5.34/2.29 YES 5.34/2.31 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 5.34/2.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.34/2.31 5.34/2.31 5.34/2.31 Termination of the given C Problem could be proven: 5.34/2.31 5.34/2.31 (0) C Problem 5.34/2.31 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.34/2.31 (2) IntTRS 5.34/2.31 (3) TerminationGraphProcessor [SOUND, 54 ms] 5.34/2.31 (4) IntTRS 5.34/2.31 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.34/2.31 (6) IntTRS 5.34/2.31 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 2 ms] 5.34/2.31 (8) IntTRS 5.34/2.31 (9) TerminationGraphProcessor [EQUIVALENT, 0 ms] 5.34/2.31 (10) IntTRS 5.34/2.31 (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.34/2.31 (12) IntTRS 5.34/2.31 (13) RankingReductionPairProof [EQUIVALENT, 5 ms] 5.34/2.31 (14) YES 5.34/2.31 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (0) 5.34/2.31 Obligation: 5.34/2.31 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (1) CToIRSProof (EQUIVALENT) 5.34/2.31 Parsed C Integer Program as IRS. 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (2) 5.34/2.31 Obligation: 5.34/2.31 Rules: 5.34/2.31 f1(x, y, z) -> f2(x_1, y, z) :|: TRUE 5.34/2.31 f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE 5.34/2.31 f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE 5.34/2.31 f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + x10 5.34/2.31 f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE 5.34/2.31 f7(x27, x28, x29) -> f8(x27, x28, x30) :|: TRUE && x30 = 0 - x29 - 1 5.34/2.31 f4(x18, x19, x20) -> f5(x18, x19, x20) :|: x18 >= 0 5.34/2.31 f8(x21, x22, x23) -> f4(x21, x22, x23) :|: TRUE 5.34/2.31 f4(x24, x25, x26) -> f9(x24, x25, x26) :|: x24 < 0 5.34/2.31 Start term: f1(x, y, z) 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (3) TerminationGraphProcessor (SOUND) 5.34/2.31 Constructed the termination graph and obtained one non-trivial SCC. 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (4) 5.34/2.31 Obligation: 5.34/2.31 Rules: 5.34/2.31 f4(x18, x19, x20) -> f5(x18, x19, x20) :|: x18 >= 0 5.34/2.31 f8(x21, x22, x23) -> f4(x21, x22, x23) :|: TRUE 5.34/2.31 f7(x27, x28, x29) -> f8(x27, x28, x30) :|: TRUE && x30 = 0 - x29 - 1 5.34/2.31 f6(x12, x13, x14) -> f7(x12, x14, x14) :|: TRUE 5.34/2.31 f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = x9 + x10 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (5) IntTRSCompressionProof (EQUIVALENT) 5.34/2.31 Compressed rules. 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (6) 5.34/2.31 Obligation: 5.34/2.31 Rules: 5.34/2.31 f6(x12:0, x13:0, x14:0) -> f6(x12:0 + x14:0, x14:0, 0 - x14:0 - 1) :|: x12:0 > -1 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.34/2.31 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.34/2.31 5.34/2.31 f6(x1, x2, x3) -> f6(x1, x3) 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (8) 5.34/2.31 Obligation: 5.34/2.31 Rules: 5.34/2.31 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > -1 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (9) TerminationGraphProcessor (EQUIVALENT) 5.34/2.31 Constructed the termination graph and obtained one non-trivial SCC. 5.34/2.31 5.34/2.31 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > -1 5.34/2.31 has been transformed into 5.34/2.31 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > -1 && x4 > -1. 5.34/2.31 5.34/2.31 5.34/2.31 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > -1 && x4 > -1 and 5.34/2.31 f6(x12:0, x14:0) -> f6(x12:0 + x14:0, 0 - x14:0 - 1) :|: x12:0 > -1 && x4 > -1 5.34/2.31 have been merged into the new rule 5.34/2.31 f6(x12, x13) -> f6(x12 + x13 + (0 - x13 - 1), 0 - (0 - x13 - 1) - 1) :|: x12 > -1 && x14 > -1 && (x12 + x13 > -1 && x15 > -1) 5.34/2.31 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (10) 5.34/2.31 Obligation: 5.34/2.31 Rules: 5.34/2.31 f6(x16, x17) -> f6(x16 + -1, x17) :|: TRUE && x16 >= 0 && x18 >= 0 && x16 + x17 >= 0 && x19 >= 0 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (11) IntTRSCompressionProof (EQUIVALENT) 5.34/2.31 Compressed rules. 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (12) 5.34/2.31 Obligation: 5.34/2.31 Rules: 5.34/2.31 f6(x16:0, x17:0) -> f6(x16:0 - 1, x17:0) :|: x16:0 + x17:0 >= 0 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (13) RankingReductionPairProof (EQUIVALENT) 5.34/2.31 Interpretation: 5.34/2.31 [ f6 ] = f6_1 5.34/2.31 5.34/2.31 The following rules are decreasing: 5.34/2.31 f6(x16:0, x17:0) -> f6(x16:0 - 1, x17:0) :|: x16:0 + x17:0 >= 0 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1 5.34/2.31 5.34/2.31 The following rules are bounded: 5.34/2.31 f6(x16:0, x17:0) -> f6(x16:0 - 1, x17:0) :|: x16:0 + x17:0 >= 0 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1 5.34/2.31 5.34/2.31 5.34/2.31 ---------------------------------------- 5.34/2.31 5.34/2.31 (14) 5.34/2.31 YES 5.92/2.34 EOF