5.83/2.35 YES 5.83/2.36 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 5.83/2.36 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.83/2.36 5.83/2.36 5.83/2.36 Termination of the given C Problem could be proven: 5.83/2.36 5.83/2.36 (0) C Problem 5.83/2.36 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.83/2.36 (2) IntTRS 5.83/2.36 (3) TerminationGraphProcessor [SOUND, 67 ms] 5.83/2.36 (4) IntTRS 5.83/2.36 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.83/2.36 (6) IntTRS 5.83/2.36 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.83/2.36 (8) IntTRS 5.83/2.36 (9) RankingReductionPairProof [EQUIVALENT, 6 ms] 5.83/2.36 (10) IntTRS 5.83/2.36 (11) RankingReductionPairProof [EQUIVALENT, 0 ms] 5.83/2.36 (12) YES 5.83/2.36 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (0) 5.83/2.36 Obligation: 5.83/2.36 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (1) CToIRSProof (EQUIVALENT) 5.83/2.36 Parsed C Integer Program as IRS. 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (2) 5.83/2.36 Obligation: 5.83/2.36 Rules: 5.83/2.36 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 5.83/2.36 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 5.83/2.36 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 5.83/2.36 f5(x8, x9, x10) -> f6(x8, x9, 0) :|: TRUE 5.83/2.36 f7(x11, x12, x13) -> f8(x11, x12, arith) :|: TRUE && arith = x13 + 1 5.83/2.36 f8(x38, x39, x40) -> f9(x41, x39, x40) :|: TRUE && x41 = x38 + 1 5.83/2.36 f6(x17, x18, x19) -> f7(x17, x18, x19) :|: x19 < x18 5.83/2.36 f9(x20, x21, x22) -> f6(x20, x21, x22) :|: TRUE 5.83/2.36 f6(x23, x24, x25) -> f10(x23, x24, x25) :|: x25 >= x24 5.83/2.36 f10(x42, x43, x44) -> f11(x42, x45, x44) :|: TRUE && x45 = x43 - 1 5.83/2.36 f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x30 > 0 5.83/2.36 f11(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE 5.83/2.36 f4(x35, x36, x37) -> f12(x35, x36, x37) :|: x36 <= 0 5.83/2.36 Start term: f1(c, x, y) 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (3) TerminationGraphProcessor (SOUND) 5.83/2.36 Constructed the termination graph and obtained one non-trivial SCC. 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (4) 5.83/2.36 Obligation: 5.83/2.36 Rules: 5.83/2.36 f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x30 > 0 5.83/2.36 f11(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE 5.83/2.36 f10(x42, x43, x44) -> f11(x42, x45, x44) :|: TRUE && x45 = x43 - 1 5.83/2.36 f6(x23, x24, x25) -> f10(x23, x24, x25) :|: x25 >= x24 5.83/2.36 f5(x8, x9, x10) -> f6(x8, x9, 0) :|: TRUE 5.83/2.36 f9(x20, x21, x22) -> f6(x20, x21, x22) :|: TRUE 5.83/2.36 f8(x38, x39, x40) -> f9(x41, x39, x40) :|: TRUE && x41 = x38 + 1 5.83/2.36 f7(x11, x12, x13) -> f8(x11, x12, arith) :|: TRUE && arith = x13 + 1 5.83/2.36 f6(x17, x18, x19) -> f7(x17, x18, x19) :|: x19 < x18 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (5) IntTRSCompressionProof (EQUIVALENT) 5.83/2.36 Compressed rules. 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (6) 5.83/2.36 Obligation: 5.83/2.36 Rules: 5.83/2.36 f6(x23:0, x24:0, x25:0) -> f6(x23:0, x24:0 - 1, 0) :|: x25:0 >= x24:0 && x24:0 > 1 5.83/2.36 f6(x17:0, x18:0, x19:0) -> f6(x17:0 + 1, x18:0, x19:0 + 1) :|: x19:0 < x18:0 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.83/2.36 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.83/2.36 5.83/2.36 f6(x1, x2, x3) -> f6(x2, x3) 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (8) 5.83/2.36 Obligation: 5.83/2.36 Rules: 5.83/2.36 f6(x24:0, x25:0) -> f6(x24:0 - 1, 0) :|: x25:0 >= x24:0 && x24:0 > 1 5.83/2.36 f6(x18:0, x19:0) -> f6(x18:0, x19:0 + 1) :|: x19:0 < x18:0 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (9) RankingReductionPairProof (EQUIVALENT) 5.83/2.36 Interpretation: 5.83/2.36 [ f6 ] = f6_1 5.83/2.36 5.83/2.36 The following rules are decreasing: 5.83/2.36 f6(x24:0, x25:0) -> f6(x24:0 - 1, 0) :|: x25:0 >= x24:0 && x24:0 > 1 5.83/2.36 5.83/2.36 The following rules are bounded: 5.83/2.36 f6(x24:0, x25:0) -> f6(x24:0 - 1, 0) :|: x25:0 >= x24:0 && x24:0 > 1 5.83/2.36 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (10) 5.83/2.36 Obligation: 5.83/2.36 Rules: 5.83/2.36 f6(x18:0, x19:0) -> f6(x18:0, x19:0 + 1) :|: x19:0 < x18:0 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (11) RankingReductionPairProof (EQUIVALENT) 5.83/2.36 Interpretation: 5.83/2.36 [ f6 ] = -1*f6_2 + f6_1 5.83/2.36 5.83/2.36 The following rules are decreasing: 5.83/2.36 f6(x18:0, x19:0) -> f6(x18:0, x19:0 + 1) :|: x19:0 < x18:0 5.83/2.36 5.83/2.36 The following rules are bounded: 5.83/2.36 f6(x18:0, x19:0) -> f6(x18:0, x19:0 + 1) :|: x19:0 < x18:0 5.83/2.36 5.83/2.36 5.83/2.36 ---------------------------------------- 5.83/2.36 5.83/2.36 (12) 5.83/2.36 YES 6.21/2.39 EOF