MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 222 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 58 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: nHAT0 <= 0 && RHAT1 = 0 && RHATpost = 0 && dobreakHATpost = dobreakHATpost && AHAT0 = AHATpost && nHAT0 = nHATpost l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x2 = x6 && x1 = x5 && x = x4 && x7 = -1 + x3 && 1 <= x3 l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 l1(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x18 <= 0 && x24 = 1 && x20 = 0 && x17 = x21 && x18 = x22 && x19 = x23 l3(x25, x26, x27, x28) -> l1(x29, x30, x31, x32) :|: x32 = x32 && x31 = x31 && x30 = 0 && x29 = 0 l4(x33, x34, x35, x36) -> l3(x37, x38, x39, x40) :|: x36 = x40 && x35 = x39 && x34 = x38 && x33 = x37 Start term: l4(AHAT0, RHAT0, dobreakHAT0, nHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: nHAT0 <= 0 && RHAT1 = 0 && RHATpost = 0 && dobreakHATpost = dobreakHATpost && AHAT0 = AHATpost && nHAT0 = nHATpost l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x2 = x6 && x1 = x5 && x = x4 && x7 = -1 + x3 && 1 <= x3 l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 l1(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x18 <= 0 && x24 = 1 && x20 = 0 && x17 = x21 && x18 = x22 && x19 = x23 l3(x25, x26, x27, x28) -> l1(x29, x30, x31, x32) :|: x32 = x32 && x31 = x31 && x30 = 0 && x29 = 0 l4(x33, x34, x35, x36) -> l3(x37, x38, x39, x40) :|: x36 = x40 && x35 = x39 && x34 = x38 && x33 = x37 Start term: l4(AHAT0, RHAT0, dobreakHAT0, nHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: nHAT0 <= 0 && RHAT1 = 0 && RHATpost = 0 && dobreakHATpost = dobreakHATpost && AHAT0 = AHATpost && nHAT0 = nHATpost (2) l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x2 = x6 && x1 = x5 && x = x4 && x7 = -1 + x3 && 1 <= x3 (3) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 (4) l1(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x18 <= 0 && x24 = 1 && x20 = 0 && x17 = x21 && x18 = x22 && x19 = x23 (5) l3(x25, x26, x27, x28) -> l1(x29, x30, x31, x32) :|: x32 = x32 && x31 = x31 && x30 = 0 && x29 = 0 (6) l4(x33, x34, x35, x36) -> l3(x37, x38, x39, x40) :|: x36 = x40 && x35 = x39 && x34 = x38 && x33 = x37 Arcs: (1) -> (4) (2) -> (3) (3) -> (1), (2) (4) -> (1), (2) (5) -> (4) (6) -> (5) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: nHAT0 <= 0 && RHAT1 = 0 && RHATpost = 0 && dobreakHATpost = dobreakHATpost && AHAT0 = AHATpost && nHAT0 = nHATpost (2) l2(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 (3) l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x2 = x6 && x1 = x5 && x = x4 && x7 = -1 + x3 && 1 <= x3 (4) l1(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x18 <= 0 && x24 = 1 && x20 = 0 && x17 = x21 && x18 = x22 && x19 = x23 Arcs: (1) -> (4) (2) -> (1), (3) (3) -> (2) (4) -> (1), (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(AHAT0:0, RHAT0:0, dobreakHAT0:0, nHAT0:0) -> l0(0, 0, dobreakHATpost:0, nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 l0(x12:0, x13:0, x14:0, x3:0) -> l0(x12:0, x13:0, x14:0, -1 + x3:0) :|: x3:0 > 0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4) -> l0(x4) ---------------------------------------- (8) Obligation: Rules: l0(nHAT0:0) -> l0(nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 l0(x3:0) -> l0(-1 + x3:0) :|: x3:0 > 0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(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: l0(nHAT0:0) -> l0(nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 l0(x3:0) -> l0(c) :|: c = -1 + x3:0 && x3:0 > 0 Found the following polynomial interpretation: [l0(x)] = -1 + x The following rules are decreasing: l0(x3:0) -> l0(c) :|: c = -1 + x3:0 && x3:0 > 0 The following rules are bounded: l0(x3:0) -> l0(c) :|: c = -1 + x3:0 && x3:0 > 0 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(nHAT0:0) -> l0(nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 ---------------------------------------- (10) Obligation: Rules: l0(nHAT0:0) -> l0(nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(nHAT0:0) -> l0(nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(nHAT0:0) -> l0(nHAT0:0) :|: nHAT0:0 < 1 && dobreakHATpost:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated!