7.55/2.79 YES 7.55/2.80 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.55/2.80 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.55/2.80 7.55/2.80 7.55/2.80 Termination of the given C Problem could be proven: 7.55/2.80 7.55/2.80 (0) C Problem 7.55/2.80 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.55/2.80 (2) IntTRS 7.55/2.80 (3) TerminationGraphProcessor [SOUND, 53 ms] 7.55/2.80 (4) IntTRS 7.55/2.80 (5) IntTRSCompressionProof [EQUIVALENT, 25 ms] 7.55/2.80 (6) IntTRS 7.55/2.80 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.55/2.80 (8) IntTRS 7.55/2.80 (9) TerminationGraphProcessor [EQUIVALENT, 0 ms] 7.55/2.80 (10) IntTRS 7.55/2.80 (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.55/2.80 (12) IntTRS 7.55/2.80 (13) RankingReductionPairProof [EQUIVALENT, 5 ms] 7.55/2.80 (14) YES 7.55/2.80 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (0) 7.55/2.80 Obligation: 7.55/2.80 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (1) CToIRSProof (EQUIVALENT) 7.55/2.80 Parsed C Integer Program as IRS. 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (2) 7.55/2.80 Obligation: 7.55/2.80 Rules: 7.55/2.80 f1(x, y, z) -> f2(x_1, y, z) :|: TRUE 7.55/2.80 f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE 7.55/2.80 f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE 7.55/2.80 f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + x10 7.55/2.80 f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE 7.55/2.80 f7(x27, x28, x29) -> f8(x27, x28, x30) :|: TRUE && x30 = 0 - x29 - 1 7.55/2.80 f4(x18, x19, x20) -> f5(x18, x19, x20) :|: x18 > 0 7.55/2.80 f8(x21, x22, x23) -> f4(x21, x22, x23) :|: TRUE 7.55/2.80 f4(x24, x25, x26) -> f9(x24, x25, x26) :|: x24 <= 0 7.55/2.80 Start term: f1(x, y, z) 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (3) TerminationGraphProcessor (SOUND) 7.55/2.80 Constructed the termination graph and obtained one non-trivial SCC. 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (4) 7.55/2.80 Obligation: 7.55/2.80 Rules: 7.55/2.80 f4(x18, x19, x20) -> f5(x18, x19, x20) :|: x18 > 0 7.55/2.80 f8(x21, x22, x23) -> f4(x21, x22, x23) :|: TRUE 7.55/2.80 f7(x27, x28, x29) -> f8(x27, x28, x30) :|: TRUE && x30 = 0 - x29 - 1 7.55/2.80 f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE 7.55/2.80 f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + x10 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (5) IntTRSCompressionProof (EQUIVALENT) 7.55/2.80 Compressed rules. 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (6) 7.55/2.80 Obligation: 7.55/2.80 Rules: 7.55/2.80 f6(x12:0, x13:0, x14:0) -> f6(x12:0 + x14:0, x14:0, 0 - x14:0 - 1) :|: x12:0 > 0 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.55/2.80 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.55/2.80 7.55/2.80 f6(x1, x2, x3) -> f6(x1, x3) 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (8) 7.55/2.80 Obligation: 7.55/2.80 Rules: 7.55/2.80 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > 0 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (9) TerminationGraphProcessor (EQUIVALENT) 7.55/2.80 Constructed the termination graph and obtained one non-trivial SCC. 7.55/2.80 7.55/2.80 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > 0 7.55/2.80 has been transformed into 7.55/2.80 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > 0 && x4 > 0. 7.55/2.80 7.55/2.80 7.55/2.80 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > 0 && x4 > 0 and 7.55/2.80 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > 0 && x4 > 0 7.55/2.80 have been merged into the new rule 7.55/2.80 f6(x12, x13) -> f6(x12 + x13 + (0 - x13 - 1), 0 - (0 - x13 - 1) - 1) :|: x12 > 0 && x14 > 0 && (x12 + x13 > 0 && x15 > 0) 7.55/2.80 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (10) 7.55/2.80 Obligation: 7.55/2.80 Rules: 7.55/2.80 f6(x16, x17) -> f6(x16 + -1, x17) :|: TRUE && x16 >= 1 && x18 >= 1 && x16 + x17 >= 1 && x19 >= 1 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (11) IntTRSCompressionProof (EQUIVALENT) 7.55/2.80 Compressed rules. 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (12) 7.55/2.80 Obligation: 7.55/2.80 Rules: 7.55/2.80 f6(x16:0, x17:0) -> f6(x16:0 - 1, x17:0) :|: x16:0 + x17:0 >= 1 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (13) RankingReductionPairProof (EQUIVALENT) 7.55/2.80 Interpretation: 7.55/2.80 [ f6 ] = f6_1 7.55/2.80 7.55/2.80 The following rules are decreasing: 7.55/2.80 f6(x16:0, x17:0) -> f6(x16:0 - 1, x17:0) :|: x16:0 + x17:0 >= 1 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0 7.55/2.80 7.55/2.80 The following rules are bounded: 7.55/2.80 f6(x16:0, x17:0) -> f6(x16:0 - 1, x17:0) :|: x16:0 + x17:0 >= 1 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0 7.55/2.80 7.55/2.80 7.55/2.80 ---------------------------------------- 7.55/2.80 7.55/2.80 (14) 7.55/2.80 YES 7.80/2.84 EOF