5.53/2.20 YES 5.53/2.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.53/2.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.53/2.21 5.53/2.21 5.53/2.21 Termination of the given C Problem could be proven: 5.53/2.21 5.53/2.21 (0) C Problem 5.53/2.21 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.53/2.21 (2) IntTRS 5.53/2.21 (3) TerminationGraphProcessor [SOUND, 73 ms] 5.53/2.21 (4) IntTRS 5.53/2.21 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.53/2.21 (6) IntTRS 5.53/2.21 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.53/2.21 (8) IntTRS 5.53/2.21 (9) PolynomialOrderProcessor [EQUIVALENT, 11 ms] 5.53/2.21 (10) IntTRS 5.53/2.21 (11) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.53/2.21 (12) IntTRS 5.53/2.21 (13) PolynomialOrderProcessor [EQUIVALENT, 3 ms] 5.53/2.21 (14) YES 5.53/2.21 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (0) 5.53/2.21 Obligation: 5.53/2.21 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (1) CToIRSProof (EQUIVALENT) 5.53/2.21 Parsed C Integer Program as IRS. 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (2) 5.53/2.21 Obligation: 5.53/2.21 Rules: 5.53/2.21 f1(i, j, c) -> f2(i, j, 0) :|: TRUE 5.53/2.21 f2(x, x1, x2) -> f3(0, x1, x2) :|: TRUE 5.53/2.21 f4(x3, x4, x5) -> f5(x3, 3, x5) :|: TRUE 5.53/2.21 f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1 5.53/2.21 f7(x36, x37, x38) -> f8(x36, x37, x39) :|: TRUE && x39 = x38 + 1 5.53/2.21 f8(x40, x41, x42) -> f9(x40, x43, x42) :|: TRUE && x43 = x41 + 2 5.53/2.21 f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x16 < 12 5.53/2.21 f9(x18, x19, x20) -> f5(x18, x19, x20) :|: TRUE 5.53/2.21 f5(x21, x22, x23) -> f10(x21, x22, x23) :|: x22 >= 12 5.53/2.21 f10(x44, x45, x46) -> f11(x47, x45, x46) :|: TRUE && x47 = x44 + 1 5.53/2.21 f3(x27, x28, x29) -> f4(x27, x28, x29) :|: x27 < 10 5.53/2.21 f11(x30, x31, x32) -> f3(x30, x31, x32) :|: TRUE 5.53/2.21 f3(x33, x34, x35) -> f12(x33, x34, x35) :|: x33 >= 10 5.53/2.21 Start term: f1(i, j, c) 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (3) TerminationGraphProcessor (SOUND) 5.53/2.21 Constructed the termination graph and obtained one non-trivial SCC. 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (4) 5.53/2.21 Obligation: 5.53/2.21 Rules: 5.53/2.21 f3(x27, x28, x29) -> f4(x27, x28, x29) :|: x27 < 10 5.53/2.21 f11(x30, x31, x32) -> f3(x30, x31, x32) :|: TRUE 5.53/2.21 f10(x44, x45, x46) -> f11(x47, x45, x46) :|: TRUE && x47 = x44 + 1 5.53/2.21 f5(x21, x22, x23) -> f10(x21, x22, x23) :|: x22 >= 12 5.53/2.21 f9(x18, x19, x20) -> f5(x18, x19, x20) :|: TRUE 5.53/2.21 f8(x40, x41, x42) -> f9(x40, x43, x42) :|: TRUE && x43 = x41 + 2 5.53/2.21 f7(x36, x37, x38) -> f8(x36, x37, x39) :|: TRUE && x39 = x38 + 1 5.53/2.21 f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1 5.53/2.21 f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x16 < 12 5.53/2.21 f4(x3, x4, x5) -> f5(x3, 3, x5) :|: TRUE 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (5) IntTRSCompressionProof (EQUIVALENT) 5.53/2.21 Compressed rules. 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (6) 5.53/2.21 Obligation: 5.53/2.21 Rules: 5.53/2.21 f5(x21:0, x22:0, x23:0) -> f5(x21:0 + 1, 3, x23:0) :|: x22:0 > 11 && x21:0 < 9 5.53/2.21 f5(x15:0, x16:0, x17:0) -> f5(x15:0, x16:0 + 1, x17:0 + 1) :|: x16:0 < 12 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.53/2.21 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.53/2.21 5.53/2.21 f5(x1, x2, x3) -> f5(x1, x2) 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (8) 5.53/2.21 Obligation: 5.53/2.21 Rules: 5.53/2.21 f5(x21:0, x22:0) -> f5(x21:0 + 1, 3) :|: x22:0 > 11 && x21:0 < 9 5.53/2.21 f5(x15:0, x16:0) -> f5(x15:0, x16:0 + 1) :|: x16:0 < 12 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (9) PolynomialOrderProcessor (EQUIVALENT) 5.53/2.21 Found the following polynomial interpretation: 5.53/2.21 [f5(x, x1)] = 8 - x 5.53/2.21 5.53/2.21 The following rules are decreasing: 5.53/2.21 f5(x21:0, x22:0) -> f5(x21:0 + 1, 3) :|: x22:0 > 11 && x21:0 < 9 5.53/2.21 The following rules are bounded: 5.53/2.21 f5(x21:0, x22:0) -> f5(x21:0 + 1, 3) :|: x22:0 > 11 && x21:0 < 9 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (10) 5.53/2.21 Obligation: 5.53/2.21 Rules: 5.53/2.21 f5(x15:0, x16:0) -> f5(x15:0, x16:0 + 1) :|: x16:0 < 12 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (11) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.53/2.21 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.53/2.21 5.53/2.21 f5(x1, x2) -> f5(x2) 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (12) 5.53/2.21 Obligation: 5.53/2.21 Rules: 5.53/2.21 f5(x16:0) -> f5(x16:0 + 1) :|: x16:0 < 12 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (13) PolynomialOrderProcessor (EQUIVALENT) 5.53/2.21 Found the following polynomial interpretation: 5.53/2.21 [f5(x)] = 11 - x 5.53/2.21 5.53/2.21 The following rules are decreasing: 5.53/2.21 f5(x16:0) -> f5(x16:0 + 1) :|: x16:0 < 12 5.53/2.21 The following rules are bounded: 5.53/2.21 f5(x16:0) -> f5(x16:0 + 1) :|: x16:0 < 12 5.53/2.21 5.53/2.21 ---------------------------------------- 5.53/2.21 5.53/2.21 (14) 5.53/2.21 YES 5.83/2.25 EOF