MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 195 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) TempFilterProof [SOUND, 189 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms] (10) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(xHAT0, yHAT0) -> l1(xHATpost, yHATpost) :|: xHAT0 = xHATpost && yHATpost = xHAT0 && 1 <= xHAT0 l1(x, x1) -> l2(x2, x3) :|: x = x2 && x3 = -1 + x1 && 1 <= x1 l2(x4, x5) -> l1(x6, x7) :|: x5 = x7 && x4 = x6 l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x8 = x10 l3(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 l3(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) :|: x = x2 && x3 = -1 + x1 && 1 <= x1 l2(x4, x5) -> l1(x6, x7) :|: x5 = x7 && x4 = x6 l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x8 = x10 l3(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 l3(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) :|: x = x2 && x3 = -1 + x1 && 1 <= x1 (3) l2(x4, x5) -> l1(x6, x7) :|: x5 = x7 && x4 = x6 (4) l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x8 = x10 (5) l3(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 (6) l3(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) -> (2), (4) (2) -> (3) (3) -> (2), (4) (4) -> (5), (6) (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) l3(x16, x17) -> l0(x18, x19) :|: x19 = 1 + x17 && x18 = -1 + x16 (3) l3(x12, x13) -> l0(x14, x15) :|: x12 = x14 && x15 = 1 + x13 (4) l1(x8, x9) -> l3(x10, x11) :|: x9 = x11 && x8 = x10 (5) l2(x4, x5) -> l1(x6, x7) :|: x5 = x7 && x4 = x6 (6) l1(x, x1) -> l2(x2, x3) :|: x = x2 && x3 = -1 + x1 && 1 <= x1 Arcs: (1) -> (4), (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(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 l1(x2:0, x1:0) -> l1(x2:0, -1 + x1:0) :|: x1:0 > 0 l1(x, x1) -> l1(-1 + x, -1 + x) :|: x > 1 ---------------------------------------- (7) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(VARIABLE, 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: l1(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 l1(x2:0, x1:0) -> l1(x2:0, c) :|: c = -1 + x1:0 && x1:0 > 0 l1(x, x1) -> l1(c1, c2) :|: c2 = -1 + x && c1 = -1 + x && x > 1 Found the following polynomial interpretation: [l1(x, x1)] = -1 + x The following rules are decreasing: l1(x, x1) -> l1(c1, c2) :|: c2 = -1 + x && c1 = -1 + x && x > 1 The following rules are bounded: l1(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 l1(x, x1) -> l1(c1, c2) :|: c2 = -1 + x && c1 = -1 + x && x > 1 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 l1(x2:0, x1:0) -> l1(x2:0, c) :|: c = -1 + x1:0 && x1:0 > 0 ---------------------------------------- (8) Obligation: Rules: l1(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 l1(x2:0, x1:0) -> l1(x2:0, -1 + x1:0) :|: x1:0 > 0 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 (2) l1(x2:0, x1:0) -> l1(x2:0, -1 + x1:0) :|: x1:0 > 0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) l1(x10:0, x11:0) -> l1(x10:0, x10:0) :|: x10:0 > 0 (2) l1(x2:0, x1:0) -> l1(x2:0, -1 + x1:0) :|: x1:0 > 0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated!