MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 645 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 43 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 80 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(retpHAT0, retppHAT0, rhoHAT0, rhopHAT0, xHAT0, xpHAT0) -> l1(retpHATpost, retppHATpost, rhoHATpost, rhopHATpost, xHATpost, xpHATpost) :|: xHAT0 = xHATpost && rhopHAT0 = rhopHATpost && rhoHAT0 = rhoHATpost && retppHAT0 = retppHATpost && retpHAT0 = retpHATpost && xpHATpost = 1 + xpHAT0 && 1 <= rhopHAT0 l0(x, x1, x2, x3, x4, x5) -> l1(x6, x7, x8, x9, x10, x11) :|: x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x11 = -1 + x5 && x3 <= 0 l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 0 && x13 <= 0 l2(x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x30 = 1 l2(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && 1 <= x45 && x45 = x45 l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x48 = x54 && x55 = 0 && x53 <= 1 l1(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x60 = x66 && x67 = 1 && 2 <= x65 l4(x72, x73, x74, x75, x76, x77) -> l1(x78, x79, x80, x81, x82, x83) :|: x74 = x80 && x73 = x79 && x72 = x78 && x81 = x74 && x83 = x82 && x82 = 2 l3(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 && x84 <= 0 l6(x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x97 = x103 && x96 = x102 Start term: l6(retpHAT0, retppHAT0, rhoHAT0, rhopHAT0, xHAT0, xpHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(retpHAT0, retppHAT0, rhoHAT0, rhopHAT0, xHAT0, xpHAT0) -> l1(retpHATpost, retppHATpost, rhoHATpost, rhopHATpost, xHATpost, xpHATpost) :|: xHAT0 = xHATpost && rhopHAT0 = rhopHATpost && rhoHAT0 = rhoHATpost && retppHAT0 = retppHATpost && retpHAT0 = retpHATpost && xpHATpost = 1 + xpHAT0 && 1 <= rhopHAT0 l0(x, x1, x2, x3, x4, x5) -> l1(x6, x7, x8, x9, x10, x11) :|: x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x11 = -1 + x5 && x3 <= 0 l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 0 && x13 <= 0 l2(x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x30 = 1 l2(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && 1 <= x45 && x45 = x45 l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x48 = x54 && x55 = 0 && x53 <= 1 l1(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x60 = x66 && x67 = 1 && 2 <= x65 l4(x72, x73, x74, x75, x76, x77) -> l1(x78, x79, x80, x81, x82, x83) :|: x74 = x80 && x73 = x79 && x72 = x78 && x81 = x74 && x83 = x82 && x82 = 2 l3(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 && x84 <= 0 l6(x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x97 = x103 && x96 = x102 Start term: l6(retpHAT0, retppHAT0, rhoHAT0, rhopHAT0, xHAT0, xpHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(retpHAT0, retppHAT0, rhoHAT0, rhopHAT0, xHAT0, xpHAT0) -> l1(retpHATpost, retppHATpost, rhoHATpost, rhopHATpost, xHATpost, xpHATpost) :|: xHAT0 = xHATpost && rhopHAT0 = rhopHATpost && rhoHAT0 = rhoHATpost && retppHAT0 = retppHATpost && retpHAT0 = retpHATpost && xpHATpost = 1 + xpHAT0 && 1 <= rhopHAT0 (2) l0(x, x1, x2, x3, x4, x5) -> l1(x6, x7, x8, x9, x10, x11) :|: x4 = x10 && x3 = x9 && x2 = x8 && x1 = x7 && x = x6 && x11 = -1 + x5 && x3 <= 0 (3) l2(x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && x16 = x22 && x15 = x21 && x14 = x20 && x13 = x19 && x18 = 0 && x13 <= 0 (4) l2(x24, x25, x26, x27, x28, x29) -> l3(x30, x31, x32, x33, x34, x35) :|: x29 = x35 && x28 = x34 && x27 = x33 && x26 = x32 && x25 = x31 && x30 = 1 (5) l2(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && 1 <= x45 && x45 = x45 (6) l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x48 = x54 && x55 = 0 && x53 <= 1 (7) l1(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x60 = x66 && x67 = 1 && 2 <= x65 (8) l4(x72, x73, x74, x75, x76, x77) -> l1(x78, x79, x80, x81, x82, x83) :|: x74 = x80 && x73 = x79 && x72 = x78 && x81 = x74 && x83 = x82 && x82 = 2 (9) l3(x84, x85, x86, x87, x88, x89) -> l5(x90, x91, x92, x93, x94, x95) :|: x89 = x95 && x88 = x94 && x87 = x93 && x86 = x92 && x85 = x91 && x84 = x90 && x84 <= 0 (10) l6(x96, x97, x98, x99, x100, x101) -> l4(x102, x103, x104, x105, x106, x107) :|: x101 = x107 && x100 = x106 && x99 = x105 && x98 = x104 && x97 = x103 && x96 = x102 Arcs: (1) -> (6), (7) (2) -> (6), (7) (3) -> (9) (5) -> (1) (6) -> (3), (4), (5) (7) -> (4), (5) (8) -> (7) (10) -> (8) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(retpHAT0, retppHAT0, rhoHAT0, rhopHAT0, xHAT0, xpHAT0) -> l1(retpHATpost, retppHATpost, rhoHATpost, rhopHATpost, xHATpost, xpHATpost) :|: xHAT0 = xHATpost && rhopHAT0 = rhopHATpost && rhoHAT0 = rhoHATpost && retppHAT0 = retppHATpost && retpHAT0 = retpHATpost && xpHATpost = 1 + xpHAT0 && 1 <= rhopHAT0 (2) l2(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x41 = x47 && x40 = x46 && x38 = x44 && x37 = x43 && x36 = x42 && 1 <= x45 && x45 = x45 (3) l1(x60, x61, x62, x63, x64, x65) -> l2(x66, x67, x68, x69, x70, x71) :|: x65 = x71 && x64 = x70 && x63 = x69 && x62 = x68 && x60 = x66 && x67 = 1 && 2 <= x65 (4) l1(x48, x49, x50, x51, x52, x53) -> l2(x54, x55, x56, x57, x58, x59) :|: x53 = x59 && x52 = x58 && x51 = x57 && x50 = x56 && x48 = x54 && x55 = 0 && x53 <= 1 Arcs: (1) -> (3), (4) (2) -> (1) (3) -> (2) (4) -> (2) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l2(retpHATpost:0, retppHATpost:0, rhoHATpost:0, x39:0, x40:0, x41:0) -> l2(retpHATpost:0, 0, rhoHATpost:0, rhopHATpost:0, x40:0, 1 + x41:0) :|: x41:0 < 1 && rhopHATpost:0 > 0 l2(x, x1, x2, x3, x4, x5) -> l2(x, 1, x2, x6, x4, 1 + x5) :|: x5 > 0 && x6 > 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4, x5, x6) -> l2(x6) ---------------------------------------- (8) Obligation: Rules: l2(x41:0) -> l2(1 + x41:0) :|: x41:0 < 1 && rhopHATpost:0 > 0 l2(x5) -> l2(1 + x5) :|: x5 > 0 && x6 > 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(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: l2(x41:0) -> l2(c) :|: c = 1 + x41:0 && (x41:0 < 1 && rhopHATpost:0 > 0) l2(x5) -> l2(c1) :|: c1 = 1 + x5 && (x5 > 0 && x6 > 0) Found the following polynomial interpretation: [l2(x)] = -x The following rules are decreasing: l2(x41:0) -> l2(c) :|: c = 1 + x41:0 && (x41:0 < 1 && rhopHATpost:0 > 0) l2(x5) -> l2(c1) :|: c1 = 1 + x5 && (x5 > 0 && x6 > 0) The following rules are bounded: l2(x41:0) -> l2(c) :|: c = 1 + x41:0 && (x41:0 < 1 && rhopHATpost:0 > 0) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l2(x5) -> l2(c1) :|: c1 = 1 + x5 && (x5 > 0 && x6 > 0) ---------------------------------------- (10) Obligation: Rules: l2(x5) -> l2(1 + x5) :|: x5 > 0 && x6 > 0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x5) -> l2(1 + x5) :|: x5 > 0 && x6 > 0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x5) -> l2(1 + x5) :|: x5 > 0 && x6 > 0 Arcs: (1) -> (1) This digraph is fully evaluated!