NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 947 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 22 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 54 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) IntTRS (14) RankingReductionPairProof [EQUIVALENT, 6 ms] (15) YES (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IRSwT (19) FilterProof [EQUIVALENT, 0 ms] (20) IntTRS (21) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (22) NO ---------------------------------------- (0) Obligation: Rules: l0(___rho_1_HAT0, ___rho_2_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0) -> l1(___rho_1_HATpost, ___rho_2_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost) :|: serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_2_HAT0 = ___rho_2_HATpost && ___rho_1_HAT0 = ___rho_1_HATpost l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 l4(x12, x13, x14, x15, x16, x17) -> l5(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 l5(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 l6(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && x45 = -1 + x39 && 1 + x38 <= x39 && x36 <= 0 l6(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && x57 = -1 + x51 && x56 = -1 + x50 && 1 <= x48 l1(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x66 = x66 && 1 <= x63 l1(x72, x73, x74, x75, x76, x77) -> l4(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x75 = x81 && x74 = x80 && x73 = x79 && x72 = x78 && x75 <= 0 l7(x84, x85, x86, x87, x88, x89) -> l4(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 && 6 <= x86 l7(x96, x97, x98, x99, x100, x101) -> l0(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x97 = x103 && x96 = x102 && x98 <= 5 l8(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x108 = x114 && x117 = x119 && x118 = 0 && x119 = 4 && 1 <= x116 && x116 = x115 && x115 = x115 l9(x120, x121, x122, x123, x124, x125) -> l8(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x123 = x129 && x122 = x128 && x121 = x127 && x120 = x126 Start term: l9(___rho_1_HAT0, ___rho_2_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(___rho_1_HAT0, ___rho_2_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0) -> l1(___rho_1_HATpost, ___rho_2_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost) :|: serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_2_HAT0 = ___rho_2_HATpost && ___rho_1_HAT0 = ___rho_1_HATpost l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 l4(x12, x13, x14, x15, x16, x17) -> l5(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 l5(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 l6(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && x45 = -1 + x39 && 1 + x38 <= x39 && x36 <= 0 l6(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && x57 = -1 + x51 && x56 = -1 + x50 && 1 <= x48 l1(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x66 = x66 && 1 <= x63 l1(x72, x73, x74, x75, x76, x77) -> l4(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x75 = x81 && x74 = x80 && x73 = x79 && x72 = x78 && x75 <= 0 l7(x84, x85, x86, x87, x88, x89) -> l4(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 && 6 <= x86 l7(x96, x97, x98, x99, x100, x101) -> l0(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x97 = x103 && x96 = x102 && x98 <= 5 l8(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x108 = x114 && x117 = x119 && x118 = 0 && x119 = 4 && 1 <= x116 && x116 = x115 && x115 = x115 l9(x120, x121, x122, x123, x124, x125) -> l8(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x123 = x129 && x122 = x128 && x121 = x127 && x120 = x126 Start term: l9(___rho_1_HAT0, ___rho_2_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(___rho_1_HAT0, ___rho_2_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0) -> l1(___rho_1_HATpost, ___rho_2_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost) :|: serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_2_HAT0 = ___rho_2_HATpost && ___rho_1_HAT0 = ___rho_1_HATpost (2) l2(x, x1, x2, x3, x4, x5) -> l3(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 (3) l4(x12, x13, x14, x15, x16, x17) -> l5(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 (4) l5(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 (5) l6(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && x45 = -1 + x39 && 1 + x38 <= x39 && x36 <= 0 (6) l6(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && x57 = -1 + x51 && x56 = -1 + x50 && 1 <= x48 (7) l1(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x66 = x66 && 1 <= x63 (8) l1(x72, x73, x74, x75, x76, x77) -> l4(x78, x79, x80, x81, x82, x83) :|: x77 = x83 && x76 = x82 && x75 = x81 && x74 = x80 && x73 = x79 && x72 = x78 && x75 <= 0 (9) l7(x84, x85, x86, x87, x88, x89) -> l4(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 && 6 <= x86 (10) l7(x96, x97, x98, x99, x100, x101) -> l0(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x97 = x103 && x96 = x102 && x98 <= 5 (11) l8(x108, x109, x110, x111, x112, x113) -> l7(x114, x115, x116, x117, x118, x119) :|: x108 = x114 && x117 = x119 && x118 = 0 && x119 = 4 && 1 <= x116 && x116 = x115 && x115 = x115 (12) l9(x120, x121, x122, x123, x124, x125) -> l8(x126, x127, x128, x129, x130, x131) :|: x125 = x131 && x124 = x130 && x123 = x129 && x122 = x128 && x121 = x127 && x120 = x126 Arcs: (1) -> (7), (8) (3) -> (4) (4) -> (3) (5) -> (1) (6) -> (1) (7) -> (5), (6) (8) -> (3) (9) -> (3) (10) -> (1) (11) -> (9), (10) (12) -> (11) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(___rho_1_HAT0, ___rho_2_HAT0, cHAT0, curr_servHAT0, respHAT0, serversHAT0) -> l1(___rho_1_HATpost, ___rho_2_HATpost, cHATpost, curr_servHATpost, respHATpost, serversHATpost) :|: serversHAT0 = serversHATpost && respHAT0 = respHATpost && curr_servHAT0 = curr_servHATpost && cHAT0 = cHATpost && ___rho_2_HAT0 = ___rho_2_HATpost && ___rho_1_HAT0 = ___rho_1_HATpost (2) l6(x48, x49, x50, x51, x52, x53) -> l0(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x49 = x55 && x48 = x54 && x58 = 1 + x52 && x57 = -1 + x51 && x56 = -1 + x50 && 1 <= x48 (3) l6(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && x45 = -1 + x39 && 1 + x38 <= x39 && x36 <= 0 (4) l1(x60, x61, x62, x63, x64, x65) -> l6(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x61 = x67 && x66 = x66 && 1 <= x63 Arcs: (1) -> (4) (2) -> (1) (3) -> (1) (4) -> (2), (3) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l6(___rho_1_HATpost:0, ___rho_2_HATpost:0, x50:0, x51:0, x52:0, serversHATpost:0) -> l6(x66:0, ___rho_2_HATpost:0, -1 + x50:0, -1 + x51:0, 1 + x52:0, serversHATpost:0) :|: ___rho_1_HATpost:0 > 0 && x51:0 > 1 l6(x, x1, x2, x3, x4, x5) -> l6(x6, x1, x2, -1 + x3, x4, x5) :|: x3 >= 1 + x2 && x3 > 1 && x < 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) -> l6(x1, x3, x4) ---------------------------------------- (9) Obligation: Rules: l6(___rho_1_HATpost:0, x50:0, x51:0) -> l6(x66:0, -1 + x50:0, -1 + x51:0) :|: ___rho_1_HATpost:0 > 0 && x51:0 > 1 l6(x, x2, x3) -> l6(x6, x2, -1 + x3) :|: x3 >= 1 + x2 && x3 > 1 && x < 1 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l6(VARIABLE, VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l6(___rho_1_HATpost:0, x50:0, x51:0) -> l6(x66:0, c, c1) :|: c1 = -1 + x51:0 && c = -1 + x50:0 && (___rho_1_HATpost:0 > 0 && x51:0 > 1) l6(x, x2, x3) -> l6(x6, x2, c2) :|: c2 = -1 + x3 && (x3 >= 1 + x2 && x3 > 1 && x < 1) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l6(x, x1, x2)] = -x1 + x2 The following rules are decreasing: l6(x, x2, x3) -> l6(x6, x2, c2) :|: c2 = -1 + x3 && (x3 >= 1 + x2 && x3 > 1 && x < 1) The following rules are bounded: l6(x, x2, x3) -> l6(x6, x2, c2) :|: c2 = -1 + x3 && (x3 >= 1 + x2 && x3 > 1 && x < 1) ---------------------------------------- (13) Obligation: Rules: l6(___rho_1_HATpost:0, x50:0, x51:0) -> l6(x66:0, c, c1) :|: c1 = -1 + x51:0 && c = -1 + x50:0 && (___rho_1_HATpost:0 > 0 && x51:0 > 1) ---------------------------------------- (14) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l6 ] = l6_3 The following rules are decreasing: l6(___rho_1_HATpost:0, x50:0, x51:0) -> l6(x66:0, c, c1) :|: c1 = -1 + x51:0 && c = -1 + x50:0 && (___rho_1_HATpost:0 > 0 && x51:0 > 1) The following rules are bounded: l6(___rho_1_HATpost:0, x50:0, x51:0) -> l6(x66:0, c, c1) :|: c1 = -1 + x51:0 && c = -1 + x50:0 && (___rho_1_HATpost:0 > 0 && x51:0 > 1) ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l4(x12, x13, x14, x15, x16, x17) -> l5(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x12 = x18 (2) l5(x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x24 = x30 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l4(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> l4(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) :|: TRUE ---------------------------------------- (19) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l4(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l4(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> l4(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) :|: TRUE ---------------------------------------- (21) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> f(1, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8, -8, -8) ---------------------------------------- (22) NO