MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 287 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 12 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 55 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, tmp_6HAT0, x_5HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_6HATpost, x_5HATpost) :|: x_5HAT0 = x_5HATpost && tmp_6HAT0 = tmp_6HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x4 = x4 && 0 <= -1 - x3 l1(x8, x9, x10, x11) -> l3(x12, x13, x14, x15) :|: x11 = x15 && x9 = x13 && x8 = x12 && 0 <= x14 && x14 <= 0 && x14 = x14 && -1 * x11 <= 0 l3(x16, x17, x18, x19) -> l1(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x25 = x29 && x24 = x28 && x30 = x30 && -1 * x27 <= 0 l5(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && x37 = x33 l6(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x47 = -1 + x43 l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 l7(x56, x57, x58, x59) -> l0(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 Start term: l7(Result_4HAT0, __disjvr_0HAT0, tmp_6HAT0, x_5HAT0) ---------------------------------------- (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_6HAT0, x_5HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_6HATpost, x_5HATpost) :|: x_5HAT0 = x_5HATpost && tmp_6HAT0 = tmp_6HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x4 = x4 && 0 <= -1 - x3 l1(x8, x9, x10, x11) -> l3(x12, x13, x14, x15) :|: x11 = x15 && x9 = x13 && x8 = x12 && 0 <= x14 && x14 <= 0 && x14 = x14 && -1 * x11 <= 0 l3(x16, x17, x18, x19) -> l1(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x25 = x29 && x24 = x28 && x30 = x30 && -1 * x27 <= 0 l5(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && x37 = x33 l6(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x47 = -1 + x43 l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 l7(x56, x57, x58, x59) -> l0(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 Start term: l7(Result_4HAT0, __disjvr_0HAT0, tmp_6HAT0, x_5HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, tmp_6HAT0, x_5HAT0) -> l1(Result_4HATpost, __disjvr_0HATpost, tmp_6HATpost, x_5HATpost) :|: x_5HAT0 = x_5HATpost && tmp_6HAT0 = tmp_6HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost (2) l1(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x4 = x4 && 0 <= -1 - x3 (3) l1(x8, x9, x10, x11) -> l3(x12, x13, x14, x15) :|: x11 = x15 && x9 = x13 && x8 = x12 && 0 <= x14 && x14 <= 0 && x14 = x14 && -1 * x11 <= 0 (4) l3(x16, x17, x18, x19) -> l1(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 (5) l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x25 = x29 && x24 = x28 && x30 = x30 && -1 * x27 <= 0 (6) l5(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && x37 = x33 (7) l6(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x47 = -1 + x43 (8) l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 (9) l7(x56, x57, x58, x59) -> l0(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 Arcs: (1) -> (2), (3), (5) (3) -> (4) (4) -> (2), (3), (5) (5) -> (6) (6) -> (7) (7) -> (8) (8) -> (2), (3), (5) (9) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x8, x9, x10, x11) -> l3(x12, x13, x14, x15) :|: x11 = x15 && x9 = x13 && x8 = x12 && 0 <= x14 && x14 <= 0 && x14 = x14 && -1 * x11 <= 0 (2) l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 (3) l6(x40, x41, x42, x43) -> l4(x44, x45, x46, x47) :|: x42 = x46 && x41 = x45 && x40 = x44 && x47 = -1 + x43 (4) l5(x32, x33, x34, x35) -> l6(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 && x37 = x33 (5) l1(x24, x25, x26, x27) -> l5(x28, x29, x30, x31) :|: x27 = x31 && x25 = x29 && x24 = x28 && x30 = x30 && -1 * x27 <= 0 (6) l3(x16, x17, x18, x19) -> l1(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 Arcs: (1) -> (6) (2) -> (1), (5) (3) -> (2) (4) -> (3) (5) -> (4) (6) -> (1), (5) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x12:0, x13:0, x10:0, x11:0) -> l1(x12:0, x13:0, x14:0, x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 l1(x24:0, x25:0, x26:0, x27:0) -> l1(x24:0, x25:0, x30:0, -1 + x27:0) :|: 0 >= -1 * x27:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3, x4) -> l1(x4) ---------------------------------------- (8) Obligation: Rules: l1(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 l1(x27:0) -> l1(-1 + x27:0) :|: 0 >= -1 * x27:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(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(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 l1(x27:0) -> l1(c) :|: c = -1 + x27:0 && 0 >= -1 * x27:0 Found the following polynomial interpretation: [l1(x)] = x The following rules are decreasing: l1(x27:0) -> l1(c) :|: c = -1 + x27:0 && 0 >= -1 * x27:0 The following rules are bounded: l1(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 l1(x27:0) -> l1(c) :|: c = -1 + x27:0 && 0 >= -1 * x27:0 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 ---------------------------------------- (10) Obligation: Rules: l1(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l1(x11:0) -> l1(x11:0) :|: x14:0 < 1 && x14:0 > -1 && 0 >= -1 * x11:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l1(x11:0:0) -> l1(x11:0:0) :|: x14:0:0 < 1 && x14:0:0 > -1 && 0 >= -1 * x11:0:0