5.47/2.30 YES 5.47/2.32 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.47/2.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.47/2.32 5.47/2.32 5.47/2.32 Termination of the given C Problem could be proven: 5.47/2.32 5.47/2.32 (0) C Problem 5.47/2.32 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.47/2.32 (2) IntTRS 5.47/2.32 (3) TerminationGraphProcessor [SOUND, 34 ms] 5.47/2.32 (4) IntTRS 5.47/2.32 (5) IntTRSCompressionProof [EQUIVALENT, 24 ms] 5.47/2.32 (6) IntTRS 5.47/2.32 (7) TerminationGraphProcessor [EQUIVALENT, 3 ms] 5.47/2.32 (8) IntTRS 5.47/2.32 (9) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.47/2.32 (10) IntTRS 5.47/2.32 (11) PolynomialOrderProcessor [EQUIVALENT, 4 ms] 5.47/2.32 (12) YES 5.47/2.32 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (0) 5.47/2.32 Obligation: 5.47/2.32 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (1) CToIRSProof (EQUIVALENT) 5.47/2.32 Parsed C Integer Program as IRS. 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (2) 5.47/2.32 Obligation: 5.47/2.32 Rules: 5.47/2.32 f1(x, y) -> f2(x_1, y) :|: TRUE 5.47/2.32 f2(x1, x2) -> f3(x1, x3) :|: TRUE 5.47/2.32 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 5.47/2.32 f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = 0 - x15 - 1 5.47/2.32 f3(x8, x9) -> f4(x8, x9) :|: x8 > 0 5.47/2.32 f6(x10, x11) -> f3(x10, x11) :|: TRUE 5.47/2.32 f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0 5.47/2.32 Start term: f1(x, y) 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (3) TerminationGraphProcessor (SOUND) 5.47/2.32 Constructed the termination graph and obtained one non-trivial SCC. 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (4) 5.47/2.32 Obligation: 5.47/2.32 Rules: 5.47/2.32 f3(x8, x9) -> f4(x8, x9) :|: x8 > 0 5.47/2.32 f6(x10, x11) -> f3(x10, x11) :|: TRUE 5.47/2.32 f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = 0 - x15 - 1 5.47/2.32 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (5) IntTRSCompressionProof (EQUIVALENT) 5.47/2.32 Compressed rules. 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (6) 5.47/2.32 Obligation: 5.47/2.32 Rules: 5.47/2.32 f5(x14:0, x15:0) -> f5(x14:0 + (0 - x15:0 - 1), 0 - x15:0 - 1) :|: x14:0 > 0 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (7) TerminationGraphProcessor (EQUIVALENT) 5.47/2.32 Constructed the termination graph and obtained one non-trivial SCC. 5.47/2.32 5.47/2.32 f5(x14:0, x15:0) -> f5(x14:0 + (0 - x15:0 - 1), 0 - x15:0 - 1) :|: x14:0 > 0 5.47/2.32 has been transformed into 5.47/2.32 f5(x14:0, x15:0) -> f5(x14:0 + (0 - x15:0 - 1), 0 - x15:0 - 1) :|: x14:0 > 0 && x4 > 0. 5.47/2.32 5.47/2.32 5.47/2.32 f5(x14:0, x15:0) -> f5(x14:0 + (0 - x15:0 - 1), 0 - x15:0 - 1) :|: x14:0 > 0 && x4 > 0 and 5.47/2.32 f5(x14:0, x15:0) -> f5(x14:0 + (0 - x15:0 - 1), 0 - x15:0 - 1) :|: x14:0 > 0 && x4 > 0 5.47/2.32 have been merged into the new rule 5.47/2.32 f5(x12, x13) -> f5(x12 + (0 - x13 - 1) + (0 - (0 - x13 - 1) - 1), 0 - (0 - x13 - 1) - 1) :|: x12 > 0 && x14 > 0 && (x12 + (0 - x13 - 1) > 0 && x15 > 0) 5.47/2.32 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (8) 5.47/2.32 Obligation: 5.47/2.32 Rules: 5.47/2.32 f5(x16, x17) -> f5(x16 + -1, x17) :|: TRUE && x16 >= 1 && x18 >= 1 && x16 + -1 * x17 >= 2 && x19 >= 1 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (9) IntTRSCompressionProof (EQUIVALENT) 5.47/2.32 Compressed rules. 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (10) 5.47/2.32 Obligation: 5.47/2.32 Rules: 5.47/2.32 f5(x16:0, x17:0) -> f5(x16:0 - 1, x17:0) :|: x16:0 + -1 * x17:0 >= 2 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (11) PolynomialOrderProcessor (EQUIVALENT) 5.47/2.32 Found the following polynomial interpretation: 5.47/2.32 [f5(x, x1)] = x 5.47/2.32 5.47/2.32 The following rules are decreasing: 5.47/2.32 f5(x16:0, x17:0) -> f5(x16:0 - 1, x17:0) :|: x16:0 + -1 * x17:0 >= 2 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0 5.47/2.32 The following rules are bounded: 5.47/2.32 f5(x16:0, x17:0) -> f5(x16:0 - 1, x17:0) :|: x16:0 + -1 * x17:0 >= 2 && x19:0 > 0 && x16:0 > 0 && x18:0 > 0 5.47/2.32 5.47/2.32 ---------------------------------------- 5.47/2.32 5.47/2.32 (12) 5.47/2.32 YES 6.09/2.38 EOF