6.65/2.45 YES 6.65/2.46 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 6.65/2.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.65/2.46 6.65/2.46 6.65/2.46 Termination of the given C Problem could be proven: 6.65/2.46 6.65/2.46 (0) C Problem 6.65/2.46 (1) CToIRSProof [EQUIVALENT, 0 ms] 6.65/2.46 (2) IntTRS 6.65/2.46 (3) TerminationGraphProcessor [SOUND, 31 ms] 6.65/2.46 (4) IntTRS 6.65/2.46 (5) IntTRSCompressionProof [EQUIVALENT, 13 ms] 6.65/2.46 (6) IntTRS 6.65/2.46 (7) TerminationGraphProcessor [EQUIVALENT, 0 ms] 6.65/2.46 (8) IntTRS 6.65/2.46 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.65/2.46 (10) IntTRS 6.65/2.46 (11) RankingReductionPairProof [EQUIVALENT, 0 ms] 6.65/2.46 (12) YES 6.65/2.46 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (0) 6.65/2.46 Obligation: 6.65/2.46 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (1) CToIRSProof (EQUIVALENT) 6.65/2.46 Parsed C Integer Program as IRS. 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (2) 6.65/2.46 Obligation: 6.65/2.46 Rules: 6.65/2.46 f1(x, y) -> f2(x_1, y) :|: TRUE 6.65/2.46 f2(x1, x2) -> f3(x1, x3) :|: TRUE 6.65/2.46 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 6.65/2.46 f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = (0 - 2) * x15 - 1 6.65/2.46 f3(x8, x9) -> f4(x8, x9) :|: x8 >= 0 6.65/2.46 f6(x10, x11) -> f3(x10, x11) :|: TRUE 6.65/2.46 f3(x12, x13) -> f7(x12, x13) :|: x12 < 0 6.65/2.46 Start term: f1(x, y) 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (3) TerminationGraphProcessor (SOUND) 6.65/2.46 Constructed the termination graph and obtained one non-trivial SCC. 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (4) 6.65/2.46 Obligation: 6.65/2.46 Rules: 6.65/2.46 f3(x8, x9) -> f4(x8, x9) :|: x8 >= 0 6.65/2.46 f6(x10, x11) -> f3(x10, x11) :|: TRUE 6.65/2.46 f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = (0 - 2) * x15 - 1 6.65/2.46 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (5) IntTRSCompressionProof (EQUIVALENT) 6.65/2.46 Compressed rules. 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (6) 6.65/2.46 Obligation: 6.65/2.46 Rules: 6.65/2.46 f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (7) TerminationGraphProcessor (EQUIVALENT) 6.65/2.46 Constructed the termination graph and obtained one non-trivial SCC. 6.65/2.46 6.65/2.46 f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 6.65/2.46 has been transformed into 6.65/2.46 f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 && x4 > -1. 6.65/2.46 6.65/2.46 6.65/2.46 f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 && x4 > -1 and 6.65/2.46 f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 && x4 > -1 6.65/2.46 have been merged into the new rule 6.65/2.46 f5(x12, x13) -> f5(x12 + (-2 * x13 - 1) + (-2 * (-2 * x13 - 1) - 1), -2 * (-2 * x13 - 1) - 1) :|: x12 > -1 && x14 > -1 && (x12 + (-2 * x13 - 1) > -1 && x15 > -1) 6.65/2.46 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (8) 6.65/2.46 Obligation: 6.65/2.46 Rules: 6.65/2.46 f5(x16, x17) -> f5(x16 + 2 * x17, 4 * x17 + 1) :|: TRUE && x16 >= 0 && x18 >= 0 && x16 + -2 * x17 >= 1 && x19 >= 0 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (9) IntTRSCompressionProof (EQUIVALENT) 6.65/2.46 Compressed rules. 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (10) 6.65/2.46 Obligation: 6.65/2.46 Rules: 6.65/2.46 f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0, 4 * x17:0 + 1) :|: x16:0 + -2 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (11) RankingReductionPairProof (EQUIVALENT) 6.65/2.46 Interpretation: 6.65/2.46 [ f5 ] = 3/2*f5_1 + -1*f5_2 6.65/2.46 6.65/2.46 The following rules are decreasing: 6.65/2.46 f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0, 4 * x17:0 + 1) :|: x16:0 + -2 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1 6.65/2.46 6.65/2.46 The following rules are bounded: 6.65/2.46 f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0, 4 * x17:0 + 1) :|: x16:0 + -2 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1 6.65/2.46 6.65/2.46 6.65/2.46 ---------------------------------------- 6.65/2.46 6.65/2.46 (12) 6.65/2.46 YES 6.65/2.49 EOF