MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 206 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 37 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 121 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(LHAT0, nHAT0, oHAT0) -> l1(LHATpost, nHATpost, oHATpost) :|: oHAT0 = oHATpost && nHAT0 = nHATpost && LHAT0 = LHATpost && 1 + oHAT0 <= nHAT0 l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x1 <= x2 l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x7 l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x16 = 1 + x13 && x15 = 0 l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 1 <= x18 && x18 <= 1 l1(x24, x25, x26) -> l3(x27, x28, x29) :|: x25 = x28 && x29 = x25 && x27 = 1 l5(x30, x31, x32) -> l1(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x33 = 0 l6(x36, x37, x38) -> l5(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 Start term: l6(LHAT0, nHAT0, oHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(LHAT0, nHAT0, oHAT0) -> l1(LHATpost, nHATpost, oHATpost) :|: oHAT0 = oHATpost && nHAT0 = nHATpost && LHAT0 = LHATpost && 1 + oHAT0 <= nHAT0 l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x1 <= x2 l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x7 l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x16 = 1 + x13 && x15 = 0 l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 1 <= x18 && x18 <= 1 l1(x24, x25, x26) -> l3(x27, x28, x29) :|: x25 = x28 && x29 = x25 && x27 = 1 l5(x30, x31, x32) -> l1(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x33 = 0 l6(x36, x37, x38) -> l5(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 Start term: l6(LHAT0, nHAT0, oHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(LHAT0, nHAT0, oHAT0) -> l1(LHATpost, nHATpost, oHATpost) :|: oHAT0 = oHATpost && nHAT0 = nHATpost && LHAT0 = LHATpost && 1 + oHAT0 <= nHAT0 (2) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 && x1 <= x2 (3) l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x7 (4) l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x16 = 1 + x13 && x15 = 0 (5) l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 1 <= x18 && x18 <= 1 (6) l1(x24, x25, x26) -> l3(x27, x28, x29) :|: x25 = x28 && x29 = x25 && x27 = 1 (7) l5(x30, x31, x32) -> l1(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x33 = 0 (8) l6(x36, x37, x38) -> l5(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 Arcs: (1) -> (5), (6) (3) -> (1), (2) (4) -> (1), (2) (6) -> (3), (4) (7) -> (6) (8) -> (7) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(LHAT0, nHAT0, oHAT0) -> l1(LHATpost, nHATpost, oHATpost) :|: oHAT0 = oHATpost && nHAT0 = nHATpost && LHAT0 = LHATpost && 1 + oHAT0 <= nHAT0 (2) l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x16 = 1 + x13 && x15 = 0 (3) l3(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x7 (4) l1(x24, x25, x26) -> l3(x27, x28, x29) :|: x25 = x28 && x29 = x25 && x27 = 1 Arcs: (1) -> (4) (2) -> (1) (3) -> (1) (4) -> (2), (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l3(x12:0, x13:0, oHATpost:0) -> l3(1, 1 + x13:0, 1 + x13:0) :|: 1 + x13:0 >= 1 + oHATpost:0 l3(x, x1, x2) -> l3(1, x1, x1) :|: x1 >= 1 + x2 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3) -> l3(x2, x3) ---------------------------------------- (8) Obligation: Rules: l3(x13:0, oHATpost:0) -> l3(1 + x13:0, 1 + x13:0) :|: 1 + x13:0 >= 1 + oHATpost:0 l3(x1, x2) -> l3(x1, x1) :|: x1 >= 1 + x2 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l3(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: l3(x13:0, oHATpost:0) -> l3(c, c1) :|: c1 = 1 + x13:0 && c = 1 + x13:0 && 1 + x13:0 >= 1 + oHATpost:0 l3(x1, x2) -> l3(x1, x1) :|: x1 >= 1 + x2 Found the following polynomial interpretation: [l3(x, x1)] = x - x1 The following rules are decreasing: l3(x1, x2) -> l3(x1, x1) :|: x1 >= 1 + x2 The following rules are bounded: l3(x13:0, oHATpost:0) -> l3(c, c1) :|: c1 = 1 + x13:0 && c = 1 + x13:0 && 1 + x13:0 >= 1 + oHATpost:0 l3(x1, x2) -> l3(x1, x1) :|: x1 >= 1 + x2 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l3(x13:0, oHATpost:0) -> l3(c, c1) :|: c1 = 1 + x13:0 && c = 1 + x13:0 && 1 + x13:0 >= 1 + oHATpost:0 ---------------------------------------- (10) Obligation: Rules: l3(x13:0, oHATpost:0) -> l3(1 + x13:0, 1 + x13:0) :|: 1 + x13:0 >= 1 + oHATpost:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l3(x13:0, oHATpost:0) -> l3(1 + x13:0, 1 + x13:0) :|: 1 + x13:0 >= 1 + oHATpost:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l3(x13:0, oHATpost:0) -> l3(1 + x13:0, 1 + x13:0) :|: 1 + x13:0 >= 1 + oHATpost:0 Arcs: (1) -> (1) This digraph is fully evaluated!