MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 155 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 53 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(iHAT0, jHAT0, tempHAT0) -> l1(iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost l2(x, x1, x2) -> l3(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 l3(x6, x7, x8) -> l2(x9, x10, x11) :|: x6 = x9 && x10 = -1 + x7 && x11 = x11 l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x15 = 1 + x12 l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 11 <= x18 l1(x24, x25, x26) -> l2(x27, x28, x29) :|: x26 = x29 && x24 = x27 && x28 = x24 && x24 <= 10 l5(x30, x31, x32) -> l0(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x33 = 2 l6(x36, x37, x38) -> l5(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 Start term: l6(iHAT0, jHAT0, tempHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(iHAT0, jHAT0, tempHAT0) -> l1(iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost l2(x, x1, x2) -> l3(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 l3(x6, x7, x8) -> l2(x9, x10, x11) :|: x6 = x9 && x10 = -1 + x7 && x11 = x11 l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x15 = 1 + x12 l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 11 <= x18 l1(x24, x25, x26) -> l2(x27, x28, x29) :|: x26 = x29 && x24 = x27 && x28 = x24 && x24 <= 10 l5(x30, x31, x32) -> l0(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x33 = 2 l6(x36, x37, x38) -> l5(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 Start term: l6(iHAT0, jHAT0, tempHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(iHAT0, jHAT0, tempHAT0) -> l1(iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost (2) l2(x, x1, x2) -> l3(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 (3) l3(x6, x7, x8) -> l2(x9, x10, x11) :|: x6 = x9 && x10 = -1 + x7 && x11 = x11 (4) l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x15 = 1 + x12 (5) l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 && 11 <= x18 (6) l1(x24, x25, x26) -> l2(x27, x28, x29) :|: x26 = x29 && x24 = x27 && x28 = x24 && x24 <= 10 (7) l5(x30, x31, x32) -> l0(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x33 = 2 (8) l6(x36, x37, x38) -> l5(x39, x40, x41) :|: x38 = x41 && x37 = x40 && x36 = x39 Arcs: (1) -> (5), (6) (2) -> (3), (4) (3) -> (2) (4) -> (1) (6) -> (2) (7) -> (1) (8) -> (7) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(iHAT0, jHAT0, tempHAT0) -> l1(iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost (2) l3(x12, x13, x14) -> l0(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x15 = 1 + x12 (3) l2(x, x1, x2) -> l3(x3, x4, x5) :|: x2 = x5 && x1 = x4 && x = x3 (4) l1(x24, x25, x26) -> l2(x27, x28, x29) :|: x26 = x29 && x24 = x27 && x28 = x24 && x24 <= 10 (5) l3(x6, x7, x8) -> l2(x9, x10, x11) :|: x6 = x9 && x10 = -1 + x7 && x11 = x11 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (5) (4) -> (3) (5) -> (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l2(x3:0, x1:0, x2:0) -> l2(x3:0, -1 + x1:0, x11:0) :|: TRUE l2(x, x1, x2) -> l2(1 + x, 1 + x, x2) :|: x < 10 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3) -> l2(x1) ---------------------------------------- (8) Obligation: Rules: l2(x3:0) -> l2(x3:0) :|: TRUE l2(x) -> l2(1 + x) :|: x < 10 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(VARIABLE) 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(x3:0) -> l2(x3:0) :|: TRUE l2(x) -> l2(c) :|: c = 1 + x && x < 10 Found the following polynomial interpretation: [l2(x)] = 9 - x The following rules are decreasing: l2(x) -> l2(c) :|: c = 1 + x && x < 10 The following rules are bounded: l2(x) -> l2(c) :|: c = 1 + x && x < 10 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l2(x3:0) -> l2(x3:0) :|: TRUE ---------------------------------------- (10) Obligation: Rules: l2(x3:0) -> l2(x3:0) :|: TRUE ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x3:0) -> l2(x3:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x3:0) -> l2(x3:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated!