5.69/2.37 YES 5.69/2.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.69/2.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.69/2.37 5.69/2.37 5.69/2.37 Termination of the given C Problem could be proven: 5.69/2.37 5.69/2.37 (0) C Problem 5.69/2.37 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.69/2.37 (2) IntTRS 5.69/2.37 (3) TerminationGraphProcessor [SOUND, 66 ms] 5.69/2.37 (4) IntTRS 5.69/2.37 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.69/2.37 (6) IntTRS 5.69/2.37 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.69/2.37 (8) IntTRS 5.69/2.37 (9) PolynomialOrderProcessor [EQUIVALENT, 15 ms] 5.69/2.37 (10) IntTRS 5.69/2.37 (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 5.69/2.37 (12) YES 5.69/2.37 5.69/2.37 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (0) 5.69/2.37 Obligation: 5.69/2.37 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (1) CToIRSProof (EQUIVALENT) 5.69/2.37 Parsed C Integer Program as IRS. 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (2) 5.69/2.37 Obligation: 5.69/2.37 Rules: 5.69/2.37 f1(c, i, j) -> f2(c, x_1, j) :|: TRUE 5.69/2.37 f2(x, x1, x2) -> f3(x, x1, x3) :|: TRUE 5.69/2.37 f3(x4, x5, x6) -> f4(0, x5, x6) :|: TRUE 5.69/2.37 f5(x7, x8, x9) -> f6(x7, x8, 0) :|: TRUE 5.69/2.37 f7(x10, x11, x12) -> f8(x10, x11, arith) :|: TRUE && arith = x12 + 1 5.69/2.37 f8(x37, x38, x39) -> f9(x40, x38, x39) :|: TRUE && x40 = x37 + 1 5.69/2.37 f6(x16, x17, x18) -> f7(x16, x17, x18) :|: x18 <= x17 - 1 5.69/2.37 f9(x19, x20, x21) -> f6(x19, x20, x21) :|: TRUE 5.69/2.37 f6(x22, x23, x24) -> f10(x22, x23, x24) :|: x24 > x23 - 1 5.69/2.37 f10(x41, x42, x43) -> f11(x41, x44, x43) :|: TRUE && x44 = x42 - 1 5.69/2.37 f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x29 >= 0 5.69/2.37 f11(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE 5.69/2.37 f4(x34, x35, x36) -> f12(x34, x35, x36) :|: x35 < 0 5.69/2.37 Start term: f1(c, i, j) 5.69/2.37 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (3) TerminationGraphProcessor (SOUND) 5.69/2.37 Constructed the termination graph and obtained one non-trivial SCC. 5.69/2.37 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (4) 5.69/2.37 Obligation: 5.69/2.37 Rules: 5.69/2.37 f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x29 >= 0 5.69/2.37 f11(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE 5.69/2.37 f10(x41, x42, x43) -> f11(x41, x44, x43) :|: TRUE && x44 = x42 - 1 5.69/2.37 f6(x22, x23, x24) -> f10(x22, x23, x24) :|: x24 > x23 - 1 5.69/2.37 f5(x7, x8, x9) -> f6(x7, x8, 0) :|: TRUE 5.69/2.37 f9(x19, x20, x21) -> f6(x19, x20, x21) :|: TRUE 5.69/2.37 f8(x37, x38, x39) -> f9(x40, x38, x39) :|: TRUE && x40 = x37 + 1 5.69/2.37 f7(x10, x11, x12) -> f8(x10, x11, arith) :|: TRUE && arith = x12 + 1 5.69/2.37 f6(x16, x17, x18) -> f7(x16, x17, x18) :|: x18 <= x17 - 1 5.69/2.37 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (5) IntTRSCompressionProof (EQUIVALENT) 5.69/2.37 Compressed rules. 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (6) 5.69/2.37 Obligation: 5.69/2.37 Rules: 5.69/2.37 f6(x16:0, x17:0, x18:0) -> f6(x16:0 + 1, x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1 5.69/2.37 f6(x22:0, x23:0, x24:0) -> f6(x22:0, x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0 5.69/2.37 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.69/2.37 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.69/2.37 5.69/2.37 f6(x1, x2, x3) -> f6(x2, x3) 5.69/2.37 5.69/2.37 ---------------------------------------- 5.69/2.37 5.69/2.37 (8) 5.69/2.37 Obligation: 5.69/2.37 Rules: 5.69/2.37 f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1 5.69/2.37 f6(x23:0, x24:0) -> f6(x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0 5.69/2.38 5.69/2.38 ---------------------------------------- 5.69/2.38 5.69/2.38 (9) PolynomialOrderProcessor (EQUIVALENT) 5.69/2.38 Found the following polynomial interpretation: 5.69/2.38 [f6(x, x1)] = x^2 5.69/2.38 5.69/2.38 The following rules are decreasing: 5.69/2.38 f6(x23:0, x24:0) -> f6(x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0 5.69/2.38 The following rules are bounded: 5.69/2.38 f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1 5.69/2.38 f6(x23:0, x24:0) -> f6(x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0 5.69/2.38 5.69/2.38 ---------------------------------------- 5.69/2.38 5.69/2.38 (10) 5.69/2.38 Obligation: 5.69/2.38 Rules: 5.69/2.38 f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1 5.69/2.38 5.69/2.38 ---------------------------------------- 5.69/2.38 5.69/2.38 (11) PolynomialOrderProcessor (EQUIVALENT) 5.69/2.38 Found the following polynomial interpretation: 5.69/2.38 [f6(x, x1)] = x - x1 5.69/2.38 5.69/2.38 The following rules are decreasing: 5.69/2.38 f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1 5.69/2.38 The following rules are bounded: 5.69/2.38 f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1 5.69/2.38 5.69/2.38 ---------------------------------------- 5.69/2.38 5.69/2.38 (12) 5.69/2.38 YES 6.18/2.70 EOF