YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.c # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToIRSProof [EQUIVALENT, 0 ms] (2) IntTRS (3) TerminationGraphProcessor [SOUND, 80 ms] (4) IntTRS (5) IntTRSCompressionProof [EQUIVALENT, 53 ms] (6) IntTRS (7) TerminationGraphProcessor [EQUIVALENT, 9 ms] (8) AND (9) IntTRS (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 5 ms] (13) YES (14) IntTRS (15) IntTRSCompressionProof [EQUIVALENT, 0 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: c file /export/starexec/sandbox2/benchmark/theBenchmark.c ---------------------------------------- (1) CToIRSProof (EQUIVALENT) Parsed C Integer Program as IRS. ---------------------------------------- (2) Obligation: Rules: f1(x, y, z) -> f2(x_1, y, z) :|: TRUE f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE f6(x9, x10, x11) -> f9(x9, x11, x11) :|: TRUE f9(x12, x13, x14) -> f10(x15, x13, x14) :|: TRUE f10(x16, x17, x18) -> f11(x16, x17, arith) :|: TRUE && arith = x16 - 1 f7(x50, x51, x52) -> f12(x50, x51, x53) :|: TRUE && x53 = x52 - 1 f12(x22, x23, x24) -> f13(x25, x23, x24) :|: TRUE f13(x54, x55, x56) -> f14(x54, x57, x56) :|: TRUE && x57 = x54 - 1 f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x29 f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x32 f11(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE f14(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x41 > 0 && x42 > 0 && x43 > 0 f8(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE f4(x47, x48, x49) -> f15(x47, x48, x49) :|: x49 <= 0 f4(x58, x59, x60) -> f15(x58, x59, x60) :|: x58 <= 0 f4(x61, x62, x63) -> f15(x61, x62, x63) :|: x62 <= 0 Start term: f1(x, y, z) ---------------------------------------- (3) TerminationGraphProcessor (SOUND) Constructed the termination graph and obtained one non-trivial SCC. ---------------------------------------- (4) Obligation: Rules: f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x41 > 0 && x42 > 0 && x43 > 0 f8(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE f11(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE f10(x16, x17, x18) -> f11(x16, x17, arith) :|: TRUE && arith = x16 - 1 f9(x12, x13, x14) -> f10(x15, x13, x14) :|: TRUE f6(x9, x10, x11) -> f9(x9, x11, x11) :|: TRUE f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x29 f14(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE f13(x54, x55, x56) -> f14(x54, x57, x56) :|: TRUE && x57 = x54 - 1 f12(x22, x23, x24) -> f13(x25, x23, x24) :|: TRUE f7(x50, x51, x52) -> f12(x50, x51, x53) :|: TRUE && x53 = x52 - 1 f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x32 ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f8(x44:0, x45:0, x46:0) -> f8(x25:0, x25:0 - 1, x46:0 - 1) :|: x46:0 > 0 && x45:0 <= x44:0 && x45:0 > 0 && x44:0 > 0 f8(x, x1, x2) -> f8(x3, x2, x3 - 1) :|: x2 > 0 && x1 > x && x1 > 0 && x > 0 ---------------------------------------- (7) TerminationGraphProcessor (EQUIVALENT) Constructed the termination graph and obtained 2 non-trivial SCCs. f8(x, x1, x2) -> f8(x3, x2, x3 - 1) :|: x2 > 0 && x1 > x && x1 > 0 && x > 0 has been transformed into f8(x, x1, x2) -> f8(x3, x2, x3 - 1) :|: x1 = x18 && (x2 > 0 && x1 > x && x1 > 0 && x > 0) && x18 > 0. f8(x44:0, x45:0, x46:0) -> f8(x25:0, x25:0 - 1, x46:0 - 1) :|: x46:0 > 0 && x45:0 <= x44:0 && x45:0 > 0 && x44:0 > 0 has been transformed into f8(x44:0, x45:0, x46:0) -> f8(x25:0, x25:0 - 1, x46:0 - 1) :|: x46:0 = x50 - 1 && (x46:0 > 0 && x45:0 <= x44:0 && x45:0 > 0 && x44:0 > 0) && x50 > 0. f8(x, x1, x2) -> f8(x3, x2, x3 - 1) :|: x1 = x18 && (x2 > 0 && x1 > x && x1 > 0 && x > 0) && x18 > 0 and f8(x, x1, x2) -> f8(x3, x2, x3 - 1) :|: x1 = x18 && (x2 > 0 && x1 > x && x1 > 0 && x > 0) && x18 > 0 have been merged into the new rule f8(x30, x31, x32) -> f8(x33, x34 - 1, x33 - 1) :|: x31 = x35 && (x32 > 0 && x31 > x30 && x31 > 0 && x30 > 0) && x35 > 0 && (x32 = x36 && (x34 - 1 > 0 && x32 > x34 && x32 > 0 && x34 > 0) && x36 > 0) f8(x44:0, x45:0, x46:0) -> f8(x25:0, x25:0 - 1, x46:0 - 1) :|: x46:0 = x50 - 1 && (x46:0 > 0 && x45:0 <= x44:0 && x45:0 > 0 && x44:0 > 0) && x50 > 0 and f8(x44:0, x45:0, x46:0) -> f8(x25:0, x25:0 - 1, x46:0 - 1) :|: x46:0 = x50 - 1 && (x46:0 > 0 && x45:0 <= x44:0 && x45:0 > 0 && x44:0 > 0) && x50 > 0 have been merged into the new rule f8(x62, x63, x64) -> f8(x65, x65 - 1, x64 - 1 - 1) :|: x64 = x66 - 1 && (x64 > 0 && x63 <= x62 && x63 > 0 && x62 > 0) && x66 > 0 && (x64 - 1 = x67 - 1 && (x64 - 1 > 0 && x68 - 1 <= x68 && x68 - 1 > 0 && x68 > 0) && x67 > 0) ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Rules: f8(x37, x38, x39) -> f8(x40, x41 + -1, x40 + -1) :|: TRUE && x38 + -1 * x42 = 0 && x39 >= 1 && x38 + -1 * x37 >= 1 && x38 >= 1 && x37 >= 1 && x42 >= 1 && x39 + -1 * x43 = 0 && x41 >= 2 && x39 + -1 * x41 >= 1 && x43 >= 1 ---------------------------------------- (10) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (11) Obligation: Rules: f8(x37:0, x38:0, x39:0) -> f8(x40:0, x41:0 - 1, x40:0 - 1) :|: x39:0 + -1 * x41:0 >= 1 && x43:0 > 0 && x41:0 > 1 && x39:0 + -1 * x43:0 = 0 && x42:0 > 0 && x37:0 > 0 && x38:0 > 0 && x38:0 + -1 * x37:0 >= 1 && x38:0 + -1 * x42:0 = 0 && x39:0 > 0 ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f8(x, x1, x2)] = -3 - x + x1 + x2 The following rules are decreasing: f8(x37:0, x38:0, x39:0) -> f8(x40:0, x41:0 - 1, x40:0 - 1) :|: x39:0 + -1 * x41:0 >= 1 && x43:0 > 0 && x41:0 > 1 && x39:0 + -1 * x43:0 = 0 && x42:0 > 0 && x37:0 > 0 && x38:0 > 0 && x38:0 + -1 * x37:0 >= 1 && x38:0 + -1 * x42:0 = 0 && x39:0 > 0 The following rules are bounded: f8(x37:0, x38:0, x39:0) -> f8(x40:0, x41:0 - 1, x40:0 - 1) :|: x39:0 + -1 * x41:0 >= 1 && x43:0 > 0 && x41:0 > 1 && x39:0 + -1 * x43:0 = 0 && x42:0 > 0 && x37:0 > 0 && x38:0 > 0 && x38:0 + -1 * x37:0 >= 1 && x38:0 + -1 * x42:0 = 0 && x39:0 > 0 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Rules: f8(x69, x70, x71) -> f8(x72, x72 + -1, x71 + -2) :|: TRUE && x71 + -1 * x73 = -1 && x70 + -1 * x69 <= 0 && x70 >= 1 && x69 >= 1 && x73 >= 1 && x71 + -1 * x74 = 0 && x71 >= 2 && 0 <= 1 && x75 >= 2 && x74 >= 1 ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: f8(x69:0, x70:0, x71:0) -> f8(x72:0, x72:0 - 1, x71:0 - 2) :|: x75:0 > 1 && x74:0 > 0 && x71:0 > 1 && x71:0 + -1 * x74:0 = 0 && x73:0 > 0 && x69:0 > 0 && x70:0 > 0 && x71:0 + -1 * x73:0 = -1 && x70:0 + -1 * x69:0 <= 0 ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f8 ] = 1/2*f8_3 The following rules are decreasing: f8(x69:0, x70:0, x71:0) -> f8(x72:0, x72:0 - 1, x71:0 - 2) :|: x75:0 > 1 && x74:0 > 0 && x71:0 > 1 && x71:0 + -1 * x74:0 = 0 && x73:0 > 0 && x69:0 > 0 && x70:0 > 0 && x71:0 + -1 * x73:0 = -1 && x70:0 + -1 * x69:0 <= 0 The following rules are bounded: f8(x69:0, x70:0, x71:0) -> f8(x72:0, x72:0 - 1, x71:0 - 2) :|: x75:0 > 1 && x74:0 > 0 && x71:0 > 1 && x71:0 + -1 * x74:0 = 0 && x73:0 > 0 && x69:0 > 0 && x70:0 > 0 && x71:0 + -1 * x73:0 = -1 && x70:0 + -1 * x69:0 <= 0 ---------------------------------------- (18) YES