7.23/2.65 YES 7.23/2.66 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.23/2.66 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.23/2.66 7.23/2.66 7.23/2.66 Termination of the given C Problem could be proven: 7.23/2.66 7.23/2.66 (0) C Problem 7.23/2.66 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.23/2.66 (2) IntTRS 7.23/2.66 (3) TerminationGraphProcessor [SOUND, 70 ms] 7.23/2.66 (4) IntTRS 7.23/2.66 (5) IntTRSCompressionProof [EQUIVALENT, 8 ms] 7.23/2.66 (6) IntTRS 7.23/2.66 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.23/2.66 (8) IntTRS 7.23/2.66 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 7.23/2.66 (10) AND 7.23/2.66 (11) IntTRS 7.23/2.66 (12) TerminationGraphProcessor [EQUIVALENT, 9 ms] 7.23/2.66 (13) IntTRS 7.23/2.66 (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.23/2.66 (15) IntTRS 7.23/2.66 (16) PolynomialOrderProcessor [EQUIVALENT, 3 ms] 7.23/2.66 (17) YES 7.23/2.66 (18) IntTRS 7.23/2.66 (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.23/2.66 (20) IntTRS 7.23/2.66 (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 7.23/2.66 (22) YES 7.23/2.66 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (0) 7.23/2.66 Obligation: 7.23/2.66 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (1) CToIRSProof (EQUIVALENT) 7.23/2.66 Parsed C Integer Program as IRS. 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (2) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f1(x, y, tmp, xtmp) -> f2(x_1, y, tmp, xtmp) :|: TRUE 7.23/2.66 f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE 7.23/2.66 f4(x6, x7, x8, x9) -> f5(x6, x7, x7, x9) :|: TRUE 7.23/2.66 f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE 7.23/2.66 f7(x14, x15, x16, x17) -> f8(x14, x15, x16, arith) :|: TRUE && arith = x17 - x15 7.23/2.66 f6(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x21 >= x19 && x19 > 0 7.23/2.66 f8(x22, x23, x24, x25) -> f6(x22, x23, x24, x25) :|: TRUE 7.23/2.66 f6(x26, x27, x28, x29) -> f9(x26, x27, x28, x29) :|: x29 < x27 7.23/2.66 f6(x50, x51, x52, x53) -> f9(x50, x51, x52, x53) :|: x51 <= 0 7.23/2.66 f9(x30, x31, x32, x33) -> f10(x30, x33, x32, x33) :|: TRUE 7.23/2.66 f10(x34, x35, x36, x37) -> f11(x36, x35, x36, x37) :|: TRUE 7.23/2.66 f3(x38, x39, x40, x41) -> f4(x38, x39, x40, x41) :|: x39 > 0 && x38 > 0 7.23/2.66 f11(x42, x43, x44, x45) -> f3(x42, x43, x44, x45) :|: TRUE 7.23/2.66 f3(x46, x47, x48, x49) -> f12(x46, x47, x48, x49) :|: x47 <= 0 7.23/2.66 f3(x54, x55, x56, x57) -> f12(x54, x55, x56, x57) :|: x54 <= 0 7.23/2.66 Start term: f1(x, y, tmp, xtmp) 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (3) TerminationGraphProcessor (SOUND) 7.23/2.66 Constructed the termination graph and obtained one non-trivial SCC. 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (4) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f3(x38, x39, x40, x41) -> f4(x38, x39, x40, x41) :|: x39 > 0 && x38 > 0 7.23/2.66 f11(x42, x43, x44, x45) -> f3(x42, x43, x44, x45) :|: TRUE 7.23/2.66 f10(x34, x35, x36, x37) -> f11(x36, x35, x36, x37) :|: TRUE 7.23/2.66 f9(x30, x31, x32, x33) -> f10(x30, x33, x32, x33) :|: TRUE 7.23/2.66 f6(x26, x27, x28, x29) -> f9(x26, x27, x28, x29) :|: x29 < x27 7.23/2.66 f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE 7.23/2.66 f4(x6, x7, x8, x9) -> f5(x6, x7, x7, x9) :|: TRUE 7.23/2.66 f8(x22, x23, x24, x25) -> f6(x22, x23, x24, x25) :|: TRUE 7.23/2.66 f7(x14, x15, x16, x17) -> f8(x14, x15, x16, arith) :|: TRUE && arith = x17 - x15 7.23/2.66 f6(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x21 >= x19 && x19 > 0 7.23/2.66 f6(x50, x51, x52, x53) -> f9(x50, x51, x52, x53) :|: x51 <= 0 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (5) IntTRSCompressionProof (EQUIVALENT) 7.23/2.66 Compressed rules. 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (6) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f6(x18:0, x19:0, x20:0, x21:0) -> f6(x18:0, x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.66 f6(x26:0, x27:0, x28:0, x29:0) -> f6(x28:0, x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 7.23/2.66 f6(x50:0, x51:0, x52:0, x53:0) -> f6(x52:0, x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.23/2.66 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.23/2.66 7.23/2.66 f6(x1, x2, x3, x4) -> f6(x2, x3, x4) 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (8) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f6(x19:0, x20:0, x21:0) -> f6(x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.66 f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 7.23/2.66 f6(x51:0, x52:0, x53:0) -> f6(x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (9) PolynomialOrderProcessor (EQUIVALENT) 7.23/2.66 Found the following polynomial interpretation: 7.23/2.66 [f6(x, x1, x2)] = -2 + x1 + x2 7.23/2.66 7.23/2.66 The following rules are decreasing: 7.23/2.66 f6(x19:0, x20:0, x21:0) -> f6(x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.66 The following rules are bounded: 7.23/2.66 f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 7.23/2.66 f6(x51:0, x52:0, x53:0) -> f6(x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (10) 7.23/2.66 Complex Obligation (AND) 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (11) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 7.23/2.66 f6(x51:0, x52:0, x53:0) -> f6(x53:0, x53:0, x52:0) :|: x53:0 > 0 && x52:0 > 0 && x51:0 < 1 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (12) TerminationGraphProcessor (EQUIVALENT) 7.23/2.66 Constructed the termination graph and obtained one non-trivial SCC. 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (13) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f6(x27:0, x28:0, x29:0) -> f6(x29:0, x29:0, x28:0) :|: x29:0 > 0 && x28:0 > 0 && x29:0 < x27:0 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (14) IntTRSCompressionProof (EQUIVALENT) 7.23/2.66 Compressed rules. 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (15) 7.23/2.66 Obligation: 7.23/2.66 Rules: 7.23/2.66 f6(x27:0:0, x28:0:0, x29:0:0) -> f6(x29:0:0, x29:0:0, x28:0:0) :|: x29:0:0 > 0 && x28:0:0 > 0 && x29:0:0 < x27:0:0 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (16) PolynomialOrderProcessor (EQUIVALENT) 7.23/2.66 Found the following polynomial interpretation: 7.23/2.66 [f6(x, x1, x2)] = x 7.23/2.66 7.23/2.66 The following rules are decreasing: 7.23/2.66 f6(x27:0:0, x28:0:0, x29:0:0) -> f6(x29:0:0, x29:0:0, x28:0:0) :|: x29:0:0 > 0 && x28:0:0 > 0 && x29:0:0 < x27:0:0 7.23/2.66 The following rules are bounded: 7.23/2.66 f6(x27:0:0, x28:0:0, x29:0:0) -> f6(x29:0:0, x29:0:0, x28:0:0) :|: x29:0:0 > 0 && x28:0:0 > 0 && x29:0:0 < x27:0:0 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.66 7.23/2.66 (17) 7.23/2.66 YES 7.23/2.66 7.23/2.66 ---------------------------------------- 7.23/2.67 7.23/2.67 (18) 7.23/2.67 Obligation: 7.23/2.67 Rules: 7.23/2.67 f6(x19:0, x20:0, x21:0) -> f6(x19:0, x20:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.67 7.23/2.67 ---------------------------------------- 7.23/2.67 7.23/2.67 (19) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.23/2.67 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.23/2.67 7.23/2.67 f6(x1, x2, x3) -> f6(x1, x3) 7.23/2.67 7.23/2.67 ---------------------------------------- 7.23/2.67 7.23/2.67 (20) 7.23/2.67 Obligation: 7.23/2.67 Rules: 7.23/2.67 f6(x19:0, x21:0) -> f6(x19:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.67 7.23/2.67 ---------------------------------------- 7.23/2.67 7.23/2.67 (21) PolynomialOrderProcessor (EQUIVALENT) 7.23/2.67 Found the following polynomial interpretation: 7.23/2.67 [f6(x, x1)] = x1 7.23/2.67 7.23/2.67 The following rules are decreasing: 7.23/2.67 f6(x19:0, x21:0) -> f6(x19:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.67 The following rules are bounded: 7.23/2.67 f6(x19:0, x21:0) -> f6(x19:0, x21:0 - x19:0) :|: x21:0 >= x19:0 && x19:0 > 0 7.23/2.67 7.23/2.67 ---------------------------------------- 7.23/2.67 7.23/2.67 (22) 7.23/2.67 YES 7.57/2.72 EOF