7.25/2.65 YES 7.25/2.66 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.25/2.66 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.25/2.66 7.25/2.66 7.25/2.66 Termination of the given C Problem could be proven: 7.25/2.66 7.25/2.66 (0) C Problem 7.25/2.66 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.25/2.66 (2) IntTRS 7.25/2.66 (3) TerminationGraphProcessor [SOUND, 60 ms] 7.25/2.66 (4) IntTRS 7.25/2.66 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.25/2.66 (6) IntTRS 7.25/2.66 (7) TerminationGraphProcessor [EQUIVALENT, 3 ms] 7.25/2.66 (8) IntTRS 7.25/2.66 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.25/2.66 (10) IntTRS 7.25/2.66 (11) PolynomialOrderProcessor [EQUIVALENT, 8 ms] 7.25/2.66 (12) YES 7.25/2.66 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (0) 7.25/2.66 Obligation: 7.25/2.66 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (1) CToIRSProof (EQUIVALENT) 7.25/2.66 Parsed C Integer Program as IRS. 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (2) 7.25/2.66 Obligation: 7.25/2.66 Rules: 7.25/2.66 f1(x, y, n) -> f2(x_1, y, n) :|: TRUE 7.25/2.66 f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE 7.25/2.66 f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE 7.25/2.66 f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 0 - x9 + x10 - 5 7.25/2.66 f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = 2 * x25 7.25/2.66 f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 > 0 && x15 < x17 7.25/2.66 f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE 7.25/2.66 f4(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 <= 0 7.25/2.66 f4(x28, x29, x30) -> f8(x28, x29, x30) :|: x28 >= x30 7.25/2.66 Start term: f1(x, y, n) 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (3) TerminationGraphProcessor (SOUND) 7.25/2.66 Constructed the termination graph and obtained one non-trivial SCC. 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (4) 7.25/2.66 Obligation: 7.25/2.66 Rules: 7.25/2.66 f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 > 0 && x15 < x17 7.25/2.66 f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE 7.25/2.66 f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = 2 * x25 7.25/2.66 f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 0 - x9 + x10 - 5 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (5) IntTRSCompressionProof (EQUIVALENT) 7.25/2.66 Compressed rules. 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (6) 7.25/2.66 Obligation: 7.25/2.66 Rules: 7.25/2.66 f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x24:0 > 0 && x26:0 > x24:0 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (7) TerminationGraphProcessor (EQUIVALENT) 7.25/2.66 Constructed the termination graph and obtained one non-trivial SCC. 7.25/2.66 7.25/2.66 f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x24:0 > 0 && x26:0 > x24:0 7.25/2.66 has been transformed into 7.25/2.66 f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x26:0 = x8 && (x24:0 > 0 && x26:0 > x24:0) && x6 > 0 && x8 > x6. 7.25/2.66 7.25/2.66 7.25/2.66 f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x26:0 = x8 && (x24:0 > 0 && x26:0 > x24:0) && x6 > 0 && x8 > x6 and 7.25/2.66 f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x26:0 = x8 && (x24:0 > 0 && x26:0 > x24:0) && x6 > 0 && x8 > x6 7.25/2.66 have been merged into the new rule 7.25/2.66 f6(x19, x20, x21) -> f6(0 - (0 - x19 + 2 * x20 - 5) + 2 * (2 * x20) - 5, 2 * (2 * x20), x21) :|: x21 = x22 && (x19 > 0 && x21 > x19) && x23 > 0 && x22 > x23 && (x21 = x24 && (0 - x19 + 2 * x20 - 5 > 0 && x21 > 0 - x19 + 2 * x20 - 5) && x25 > 0 && x24 > x25) 7.25/2.66 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (8) 7.25/2.66 Obligation: 7.25/2.66 Rules: 7.25/2.66 f6(x26, x27, x28) -> f6(x26 + 2 * x27, 4 * x27, x28) :|: TRUE && x28 + -1 * x29 = 0 && x26 >= 1 && x28 + -1 * x26 >= 1 && x30 >= 1 && x29 + -1 * x30 >= 1 && x28 + -1 * x31 = 0 && -1 * x26 + 2 * x27 >= 6 && x28 + x26 + -2 * x27 >= -4 && x32 >= 1 && x31 + -1 * x32 >= 1 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (9) IntTRSCompressionProof (EQUIVALENT) 7.25/2.66 Compressed rules. 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (10) 7.25/2.66 Obligation: 7.25/2.66 Rules: 7.25/2.66 f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 2 * x27:0, 4 * x27:0, x28:0) :|: x32:0 > 0 && x31:0 + -1 * x32:0 >= 1 && x28:0 + x26:0 + -2 * x27:0 >= -4 && 6 <= -1 * x26:0 + 2 * x27:0 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 1 && x30:0 > 0 && x28:0 + -1 * x26:0 >= 1 && x28:0 + -1 * x29:0 = 0 && x26:0 > 0 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (11) PolynomialOrderProcessor (EQUIVALENT) 7.25/2.66 Found the following polynomial interpretation: 7.25/2.66 [f6(x, x1, x2)] = x - x1 + x2 7.25/2.66 7.25/2.66 The following rules are decreasing: 7.25/2.66 f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 2 * x27:0, 4 * x27:0, x28:0) :|: x32:0 > 0 && x31:0 + -1 * x32:0 >= 1 && x28:0 + x26:0 + -2 * x27:0 >= -4 && 6 <= -1 * x26:0 + 2 * x27:0 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 1 && x30:0 > 0 && x28:0 + -1 * x26:0 >= 1 && x28:0 + -1 * x29:0 = 0 && x26:0 > 0 7.25/2.66 The following rules are bounded: 7.25/2.66 f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 2 * x27:0, 4 * x27:0, x28:0) :|: x32:0 > 0 && x31:0 + -1 * x32:0 >= 1 && x28:0 + x26:0 + -2 * x27:0 >= -4 && 6 <= -1 * x26:0 + 2 * x27:0 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 1 && x30:0 > 0 && x28:0 + -1 * x26:0 >= 1 && x28:0 + -1 * x29:0 = 0 && x26:0 > 0 7.25/2.66 7.25/2.66 ---------------------------------------- 7.25/2.66 7.25/2.66 (12) 7.25/2.66 YES 7.40/2.71 EOF