7.24/2.62 YES 7.24/2.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.24/2.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.24/2.63 7.24/2.63 7.24/2.63 Termination of the given C Problem could be proven: 7.24/2.63 7.24/2.63 (0) C Problem 7.24/2.63 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.24/2.63 (2) IntTRS 7.24/2.63 (3) TerminationGraphProcessor [SOUND, 90 ms] 7.24/2.63 (4) IntTRS 7.24/2.63 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.24/2.63 (6) IntTRS 7.24/2.63 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.24/2.63 (8) IntTRS 7.24/2.63 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 7.24/2.63 (10) YES 7.24/2.63 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (0) 7.24/2.63 Obligation: 7.24/2.63 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (1) CToIRSProof (EQUIVALENT) 7.24/2.63 Parsed C Integer Program as IRS. 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (2) 7.24/2.63 Obligation: 7.24/2.63 Rules: 7.24/2.63 f1(a, x, max) -> f2(x_1, x, max) :|: TRUE 7.24/2.63 f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE 7.24/2.63 f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE 7.24/2.63 f5(x9, x10, x11) -> f8(0, x10, x11) :|: TRUE 7.24/2.63 f8(x12, x13, x14) -> f9(x12, 1, x14) :|: TRUE 7.24/2.63 f11(x15, x16, x17) -> f14(arith, x16, x17) :|: TRUE && arith = x15 + 1 7.24/2.63 f12(x59, x60, x61) -> f15(x62, x60, x61) :|: TRUE && x62 = x59 - 1 7.24/2.63 f10(x21, x22, x23) -> f11(x21, x22, x23) :|: x24 < 0 7.24/2.63 f10(x63, x64, x65) -> f11(x63, x64, x65) :|: x66 > 0 7.24/2.63 f10(x25, x26, x27) -> f12(x25, x26, x27) :|: x28 = 0 7.24/2.63 f14(x29, x30, x31) -> f13(x29, x30, x31) :|: TRUE 7.24/2.63 f15(x32, x33, x34) -> f13(x32, x33, x34) :|: TRUE 7.24/2.63 f13(x67, x68, x69) -> f16(x67, x70, x69) :|: TRUE && x70 = x68 + 1 7.24/2.63 f9(x38, x39, x40) -> f10(x38, x39, x40) :|: x39 <= x40 7.24/2.63 f16(x41, x42, x43) -> f9(x41, x42, x43) :|: TRUE 7.24/2.63 f9(x44, x45, x46) -> f17(x44, x45, x46) :|: x45 > x46 7.24/2.63 f4(x47, x48, x49) -> f5(x47, x48, x49) :|: x49 > 0 7.24/2.63 f4(x50, x51, x52) -> f6(x50, x51, x52) :|: x52 <= 0 7.24/2.63 f17(x53, x54, x55) -> f7(x53, x54, x55) :|: TRUE 7.24/2.63 f6(x56, x57, x58) -> f7(x56, x57, x58) :|: TRUE 7.24/2.63 Start term: f1(a, x, max) 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (3) TerminationGraphProcessor (SOUND) 7.24/2.63 Constructed the termination graph and obtained one non-trivial SCC. 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (4) 7.24/2.63 Obligation: 7.24/2.63 Rules: 7.24/2.63 f9(x38, x39, x40) -> f10(x38, x39, x40) :|: x39 <= x40 7.24/2.63 f16(x41, x42, x43) -> f9(x41, x42, x43) :|: TRUE 7.24/2.63 f13(x67, x68, x69) -> f16(x67, x70, x69) :|: TRUE && x70 = x68 + 1 7.24/2.63 f14(x29, x30, x31) -> f13(x29, x30, x31) :|: TRUE 7.24/2.63 f11(x15, x16, x17) -> f14(arith, x16, x17) :|: TRUE && arith = x15 + 1 7.24/2.63 f10(x21, x22, x23) -> f11(x21, x22, x23) :|: x24 < 0 7.24/2.63 f10(x63, x64, x65) -> f11(x63, x64, x65) :|: x66 > 0 7.24/2.63 f15(x32, x33, x34) -> f13(x32, x33, x34) :|: TRUE 7.24/2.63 f12(x59, x60, x61) -> f15(x62, x60, x61) :|: TRUE && x62 = x59 - 1 7.24/2.63 f10(x25, x26, x27) -> f12(x25, x26, x27) :|: x28 = 0 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (5) IntTRSCompressionProof (EQUIVALENT) 7.24/2.63 Compressed rules. 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (6) 7.24/2.63 Obligation: 7.24/2.63 Rules: 7.24/2.63 f13(x67:0, x68:0, x69:0) -> f13(x67:0 - 1, x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1 7.24/2.63 f13(x, x1, x2) -> f13(x + 1, x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0 7.24/2.63 f13(x4, x5, x6) -> f13(x4 + 1, x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.24/2.63 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.24/2.63 7.24/2.63 f13(x1, x2, x3) -> f13(x2, x3) 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (8) 7.24/2.63 Obligation: 7.24/2.63 Rules: 7.24/2.63 f13(x68:0, x69:0) -> f13(x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1 7.24/2.63 f13(x1, x2) -> f13(x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0 7.24/2.63 f13(x5, x6) -> f13(x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (9) PolynomialOrderProcessor (EQUIVALENT) 7.24/2.63 Found the following polynomial interpretation: 7.24/2.63 [f13(x, x1)] = -x + x1 7.24/2.63 7.24/2.63 The following rules are decreasing: 7.24/2.63 f13(x68:0, x69:0) -> f13(x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1 7.24/2.63 f13(x1, x2) -> f13(x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0 7.24/2.63 f13(x5, x6) -> f13(x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0 7.24/2.63 The following rules are bounded: 7.24/2.63 f13(x68:0, x69:0) -> f13(x68:0 + 1, x69:0) :|: x69:0 >= x68:0 + 1 7.24/2.63 f13(x1, x2) -> f13(x1 + 1, x2) :|: x2 >= x1 + 1 && x3 > 0 7.24/2.63 f13(x5, x6) -> f13(x5 + 1, x6) :|: x6 >= x5 + 1 && x7 < 0 7.24/2.63 7.24/2.63 ---------------------------------------- 7.24/2.63 7.24/2.63 (10) 7.24/2.63 YES 7.24/2.68 EOF