5.92/2.34 YES 5.92/2.34 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 5.92/2.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.92/2.34 5.92/2.34 5.92/2.34 Termination of the given C Problem could be proven: 5.92/2.34 5.92/2.34 (0) C Problem 5.92/2.34 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.92/2.34 (2) IntTRS 5.92/2.34 (3) TerminationGraphProcessor [SOUND, 47 ms] 5.92/2.34 (4) IntTRS 5.92/2.34 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.92/2.34 (6) IntTRS 5.92/2.34 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.92/2.34 (8) IntTRS 5.92/2.34 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 5.92/2.34 (10) IntTRS 5.92/2.34 (11) RankingReductionPairProof [EQUIVALENT, 0 ms] 5.92/2.34 (12) YES 5.92/2.34 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (0) 5.92/2.34 Obligation: 5.92/2.34 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (1) CToIRSProof (EQUIVALENT) 5.92/2.34 Parsed C Integer Program as IRS. 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (2) 5.92/2.34 Obligation: 5.92/2.34 Rules: 5.92/2.34 f1(i, c) -> f2(0, c) :|: TRUE 5.92/2.34 f2(x, x1) -> f3(x, 0) :|: TRUE 5.92/2.34 f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1 5.92/2.34 f7(x20, x21) -> f9(x20, x22) :|: TRUE && x22 = x21 + 1 5.92/2.34 f5(x6, x7) -> f6(x6, x7) :|: x6 <= 10 5.92/2.34 f5(x8, x9) -> f7(x8, x9) :|: x8 > 10 5.92/2.34 f6(x10, x11) -> f8(x10, x11) :|: TRUE 5.92/2.34 f9(x12, x13) -> f8(x12, x13) :|: TRUE 5.92/2.34 f3(x14, x15) -> f4(x14, x15) :|: x14 < 20 5.92/2.34 f8(x16, x17) -> f3(x16, x17) :|: TRUE 5.92/2.34 f3(x18, x19) -> f10(x18, x19) :|: x18 >= 20 5.92/2.34 Start term: f1(i, c) 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (3) TerminationGraphProcessor (SOUND) 5.92/2.34 Constructed the termination graph and obtained one non-trivial SCC. 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (4) 5.92/2.34 Obligation: 5.92/2.34 Rules: 5.92/2.34 f3(x14, x15) -> f4(x14, x15) :|: x14 < 20 5.92/2.34 f8(x16, x17) -> f3(x16, x17) :|: TRUE 5.92/2.34 f6(x10, x11) -> f8(x10, x11) :|: TRUE 5.92/2.34 f5(x6, x7) -> f6(x6, x7) :|: x6 <= 10 5.92/2.34 f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1 5.92/2.34 f9(x12, x13) -> f8(x12, x13) :|: TRUE 5.92/2.34 f7(x20, x21) -> f9(x20, x22) :|: TRUE && x22 = x21 + 1 5.92/2.34 f5(x8, x9) -> f7(x8, x9) :|: x8 > 10 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (5) IntTRSCompressionProof (EQUIVALENT) 5.92/2.34 Compressed rules. 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (6) 5.92/2.34 Obligation: 5.92/2.34 Rules: 5.92/2.34 f5(x8:0, x9:0) -> f5(x8:0 + 1, x9:0 + 1) :|: x8:0 > 10 && x8:0 < 20 5.92/2.34 f5(x6:0, x7:0) -> f5(x6:0 + 1, x7:0) :|: x6:0 < 11 && x6:0 < 20 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.92/2.34 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.92/2.34 5.92/2.34 f5(x1, x2) -> f5(x1) 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (8) 5.92/2.34 Obligation: 5.92/2.34 Rules: 5.92/2.34 f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20 5.92/2.34 f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 11 && x6:0 < 20 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (9) PolynomialOrderProcessor (EQUIVALENT) 5.92/2.34 Found the following polynomial interpretation: 5.92/2.34 [f5(x)] = 297 - 39*x + x^2 5.92/2.34 5.92/2.34 The following rules are decreasing: 5.92/2.34 f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 11 && x6:0 < 20 5.92/2.34 The following rules are bounded: 5.92/2.34 f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 11 && x6:0 < 20 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (10) 5.92/2.34 Obligation: 5.92/2.34 Rules: 5.92/2.34 f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (11) RankingReductionPairProof (EQUIVALENT) 5.92/2.34 Interpretation: 5.92/2.34 [ f5 ] = -1*f5_1 5.92/2.34 5.92/2.34 The following rules are decreasing: 5.92/2.34 f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20 5.92/2.34 5.92/2.34 The following rules are bounded: 5.92/2.34 f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20 5.92/2.34 5.92/2.34 5.92/2.34 ---------------------------------------- 5.92/2.34 5.92/2.34 (12) 5.92/2.34 YES 6.15/2.38 EOF