7.49/2.75 YES 7.49/2.77 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.49/2.77 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.49/2.77 7.49/2.77 7.49/2.77 Termination of the given C Problem could be proven: 7.49/2.77 7.49/2.77 (0) C Problem 7.49/2.77 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.49/2.77 (2) IntTRS 7.49/2.77 (3) TerminationGraphProcessor [SOUND, 64 ms] 7.49/2.77 (4) IntTRS 7.49/2.77 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.49/2.77 (6) IntTRS 7.49/2.77 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.49/2.77 (8) IntTRS 7.49/2.77 (9) PolynomialOrderProcessor [EQUIVALENT, 28 ms] 7.49/2.77 (10) AND 7.49/2.77 (11) IntTRS 7.49/2.77 (12) PolynomialOrderProcessor [EQUIVALENT, 3 ms] 7.49/2.77 (13) YES 7.49/2.77 (14) IntTRS 7.49/2.77 (15) PolynomialOrderProcessor [EQUIVALENT, 2 ms] 7.49/2.77 (16) YES 7.49/2.77 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (0) 7.49/2.77 Obligation: 7.49/2.77 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (1) CToIRSProof (EQUIVALENT) 7.49/2.77 Parsed C Integer Program as IRS. 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (2) 7.49/2.77 Obligation: 7.49/2.77 Rules: 7.49/2.77 f1(c, x, y, z) -> f2(c, x_1, y, z) :|: TRUE 7.49/2.77 f2(x1, x2, x3, x4) -> f3(x1, x2, x5, x4) :|: TRUE 7.49/2.77 f3(x6, x7, x8, x9) -> f4(x6, x7, x8, x10) :|: TRUE 7.49/2.77 f4(x11, x12, x13, x14) -> f5(0, x12, x13, x14) :|: TRUE 7.49/2.77 f7(x15, x16, x17, x18) -> f10(x15, arith, x17, x18) :|: TRUE && arith = x16 + 1 7.49/2.77 f8(x55, x56, x57, x58) -> f11(x55, x56, x57, x59) :|: TRUE && x59 = x58 + 1 7.49/2.77 f6(x23, x24, x25, x26) -> f7(x23, x24, x25, x26) :|: x24 < x26 7.49/2.77 f6(x27, x28, x29, x30) -> f8(x27, x28, x29, x30) :|: x28 >= x30 7.49/2.77 f10(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE 7.49/2.77 f11(x35, x36, x37, x38) -> f9(x35, x36, x37, x38) :|: TRUE 7.49/2.77 f9(x60, x61, x62, x63) -> f12(x64, x61, x62, x63) :|: TRUE && x64 = x60 + 1 7.49/2.77 f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x44 < x45 7.49/2.77 f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE 7.49/2.77 f5(x51, x52, x53, x54) -> f13(x51, x52, x53, x54) :|: x52 >= x53 7.49/2.77 Start term: f1(c, x, y, z) 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (3) TerminationGraphProcessor (SOUND) 7.49/2.77 Constructed the termination graph and obtained one non-trivial SCC. 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (4) 7.49/2.77 Obligation: 7.49/2.77 Rules: 7.49/2.77 f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x44 < x45 7.49/2.77 f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE 7.49/2.77 f9(x60, x61, x62, x63) -> f12(x64, x61, x62, x63) :|: TRUE && x64 = x60 + 1 7.49/2.77 f10(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE 7.49/2.77 f7(x15, x16, x17, x18) -> f10(x15, arith, x17, x18) :|: TRUE && arith = x16 + 1 7.49/2.77 f6(x23, x24, x25, x26) -> f7(x23, x24, x25, x26) :|: x24 < x26 7.49/2.77 f11(x35, x36, x37, x38) -> f9(x35, x36, x37, x38) :|: TRUE 7.49/2.77 f8(x55, x56, x57, x58) -> f11(x55, x56, x57, x59) :|: TRUE && x59 = x58 + 1 7.49/2.77 f6(x27, x28, x29, x30) -> f8(x27, x28, x29, x30) :|: x28 >= x30 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (5) IntTRSCompressionProof (EQUIVALENT) 7.49/2.77 Compressed rules. 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (6) 7.49/2.77 Obligation: 7.49/2.77 Rules: 7.49/2.77 f9(x60:0, x61:0, x62:0, x63:0) -> f9(x60:0 + 1, x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0 7.49/2.77 f9(x, x1, x2, x3) -> f9(x + 1, x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.49/2.77 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.49/2.77 7.49/2.77 f9(x1, x2, x3, x4) -> f9(x2, x3, x4) 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (8) 7.49/2.77 Obligation: 7.49/2.77 Rules: 7.49/2.77 f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0 7.49/2.77 f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (9) PolynomialOrderProcessor (EQUIVALENT) 7.49/2.77 Found the following polynomial interpretation: 7.49/2.77 [f9(x, x1, x2)] = -x - x1 + x1^2 7.49/2.77 7.49/2.77 The following rules are decreasing: 7.49/2.77 f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1 7.49/2.77 The following rules are bounded: 7.49/2.77 f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (10) 7.49/2.77 Complex Obligation (AND) 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (11) 7.49/2.77 Obligation: 7.49/2.77 Rules: 7.49/2.77 f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (12) PolynomialOrderProcessor (EQUIVALENT) 7.49/2.77 Found the following polynomial interpretation: 7.49/2.77 [f9(x, x1, x2)] = x - x2 7.49/2.77 7.49/2.77 The following rules are decreasing: 7.49/2.77 f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0 7.49/2.77 The following rules are bounded: 7.49/2.77 f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (13) 7.49/2.77 YES 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (14) 7.49/2.77 Obligation: 7.49/2.77 Rules: 7.49/2.77 f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (15) PolynomialOrderProcessor (EQUIVALENT) 7.49/2.77 Found the following polynomial interpretation: 7.49/2.77 [f9(x, x1, x2)] = -x + x2 7.49/2.77 7.49/2.77 The following rules are decreasing: 7.49/2.77 f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1 7.49/2.77 The following rules are bounded: 7.49/2.77 f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1 7.49/2.77 7.49/2.77 ---------------------------------------- 7.49/2.77 7.49/2.77 (16) 7.49/2.77 YES 7.70/2.85 EOF