MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 494 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 40 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 65 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, tmp_6HAT0, x_5HAT0) -> l1(Result_4HATpost, tmp_6HATpost, x_5HATpost) :|: x_5HAT0 = x_5HATpost && tmp_6HAT0 = tmp_6HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x3 = x3 && x2 <= 0 && 0 <= x4 && x4 <= 0 && x4 = x4 l1(x6, x7, x8) -> l3(x9, x10, x11) :|: x8 = x11 && x6 = x9 && 0 <= -1 + x8 && 0 <= x10 && x10 <= 0 && x10 = x10 l3(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x18 = x21 && x22 = x22 l4(x24, x25, x26) -> l5(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 + x25 <= 0 l4(x30, x31, x32) -> l5(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 <= x31 l5(x36, x37, x38) -> l2(x39, x40, x41) :|: x37 = x40 && x39 = x39 && x41 <= 0 && x41 = -1 + x38 l1(x42, x43, x44) -> l7(x45, x46, x47) :|: x44 = x47 && x42 = x45 && x46 = x46 l7(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51 && 1 + x49 <= 0 l7(x54, x55, x56) -> l8(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 1 <= x55 l8(x60, x61, x62) -> l6(x63, x64, x65) :|: x61 = x64 && x60 = x63 && 0 <= -1 + x65 && x65 = -1 + x62 l6(x66, x67, x68) -> l1(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x66 = x69 l9(x72, x73, x74) -> l0(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75 Start term: l9(Result_4HAT0, 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, tmp_6HAT0, x_5HAT0) -> l1(Result_4HATpost, tmp_6HATpost, x_5HATpost) :|: x_5HAT0 = x_5HATpost && tmp_6HAT0 = tmp_6HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x3 = x3 && x2 <= 0 && 0 <= x4 && x4 <= 0 && x4 = x4 l1(x6, x7, x8) -> l3(x9, x10, x11) :|: x8 = x11 && x6 = x9 && 0 <= -1 + x8 && 0 <= x10 && x10 <= 0 && x10 = x10 l3(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x18 = x21 && x22 = x22 l4(x24, x25, x26) -> l5(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 + x25 <= 0 l4(x30, x31, x32) -> l5(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 <= x31 l5(x36, x37, x38) -> l2(x39, x40, x41) :|: x37 = x40 && x39 = x39 && x41 <= 0 && x41 = -1 + x38 l1(x42, x43, x44) -> l7(x45, x46, x47) :|: x44 = x47 && x42 = x45 && x46 = x46 l7(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51 && 1 + x49 <= 0 l7(x54, x55, x56) -> l8(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 1 <= x55 l8(x60, x61, x62) -> l6(x63, x64, x65) :|: x61 = x64 && x60 = x63 && 0 <= -1 + x65 && x65 = -1 + x62 l6(x66, x67, x68) -> l1(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x66 = x69 l9(x72, x73, x74) -> l0(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75 Start term: l9(Result_4HAT0, tmp_6HAT0, x_5HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, tmp_6HAT0, x_5HAT0) -> l1(Result_4HATpost, tmp_6HATpost, x_5HATpost) :|: x_5HAT0 = x_5HATpost && tmp_6HAT0 = tmp_6HATpost && Result_4HAT0 = Result_4HATpost (2) l1(x, x1, x2) -> l2(x3, x4, x5) :|: x2 = x5 && x3 = x3 && x2 <= 0 && 0 <= x4 && x4 <= 0 && x4 = x4 (3) l1(x6, x7, x8) -> l3(x9, x10, x11) :|: x8 = x11 && x6 = x9 && 0 <= -1 + x8 && 0 <= x10 && x10 <= 0 && x10 = x10 (4) l3(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 (5) l1(x18, x19, x20) -> l4(x21, x22, x23) :|: x20 = x23 && x18 = x21 && x22 = x22 (6) l4(x24, x25, x26) -> l5(x27, x28, x29) :|: x26 = x29 && x25 = x28 && x24 = x27 && 1 + x25 <= 0 (7) l4(x30, x31, x32) -> l5(x33, x34, x35) :|: x32 = x35 && x31 = x34 && x30 = x33 && 1 <= x31 (8) l5(x36, x37, x38) -> l2(x39, x40, x41) :|: x37 = x40 && x39 = x39 && x41 <= 0 && x41 = -1 + x38 (9) l1(x42, x43, x44) -> l7(x45, x46, x47) :|: x44 = x47 && x42 = x45 && x46 = x46 (10) l7(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51 && 1 + x49 <= 0 (11) l7(x54, x55, x56) -> l8(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 1 <= x55 (12) l8(x60, x61, x62) -> l6(x63, x64, x65) :|: x61 = x64 && x60 = x63 && 0 <= -1 + x65 && x65 = -1 + x62 (13) l6(x66, x67, x68) -> l1(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x66 = x69 (14) l9(x72, x73, x74) -> l0(x75, x76, x77) :|: x74 = x77 && x73 = x76 && x72 = x75 Arcs: (1) -> (2), (3), (5), (9) (3) -> (4) (4) -> (2), (3), (5), (9) (5) -> (6), (7) (6) -> (8) (7) -> (8) (9) -> (10), (11) (10) -> (12) (11) -> (12) (12) -> (13) (13) -> (2), (3), (5), (9) (14) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x6, x7, x8) -> l3(x9, x10, x11) :|: x8 = x11 && x6 = x9 && 0 <= -1 + x8 && 0 <= x10 && x10 <= 0 && x10 = x10 (2) l6(x66, x67, x68) -> l1(x69, x70, x71) :|: x68 = x71 && x67 = x70 && x66 = x69 (3) l8(x60, x61, x62) -> l6(x63, x64, x65) :|: x61 = x64 && x60 = x63 && 0 <= -1 + x65 && x65 = -1 + x62 (4) l7(x54, x55, x56) -> l8(x57, x58, x59) :|: x56 = x59 && x55 = x58 && x54 = x57 && 1 <= x55 (5) l7(x48, x49, x50) -> l8(x51, x52, x53) :|: x50 = x53 && x49 = x52 && x48 = x51 && 1 + x49 <= 0 (6) l1(x42, x43, x44) -> l7(x45, x46, x47) :|: x44 = x47 && x42 = x45 && x46 = x46 (7) l3(x12, x13, x14) -> l1(x15, x16, x17) :|: x14 = x17 && x13 = x16 && x12 = x15 Arcs: (1) -> (7) (2) -> (1), (6) (3) -> (2) (4) -> (3) (5) -> (3) (6) -> (4), (5) (7) -> (1), (6) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x42:0, x43:0, x44:0) -> l1(x42:0, x46:0, -1 + x44:0) :|: x46:0 < 0 && x44:0 > 1 l1(x15:0, x7:0, x11:0) -> l1(x15:0, x10:0, x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 l1(x, x1, x2) -> l1(x, x3, -1 + x2) :|: x3 > 0 && x2 > 1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3) -> l1(x3) ---------------------------------------- (8) Obligation: Rules: l1(x44:0) -> l1(-1 + x44:0) :|: x46:0 < 0 && x44:0 > 1 l1(x11:0) -> l1(x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 l1(x2) -> l1(-1 + x2) :|: x3 > 0 && x2 > 1 ---------------------------------------- (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(x44:0) -> l1(c) :|: c = -1 + x44:0 && (x46:0 < 0 && x44:0 > 1) l1(x11:0) -> l1(x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 l1(x2) -> l1(c1) :|: c1 = -1 + x2 && (x3 > 0 && x2 > 1) Found the following polynomial interpretation: [l1(x)] = -2 + x The following rules are decreasing: l1(x44:0) -> l1(c) :|: c = -1 + x44:0 && (x46:0 < 0 && x44:0 > 1) l1(x2) -> l1(c1) :|: c1 = -1 + x2 && (x3 > 0 && x2 > 1) The following rules are bounded: l1(x44:0) -> l1(c) :|: c = -1 + x44:0 && (x46:0 < 0 && x44:0 > 1) l1(x2) -> l1(c1) :|: c1 = -1 + x2 && (x3 > 0 && x2 > 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x11:0) -> l1(x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 ---------------------------------------- (10) Obligation: Rules: l1(x11:0) -> l1(x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x11:0) -> l1(x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l1(x11:0) -> l1(x11:0) :|: x10:0 > -1 && x11:0 > 0 && x10:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l1(x11:0:0) -> l1(x11:0:0) :|: x10:0:0 > -1 && x11:0:0 > 0 && x10:0:0 < 1