15.13/4.63 YES 15.13/4.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 15.13/4.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.13/4.63 15.13/4.63 15.13/4.63 Termination of the given C Problem could be proven: 15.13/4.63 15.13/4.63 (0) C Problem 15.13/4.63 (1) CToIRSProof [EQUIVALENT, 0 ms] 15.13/4.63 (2) IntTRS 15.13/4.63 (3) TerminationGraphProcessor [SOUND, 78 ms] 15.13/4.63 (4) IntTRS 15.13/4.63 (5) IntTRSCompressionProof [EQUIVALENT, 6 ms] 15.13/4.63 (6) IntTRS 15.13/4.63 (7) CaseAnalysis [EQUIVALENT, 24 ms] 15.13/4.63 (8) AND 15.13/4.63 (9) IntTRS 15.13/4.63 (10) TerminationGraphProcessor [EQUIVALENT, 14 ms] 15.13/4.63 (11) IntTRS 15.13/4.63 (12) IntTRSCompressionProof [EQUIVALENT, 0 ms] 15.13/4.63 (13) IntTRS 15.13/4.63 (14) RankingReductionPairProof [EQUIVALENT, 91 ms] 15.13/4.63 (15) YES 15.13/4.63 (16) IntTRS 15.13/4.63 (17) TerminationGraphProcessor [EQUIVALENT, 13 ms] 15.13/4.63 (18) IntTRS 15.13/4.63 (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] 15.13/4.63 (20) IntTRS 15.13/4.63 (21) RankingReductionPairProof [EQUIVALENT, 0 ms] 15.13/4.63 (22) YES 15.13/4.63 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (0) 15.13/4.63 Obligation: 15.13/4.63 c file /export/starexec/sandbox/benchmark/theBenchmark.c 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (1) CToIRSProof (EQUIVALENT) 15.13/4.63 Parsed C Integer Program as IRS. 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (2) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f1(x, y) -> f2(x_1, y) :|: TRUE 15.13/4.63 f2(x1, x2) -> f3(x1, x3) :|: TRUE 15.13/4.63 f8(x4, x5) -> f11(arith, x5) :|: TRUE && arith = x4 + 1 15.13/4.63 f9(x30, x31) -> f12(x30, x32) :|: TRUE && x32 = x31 + 1 15.13/4.63 f7(x8, x9) -> f8(x8, x9) :|: x8 < x9 15.13/4.63 f7(x10, x11) -> f9(x10, x11) :|: x10 >= x11 15.13/4.63 f11(x12, x13) -> f10(x12, x13) :|: TRUE 15.13/4.63 f12(x14, x15) -> f10(x14, x15) :|: TRUE 15.13/4.63 f4(x16, x17) -> f7(x16, x17) :|: x16 - x17 > 2 15.13/4.63 f4(x33, x34) -> f7(x33, x34) :|: x34 - x33 > 2 15.13/4.63 f10(x18, x19) -> f4(x18, x19) :|: TRUE 15.13/4.63 f4(x20, x21) -> f13(x20, x21) :|: x20 - x21 <= 2 && x21 - x20 <= 2 15.13/4.63 f3(x22, x23) -> f4(x22, x23) :|: x22 >= 0 && x23 >= 0 15.13/4.63 f3(x24, x25) -> f5(x24, x25) :|: x24 < 0 15.13/4.63 f3(x35, x36) -> f5(x35, x36) :|: x36 < 0 15.13/4.63 f13(x26, x27) -> f6(x26, x27) :|: TRUE 15.13/4.63 f5(x28, x29) -> f6(x28, x29) :|: TRUE 15.13/4.63 Start term: f1(x, y) 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (3) TerminationGraphProcessor (SOUND) 15.13/4.63 Constructed the termination graph and obtained one non-trivial SCC. 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (4) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f4(x16, x17) -> f7(x16, x17) :|: x16 - x17 > 2 15.13/4.63 f10(x18, x19) -> f4(x18, x19) :|: TRUE 15.13/4.63 f11(x12, x13) -> f10(x12, x13) :|: TRUE 15.13/4.63 f8(x4, x5) -> f11(arith, x5) :|: TRUE && arith = x4 + 1 15.13/4.63 f7(x8, x9) -> f8(x8, x9) :|: x8 < x9 15.13/4.63 f4(x33, x34) -> f7(x33, x34) :|: x34 - x33 > 2 15.13/4.63 f12(x14, x15) -> f10(x14, x15) :|: TRUE 15.13/4.63 f9(x30, x31) -> f12(x30, x32) :|: TRUE && x32 = x31 + 1 15.13/4.63 f7(x10, x11) -> f9(x10, x11) :|: x10 >= x11 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (5) IntTRSCompressionProof (EQUIVALENT) 15.13/4.63 Compressed rules. 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (6) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 15.13/4.63 f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 15.13/4.63 f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 15.13/4.63 f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (7) CaseAnalysis (EQUIVALENT) 15.13/4.63 Found the following inductive condition: 15.13/4.63 f10(x, x1): 3 + 3*x - 3*x1>=0 15.13/4.63 f7(x2, x3): 3 + 3*x2 - 3*x3>=0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (8) 15.13/4.63 Complex Obligation (AND) 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (9) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 && 3 + 3 * x18:0 + -3 * x19:0 >= 0 15.13/4.63 f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 && 3 + 3 * x + -3 * x1 >= 0 15.13/4.63 f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && 3 + 3 * x10:0 + -3 * x11:0 >= 0 15.13/4.63 f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 >= 0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (10) TerminationGraphProcessor (EQUIVALENT) 15.13/4.63 Constructed the termination graph and obtained one non-trivial SCC. 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (11) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 && 3 + 3 * x18:0 + -3 * x19:0 >= 0 15.13/4.63 f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && 3 + 3 * x10:0 + -3 * x11:0 >= 0 15.13/4.63 f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 >= 0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (12) IntTRSCompressionProof (EQUIVALENT) 15.13/4.63 Compressed rules. 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (13) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x18:0:0, x19:0:0) -> f10(x18:0:0, x19:0:0 + 1) :|: x18:0:0 - x19:0:0 > 2 && 3 + 3 * x18:0:0 + -3 * x19:0:0 >= 0 && x19:0:0 <= x18:0:0 15.13/4.63 f10(x, x1) -> f10(x + 1, x1) :|: x - x1 > 2 && 3 + 3 * x + -3 * x1 >= 0 && x1 > x 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (14) RankingReductionPairProof (EQUIVALENT) 15.13/4.63 Interpretation: 15.13/4.63 [ f10 ] = f10_1 + -1*f10_2 15.13/4.63 15.13/4.63 The following rules are decreasing: 15.13/4.63 f10(x18:0:0, x19:0:0) -> f10(x18:0:0, x19:0:0 + 1) :|: x18:0:0 - x19:0:0 > 2 && 3 + 3 * x18:0:0 + -3 * x19:0:0 >= 0 && x19:0:0 <= x18:0:0 15.13/4.63 f10(x, x1) -> f10(x + 1, x1) :|: x - x1 > 2 && 3 + 3 * x + -3 * x1 >= 0 && x1 > x 15.13/4.63 15.13/4.63 The following rules are bounded: 15.13/4.63 f10(x18:0:0, x19:0:0) -> f10(x18:0:0, x19:0:0 + 1) :|: x18:0:0 - x19:0:0 > 2 && 3 + 3 * x18:0:0 + -3 * x19:0:0 >= 0 && x19:0:0 <= x18:0:0 15.13/4.63 f10(x, x1) -> f10(x + 1, x1) :|: x - x1 > 2 && 3 + 3 * x + -3 * x1 >= 0 && x1 > x 15.13/4.63 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (15) 15.13/4.63 YES 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (16) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x18:0, x19:0) -> f7(x18:0, x19:0) :|: x18:0 - x19:0 > 2 && 3 + 3 * x18:0 + -3 * x19:0 < 0 15.13/4.63 f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 && 3 + 3 * x + -3 * x1 < 0 15.13/4.63 f7(x10:0, x11:0) -> f10(x10:0, x11:0 + 1) :|: x11:0 <= x10:0 && 3 + 3 * x10:0 + -3 * x11:0 < 0 15.13/4.63 f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 < 0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (17) TerminationGraphProcessor (EQUIVALENT) 15.13/4.63 Constructed the termination graph and obtained one non-trivial SCC. 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (18) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x, x1) -> f7(x, x1) :|: x1 - x > 2 && 3 + 3 * x + -3 * x1 < 0 15.13/4.63 f7(x8:0, x9:0) -> f10(x8:0 + 1, x9:0) :|: x9:0 > x8:0 && 3 + 3 * x8:0 + -3 * x9:0 < 0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (19) IntTRSCompressionProof (EQUIVALENT) 15.13/4.63 Compressed rules. 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (20) 15.13/4.63 Obligation: 15.13/4.63 Rules: 15.13/4.63 f10(x:0, x1:0) -> f10(x:0 + 1, x1:0) :|: x1:0 - x:0 > 2 && 3 + 3 * x:0 + -3 * x1:0 < 0 && x:0 < x1:0 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (21) RankingReductionPairProof (EQUIVALENT) 15.13/4.63 Interpretation: 15.13/4.63 [ f10 ] = f10_2 + -1*f10_1 15.13/4.63 15.13/4.63 The following rules are decreasing: 15.13/4.63 f10(x:0, x1:0) -> f10(x:0 + 1, x1:0) :|: x1:0 - x:0 > 2 && 3 + 3 * x:0 + -3 * x1:0 < 0 && x:0 < x1:0 15.13/4.63 15.13/4.63 The following rules are bounded: 15.13/4.63 f10(x:0, x1:0) -> f10(x:0 + 1, x1:0) :|: x1:0 - x:0 > 2 && 3 + 3 * x:0 + -3 * x1:0 < 0 && x:0 < x1:0 15.13/4.63 15.13/4.63 15.13/4.63 ---------------------------------------- 15.13/4.63 15.13/4.63 (22) 15.13/4.63 YES 15.13/4.67 EOF