MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 230 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 112 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && Result_4HATpost = Result_4HATpost && x_5HAT0 - y_6HAT0 <= 0 && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x = x3 && x4 = 1 + x1 && 0 <= -1 + x1 - x2 && -1 * x1 + x2 <= 0 l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 l0(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = 1 + x13 && 0 <= -1 - x13 + x14 l3(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 l4(x24, x25, x26) -> l0(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 l5(x30, x31, x32) -> l4(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 Start term: l5(Result_4HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && Result_4HATpost = Result_4HATpost && x_5HAT0 - y_6HAT0 <= 0 && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x = x3 && x4 = 1 + x1 && 0 <= -1 + x1 - x2 && -1 * x1 + x2 <= 0 l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 l0(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = 1 + x13 && 0 <= -1 - x13 + x14 l3(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 l4(x24, x25, x26) -> l0(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 l5(x30, x31, x32) -> l4(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 Start term: l5(Result_4HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && Result_4HATpost = Result_4HATpost && x_5HAT0 - y_6HAT0 <= 0 && -1 * x_5HAT0 + y_6HAT0 <= 0 (2) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x = x3 && x4 = 1 + x1 && 0 <= -1 + x1 - x2 && -1 * x1 + x2 <= 0 (3) l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 (4) l0(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = 1 + x13 && 0 <= -1 - x13 + x14 (5) l3(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 (6) l4(x24, x25, x26) -> l0(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 (7) l5(x30, x31, x32) -> l4(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 Arcs: (2) -> (3) (3) -> (1), (2), (4) (4) -> (5) (5) -> (1), (2), (4) (6) -> (1), (2), (4) (7) -> (6) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x = x3 && x4 = 1 + x1 && 0 <= -1 + x1 - x2 && -1 * x1 + x2 <= 0 (2) l3(x18, x19, x20) -> l0(x21, x22, x23) :|: x20 = x23 && x19 = x22 && x18 = x21 (3) l0(x12, x13, x14) -> l3(x15, x16, x17) :|: x14 = x17 && x12 = x15 && x16 = 1 + x13 && 0 <= -1 - x13 + x14 (4) l2(x6, x7, x8) -> l0(x9, x10, x11) :|: x8 = x11 && x7 = x10 && x6 = x9 Arcs: (1) -> (4) (2) -> (1), (3) (3) -> (2) (4) -> (1), (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x3:0, x1:0, x11:0) -> l0(x3:0, 1 + x1:0, x11:0) :|: 0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0 l0(x12:0, x13:0, x14:0) -> l0(x12:0, 1 + x13:0, x14:0) :|: 0 <= -1 - x13:0 + x14:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3) -> l0(x2, x3) ---------------------------------------- (8) Obligation: Rules: l0(x1:0, x11:0) -> l0(1 + x1:0, x11:0) :|: 0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0 l0(x13:0, x14:0) -> l0(1 + x13:0, x14:0) :|: 0 <= -1 - x13:0 + x14:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(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(x1:0, x11:0) -> l0(c, x11:0) :|: c = 1 + x1:0 && (0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0) l0(x13:0, x14:0) -> l0(c1, x14:0) :|: c1 = 1 + x13:0 && 0 <= -1 - x13:0 + x14:0 Found the following polynomial interpretation: [l0(x, x1)] = -x + x1 The following rules are decreasing: l0(x1:0, x11:0) -> l0(c, x11:0) :|: c = 1 + x1:0 && (0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0) l0(x13:0, x14:0) -> l0(c1, x14:0) :|: c1 = 1 + x13:0 && 0 <= -1 - x13:0 + x14:0 The following rules are bounded: l0(x13:0, x14:0) -> l0(c1, x14:0) :|: c1 = 1 + x13:0 && 0 <= -1 - x13:0 + x14:0 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(x1:0, x11:0) -> l0(c, x11:0) :|: c = 1 + x1:0 && (0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0) ---------------------------------------- (10) Obligation: Rules: l0(x1:0, x11:0) -> l0(1 + x1:0, x11:0) :|: 0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x1:0, x11:0) -> l0(1 + x1:0, x11:0) :|: 0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(x1:0, x11:0) -> l0(1 + x1:0, x11:0) :|: 0 >= -1 * x1:0 + x11:0 && 0 <= -1 + x1:0 - x11:0 Arcs: (1) -> (1) This digraph is fully evaluated!