YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToIRSProof [EQUIVALENT, 0 ms] (2) IntTRS (3) TerminationGraphProcessor [SOUND, 64 ms] (4) IntTRS (5) IntTRSCompressionProof [EQUIVALENT, 13 ms] (6) IntTRS (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IntTRS (9) PolynomialOrderProcessor [EQUIVALENT, 10 ms] (10) AND (11) IntTRS (12) TerminationGraphProcessor [EQUIVALENT, 8 ms] (13) IntTRS (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IntTRS (16) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (17) YES (18) IntTRS (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 4 ms] (22) YES ---------------------------------------- (0) Obligation: c file /export/starexec/sandbox/benchmark/theBenchmark.c ---------------------------------------- (1) CToIRSProof (EQUIVALENT) Parsed C Integer Program as IRS. ---------------------------------------- (2) Obligation: Rules: f1(x, y, tmp, xtmp) -> f2(x_1, y, tmp, xtmp) :|: TRUE f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE f4(x6, x7, x8, x9) -> f5(x6, x7, x7, x9) :|: TRUE f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE f7(x14, x15, x16, x17) -> f8(x14, x15, x16, arith) :|: TRUE && arith = x17 - x15 f6(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x21 >= x19 && x19 > 0 f8(x22, x23, x24, x25) -> f6(x22, x23, x24, x25) :|: TRUE f6(x26, x27, x28, x29) -> f9(x26, x27, x28, x29) :|: x29 < x27 f6(x50, x51, x52, x53) -> f9(x50, x51, x52, x53) :|: x51 <= 0 f9(x30, x31, x32, x33) -> f10(x30, x33, x32, x33) :|: TRUE f10(x34, x35, x36, x37) -> f11(x36, x35, x36, x37) :|: TRUE f3(x38, x39, x40, x41) -> f4(x38, x39, x40, x41) :|: x39 > 0 && x38 > 0 f11(x42, x43, x44, x45) -> f3(x42, x43, x44, x45) :|: TRUE f3(x46, x47, x48, x49) -> f12(x46, x47, x48, x49) :|: x47 <= 0 f3(x54, x55, x56, x57) -> f12(x54, x55, x56, x57) :|: x54 <= 0 Start term: f1(x, y, tmp, xtmp) ---------------------------------------- (3) TerminationGraphProcessor (SOUND) Constructed the termination graph and obtained one non-trivial SCC. ---------------------------------------- (4) Obligation: Rules: f3(x38, x39, x40, x41) -> f4(x38, x39, x40, x41) :|: x39 > 0 && x38 > 0 f11(x42, x43, x44, x45) -> f3(x42, x43, x44, x45) :|: TRUE f10(x34, x35, x36, x37) -> f11(x36, x35, x36, x37) :|: TRUE f9(x30, x31, x32, x33) -> f10(x30, x33, x32, x33) :|: TRUE f6(x26, x27, x28, x29) -> f9(x26, x27, x28, x29) :|: x29 < x27 f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE f4(x6, x7, x8, x9) -> f5(x6, x7, x7, x9) :|: TRUE f8(x22, x23, x24, x25) -> f6(x22, x23, x24, x25) :|: TRUE f7(x14, x15, x16, x17) -> f8(x14, x15, x16, arith) :|: TRUE && arith = x17 - x15 f6(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x21 >= x19 && x19 > 0 f6(x50, x51, x52, x53) -> f9(x50, x51, x52, x53) :|: x51 <= 0 ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f6(x18:0, x19:0, x20:0, x21:0) -> f6(x18:0, x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 f6(x26:0, x27:0, x28:0, x29:0) -> f6(x28:0, x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 f6(x50:0, x51:0, x52:0, x53:0) -> f6(x52:0, x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f6(x1, x2, x3, x4) -> f6(x2, x3, x4) ---------------------------------------- (8) Obligation: Rules: f6(x19:0, x20:0, x21:0) -> f6(x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 f6(x51:0, x52:0, x53:0) -> f6(x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 ---------------------------------------- (9) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f6(x, x1, x2)] = -2 + x1 + x2 The following rules are decreasing: f6(x19:0, x20:0, x21:0) -> f6(x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 The following rules are bounded: f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 f6(x51:0, x52:0, x53:0) -> f6(x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Rules: f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 f6(x51:0, x52:0, x53:0) -> f6(x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 ---------------------------------------- (12) TerminationGraphProcessor (EQUIVALENT) Constructed the termination graph and obtained one non-trivial SCC. ---------------------------------------- (13) Obligation: Rules: f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f6(x27:0:0, x28:0:0, x29:0:0) -> f6(x29:0:0, x29:0:0, x28:0:0) :|: x29:0:0 > 0 && x28:0:0 > 0 && x29:0:0 < x27:0:0 ---------------------------------------- (16) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f6(x, x1, x2)] = x The following rules are decreasing: f6(x27:0:0, x28:0:0, x29:0:0) -> f6(x29:0:0, x29:0:0, x28:0:0) :|: x29:0:0 > 0 && x28:0:0 > 0 && x29:0:0 < x27:0:0 The following rules are bounded: f6(x27:0:0, x28:0:0, x29:0:0) -> f6(x29:0:0, x29:0:0, x28:0:0) :|: x29:0:0 > 0 && x28:0:0 > 0 && x29:0:0 < x27:0:0 ---------------------------------------- (17) YES ---------------------------------------- (18) Obligation: Rules: f6(x19:0, x20:0, x21:0) -> f6(x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 ---------------------------------------- (19) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f6(x1, x2, x3) -> f6(x1, x3) ---------------------------------------- (20) Obligation: Rules: f6(x19:0, x21:0) -> f6(x19:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f6 ] = f6_2 The following rules are decreasing: f6(x19:0, x21:0) -> f6(x19:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 The following rules are bounded: f6(x19:0, x21:0) -> f6(x19:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 ---------------------------------------- (22) YES