NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 358 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 10 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) FilterProof [EQUIVALENT, 0 ms] (11) IntTRS (12) IntTRSCompressionProof [EQUIVALENT, 0 ms] (13) IntTRS (14) IntTRSNonPeriodicNontermProof [COMPLETE, 4 ms] (15) NO (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 7 ms] (18) IRSwT (19) FilterProof [EQUIVALENT, 0 ms] (20) IntTRS (21) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (22) NO ---------------------------------------- (0) Obligation: Rules: l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: dobreakHAT0 <= 0 && AHAT1 = 1 && AHATpost = 0 && nHATpost = nHATpost && 1 <= nHATpost && RHAT0 = RHATpost && dobreakHAT0 = dobreakHATpost l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 1 <= x2 l3(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 l1(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 l5(x24, x25, x26, x27) -> l6(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 l2(x32, x33, x34, x35) -> l7(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 l7(x40, x41, x42, x43) -> l2(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 <= x51 l4(x56, x57, x58, x59) -> l3(x60, x61, x62, x63) :|: x59 <= 0 && x64 = 1 && x61 = 0 && x62 = x62 && x56 = x60 && x59 = x63 l8(x65, x66, x67, x68) -> l3(x69, x70, x71, x72) :|: x68 = x72 && x71 = x71 && x70 = 0 && x69 = 0 l9(x73, x74, x75, x76) -> l8(x77, x78, x79, x80) :|: x76 = x80 && x75 = x79 && x74 = x78 && x73 = x77 Start term: l9(AHAT0, RHAT0, dobreakHAT0, nHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: dobreakHAT0 <= 0 && AHAT1 = 1 && AHATpost = 0 && nHATpost = nHATpost && 1 <= nHATpost && RHAT0 = RHATpost && dobreakHAT0 = dobreakHATpost l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 1 <= x2 l3(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 l1(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 l5(x24, x25, x26, x27) -> l6(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 l2(x32, x33, x34, x35) -> l7(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 l7(x40, x41, x42, x43) -> l2(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 <= x51 l4(x56, x57, x58, x59) -> l3(x60, x61, x62, x63) :|: x59 <= 0 && x64 = 1 && x61 = 0 && x62 = x62 && x56 = x60 && x59 = x63 l8(x65, x66, x67, x68) -> l3(x69, x70, x71, x72) :|: x68 = x72 && x71 = x71 && x70 = 0 && x69 = 0 l9(x73, x74, x75, x76) -> l8(x77, x78, x79, x80) :|: x76 = x80 && x75 = x79 && x74 = x78 && x73 = x77 Start term: l9(AHAT0, RHAT0, dobreakHAT0, nHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: dobreakHAT0 <= 0 && AHAT1 = 1 && AHATpost = 0 && nHATpost = nHATpost && 1 <= nHATpost && RHAT0 = RHATpost && dobreakHAT0 = dobreakHATpost (2) l0(x, x1, x2, x3) -> l2(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && 1 <= x2 (3) l3(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 (4) l1(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 (5) l5(x24, x25, x26, x27) -> l6(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 (6) l2(x32, x33, x34, x35) -> l7(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 (7) l7(x40, x41, x42, x43) -> l2(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 (8) l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 <= x51 (9) l4(x56, x57, x58, x59) -> l3(x60, x61, x62, x63) :|: x59 <= 0 && x64 = 1 && x61 = 0 && x62 = x62 && x56 = x60 && x59 = x63 (10) l8(x65, x66, x67, x68) -> l3(x69, x70, x71, x72) :|: x68 = x72 && x71 = x71 && x70 = 0 && x69 = 0 (11) l9(x73, x74, x75, x76) -> l8(x77, x78, x79, x80) :|: x76 = x80 && x75 = x79 && x74 = x78 && x73 = x77 Arcs: (1) -> (4) (2) -> (6) (3) -> (1), (2) (4) -> (8), (9) (6) -> (7) (7) -> (6) (8) -> (4) (9) -> (3) (10) -> (3) (11) -> (10) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(AHAT0, RHAT0, dobreakHAT0, nHAT0) -> l1(AHATpost, RHATpost, dobreakHATpost, nHATpost) :|: dobreakHAT0 <= 0 && AHAT1 = 1 && AHATpost = 0 && nHATpost = nHATpost && 1 <= nHATpost && RHAT0 = RHATpost && dobreakHAT0 = dobreakHATpost (2) l3(x8, x9, x10, x11) -> l0(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 (3) l4(x56, x57, x58, x59) -> l3(x60, x61, x62, x63) :|: x59 <= 0 && x64 = 1 && x61 = 0 && x62 = x62 && x56 = x60 && x59 = x63 (4) l1(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 (5) l4(x48, x49, x50, x51) -> l1(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 && 1 <= x51 Arcs: (1) -> (4) (2) -> (1) (3) -> (2) (4) -> (3), (5) (5) -> (4) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l4(x20:0, x21:0, x22:0, x23:0) -> l4(x20:0, x21:0, x22:0, x23:0) :|: x23:0 > 0 l4(x12:0, x57:0, x58:0, x15:0) -> l4(0, 0, dobreakHATpost:0, nHATpost:0) :|: nHATpost:0 > 0 && dobreakHATpost:0 < 1 && x15:0 < 1 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l4(x1, x2, x3, x4) -> l4(x4) ---------------------------------------- (9) Obligation: Rules: l4(x23:0) -> l4(x23:0) :|: x23:0 > 0 l4(x15:0) -> l4(nHATpost:0) :|: nHATpost:0 > 0 && dobreakHATpost:0 < 1 && x15:0 < 1 ---------------------------------------- (10) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l4(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l4(x23:0) -> l4(x23:0) :|: x23:0 > 0 l4(x15:0) -> l4(nHATpost:0) :|: nHATpost:0 > 0 && dobreakHATpost:0 < 1 && x15:0 < 1 ---------------------------------------- (12) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (13) Obligation: Rules: l4(x15:0:0) -> l4(nHATpost:0:0) :|: nHATpost:0:0 > 0 && dobreakHATpost:0:0 < 1 && x15:0:0 < 1 l4(x23:0:0) -> l4(x23:0:0) :|: x23:0:0 > 0 ---------------------------------------- (14) IntTRSNonPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x15:0:0) -> f(1, nHATpost:0:0) :|: pc = 1 && (nHATpost:0:0 > 0 && dobreakHATpost:0:0 < 1 && x15:0:0 < 1) f(pc, x23:0:0) -> f(1, x23:0:0) :|: pc = 1 && x23:0:0 > 0 Proved unsatisfiability of the following formula, indicating that the system is never left after entering: ((((run2_0 = ((1 * 1)) and run2_1 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((((run1_2 * 1)) > 0 and ((run1_3 * 1)) < ((1 * 1))) and ((run1_1 * 1)) < ((1 * 1))))) or ((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((run1_1 * 1)) > 0))) and (!(((run2_0 * 1)) = ((1 * 1)) and ((((run2_2 * 1)) > 0 and ((run2_3 * 1)) < ((1 * 1))) and ((run2_1 * 1)) < ((1 * 1)))) and !(((run2_0 * 1)) = ((1 * 1)) and ((run2_1 * 1)) > 0))) Proved satisfiability of the following formula, indicating that the system is entered at least once: (((run2_0 = ((1 * 1)) and run2_1 = ((run1_2 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((((run1_2 * 1)) > 0 and ((run1_3 * 1)) < ((1 * 1))) and ((run1_1 * 1)) < ((1 * 1))))) or ((run2_0 = ((1 * 1)) and run2_1 = ((run1_1 * 1))) and (((run1_0 * 1)) = ((1 * 1)) and ((run1_1 * 1)) > 0))) ---------------------------------------- (15) NO ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l2(x32, x33, x34, x35) -> l7(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x33 = x37 && x32 = x36 (2) l7(x40, x41, x42, x43) -> l2(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l2(x32:0, x33:0, x34:0, x35:0) -> l2(x32:0, x33:0, x34:0, x35:0) :|: TRUE ---------------------------------------- (19) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: l2(VARIABLE, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l2(x32:0, x33:0, x34:0, x35:0) -> l2(x32:0, x33:0, x34:0, x35:0) :|: TRUE ---------------------------------------- (21) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x32:0, x33:0, x34:0, x35:0) -> f(1, x32:0, x33:0, x34:0, x35:0) :|: pc = 1 && TRUE Witness term starting non-terminating reduction: f(1, -8, -8, -8, -8) ---------------------------------------- (22) NO