MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 127 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 25 ms] (6) IRSwT (7) TempFilterProof [SOUND, 259 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 3 ms] (10) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(xHAT0, yHAT0, zHAT0) -> l1(xHATpost, yHATpost, zHATpost) :|: xHAT0 = xHATpost && zHATpost = yHATpost + zHAT0 && yHATpost = -1 + yHAT0 l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x4 = -1 + x1 && x3 = -1 + x l1(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x8 && 0 <= x6 l2(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 l3(x18, x19, x20) -> l2(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 Start term: l3(xHAT0, yHAT0, zHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(xHAT0, yHAT0, zHAT0) -> l1(xHATpost, yHATpost, zHATpost) :|: xHAT0 = xHATpost && zHATpost = yHATpost + zHAT0 && yHATpost = -1 + yHAT0 l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x4 = -1 + x1 && x3 = -1 + x l1(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x8 && 0 <= x6 l2(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 l3(x18, x19, x20) -> l2(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 Start term: l3(xHAT0, yHAT0, zHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(xHAT0, yHAT0, zHAT0) -> l1(xHATpost, yHATpost, zHATpost) :|: xHAT0 = xHATpost && zHATpost = yHATpost + zHAT0 && yHATpost = -1 + yHAT0 (2) l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x4 = -1 + x1 && x3 = -1 + x (3) l1(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x8 && 0 <= x6 (4) l2(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 (5) l3(x18, x19, x20) -> l2(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 Arcs: (1) -> (3) (2) -> (3) (3) -> (1), (2) (4) -> (3) (5) -> (4) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(xHAT0, yHAT0, zHAT0) -> l1(xHATpost, yHATpost, zHATpost) :|: xHAT0 = xHATpost && zHATpost = yHATpost + zHAT0 && yHATpost = -1 + yHAT0 (2) l1(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 && x7 <= x8 && 0 <= x6 (3) l0(x, x1, x2) -> l1(x3, x4, x5) :|: x2 = x5 && x4 = -1 + x1 && x3 = -1 + x Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, -1 + yHAT0:0, -1 + yHAT0:0 + zHAT0:0) :|: x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0 l0(x:0, x1:0, x11:0) -> l0(-1 + x:0, -1 + x1:0, x11:0) :|: x:0 > 0 && x11:0 >= -1 + x1:0 ---------------------------------------- (7) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER, 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: l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, c, c1) :|: c1 = -1 + yHAT0:0 + zHAT0:0 && c = -1 + yHAT0:0 && (x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0) l0(x:0, x1:0, x11:0) -> l0(c2, c3, x11:0) :|: c3 = -1 + x1:0 && c2 = -1 + x:0 && (x:0 > 0 && x11:0 >= -1 + x1:0) Found the following polynomial interpretation: [l0(x, x1, x2)] = x The following rules are decreasing: l0(x:0, x1:0, x11:0) -> l0(c2, c3, x11:0) :|: c3 = -1 + x1:0 && c2 = -1 + x:0 && (x:0 > 0 && x11:0 >= -1 + x1:0) The following rules are bounded: l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, c, c1) :|: c1 = -1 + yHAT0:0 + zHAT0:0 && c = -1 + yHAT0:0 && (x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0) l0(x:0, x1:0, x11:0) -> l0(c2, c3, x11:0) :|: c3 = -1 + x1:0 && c2 = -1 + x:0 && (x:0 > 0 && x11:0 >= -1 + x1:0) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, c, c1) :|: c1 = -1 + yHAT0:0 + zHAT0:0 && c = -1 + yHAT0:0 && (x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0) ---------------------------------------- (8) Obligation: Rules: l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, -1 + yHAT0:0, -1 + yHAT0:0 + zHAT0:0) :|: x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, -1 + yHAT0:0, -1 + yHAT0:0 + zHAT0:0) :|: x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) l0(x9:0, yHAT0:0, zHAT0:0) -> l0(x9:0, -1 + yHAT0:0, -1 + yHAT0:0 + zHAT0:0) :|: x9:0 > -1 && -1 + yHAT0:0 + zHAT0:0 >= -1 + yHAT0:0 Arcs: (1) -> (1) This digraph is fully evaluated!