MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 375 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 84 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x1 = x6 && x = x5 && x9 = -1 + x4 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 l4(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 l3(x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 l5(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l6(x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 Start term: l6(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, 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, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x1 = x6 && x = x5 && x9 = -1 + x4 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 l4(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 l3(x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 l5(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 l6(x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 Start term: l6(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HATpost = Result_4HATpost && -1 * x_5HAT0 + y_6HAT0 <= 0 (2) l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x1 = x6 && x = x5 && x9 = -1 + x4 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 (3) l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 (4) l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 (5) l4(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 (6) l3(x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 (7) l5(x50, x51, x52, x53, x54) -> l0(x55, x56, x57, x58, x59) :|: x54 = x59 && x53 = x58 && x52 = x57 && x51 = x56 && x50 = x55 (8) l6(x60, x61, x62, x63, x64) -> l5(x65, x66, x67, x68, x69) :|: x64 = x69 && x63 = x68 && x62 = x67 && x61 = x66 && x60 = x65 Arcs: (2) -> (3) (3) -> (1), (2), (4) (4) -> (5) (5) -> (6) (6) -> (1), (2), (4) (7) -> (1), (2), (4) (8) -> (7) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4) -> l2(x5, x6, x7, x8, x9) :|: x3 = x8 && x1 = x6 && x = x5 && x9 = -1 + x4 && 0 <= x7 && x7 <= 0 && x7 = x7 && 0 <= -1 - x3 + x4 (2) l3(x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49) :|: x44 = x49 && x43 = x48 && x42 = x47 && x41 = x46 && x40 = x45 (3) l4(x30, x31, x32, x33, x34) -> l3(x35, x36, x37, x38, x39) :|: x34 = x39 && x33 = x38 && x32 = x37 && x31 = x36 && x30 = x35 && x36 = x31 (4) l0(x20, x21, x22, x23, x24) -> l4(x25, x26, x27, x28, x29) :|: x24 = x29 && x23 = x28 && x21 = x26 && x20 = x25 && x27 = x27 && 0 <= -1 - x23 + x24 (5) l2(x10, x11, x12, x13, x14) -> l0(x15, x16, x17, x18, x19) :|: x14 = x19 && x13 = x18 && x12 = x17 && x11 = x16 && x10 = x15 Arcs: (1) -> (5) (2) -> (1), (4) (3) -> (2) (4) -> (3) (5) -> (1), (4) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x20:0, x21:0, x22:0, x23:0, x24:0) -> l0(x20:0, x21:0, x27:0, x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 l0(x15:0, x16:0, x2:0, x18:0, x4:0) -> l0(x15:0, x16:0, x17:0, x18:0, -1 + x4:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x4:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5) -> l0(x4, x5) ---------------------------------------- (8) Obligation: Rules: l0(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 l0(x18:0, x4:0) -> l0(x18:0, -1 + x4:0) :|: x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x4:0 ---------------------------------------- (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(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 l0(x18:0, x4:0) -> l0(x18:0, c) :|: c = -1 + x4:0 && (x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x4:0) Found the following polynomial interpretation: [l0(x, x1)] = -x + x1 The following rules are decreasing: l0(x18:0, x4:0) -> l0(x18:0, c) :|: c = -1 + x4:0 && (x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x4:0) The following rules are bounded: l0(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 l0(x18:0, x4:0) -> l0(x18:0, c) :|: c = -1 + x4:0 && (x17:0 < 1 && x17:0 > -1 && 0 <= -1 - x18:0 + x4:0) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 ---------------------------------------- (10) Obligation: Rules: l0(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(x23:0, x24:0) -> l0(x23:0, x24:0) :|: 0 <= -1 - x23:0 + x24:0 Arcs: (1) -> (1) This digraph is fully evaluated!