7.20/2.61 YES 7.20/2.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 7.20/2.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.20/2.62 7.20/2.62 7.20/2.62 Termination of the given C Problem could be proven: 7.20/2.62 7.20/2.62 (0) C Problem 7.20/2.62 (1) CToIRSProof [EQUIVALENT, 0 ms] 7.20/2.62 (2) IntTRS 7.20/2.62 (3) TerminationGraphProcessor [SOUND, 90 ms] 7.20/2.62 (4) IntTRS 7.20/2.62 (5) IntTRSCompressionProof [EQUIVALENT, 29 ms] 7.20/2.62 (6) IntTRS 7.20/2.62 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 7.20/2.62 (8) IntTRS 7.20/2.62 (9) RankingReductionPairProof [EQUIVALENT, 31 ms] 7.20/2.62 (10) YES 7.20/2.62 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (0) 7.20/2.62 Obligation: 7.20/2.62 c file /export/starexec/sandbox/benchmark/theBenchmark.c 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (1) CToIRSProof (EQUIVALENT) 7.20/2.62 Parsed C Integer Program as IRS. 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (2) 7.20/2.62 Obligation: 7.20/2.62 Rules: 7.20/2.62 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 7.20/2.62 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 7.20/2.62 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 7.20/2.62 f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1 7.20/2.62 f10(x53, x54, x55) -> f13(x53, x56, x55) :|: TRUE && x56 = x54 - 1 7.20/2.62 f11(x57, x58, x59) -> f14(x57, x58, x60) :|: TRUE && x60 = x59 - 1 7.20/2.62 f7(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 = x19 7.20/2.62 f7(x20, x21, x22) -> f11(x20, x21, x22) :|: x21 < x22 7.20/2.62 f7(x61, x62, x63) -> f11(x61, x62, x63) :|: x62 > x63 7.20/2.62 f13(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE 7.20/2.62 f14(x26, x27, x28) -> f12(x26, x27, x28) :|: TRUE 7.20/2.62 f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x31 7.20/2.62 f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x34 7.20/2.62 f9(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE 7.20/2.62 f12(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE 7.20/2.62 f8(x64, x65, x66) -> f15(x67, x65, x66) :|: TRUE && x67 = x64 + 1 7.20/2.62 f4(x44, x45, x46) -> f5(x44, x45, x46) :|: x45 + x46 > 0 7.20/2.62 f15(x47, x48, x49) -> f4(x47, x48, x49) :|: TRUE 7.20/2.62 f4(x50, x51, x52) -> f16(x50, x51, x52) :|: x51 + x52 <= 0 7.20/2.62 Start term: f1(c, x, y) 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (3) TerminationGraphProcessor (SOUND) 7.20/2.62 Constructed the termination graph and obtained one non-trivial SCC. 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (4) 7.20/2.62 Obligation: 7.20/2.62 Rules: 7.20/2.62 f4(x44, x45, x46) -> f5(x44, x45, x46) :|: x45 + x46 > 0 7.20/2.62 f15(x47, x48, x49) -> f4(x47, x48, x49) :|: TRUE 7.20/2.62 f8(x64, x65, x66) -> f15(x67, x65, x66) :|: TRUE && x67 = x64 + 1 7.20/2.62 f9(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE 7.20/2.62 f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1 7.20/2.62 f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x31 7.20/2.62 f12(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE 7.20/2.62 f13(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE 7.20/2.62 f10(x53, x54, x55) -> f13(x53, x56, x55) :|: TRUE && x56 = x54 - 1 7.20/2.62 f7(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 = x19 7.20/2.62 f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x34 7.20/2.62 f14(x26, x27, x28) -> f12(x26, x27, x28) :|: TRUE 7.20/2.62 f11(x57, x58, x59) -> f14(x57, x58, x60) :|: TRUE && x60 = x59 - 1 7.20/2.62 f7(x20, x21, x22) -> f11(x20, x21, x22) :|: x21 < x22 7.20/2.62 f7(x61, x62, x63) -> f11(x61, x62, x63) :|: x62 > x63 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (5) IntTRSCompressionProof (EQUIVALENT) 7.20/2.62 Compressed rules. 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (6) 7.20/2.62 Obligation: 7.20/2.62 Rules: 7.20/2.62 f8(x64:0, x65:0, x66:0) -> f8(x64:0 + 1, x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0 7.20/2.62 f8(x, x1, x2) -> f8(x + 1, x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1 7.20/2.62 f8(x3, x4, x5) -> f8(x3 + 1, x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 7.20/2.62 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 7.20/2.62 7.20/2.62 f8(x1, x2, x3) -> f8(x2, x3) 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (8) 7.20/2.62 Obligation: 7.20/2.62 Rules: 7.20/2.62 f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0 7.20/2.62 f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1 7.20/2.62 f8(x4, x5) -> f8(x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (9) RankingReductionPairProof (EQUIVALENT) 7.20/2.62 Interpretation: 7.20/2.62 [ f8 ] = f8_1 + f8_2 7.20/2.62 7.20/2.62 The following rules are decreasing: 7.20/2.62 f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0 7.20/2.62 f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1 7.20/2.62 f8(x4, x5) -> f8(x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5 7.20/2.62 7.20/2.62 The following rules are bounded: 7.20/2.62 f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0 7.20/2.62 f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1 7.20/2.62 f8(x4, x5) -> f8(x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5 7.20/2.62 7.20/2.62 7.20/2.62 ---------------------------------------- 7.20/2.62 7.20/2.62 (10) 7.20/2.62 YES 7.56/2.67 EOF