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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given C Problem could be proven: (0) C Problem (1) CToIRSProof [EQUIVALENT, 0 ms] (2) IntTRS (3) TerminationGraphProcessor [SOUND, 68 ms] (4) IntTRS (5) IntTRSCompressionProof [EQUIVALENT, 22 ms] (6) IntTRS (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IntTRS (9) TerminationGraphProcessor [EQUIVALENT, 17 ms] (10) IntTRS (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IntTRS (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (14) 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, z, n) -> f2(x_1, y, z, n) :|: TRUE f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE f4(x11, x12, x13, x14) -> f5(x11, x12, x13, x15) :|: TRUE f6(x16, x17, x18, x19) -> f7(arith, x17, x18, x19) :|: TRUE && arith = 2 * x16 + x17 f7(x20, x21, x22, x23) -> f8(x20, x22, x22, x23) :|: TRUE f8(x24, x25, x26, x27) -> f9(x24, x25, x26, x27) :|: TRUE f9(x44, x45, x46, x47) -> f10(x44, x45, x48, x47) :|: TRUE && x48 = x46 + 1 f5(x32, x33, x34, x35) -> f6(x32, x33, x34, x35) :|: x32 + x33 >= 0 && x32 <= x35 f10(x36, x37, x38, x39) -> f5(x36, x37, x38, x39) :|: TRUE f5(x40, x41, x42, x43) -> f11(x40, x41, x42, x43) :|: x40 + x41 < 0 f5(x49, x50, x51, x52) -> f11(x49, x50, x51, x52) :|: x49 > x52 Start term: f1(x, y, z, n) ---------------------------------------- (3) TerminationGraphProcessor (SOUND) Constructed the termination graph and obtained one non-trivial SCC. ---------------------------------------- (4) Obligation: Rules: f5(x32, x33, x34, x35) -> f6(x32, x33, x34, x35) :|: x32 + x33 >= 0 && x32 <= x35 f10(x36, x37, x38, x39) -> f5(x36, x37, x38, x39) :|: TRUE f9(x44, x45, x46, x47) -> f10(x44, x45, x48, x47) :|: TRUE && x48 = x46 + 1 f8(x24, x25, x26, x27) -> f9(x24, x25, x26, x27) :|: TRUE f7(x20, x21, x22, x23) -> f8(x20, x22, x22, x23) :|: TRUE f6(x16, x17, x18, x19) -> f7(arith, x17, x18, x19) :|: TRUE && arith = 2 * x16 + x17 ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f7(x20:0, x21:0, x22:0, x23:0) -> f7(2 * x20:0 + x22:0, x22:0, x22:0 + 1, x23:0) :|: x20:0 + x22:0 >= 0 && x23:0 >= x20:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f7(x1, x2, x3, x4) -> f7(x1, x3, x4) ---------------------------------------- (8) Obligation: Rules: f7(x20:0, x22:0, x23:0) -> f7(2 * x20:0 + x22:0, x22:0 + 1, x23:0) :|: x20:0 + x22:0 >= 0 && x23:0 >= x20:0 ---------------------------------------- (9) TerminationGraphProcessor (EQUIVALENT) Constructed the termination graph and obtained one non-trivial SCC. f7(x20:0, x22:0, x23:0) -> f7(2 * x20:0 + x22:0, x22:0 + 1, x23:0) :|: x20:0 + x22:0 >= 0 && x23:0 >= x20:0 has been transformed into f7(x20:0, x22:0, x23:0) -> f7(2 * x20:0 + x22:0, x22:0 + 1, x23:0) :|: x23:0 = x8 && (x22:0 = x7 + 1 && (x20:0 = 2 * x6 + x7 && (x20:0 + x22:0 >= 0 && x23:0 >= x20:0))) && x6 + x7 >= 0 && x8 >= x6. f7(x20:0, x22:0, x23:0) -> f7(2 * x20:0 + x22:0, x22:0 + 1, x23:0) :|: x23:0 = x8 && (x22:0 = x7 + 1 && (x20:0 = 2 * x6 + x7 && (x20:0 + x22:0 >= 0 && x23:0 >= x20:0))) && x6 + x7 >= 0 && x8 >= x6 and f7(x20:0, x22:0, x23:0) -> f7(2 * x20:0 + x22:0, x22:0 + 1, x23:0) :|: x23:0 = x8 && (x22:0 = x7 + 1 && (x20:0 = 2 * x6 + x7 && (x20:0 + x22:0 >= 0 && x23:0 >= x20:0))) && x6 + x7 >= 0 && x8 >= x6 have been merged into the new rule f7(x21, x22, x23) -> f7(2 * (2 * x21 + x22) + (x22 + 1), x22 + 1 + 1, x23) :|: x23 = x24 && (x22 = x25 + 1 && (x21 = 2 * x26 + x25 && (x21 + x22 >= 0 && x23 >= x21))) && x26 + x25 >= 0 && x24 >= x26 && (x23 = x27 && (x22 + 1 = x28 + 1 && (2 * x21 + x22 = 2 * x29 + x28 && (2 * x21 + x22 + (x22 + 1) >= 0 && x23 >= 2 * x21 + x22))) && x29 + x28 >= 0 && x27 >= x29) ---------------------------------------- (10) Obligation: Rules: f7(x30, x31, x32) -> f7(4 * x30 + 3 * x31 + 1, x31 + 2, x32) :|: TRUE && x32 + -1 * x33 = 0 && x31 + -1 * x34 = 1 && x30 + -2 * x35 + -1 * x34 = 0 && x30 + x31 >= 0 && x32 + -1 * x30 >= 0 && x35 + x34 >= 0 && x33 + -1 * x35 >= 0 && x32 + -1 * x36 = 0 && x31 + -1 * x37 = 0 && 2 * x30 + x31 + -2 * x38 + -1 * x37 = 0 && x32 + -2 * x30 + -1 * x31 >= 0 && x38 + x37 >= 0 && x36 + -1 * x38 >= 0 ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f7(x30:0, x31:0, x32:0) -> f7(4 * x30:0 + 3 * x31:0 + 1, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= 0 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 0 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= 0 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= 0 && x30:0 + -2 * x35:0 + -1 * x34:0 = 0 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1 ---------------------------------------- (13) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f7(x, x1, x2)] = -x + x2 The following rules are decreasing: f7(x30:0, x31:0, x32:0) -> f7(4 * x30:0 + 3 * x31:0 + 1, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= 0 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 0 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= 0 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= 0 && x30:0 + -2 * x35:0 + -1 * x34:0 = 0 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1 The following rules are bounded: f7(x30:0, x31:0, x32:0) -> f7(4 * x30:0 + 3 * x31:0 + 1, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= 0 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 0 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= 0 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= 0 && x30:0 + -2 * x35:0 + -1 * x34:0 = 0 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1 ---------------------------------------- (14) YES