5.12/2.13 YES 5.12/2.15 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 5.12/2.15 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.12/2.15 5.12/2.15 5.12/2.15 Termination of the given C Problem could be proven: 5.12/2.15 5.12/2.15 (0) C Problem 5.12/2.15 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.12/2.15 (2) IntTRS 5.12/2.15 (3) TerminationGraphProcessor [SOUND, 36 ms] 5.12/2.15 (4) IntTRS 5.12/2.15 (5) IntTRSCompressionProof [EQUIVALENT, 5 ms] 5.12/2.15 (6) IntTRS 5.12/2.15 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.12/2.15 (8) IntTRS 5.12/2.15 (9) PolynomialOrderProcessor [EQUIVALENT, 12 ms] 5.12/2.15 (10) YES 5.12/2.15 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (0) 5.12/2.15 Obligation: 5.12/2.15 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (1) CToIRSProof (EQUIVALENT) 5.12/2.15 Parsed C Integer Program as IRS. 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (2) 5.12/2.15 Obligation: 5.12/2.15 Rules: 5.12/2.15 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 5.12/2.15 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 5.12/2.15 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 5.12/2.15 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 * x9 5.12/2.15 f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1 5.12/2.15 f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > 1 && x15 < x16 5.12/2.15 f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE 5.12/2.15 f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 <= 1 5.12/2.15 f4(x27, x28, x29) -> f8(x27, x28, x29) :|: x28 >= x29 5.12/2.15 Start term: f1(c, x, y) 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (3) TerminationGraphProcessor (SOUND) 5.12/2.15 Constructed the termination graph and obtained one non-trivial SCC. 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (4) 5.12/2.15 Obligation: 5.12/2.15 Rules: 5.12/2.15 f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > 1 && x15 < x16 5.12/2.15 f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE 5.12/2.15 f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1 5.12/2.15 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 * x9 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (5) IntTRSCompressionProof (EQUIVALENT) 5.12/2.15 Compressed rules. 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (6) 5.12/2.15 Obligation: 5.12/2.15 Rules: 5.12/2.15 f6(x23:0, x24:0, x25:0) -> f6(x23:0 + 1, x24:0 * x24:0, x25:0) :|: x24:0 > 1 && x25:0 > x24:0 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.12/2.15 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.12/2.15 5.12/2.15 f6(x1, x2, x3) -> f6(x2, x3) 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (8) 5.12/2.15 Obligation: 5.12/2.15 Rules: 5.12/2.15 f6(x24:0, x25:0) -> f6(x24:0 * x24:0, x25:0) :|: x24:0 > 1 && x25:0 > x24:0 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (9) PolynomialOrderProcessor (EQUIVALENT) 5.12/2.15 Found the following polynomial interpretation: 5.12/2.15 [f6(x, x1)] = -x + x1 5.12/2.15 5.12/2.15 The following rules are decreasing: 5.12/2.15 f6(x24:0, x25:0) -> f6(x24:0 * x24:0, x25:0) :|: x24:0 > 1 && x25:0 > x24:0 5.12/2.15 The following rules are bounded: 5.12/2.15 f6(x24:0, x25:0) -> f6(x24:0 * x24:0, x25:0) :|: x24:0 > 1 && x25:0 > x24:0 5.12/2.15 5.12/2.15 ---------------------------------------- 5.12/2.15 5.12/2.15 (10) 5.12/2.15 YES 5.12/2.19 EOF