MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 198 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) TempFilterProof [SOUND, 246 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (10) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: xHAT0 = xHATpost && yHATpost = xHAT0 && 1 <= xHAT0 l1(x, x1) -> l2(x2, x3) :|: x1 = x3 && x = x2 && x1 <= 0 l1(x4, x5) -> l3(x6, x7) :|: x4 = x6 && x7 = -1 + x5 && 1 <= x5 l3(x8, x9) -> l1(x10, x11) :|: x9 = x11 && x8 = x10 l2(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 l2(x16, x17) -> l0(x18, x19) :|: x19 = 1 + x17 && x18 = -1 + x16 l4(x20, x21) -> l0(x22, x23) :|: x21 = x23 && x20 = x22 l5(x24, x25) -> l4(x26, x27) :|: x25 = x27 && x24 = x26 Start term: l5(xHAT0, yHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: xHAT0 = xHATpost && yHATpost = xHAT0 && 1 <= xHAT0 l1(x, x1) -> l2(x2, x3) :|: x1 = x3 && x = x2 && x1 <= 0 l1(x4, x5) -> l3(x6, x7) :|: x4 = x6 && x7 = -1 + x5 && 1 <= x5 l3(x8, x9) -> l1(x10, x11) :|: x9 = x11 && x8 = x10 l2(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 l2(x16, x17) -> l0(x18, x19) :|: x19 = 1 + x17 && x18 = -1 + x16 l4(x20, x21) -> l0(x22, x23) :|: x21 = x23 && x20 = x22 l5(x24, x25) -> l4(x26, x27) :|: x25 = x27 && x24 = x26 Start term: l5(xHAT0, yHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: xHAT0 = xHATpost && yHATpost = xHAT0 && 1 <= xHAT0 (2) l1(x, x1) -> l2(x2, x3) :|: x1 = x3 && x = x2 && x1 <= 0 (3) l1(x4, x5) -> l3(x6, x7) :|: x4 = x6 && x7 = -1 + x5 && 1 <= x5 (4) l3(x8, x9) -> l1(x10, x11) :|: x9 = x11 && x8 = x10 (5) l2(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 (6) l2(x16, x17) -> l0(x18, x19) :|: x19 = 1 + x17 && x18 = -1 + x16 (7) l4(x20, x21) -> l0(x22, x23) :|: x21 = x23 && x20 = x22 (8) l5(x24, x25) -> l4(x26, x27) :|: x25 = x27 && x24 = x26 Arcs: (1) -> (3) (2) -> (5), (6) (3) -> (4) (4) -> (2), (3) (5) -> (1) (6) -> (1) (7) -> (1) (8) -> (7) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: xHAT0 = xHATpost && yHATpost = xHAT0 && 1 <= xHAT0 (2) l2(x16, x17) -> l0(x18, x19) :|: x19 = 1 + x17 && x18 = -1 + x16 (3) l2(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 (4) l1(x, x1) -> l2(x2, x3) :|: x1 = x3 && x = x2 && x1 <= 0 (5) l3(x8, x9) -> l1(x10, x11) :|: x9 = x11 && x8 = x10 (6) l1(x4, x5) -> l3(x6, x7) :|: x4 = x6 && x7 = -1 + x5 && 1 <= x5 Arcs: (1) -> (6) (2) -> (1) (3) -> (1) (4) -> (2), (3) (5) -> (4), (6) (6) -> (5) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 l1(x, x1) -> l1(-1 + x, -1 + x) :|: x1 < 1 && x > 1 l1(x10:0, x5:0) -> l1(x10:0, -1 + x5:0) :|: x5:0 > 0 ---------------------------------------- (7) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(VARIABLE, 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: l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 l1(x, x1) -> l1(c, c1) :|: c1 = -1 + x && c = -1 + x && (x1 < 1 && x > 1) l1(x10:0, x5:0) -> l1(x10:0, c2) :|: c2 = -1 + x5:0 && x5:0 > 0 Found the following polynomial interpretation: [l1(x, x1)] = -1 + x The following rules are decreasing: l1(x, x1) -> l1(c, c1) :|: c1 = -1 + x && c = -1 + x && (x1 < 1 && x > 1) The following rules are bounded: l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 l1(x, x1) -> l1(c, c1) :|: c1 = -1 + x && c = -1 + x && (x1 < 1 && x > 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 l1(x10:0, x5:0) -> l1(x10:0, c2) :|: c2 = -1 + x5:0 && x5:0 > 0 ---------------------------------------- (8) Obligation: Rules: l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 l1(x10:0, x5:0) -> l1(x10:0, -1 + x5:0) :|: x5:0 > 0 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 (2) l1(x10:0, x5:0) -> l1(x10:0, -1 + x5:0) :|: x5:0 > 0 Arcs: (1) -> (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) l1(x14:0, x1:0) -> l1(x14:0, x14:0) :|: x1:0 < 1 && x14:0 > 0 (2) l1(x10:0, x5:0) -> l1(x10:0, -1 + x5:0) :|: x5:0 > 0 Arcs: (1) -> (2) (2) -> (1), (2) This digraph is fully evaluated!