NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 4664 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 13 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 78 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) IntTRS (14) PolynomialOrderProcessor [EQUIVALENT, 6 ms] (15) IntTRS (16) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (17) YES (18) IRSwT (19) IntTRSCompressionProof [EQUIVALENT, 16 ms] (20) IRSwT (21) FilterProof [EQUIVALENT, 0 ms] (22) IntTRS (23) IntTRSPeriodicNontermProof [COMPLETE, 6 ms] (24) NO ---------------------------------------- (0) Obligation: Rules: l0(IsochResourceDataHAT0, ResourceIrpHAT0, StackSizeHAT0, ___rho_99_HAT0, k4HAT0, keAHAT0, keRHAT0, ntStatusHAT0, pIrbHAT0) -> l1(IsochResourceDataHATpost, ResourceIrpHATpost, StackSizeHATpost, ___rho_99_HATpost, k4HATpost, keAHATpost, keRHATpost, ntStatusHATpost, pIrbHATpost) :|: pIrbHAT0 = pIrbHATpost && ntStatusHAT0 = ntStatusHATpost && keRHAT0 = keRHATpost && keAHAT0 = keAHATpost && k4HAT0 = k4HATpost && ___rho_99_HAT0 = ___rho_99_HATpost && StackSizeHAT0 = StackSizeHATpost && ResourceIrpHAT0 = ResourceIrpHATpost && IsochResourceDataHAT0 = IsochResourceDataHATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 l4(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l2(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x52 = x52 && 1 <= x44 l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x62 <= 0 l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l4(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && 1 + x91 <= 0 l6(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && x108 = x117 && 1 <= x109 l6(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && 0 <= x127 && x127 <= 0 l7(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l2(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x144 <= 0 l7(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l6(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 1 <= x162 && x180 = x180 && x173 = x173 && x174 = x174 && x172 = x174 && x162 = x171 && x166 = x175 && x167 = x176 && x168 = x177 && x169 = x178 && x170 = x179 l8(x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l0(x190, x191, x192, x193, x194, x195, x196, x197, x198) :|: x185 <= 0 && x199 = 1 && x196 = 0 && x181 = x190 && x182 = x191 && x183 = x192 && x184 = x193 && x185 = x194 && x186 = x195 && x188 = x197 && x189 = x198 l8(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l7(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: 1 <= x204 && x213 = -1 + x204 && x218 = 1 && x215 = 0 && x200 = x209 && x201 = x210 && x202 = x211 && x203 = x212 && x205 = x214 && x207 = x216 && x208 = x217 l3(x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l8(x228, x229, x230, x231, x232, x233, x234, x235, x236) :|: x237 = 1 && x233 = 0 && x219 = x228 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235 && x227 = x236 l9(x238, x239, x240, x241, x242, x243, x244, x245, x246) -> l3(x247, x248, x249, x250, x251, x252, x253, x254, x255) :|: x246 = x255 && x245 = x254 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x253 = 0 && x252 = 0 l10(x256, x257, x258, x259, x260, x261, x262, x263, x264) -> l9(x265, x266, x267, x268, x269, x270, x271, x272, x273) :|: x264 = x273 && x263 = x272 && x262 = x271 && x261 = x270 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 Start term: l10(IsochResourceDataHAT0, ResourceIrpHAT0, StackSizeHAT0, ___rho_99_HAT0, k4HAT0, keAHAT0, keRHAT0, ntStatusHAT0, pIrbHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(IsochResourceDataHAT0, ResourceIrpHAT0, StackSizeHAT0, ___rho_99_HAT0, k4HAT0, keAHAT0, keRHAT0, ntStatusHAT0, pIrbHAT0) -> l1(IsochResourceDataHATpost, ResourceIrpHATpost, StackSizeHATpost, ___rho_99_HATpost, k4HATpost, keAHATpost, keRHATpost, ntStatusHATpost, pIrbHATpost) :|: pIrbHAT0 = pIrbHATpost && ntStatusHAT0 = ntStatusHATpost && keRHAT0 = keRHATpost && keAHAT0 = keAHATpost && k4HAT0 = k4HATpost && ___rho_99_HAT0 = ___rho_99_HATpost && StackSizeHAT0 = StackSizeHATpost && ResourceIrpHAT0 = ResourceIrpHATpost && IsochResourceDataHAT0 = IsochResourceDataHATpost l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 l4(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l2(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x52 = x52 && 1 <= x44 l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x62 <= 0 l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l4(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && 1 + x91 <= 0 l6(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && x108 = x117 && 1 <= x109 l6(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && 0 <= x127 && x127 <= 0 l7(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l2(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x144 <= 0 l7(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l6(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 1 <= x162 && x180 = x180 && x173 = x173 && x174 = x174 && x172 = x174 && x162 = x171 && x166 = x175 && x167 = x176 && x168 = x177 && x169 = x178 && x170 = x179 l8(x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l0(x190, x191, x192, x193, x194, x195, x196, x197, x198) :|: x185 <= 0 && x199 = 1 && x196 = 0 && x181 = x190 && x182 = x191 && x183 = x192 && x184 = x193 && x185 = x194 && x186 = x195 && x188 = x197 && x189 = x198 l8(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l7(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: 1 <= x204 && x213 = -1 + x204 && x218 = 1 && x215 = 0 && x200 = x209 && x201 = x210 && x202 = x211 && x203 = x212 && x205 = x214 && x207 = x216 && x208 = x217 l3(x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l8(x228, x229, x230, x231, x232, x233, x234, x235, x236) :|: x237 = 1 && x233 = 0 && x219 = x228 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235 && x227 = x236 l9(x238, x239, x240, x241, x242, x243, x244, x245, x246) -> l3(x247, x248, x249, x250, x251, x252, x253, x254, x255) :|: x246 = x255 && x245 = x254 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x253 = 0 && x252 = 0 l10(x256, x257, x258, x259, x260, x261, x262, x263, x264) -> l9(x265, x266, x267, x268, x269, x270, x271, x272, x273) :|: x264 = x273 && x263 = x272 && x262 = x271 && x261 = x270 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 Start term: l10(IsochResourceDataHAT0, ResourceIrpHAT0, StackSizeHAT0, ___rho_99_HAT0, k4HAT0, keAHAT0, keRHAT0, ntStatusHAT0, pIrbHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(IsochResourceDataHAT0, ResourceIrpHAT0, StackSizeHAT0, ___rho_99_HAT0, k4HAT0, keAHAT0, keRHAT0, ntStatusHAT0, pIrbHAT0) -> l1(IsochResourceDataHATpost, ResourceIrpHATpost, StackSizeHATpost, ___rho_99_HATpost, k4HATpost, keAHATpost, keRHATpost, ntStatusHATpost, pIrbHATpost) :|: pIrbHAT0 = pIrbHATpost && ntStatusHAT0 = ntStatusHATpost && keRHAT0 = keRHATpost && keAHAT0 = keAHATpost && k4HAT0 = k4HATpost && ___rho_99_HAT0 = ___rho_99_HATpost && StackSizeHAT0 = StackSizeHATpost && ResourceIrpHAT0 = ResourceIrpHATpost && IsochResourceDataHAT0 = IsochResourceDataHATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 (3) l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 (4) l4(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l2(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x52 = x52 && 1 <= x44 (5) l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x62 <= 0 (6) l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l4(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 (7) l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && 1 + x91 <= 0 (8) l6(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && x108 = x117 && 1 <= x109 (9) l6(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && 0 <= x127 && x127 <= 0 (10) l7(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l2(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x144 <= 0 (11) l7(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l6(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 1 <= x162 && x180 = x180 && x173 = x173 && x174 = x174 && x172 = x174 && x162 = x171 && x166 = x175 && x167 = x176 && x168 = x177 && x169 = x178 && x170 = x179 (12) l8(x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l0(x190, x191, x192, x193, x194, x195, x196, x197, x198) :|: x185 <= 0 && x199 = 1 && x196 = 0 && x181 = x190 && x182 = x191 && x183 = x192 && x184 = x193 && x185 = x194 && x186 = x195 && x188 = x197 && x189 = x198 (13) l8(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l7(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: 1 <= x204 && x213 = -1 + x204 && x218 = 1 && x215 = 0 && x200 = x209 && x201 = x210 && x202 = x211 && x203 = x212 && x205 = x214 && x207 = x216 && x208 = x217 (14) l3(x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l8(x228, x229, x230, x231, x232, x233, x234, x235, x236) :|: x237 = 1 && x233 = 0 && x219 = x228 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235 && x227 = x236 (15) l9(x238, x239, x240, x241, x242, x243, x244, x245, x246) -> l3(x247, x248, x249, x250, x251, x252, x253, x254, x255) :|: x246 = x255 && x245 = x254 && x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x253 = 0 && x252 = 0 (16) l10(x256, x257, x258, x259, x260, x261, x262, x263, x264) -> l9(x265, x266, x267, x268, x269, x270, x271, x272, x273) :|: x264 = x273 && x263 = x272 && x262 = x271 && x261 = x270 && x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 Arcs: (1) -> (2) (2) -> (1) (3) -> (14) (4) -> (3) (5) -> (3) (6) -> (4), (5) (7) -> (6) (8) -> (6) (9) -> (3) (10) -> (3) (11) -> (7), (8), (9) (12) -> (1) (13) -> (10), (11) (14) -> (12), (13) (15) -> (14) (16) -> (15) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l2(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l3(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x21 = x30 && x20 = x29 && x19 = x28 && x18 = x27 (2) l7(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l2(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x147 = x156 && x146 = x155 && x145 = x154 && x144 = x153 && x144 <= 0 (3) l6(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l2(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x134 = x143 && x133 = x142 && x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && 0 <= x127 && x127 <= 0 (4) l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x57 = x66 && x56 = x65 && x55 = x64 && x54 = x63 && x62 <= 0 (5) l4(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l2(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 && x52 = x52 && 1 <= x44 (6) l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l4(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x79 = x88 && x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 (7) l6(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x111 = x120 && x110 = x119 && x109 = x118 && x108 = x117 && 1 <= x109 (8) l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x94 = x103 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && 1 + x91 <= 0 (9) l7(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l6(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: 1 <= x162 && x180 = x180 && x173 = x173 && x174 = x174 && x172 = x174 && x162 = x171 && x166 = x175 && x167 = x176 && x168 = x177 && x169 = x178 && x170 = x179 (10) l8(x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l7(x209, x210, x211, x212, x213, x214, x215, x216, x217) :|: 1 <= x204 && x213 = -1 + x204 && x218 = 1 && x215 = 0 && x200 = x209 && x201 = x210 && x202 = x211 && x203 = x212 && x205 = x214 && x207 = x216 && x208 = x217 (11) l3(x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l8(x228, x229, x230, x231, x232, x233, x234, x235, x236) :|: x237 = 1 && x233 = 0 && x219 = x228 && x220 = x229 && x221 = x230 && x222 = x231 && x223 = x232 && x225 = x234 && x226 = x235 && x227 = x236 Arcs: (1) -> (11) (2) -> (1) (3) -> (1) (4) -> (1) (5) -> (1) (6) -> (4), (5) (7) -> (6) (8) -> (6) (9) -> (3), (7), (8) (10) -> (2), (9) (11) -> (10) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l8(x117:0, x201:0, x202:0, x203:0, x204:0, x122:0, x206:0, x124:0, x125:0) -> l5(x117:0, x118:0, x119:0, x118:0, -1 + x204:0, x122:0, 0, x124:0, x125:0) :|: x204:0 > 0 && x117:0 > 0 && x118:0 > 0 l8(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l5(x, x9, x10, x9, -1 + x4, x5, 0, x7, x8) :|: x4 > 0 && x > 0 && x9 < 0 l8(x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l8(x11, x20, x21, x20, -1 + x15, 0, 0, x18, x19) :|: x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0 l5(x228:0, x229:0, x230:0, x231:0, x232:0, x32:0, x234:0, x79:0, x80:0) -> l8(x228:0, x229:0, x230:0, x231:0, x232:0, 0, x234:0, x235:0, x236:0) :|: x236:0 > 0 l5(x22, x23, x24, x25, x26, x27, x28, x29, x30) -> l8(x22, x23, x24, x25, x26, 0, x28, x29, x31) :|: x31 < 1 l8(x32, x33, x34, x35, x36, x37, x38, x39, x40) -> l8(x32, x33, x34, x35, -1 + x36, 0, 0, x39, x40) :|: x32 < 1 && x36 > 0 ---------------------------------------- (8) 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, x8, x9) -> l8(x1, x5) l5(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l5(x1, x5) ---------------------------------------- (9) Obligation: Rules: l8(x117:0, x204:0) -> l5(x117:0, -1 + x204:0) :|: x204:0 > 0 && x117:0 > 0 && x118:0 > 0 l8(x, x4) -> l5(x, -1 + x4) :|: x4 > 0 && x > 0 && x9 < 0 l8(x11, x15) -> l8(x11, -1 + x15) :|: x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0 l5(x228:0, x232:0) -> l8(x228:0, x232:0) :|: x236:0 > 0 l5(x22, x26) -> l8(x22, x26) :|: x31 < 1 l8(x32, x36) -> l8(x32, -1 + x36) :|: x32 < 1 && x36 > 0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l8(VARIABLE, VARIABLE) l5(VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l8(x117:0, x204:0) -> l5(x117:0, c) :|: c = -1 + x204:0 && (x204:0 > 0 && x117:0 > 0 && x118:0 > 0) l8(x, x4) -> l5(x, c1) :|: c1 = -1 + x4 && (x4 > 0 && x > 0 && x9 < 0) l8(x11, x15) -> l8(x11, c2) :|: c2 = -1 + x15 && (x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0) l5(x228:0, x232:0) -> l8(x228:0, x232:0) :|: x236:0 > 0 l5(x22, x26) -> l8(x22, x26) :|: x31 < 1 l8(x32, x36) -> l8(x32, c3) :|: c3 = -1 + x36 && (x32 < 1 && x36 > 0) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l8(x, x1)] = -1 - x + x1 [l5(x2, x3)] = -1 - x2 + x3 The following rules are decreasing: l8(x117:0, x204:0) -> l5(x117:0, c) :|: c = -1 + x204:0 && (x204:0 > 0 && x117:0 > 0 && x118:0 > 0) l8(x, x4) -> l5(x, c1) :|: c1 = -1 + x4 && (x4 > 0 && x > 0 && x9 < 0) l8(x11, x15) -> l8(x11, c2) :|: c2 = -1 + x15 && (x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0) l8(x32, x36) -> l8(x32, c3) :|: c3 = -1 + x36 && (x32 < 1 && x36 > 0) The following rules are bounded: l8(x32, x36) -> l8(x32, c3) :|: c3 = -1 + x36 && (x32 < 1 && x36 > 0) ---------------------------------------- (13) Obligation: Rules: l8(x117:0, x204:0) -> l5(x117:0, c) :|: c = -1 + x204:0 && (x204:0 > 0 && x117:0 > 0 && x118:0 > 0) l8(x, x4) -> l5(x, c1) :|: c1 = -1 + x4 && (x4 > 0 && x > 0 && x9 < 0) l8(x11, x15) -> l8(x11, c2) :|: c2 = -1 + x15 && (x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0) l5(x228:0, x232:0) -> l8(x228:0, x232:0) :|: x236:0 > 0 l5(x22, x26) -> l8(x22, x26) :|: x31 < 1 ---------------------------------------- (14) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l8(x, x1)] = -1 + x + x1 [l5(x2, x3)] = -1 + x2 + x3 The following rules are decreasing: l8(x117:0, x204:0) -> l5(x117:0, c) :|: c = -1 + x204:0 && (x204:0 > 0 && x117:0 > 0 && x118:0 > 0) l8(x, x4) -> l5(x, c1) :|: c1 = -1 + x4 && (x4 > 0 && x > 0 && x9 < 0) l8(x11, x15) -> l8(x11, c2) :|: c2 = -1 + x15 && (x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0) The following rules are bounded: l8(x117:0, x204:0) -> l5(x117:0, c) :|: c = -1 + x204:0 && (x204:0 > 0 && x117:0 > 0 && x118:0 > 0) l8(x, x4) -> l5(x, c1) :|: c1 = -1 + x4 && (x4 > 0 && x > 0 && x9 < 0) l8(x11, x15) -> l8(x11, c2) :|: c2 = -1 + x15 && (x20 > -1 && x20 < 1 && x11 > 0 && x15 > 0) ---------------------------------------- (15) Obligation: Rules: l5(x228:0, x232:0) -> l8(x228:0, x232:0) :|: x236:0 > 0 l5(x22, x26) -> l8(x22, x26) :|: x31 < 1 ---------------------------------------- (16) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l5(x, x1)] = 0 [l8(x2, x3)] = -1 The following rules are decreasing: l5(x228:0, x232:0) -> l8(x228:0, x232:0) :|: x236:0 > 0 l5(x22, x26) -> l8(x22, x26) :|: x31 < 1 The following rules are bounded: l5(x228:0, x232:0) -> l8(x228:0, x232:0) :|: x236:0 > 0 l5(x22, x26) -> l8(x22, x26) :|: x31 < 1 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Termination digraph: Nodes: (1) l0(IsochResourceDataHAT0, ResourceIrpHAT0, StackSizeHAT0, ___rho_99_HAT0, k4HAT0, keAHAT0, keRHAT0, ntStatusHAT0, pIrbHAT0) -> l1(IsochResourceDataHATpost, ResourceIrpHATpost, StackSizeHATpost, ___rho_99_HATpost, k4HATpost, keAHATpost, keRHATpost, ntStatusHATpost, pIrbHATpost) :|: pIrbHAT0 = pIrbHATpost && ntStatusHAT0 = ntStatusHATpost && keRHAT0 = keRHATpost && keAHAT0 = keAHATpost && k4HAT0 = k4HATpost && ___rho_99_HAT0 = ___rho_99_HATpost && StackSizeHAT0 = StackSizeHATpost && ResourceIrpHAT0 = ResourceIrpHATpost && IsochResourceDataHAT0 = IsochResourceDataHATpost (2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x3 = x12 && x2 = x11 && x1 = x10 && x = x9 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: l0(IsochResourceDataHAT0:0, ResourceIrpHAT0:0, StackSizeHAT0:0, ___rho_99_HAT0:0, k4HAT0:0, keAHAT0:0, keRHAT0:0, ntStatusHAT0:0, pIrbHAT0:0) -> l0(IsochResourceDataHAT0:0, ResourceIrpHAT0:0, StackSizeHAT0:0, ___rho_99_HAT0:0, k4HAT0:0, keAHAT0:0, keRHAT0:0, ntStatusHAT0:0, pIrbHAT0:0) :|: TRUE ---------------------------------------- (21) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l0(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: l0(IsochResourceDataHAT0:0, ResourceIrpHAT0:0, StackSizeHAT0:0, ___rho_99_HAT0:0, k4HAT0:0, keAHAT0:0, keRHAT0:0, ntStatusHAT0:0, pIrbHAT0:0) -> l0(IsochResourceDataHAT0:0, ResourceIrpHAT0:0, StackSizeHAT0:0, ___rho_99_HAT0:0, k4HAT0:0, keAHAT0:0, keRHAT0:0, ntStatusHAT0:0, pIrbHAT0:0) :|: TRUE ---------------------------------------- (23) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, IsochResourceDataHAT0:0, ResourceIrpHAT0:0, StackSizeHAT0:0, ___rho_99_HAT0:0, k4HAT0:0, keAHAT0:0, keRHAT0:0, ntStatusHAT0:0, pIrbHAT0:0) -> f(1, IsochResourceDataHAT0:0, ResourceIrpHAT0:0, StackSizeHAT0:0, ___rho_99_HAT0:0, k4HAT0:0, keAHAT0:0, keRHAT0:0, ntStatusHAT0:0, pIrbHAT0:0) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8, -8, -8, -8, -8, -8) ---------------------------------------- (24) NO