7.11/2.67 YES 7.11/2.68 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.11/2.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.11/2.68 7.11/2.68 7.11/2.68 Termination of the given C Problem could be proven: 7.11/2.68 7.11/2.68 (0) C Problem 7.11/2.68 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.11/2.68 (2) IntTRS 7.11/2.68 (3) TerminationGraphProcessor [SOUND, 79 ms] 7.11/2.68 (4) IntTRS 7.11/2.68 (5) IntTRSCompressionProof [EQUIVALENT, 17 ms] 7.11/2.68 (6) IntTRS 7.11/2.68 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.11/2.68 (8) IntTRS 7.11/2.68 (9) PolynomialOrderProcessor [EQUIVALENT, 36 ms] 7.11/2.68 (10) IntTRS 7.11/2.68 (11) TerminationGraphProcessor [EQUIVALENT, 6 ms] 7.11/2.68 (12) YES 7.11/2.68 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (0) 7.11/2.68 Obligation: 7.11/2.68 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (1) CToIRSProof (EQUIVALENT) 7.11/2.68 Parsed C Integer Program as IRS. 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (2) 7.11/2.68 Obligation: 7.11/2.68 Rules: 7.11/2.68 f1(flag, c, x, y) -> f2(1, c, x, y) :|: TRUE 7.11/2.68 f2(x1, x2, x3, x4) -> f3(x1, 0, x3, x4) :|: TRUE 7.11/2.68 f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE 7.11/2.68 f4(x10, x11, x12, x13) -> f5(x10, x11, x12, x14) :|: TRUE 7.11/2.68 f7(x15, x16, x17, x18) -> f10(0, x16, x17, x18) :|: TRUE 7.11/2.68 f6(x19, x20, x21, x22) -> f7(x19, x20, x21, x22) :|: x21 >= x22 7.11/2.68 f6(x23, x24, x25, x26) -> f8(x23, x24, x25, x26) :|: x25 < x26 7.11/2.68 f10(x27, x28, x29, x30) -> f9(x27, x28, x29, x30) :|: TRUE 7.11/2.68 f8(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE 7.11/2.68 f9(x35, x36, x37, x38) -> f11(x35, x36, arith, x38) :|: TRUE && arith = x37 + 1 7.11/2.68 f11(x55, x56, x57, x58) -> f12(x55, x59, x57, x58) :|: TRUE && x59 = x56 + 1 7.11/2.68 f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x43 < 0 7.11/2.68 f5(x60, x61, x62, x63) -> f6(x60, x61, x62, x63) :|: x60 > 0 7.11/2.68 f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE 7.11/2.68 f5(x51, x52, x53, x54) -> f13(x51, x52, x53, x54) :|: x51 = 0 7.11/2.68 Start term: f1(flag, c, x, y) 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (3) TerminationGraphProcessor (SOUND) 7.11/2.68 Constructed the termination graph and obtained one non-trivial SCC. 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (4) 7.11/2.68 Obligation: 7.11/2.68 Rules: 7.11/2.68 f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x43 < 0 7.11/2.68 f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE 7.11/2.68 f11(x55, x56, x57, x58) -> f12(x55, x59, x57, x58) :|: TRUE && x59 = x56 + 1 7.11/2.68 f9(x35, x36, x37, x38) -> f11(x35, x36, arith, x38) :|: TRUE && arith = x37 + 1 7.11/2.68 f10(x27, x28, x29, x30) -> f9(x27, x28, x29, x30) :|: TRUE 7.11/2.68 f7(x15, x16, x17, x18) -> f10(0, x16, x17, x18) :|: TRUE 7.11/2.68 f6(x19, x20, x21, x22) -> f7(x19, x20, x21, x22) :|: x21 >= x22 7.11/2.68 f5(x60, x61, x62, x63) -> f6(x60, x61, x62, x63) :|: x60 > 0 7.11/2.68 f8(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE 7.11/2.68 f6(x23, x24, x25, x26) -> f8(x23, x24, x25, x26) :|: x25 < x26 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (5) IntTRSCompressionProof (EQUIVALENT) 7.11/2.68 Compressed rules. 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (6) 7.11/2.68 Obligation: 7.11/2.68 Rules: 7.11/2.68 f9(x35:0, x36:0, x37:0, x38:0) -> f6(x35:0, x36:0 + 1, x37:0 + 1, x38:0) :|: x35:0 > 0 7.11/2.68 f9(x, x1, x2, x3) -> f6(x, x1 + 1, x2 + 1, x3) :|: x < 0 7.11/2.68 f6(x23:0, x24:0, x25:0, x26:0) -> f9(x23:0, x24:0, x25:0, x26:0) :|: x26:0 > x25:0 7.11/2.68 f6(x19:0, x20:0, x21:0, x22:0) -> f9(0, x20:0, x21:0, x22:0) :|: x22:0 <= x21:0 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.11/2.68 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.11/2.68 7.11/2.68 f9(x1, x2, x3, x4) -> f9(x1, x3, x4) 7.11/2.68 f6(x1, x2, x3, x4) -> f6(x1, x3, x4) 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (8) 7.11/2.68 Obligation: 7.11/2.68 Rules: 7.11/2.68 f9(x35:0, x37:0, x38:0) -> f6(x35:0, x37:0 + 1, x38:0) :|: x35:0 > 0 7.11/2.68 f9(x, x2, x3) -> f6(x, x2 + 1, x3) :|: x < 0 7.11/2.68 f6(x23:0, x25:0, x26:0) -> f9(x23:0, x25:0, x26:0) :|: x26:0 > x25:0 7.11/2.68 f6(x19:0, x21:0, x22:0) -> f9(0, x21:0, x22:0) :|: x22:0 <= x21:0 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (9) PolynomialOrderProcessor (EQUIVALENT) 7.11/2.68 Found the following polynomial interpretation: 7.11/2.68 [f9(x, x1, x2)] = -2 - x1 + x2 7.11/2.68 [f6(x3, x4, x5)] = -1 - x4 + x5 7.11/2.68 7.11/2.68 The following rules are decreasing: 7.11/2.68 f6(x23:0, x25:0, x26:0) -> f9(x23:0, x25:0, x26:0) :|: x26:0 > x25:0 7.11/2.68 f6(x19:0, x21:0, x22:0) -> f9(0, x21:0, x22:0) :|: x22:0 <= x21:0 7.11/2.68 The following rules are bounded: 7.11/2.68 f6(x23:0, x25:0, x26:0) -> f9(x23:0, x25:0, x26:0) :|: x26:0 > x25:0 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (10) 7.11/2.68 Obligation: 7.11/2.68 Rules: 7.11/2.68 f9(x35:0, x37:0, x38:0) -> f6(x35:0, x37:0 + 1, x38:0) :|: x35:0 > 0 7.11/2.68 f9(x, x2, x3) -> f6(x, x2 + 1, x3) :|: x < 0 7.11/2.68 f6(x19:0, x21:0, x22:0) -> f9(0, x21:0, x22:0) :|: x22:0 <= x21:0 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (11) TerminationGraphProcessor (EQUIVALENT) 7.11/2.68 Constructed the termination graph and obtained no non-trivial SCC(s). 7.11/2.68 7.11/2.68 ---------------------------------------- 7.11/2.68 7.11/2.68 (12) 7.11/2.68 YES 7.27/2.71 EOF