6.00/2.32 YES 6.00/2.33 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 6.00/2.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.00/2.33 6.00/2.33 6.00/2.33 Termination of the given C Problem could be proven: 6.00/2.33 6.00/2.33 (0) C Problem 6.00/2.33 (1) CToIRSProof [EQUIVALENT, 0 ms] 6.00/2.33 (2) IntTRS 6.00/2.33 (3) TerminationGraphProcessor [SOUND, 78 ms] 6.00/2.33 (4) IntTRS 6.00/2.33 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.00/2.33 (6) IntTRS 6.00/2.33 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 6.00/2.33 (8) IntTRS 6.00/2.33 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 6.00/2.33 (10) YES 6.00/2.33 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (0) 6.00/2.33 Obligation: 6.00/2.33 c file /export/starexec/sandbox/benchmark/theBenchmark.c 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (1) CToIRSProof (EQUIVALENT) 6.00/2.33 Parsed C Integer Program as IRS. 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (2) 6.00/2.33 Obligation: 6.00/2.33 Rules: 6.00/2.33 f1(c, x, y, z) -> f2(c, x_1, y, z) :|: TRUE 6.00/2.33 f2(x1, x2, x3, x4) -> f3(x1, x2, x5, x4) :|: TRUE 6.00/2.33 f3(x6, x7, x8, x9) -> f4(x6, x7, x8, x10) :|: TRUE 6.00/2.33 f4(x11, x12, x13, x14) -> f5(0, x12, x13, x14) :|: TRUE 6.00/2.33 f7(x15, x16, x17, x18) -> f8(x15, arith, x17, x18) :|: TRUE && arith = x16 - 1 6.00/2.33 f8(x51, x52, x53, x54) -> f9(x51, x52, x55, x54) :|: TRUE && x55 = x53 - 1 6.00/2.33 f9(x56, x57, x58, x59) -> f10(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1 6.00/2.33 f6(x27, x28, x29, x30) -> f7(x27, x28, x29, x30) :|: x29 > x30 6.00/2.33 f10(x31, x32, x33, x34) -> f6(x31, x32, x33, x34) :|: TRUE 6.00/2.33 f6(x35, x36, x37, x38) -> f11(x35, x36, x37, x38) :|: x37 <= x38 6.00/2.33 f5(x39, x40, x41, x42) -> f6(x39, x40, x41, x42) :|: x40 = x41 && x40 > x42 6.00/2.33 f11(x43, x44, x45, x46) -> f5(x43, x44, x45, x46) :|: TRUE 6.00/2.33 f5(x47, x48, x49, x50) -> f12(x47, x48, x49, x50) :|: x48 <= x50 6.00/2.33 f5(x61, x62, x63, x64) -> f12(x61, x62, x63, x64) :|: x62 < x63 6.00/2.33 f5(x65, x66, x67, x68) -> f12(x65, x66, x67, x68) :|: x66 > x67 6.00/2.33 Start term: f1(c, x, y, z) 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (3) TerminationGraphProcessor (SOUND) 6.00/2.33 Constructed the termination graph and obtained one non-trivial SCC. 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (4) 6.00/2.33 Obligation: 6.00/2.33 Rules: 6.00/2.33 f5(x39, x40, x41, x42) -> f6(x39, x40, x41, x42) :|: x40 = x41 && x40 > x42 6.00/2.33 f11(x43, x44, x45, x46) -> f5(x43, x44, x45, x46) :|: TRUE 6.00/2.33 f6(x35, x36, x37, x38) -> f11(x35, x36, x37, x38) :|: x37 <= x38 6.00/2.33 f10(x31, x32, x33, x34) -> f6(x31, x32, x33, x34) :|: TRUE 6.00/2.33 f9(x56, x57, x58, x59) -> f10(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1 6.00/2.33 f8(x51, x52, x53, x54) -> f9(x51, x52, x55, x54) :|: TRUE && x55 = x53 - 1 6.00/2.33 f7(x15, x16, x17, x18) -> f8(x15, arith, x17, x18) :|: TRUE && arith = x16 - 1 6.00/2.33 f6(x27, x28, x29, x30) -> f7(x27, x28, x29, x30) :|: x29 > x30 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (5) IntTRSCompressionProof (EQUIVALENT) 6.00/2.33 Compressed rules. 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (6) 6.00/2.33 Obligation: 6.00/2.33 Rules: 6.00/2.33 f6(x27:0, x28:0, x29:0, x30:0) -> f6(x27:0 + 1, x28:0 - 1, x29:0 - 1, x30:0) :|: x30:0 < x29:0 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 6.00/2.33 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 6.00/2.33 6.00/2.33 f6(x1, x2, x3, x4) -> f6(x3, x4) 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (8) 6.00/2.33 Obligation: 6.00/2.33 Rules: 6.00/2.33 f6(x29:0, x30:0) -> f6(x29:0 - 1, x30:0) :|: x30:0 < x29:0 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (9) PolynomialOrderProcessor (EQUIVALENT) 6.00/2.33 Found the following polynomial interpretation: 6.00/2.33 [f6(x, x1)] = x - x1 6.00/2.33 6.00/2.33 The following rules are decreasing: 6.00/2.33 f6(x29:0, x30:0) -> f6(x29:0 - 1, x30:0) :|: x30:0 < x29:0 6.00/2.33 The following rules are bounded: 6.00/2.33 f6(x29:0, x30:0) -> f6(x29:0 - 1, x30:0) :|: x30:0 < x29:0 6.00/2.33 6.00/2.33 ---------------------------------------- 6.00/2.33 6.00/2.33 (10) 6.00/2.33 YES 6.22/2.38 EOF