6.10/2.43 YES 6.10/2.44 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 6.10/2.44 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.10/2.44 6.10/2.44 6.10/2.44 Termination of the given C Problem could be proven: 6.10/2.44 6.10/2.44 (0) C Problem 6.10/2.44 (1) CToIRSProof [EQUIVALENT, 0 ms] 6.10/2.44 (2) IntTRS 6.10/2.44 (3) TerminationGraphProcessor [SOUND, 60 ms] 6.10/2.44 (4) IntTRS 6.10/2.44 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.10/2.44 (6) IntTRS 6.10/2.44 (7) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 6.10/2.44 (8) IntTRS 6.10/2.44 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 6.10/2.44 (10) YES 6.10/2.44 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (0) 6.10/2.44 Obligation: 6.10/2.44 c file /export/starexec/sandbox/benchmark/theBenchmark.c 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (1) CToIRSProof (EQUIVALENT) 6.10/2.44 Parsed C Integer Program as IRS. 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (2) 6.10/2.44 Obligation: 6.10/2.44 Rules: 6.10/2.44 f1(x, y) -> f2(x_1, y) :|: TRUE 6.10/2.44 f2(x1, x2) -> f3(x1, x3) :|: TRUE 6.10/2.44 f4(x4, x5) -> f5(x4, 1) :|: TRUE 6.10/2.44 f6(x6, x7) -> f7(x6, arith) :|: TRUE && arith = x7 + 1 6.10/2.44 f5(x8, x9) -> f6(x8, x9) :|: x9 < x8 6.10/2.44 f7(x10, x11) -> f5(x10, x11) :|: TRUE 6.10/2.44 f5(x12, x13) -> f8(x12, x13) :|: x13 >= x12 6.10/2.44 f8(x22, x23) -> f9(x24, x23) :|: TRUE && x24 = x22 - 1 6.10/2.44 f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0 6.10/2.44 f9(x18, x19) -> f3(x18, x19) :|: TRUE 6.10/2.44 f3(x20, x21) -> f10(x20, x21) :|: x20 < 0 6.10/2.44 Start term: f1(x, y) 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (3) TerminationGraphProcessor (SOUND) 6.10/2.44 Constructed the termination graph and obtained one non-trivial SCC. 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (4) 6.10/2.44 Obligation: 6.10/2.44 Rules: 6.10/2.44 f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0 6.10/2.44 f9(x18, x19) -> f3(x18, x19) :|: TRUE 6.10/2.44 f8(x22, x23) -> f9(x24, x23) :|: TRUE && x24 = x22 - 1 6.10/2.44 f5(x12, x13) -> f8(x12, x13) :|: x13 >= x12 6.10/2.44 f4(x4, x5) -> f5(x4, 1) :|: TRUE 6.10/2.44 f7(x10, x11) -> f5(x10, x11) :|: TRUE 6.10/2.44 f6(x6, x7) -> f7(x6, arith) :|: TRUE && arith = x7 + 1 6.10/2.44 f5(x8, x9) -> f6(x8, x9) :|: x9 < x8 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (5) IntTRSCompressionProof (EQUIVALENT) 6.10/2.44 Compressed rules. 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (6) 6.10/2.44 Obligation: 6.10/2.44 Rules: 6.10/2.44 f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0 6.10/2.44 f5(x12:0, x13:0) -> f5(x12:0 - 1, 1) :|: x13:0 >= x12:0 && x12:0 > 0 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (7) PolynomialOrderProcessor (EQUIVALENT) 6.10/2.44 Found the following polynomial interpretation: 6.10/2.44 [f5(x, x1)] = -1 + x 6.10/2.44 6.10/2.44 The following rules are decreasing: 6.10/2.44 f5(x12:0, x13:0) -> f5(x12:0 - 1, 1) :|: x13:0 >= x12:0 && x12:0 > 0 6.10/2.44 The following rules are bounded: 6.10/2.44 f5(x12:0, x13:0) -> f5(x12:0 - 1, 1) :|: x13:0 >= x12:0 && x12:0 > 0 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (8) 6.10/2.44 Obligation: 6.10/2.44 Rules: 6.10/2.44 f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (9) PolynomialOrderProcessor (EQUIVALENT) 6.10/2.44 Found the following polynomial interpretation: 6.10/2.44 [f5(x, x1)] = x - x1 6.10/2.44 6.10/2.44 The following rules are decreasing: 6.10/2.44 f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0 6.10/2.44 The following rules are bounded: 6.10/2.44 f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0 6.10/2.44 6.10/2.44 ---------------------------------------- 6.10/2.44 6.10/2.44 (10) 6.10/2.44 YES 6.10/2.47 EOF