusHAT0) -> l1(DNameHATpost, IoCreateDeviceHATpost, PPBlockInitsHATpost, PPBunlockInitsHATpost, PdoHATpost, PdolenHATpost, conditionalHATpost, iHATpost, numHATpost, rho_1HATpost, statusHATpost) :|: statusHAT0 = statusHATpost && rho_1HAT0 = rho_1HATpost && 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, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x19 = 1 + x8 && 2 <= x6 l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x31 = x42 && x30 = x41 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x22 = x33 && x40 = 1 + x29 && x43 = 1 && x34 = 0 && x28 <= 1 l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x49 = x60 && x47 = x58 && x46 = x57 && x44 = x55 && x61 = x61 && x59 = 0 && x56 = 0 && 2 <= x50 l1(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l4(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x86 = -1 + x75 && 1 <= x75 l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 l1(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x112 = x123 && x111 = x122 && x110 = x121 && x124 = 1 && x129 = 0 && x119 <= 0 l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l1(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x132 <= 0 l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x171 = x171 && x166 = 1 && 1 <= x154 l2(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 && x197 = 0 && x181 <= x183 l2(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x219 = 0 && x209 = x209 && 1 + x205 <= x203 && x211 = 1 l7(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l2(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x229 = x240 && x228 = x239 && x226 = x237 && x224 = x235 && x220 = x231 && x232 = 0 && x241 = 0 && x233 = 1 && x234 = 0 && x236 = x236 && x238 = x238 l8(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l7(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x252 = x263 && x251 = x262 && x250 = x261 && x249 = x260 && x248 = x259 && x247 = x258 && x246 = x257 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 Start term: l8(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, rho_1HAT0, statusHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(DNameHAT0, IoCreateDeviceHAT0, PPBlockInitsHAT0, PPBunlockInitsHAT0, PdoHAT0, PdolenHAT0, conditionalHAT0, iHAT0, numHAT0, rho_1HAT0, statusHAT0) -> l1(DNameHATpost, IoCreateDeviceHATpost, PPBlockInitsHATpost, PPBunlockInitsHATpost, PdoHATpost, PdolenHATpost, conditionalHATpost, iHATpost, numHATpost, rho_1HATpost, statusHATpost) :|: statusHAT0 = statusHATpost && rho_1HAT0 = rho_1HATpost && 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, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x19 = 1 + x8 && 2 <= x6 (3) l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x31 = x42 && x30 = x41 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x22 = x33 && x40 = 1 + x29 && x43 = 1 && x34 = 0 && x28 <= 1 (4) l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x49 = x60 && x47 = x58 && x46 = x57 && x44 = x55 && x61 = x61 && x59 = 0 && x56 = 0 && 2 <= x50 (5) l1(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l4(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x86 = -1 + x75 && 1 <= x75 (6) l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 (7) l1(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l5(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x112 = x123 && x111 = x122 && x110 = x121 && x124 = 1 && x129 = 0 && x119 <= 0 (8) l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l1(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 && x132 <= 0 (9) l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x171 = x171 && x166 = 1 && 1 <= x154 (10) l2(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x181 = x192 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 && x197 = 0 && x181 <= x183 (11) l2(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x219 = 0 && x209 = x209 && 1 + x205 <= x203 && x211 = 1 (12) l7(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l2(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x229 = x240 && x228 = x239 && x226 = x237 && x224 = x235 && x220 = x231 && x232 = 0 && x241 = 0 && x233 = 1 && x234 = 0 && x236 = x236 && x238 = x238 (13) l8(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l7(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x252 = x263 && x251 = x262 && x250 = x261 && x249 = x260 && x248 = x259 && x247 = x258 && x246 = x257 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 Arcs: (1) -> (5), (7) (2) -> (10), (11) (3) -> (10), (11) (4) -> (1), (2) (5) -> (6) (6) -> (5), (7) (8) -> (5), (7) (9) -> (3), (4) (10) -> (5), (7) (11) -> (8), (9) (12) -> (10), (11) (13) -> (12) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x7 = x18 && x6 = x17 && x5 = x16 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x19 = 1 + x8 && 2 <= x6 (2) l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x49 = x60 && x47 = x58 && x46 = x57 && x44 = x55 && x61 = x61 && x59 = 0 && x56 = 0 && 2 <= x50 (3) l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x154 = x165 && x171 = x171 && x166 = 1 && 1 <= x154 (4) l2(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x219 = 0 && x209 = x209 && 1 + x205 <= x203 && x211 = 1 (5) l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x31 = x42 && x30 = x41 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x22 = x33 && x40 = 1 + x29 && x43 = 1 && x34 = 0 && x28 <= 1 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (5) (4) -> (3) (5) -> (4) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l6(x154:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0, x161:0, x162:0, x163:0, x164:0) -> l6(x209:0, 0, 1, x157:0, x158:0, x159:0, x171:0, 1 + x161:0, x162:0, x163:0, 0) :|: x171:0 < 2 && x159:0 >= 1 + (1 + x161:0) && x154:0 > 0 l6(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l6(x11, 0, 1, x3, 0, x5, x12, x7, 1 + x8, x9, 0) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l6(x1, x6, x8) ---------------------------------------- (9) Obligation: Rules: l6(x154:0, x159:0, x161:0) -> l6(x209:0, x159:0, 1 + x161:0) :|: x171:0 < 2 && x159:0 >= 1 + (1 + x161:0) && x154:0 > 0 l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l6(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: l6(x154:0, x159:0, x161:0) -> l6(x209:0, x159:0, c) :|: c = 1 + x161:0 && (x171:0 < 2 && x159:0 >= 1 + (1 + x161:0) && x154:0 > 0) l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 Found the following polynomial interpretation: [l6(x, x1, x2)] = x1 - x2 The following rules are decreasing: l6(x154:0, x159:0, x161:0) -> l6(x209:0, x159:0, c) :|: c = 1 + x161:0 && (x171:0 < 2 && x159:0 >= 1 + (1 + x161:0) && x154:0 > 0) The following rules are bounded: l6(x154:0, x159:0, x161:0) -> l6(x209:0, x159:0, c) :|: c = 1 + x161:0 && (x171:0 < 2 && x159:0 >= 1 + (1 + x161:0) && x154:0 > 0) l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 ---------------------------------------- (11) Obligation: Rules: l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 ---------------------------------------- (12) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) l6(x, x5, x7) -> l6(x11, x5, x7) :|: x13 > 1 && x > 0 && x5 >= 1 + x7 && x12 > 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: l6(x:0, x5:0, x7:0) -> l6(x11:0, x5:0, x7:0) :|: x5:0 >= 1 + x7:0 && x12:0 > 1 && x:0 > 0 && x13:0 > 1 ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l1(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l4(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x74 = x85 && x73 = x84 && x72 = x83 && x71 = x82 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x86 = -1 + x75 && 1 <= x75 (2) l4(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l1(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l1(x66:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x75:0, x109:0) -> l1(x66:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, -1 + x75:0, x109:0) :|: x75:0 > 0 ---------------------------------------- (19) 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, x8, x9, x10, x11) -> l1(x10) ---------------------------------------- (20) Obligation: Rules: l1(x75:0) -> l1(-1 + x75:0) :|: x75:0 > 0 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: l1(x75:0) -> l1(c) :|: c = -1 + x75:0 && x75:0 > 0 ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l1(x)] = x The following rules are decreasing: l1(x75:0) -> l1(c) :|: c = -1 + x75:0 && x75:0 > 0 The following rules are bounded: l1(x75:0) -> l1(c) :|: c = -1 + x75:0 && x75:0 > 0 ---------------------------------------- (24) YES