5.34/2.11 YES 5.34/2.13 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 5.34/2.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.34/2.13 5.34/2.13 5.34/2.13 Termination of the given C Problem could be proven: 5.34/2.13 5.34/2.13 (0) C Problem 5.34/2.13 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.34/2.13 (2) IntTRS 5.34/2.13 (3) TerminationGraphProcessor [SOUND, 71 ms] 5.34/2.13 (4) IntTRS 5.34/2.13 (5) IntTRSCompressionProof [EQUIVALENT, 21 ms] 5.34/2.13 (6) IntTRS 5.34/2.13 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.34/2.13 (8) IntTRS 5.34/2.13 (9) PolynomialOrderProcessor [EQUIVALENT, 14 ms] 5.34/2.13 (10) YES 5.34/2.13 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (0) 5.34/2.13 Obligation: 5.34/2.13 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (1) CToIRSProof (EQUIVALENT) 5.34/2.13 Parsed C Integer Program as IRS. 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (2) 5.34/2.13 Obligation: 5.34/2.13 Rules: 5.34/2.13 f1(a, x, max) -> f2(a, x, x_1) :|: TRUE 5.34/2.13 f3(x1, x2, x3) -> f6(0, x2, x3) :|: TRUE 5.34/2.13 f6(x4, x5, x6) -> f7(x4, 1, x6) :|: TRUE 5.34/2.13 f9(x7, x8, x9) -> f12(arith, x8, x9) :|: TRUE && arith = x7 + 1 5.34/2.13 f10(x51, x52, x53) -> f13(x54, x52, x53) :|: TRUE && x54 = x51 - 1 5.34/2.13 f8(x13, x14, x15) -> f9(x13, x14, x15) :|: x16 < 0 5.34/2.13 f8(x55, x56, x57) -> f9(x55, x56, x57) :|: x58 > 0 5.34/2.13 f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x20 = 0 5.34/2.13 f12(x21, x22, x23) -> f11(x21, x22, x23) :|: TRUE 5.34/2.13 f13(x24, x25, x26) -> f11(x24, x25, x26) :|: TRUE 5.34/2.13 f11(x59, x60, x61) -> f14(x59, x62, x61) :|: TRUE && x62 = x60 + 1 5.34/2.13 f7(x30, x31, x32) -> f8(x30, x31, x32) :|: x31 <= x32 5.34/2.13 f14(x33, x34, x35) -> f7(x33, x34, x35) :|: TRUE 5.34/2.13 f7(x36, x37, x38) -> f15(x36, x37, x38) :|: x37 > x38 5.34/2.13 f2(x39, x40, x41) -> f3(x39, x40, x41) :|: x41 > 0 5.34/2.13 f2(x42, x43, x44) -> f4(x42, x43, x44) :|: x44 <= 0 5.34/2.13 f15(x45, x46, x47) -> f5(x45, x46, x47) :|: TRUE 5.34/2.13 f4(x48, x49, x50) -> f5(x48, x49, x50) :|: TRUE 5.34/2.13 Start term: f1(a, x, max) 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (3) TerminationGraphProcessor (SOUND) 5.34/2.13 Constructed the termination graph and obtained one non-trivial SCC. 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (4) 5.34/2.13 Obligation: 5.34/2.13 Rules: 5.34/2.13 f7(x30, x31, x32) -> f8(x30, x31, x32) :|: x31 <= x32 5.34/2.13 f14(x33, x34, x35) -> f7(x33, x34, x35) :|: TRUE 5.34/2.13 f11(x59, x60, x61) -> f14(x59, x62, x61) :|: TRUE && x62 = x60 + 1 5.34/2.13 f12(x21, x22, x23) -> f11(x21, x22, x23) :|: TRUE 5.34/2.13 f9(x7, x8, x9) -> f12(arith, x8, x9) :|: TRUE && arith = x7 + 1 5.34/2.13 f8(x13, x14, x15) -> f9(x13, x14, x15) :|: x16 < 0 5.34/2.13 f8(x55, x56, x57) -> f9(x55, x56, x57) :|: x58 > 0 5.34/2.13 f13(x24, x25, x26) -> f11(x24, x25, x26) :|: TRUE 5.34/2.13 f10(x51, x52, x53) -> f13(x54, x52, x53) :|: TRUE && x54 = x51 - 1 5.34/2.13 f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x20 = 0 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (5) IntTRSCompressionProof (EQUIVALENT) 5.34/2.13 Compressed rules. 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (6) 5.34/2.13 Obligation: 5.34/2.13 Rules: 5.34/2.13 f11(x59:0, x60:0, x61:0) -> f11(x59:0 + 1, x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0 5.34/2.13 f11(x, x1, x2) -> f11(x - 1, x1 + 1, x2) :|: x2 >= x1 + 1 5.34/2.13 f11(x3, x4, x5) -> f11(x3 + 1, x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.34/2.13 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.34/2.13 5.34/2.13 f11(x1, x2, x3) -> f11(x2, x3) 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (8) 5.34/2.13 Obligation: 5.34/2.13 Rules: 5.34/2.13 f11(x60:0, x61:0) -> f11(x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0 5.34/2.13 f11(x1, x2) -> f11(x1 + 1, x2) :|: x2 >= x1 + 1 5.34/2.13 f11(x4, x5) -> f11(x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (9) PolynomialOrderProcessor (EQUIVALENT) 5.34/2.13 Found the following polynomial interpretation: 5.34/2.13 [f11(x, x1)] = -x + x1 5.34/2.13 5.34/2.13 The following rules are decreasing: 5.34/2.13 f11(x60:0, x61:0) -> f11(x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0 5.34/2.13 f11(x1, x2) -> f11(x1 + 1, x2) :|: x2 >= x1 + 1 5.34/2.13 f11(x4, x5) -> f11(x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0 5.34/2.13 The following rules are bounded: 5.34/2.13 f11(x60:0, x61:0) -> f11(x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0 5.34/2.13 f11(x1, x2) -> f11(x1 + 1, x2) :|: x2 >= x1 + 1 5.34/2.13 f11(x4, x5) -> f11(x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0 5.34/2.13 5.34/2.13 ---------------------------------------- 5.34/2.13 5.34/2.13 (10) 5.34/2.13 YES 5.34/2.17 EOF