13.51/4.27 YES 13.51/4.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 13.51/4.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.51/4.28 13.51/4.28 13.51/4.28 Termination of the given C Problem could be proven: 13.51/4.28 13.51/4.28 (0) C Problem 13.51/4.28 (1) CToIRSProof [EQUIVALENT, 0 ms] 13.51/4.28 (2) IntTRS 13.51/4.28 (3) TerminationGraphProcessor [SOUND, 64 ms] 13.51/4.28 (4) IntTRS 13.51/4.28 (5) IntTRSCompressionProof [EQUIVALENT, 36 ms] 13.51/4.28 (6) IntTRS 13.51/4.28 (7) CaseAnalysis [EQUIVALENT, 25 ms] 13.51/4.28 (8) AND 13.51/4.28 (9) IntTRS 13.51/4.28 (10) TerminationGraphProcessor [EQUIVALENT, 17 ms] 13.51/4.28 (11) IntTRS 13.51/4.28 (12) IntTRSCompressionProof [EQUIVALENT, 0 ms] 13.51/4.28 (13) IntTRS 13.51/4.28 (14) RankingReductionPairProof [EQUIVALENT, 0 ms] 13.51/4.28 (15) YES 13.51/4.28 (16) IntTRS 13.51/4.28 (17) TerminationGraphProcessor [EQUIVALENT, 14 ms] 13.51/4.28 (18) IntTRS 13.51/4.28 (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] 13.51/4.28 (20) IntTRS 13.51/4.28 (21) RankingReductionPairProof [EQUIVALENT, 0 ms] 13.51/4.28 (22) YES 13.51/4.28 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (0) 13.51/4.28 Obligation: 13.51/4.28 c file /export/starexec/sandbox/benchmark/theBenchmark.c 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (1) CToIRSProof (EQUIVALENT) 13.51/4.28 Parsed C Integer Program as IRS. 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (2) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f1(K, x) -> f2(x_1, x) :|: TRUE 13.51/4.28 f2(x1, x2) -> f3(x1, x3) :|: TRUE 13.51/4.28 f5(x4, x5) -> f8(x4, arith) :|: TRUE && arith = x5 - 1 13.51/4.28 f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 + 1 13.51/4.28 f4(x8, x9) -> f5(x8, x9) :|: x9 > x8 13.51/4.28 f4(x10, x11) -> f6(x10, x11) :|: x11 <= x10 13.51/4.28 f8(x12, x13) -> f7(x12, x13) :|: TRUE 13.51/4.28 f9(x14, x15) -> f7(x14, x15) :|: TRUE 13.51/4.28 f3(x16, x17) -> f4(x16, x17) :|: x17 < x16 13.51/4.28 f3(x25, x26) -> f4(x25, x26) :|: x26 > x25 13.51/4.28 f7(x18, x19) -> f3(x18, x19) :|: TRUE 13.51/4.28 f3(x20, x21) -> f10(x20, x21) :|: x21 = x20 13.51/4.28 Start term: f1(K, x) 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (3) TerminationGraphProcessor (SOUND) 13.51/4.28 Constructed the termination graph and obtained one non-trivial SCC. 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (4) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f3(x16, x17) -> f4(x16, x17) :|: x17 < x16 13.51/4.28 f7(x18, x19) -> f3(x18, x19) :|: TRUE 13.51/4.28 f8(x12, x13) -> f7(x12, x13) :|: TRUE 13.51/4.28 f5(x4, x5) -> f8(x4, arith) :|: TRUE && arith = x5 - 1 13.51/4.28 f4(x8, x9) -> f5(x8, x9) :|: x9 > x8 13.51/4.28 f3(x25, x26) -> f4(x25, x26) :|: x26 > x25 13.51/4.28 f9(x14, x15) -> f7(x14, x15) :|: TRUE 13.51/4.28 f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 + 1 13.51/4.28 f4(x10, x11) -> f6(x10, x11) :|: x11 <= x10 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (5) IntTRSCompressionProof (EQUIVALENT) 13.51/4.28 Compressed rules. 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (6) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > x18:0 13.51/4.28 f4(x10:0, x11:0) -> f7(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 13.51/4.28 f4(x8:0, x9:0) -> f7(x8:0, x9:0 - 1) :|: x9:0 > x8:0 13.51/4.28 f7(x, x1) -> f4(x, x1) :|: x1 < x 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (7) CaseAnalysis (EQUIVALENT) 13.51/4.28 Found the following inductive condition: 13.51/4.28 f7(x, x1): -3*x + 3*x1>=0 13.51/4.28 f4(x2, x3): -3*x2 + 3*x3>=0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (8) 13.51/4.28 Complex Obligation (AND) 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (9) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > x18:0 && -3 * x18:0 + 3 * x19:0 >= 0 13.51/4.28 f4(x10:0, x11:0) -> f7(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && -3 * x10:0 + 3 * x11:0 >= 0 13.51/4.28 f4(x8:0, x9:0) -> f7(x8:0, x9:0 - 1) :|: x9:0 > x8:0 && -3 * x8:0 + 3 * x9:0 >= 0 13.51/4.28 f7(x, x1) -> f4(x, x1) :|: x1 < x && -3 * x + 3 * x1 >= 0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (10) TerminationGraphProcessor (EQUIVALENT) 13.51/4.28 Constructed the termination graph and obtained one non-trivial SCC. 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (11) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > x18:0 && -3 * x18:0 + 3 * x19:0 >= 0 13.51/4.28 f4(x10:0, x11:0) -> f7(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && -3 * x10:0 + 3 * x11:0 >= 0 13.51/4.28 f4(x8:0, x9:0) -> f7(x8:0, x9:0 - 1) :|: x9:0 > x8:0 && -3 * x8:0 + 3 * x9:0 >= 0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (12) IntTRSCompressionProof (EQUIVALENT) 13.51/4.28 Compressed rules. 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (13) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: 0 <= -3 * x18:0:0 + 3 * x19:0:0 && x19:0:0 > x18:0:0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (14) RankingReductionPairProof (EQUIVALENT) 13.51/4.28 Interpretation: 13.51/4.28 [ f7 ] = f7_2 + -1*f7_1 13.51/4.28 13.51/4.28 The following rules are decreasing: 13.51/4.28 f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: 0 <= -3 * x18:0:0 + 3 * x19:0:0 && x19:0:0 > x18:0:0 13.51/4.28 13.51/4.28 The following rules are bounded: 13.51/4.28 f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: 0 <= -3 * x18:0:0 + 3 * x19:0:0 && x19:0:0 > x18:0:0 13.51/4.28 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (15) 13.51/4.28 YES 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (16) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > x18:0 && -3 * x18:0 + 3 * x19:0 < 0 13.51/4.28 f4(x10:0, x11:0) -> f7(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && -3 * x10:0 + 3 * x11:0 < 0 13.51/4.28 f4(x8:0, x9:0) -> f7(x8:0, x9:0 - 1) :|: x9:0 > x8:0 && -3 * x8:0 + 3 * x9:0 < 0 13.51/4.28 f7(x, x1) -> f4(x, x1) :|: x1 < x && -3 * x + 3 * x1 < 0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (17) TerminationGraphProcessor (EQUIVALENT) 13.51/4.28 Constructed the termination graph and obtained one non-trivial SCC. 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (18) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f4(x10:0, x11:0) -> f7(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && -3 * x10:0 + 3 * x11:0 < 0 13.51/4.28 f7(x, x1) -> f4(x, x1) :|: x1 < x && -3 * x + 3 * x1 < 0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (19) IntTRSCompressionProof (EQUIVALENT) 13.51/4.28 Compressed rules. 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (20) 13.51/4.28 Obligation: 13.51/4.28 Rules: 13.51/4.28 f4(x10:0:0, x11:0:0) -> f4(x10:0:0, x11:0:0 + 1) :|: 0 > -3 * x10:0:0 + 3 * x11:0:0 && x11:0:0 <= x10:0:0 && 0 > -3 * x10:0:0 + 3 * (x11:0:0 + 1) && x11:0:0 + 1 < x10:0:0 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (21) RankingReductionPairProof (EQUIVALENT) 13.51/4.28 Interpretation: 13.51/4.28 [ f4 ] = f4_1 + -1*f4_2 13.51/4.28 13.51/4.28 The following rules are decreasing: 13.51/4.28 f4(x10:0:0, x11:0:0) -> f4(x10:0:0, x11:0:0 + 1) :|: 0 > -3 * x10:0:0 + 3 * x11:0:0 && x11:0:0 <= x10:0:0 && 0 > -3 * x10:0:0 + 3 * (x11:0:0 + 1) && x11:0:0 + 1 < x10:0:0 13.51/4.28 13.51/4.28 The following rules are bounded: 13.51/4.28 f4(x10:0:0, x11:0:0) -> f4(x10:0:0, x11:0:0 + 1) :|: 0 > -3 * x10:0:0 + 3 * x11:0:0 && x11:0:0 <= x10:0:0 && 0 > -3 * x10:0:0 + 3 * (x11:0:0 + 1) && x11:0:0 + 1 < x10:0:0 13.51/4.28 13.51/4.28 13.51/4.28 ---------------------------------------- 13.51/4.28 13.51/4.28 (22) 13.51/4.28 YES 13.71/4.39 EOF