4.48/1.90 YES 4.48/1.91 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 4.48/1.91 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.48/1.91 4.48/1.91 4.48/1.91 Termination of the given C Problem could be proven: 4.48/1.91 4.48/1.91 (0) C Problem 4.48/1.91 (1) CToIRSProof [EQUIVALENT, 0 ms] 4.48/1.91 (2) IntTRS 4.48/1.91 (3) TerminationGraphProcessor [SOUND, 48 ms] 4.48/1.91 (4) IntTRS 4.48/1.91 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 4.48/1.91 (6) IntTRS 4.48/1.91 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 4.48/1.91 (8) IntTRS 4.48/1.91 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 4.48/1.91 (10) YES 4.48/1.91 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (0) 4.48/1.91 Obligation: 4.48/1.91 c file /export/starexec/sandbox/benchmark/theBenchmark.c 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (1) CToIRSProof (EQUIVALENT) 4.48/1.91 Parsed C Integer Program as IRS. 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (2) 4.48/1.91 Obligation: 4.48/1.91 Rules: 4.48/1.91 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 4.48/1.91 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 4.48/1.91 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 4.48/1.91 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 - 1 4.48/1.91 f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1 4.48/1.91 f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > x16 4.48/1.91 f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE 4.48/1.91 f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 <= x22 4.48/1.91 Start term: f1(c, x, y) 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (3) TerminationGraphProcessor (SOUND) 4.48/1.91 Constructed the termination graph and obtained one non-trivial SCC. 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (4) 4.48/1.91 Obligation: 4.48/1.91 Rules: 4.48/1.91 f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > x16 4.48/1.91 f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE 4.48/1.91 f6(x23, x24, x25) -> f7(x26, x24, x25) :|: TRUE && x26 = x23 + 1 4.48/1.91 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 - 1 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (5) IntTRSCompressionProof (EQUIVALENT) 4.48/1.91 Compressed rules. 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (6) 4.48/1.91 Obligation: 4.48/1.91 Rules: 4.48/1.91 f6(x23:0, x24:0, x25:0) -> f6(x23:0 + 1, x24:0 - 1, x25:0) :|: x25:0 < x24:0 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 4.48/1.91 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 4.48/1.91 4.48/1.91 f6(x1, x2, x3) -> f6(x2, x3) 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (8) 4.48/1.91 Obligation: 4.48/1.91 Rules: 4.48/1.91 f6(x24:0, x25:0) -> f6(x24:0 - 1, x25:0) :|: x25:0 < x24:0 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (9) PolynomialOrderProcessor (EQUIVALENT) 4.48/1.91 Found the following polynomial interpretation: 4.48/1.91 [f6(x, x1)] = x - x1 4.48/1.91 4.48/1.91 The following rules are decreasing: 4.48/1.91 f6(x24:0, x25:0) -> f6(x24:0 - 1, x25:0) :|: x25:0 < x24:0 4.48/1.91 The following rules are bounded: 4.48/1.91 f6(x24:0, x25:0) -> f6(x24:0 - 1, x25:0) :|: x25:0 < x24:0 4.48/1.91 4.48/1.91 ---------------------------------------- 4.48/1.91 4.48/1.91 (10) 4.48/1.91 YES 4.61/1.94 EOF