5.40/2.24 YES 5.40/2.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.40/2.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.40/2.25 5.40/2.25 5.40/2.25 Termination of the given C Problem could be proven: 5.40/2.25 5.40/2.25 (0) C Problem 5.40/2.25 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.40/2.25 (2) IntTRS 5.40/2.25 (3) TerminationGraphProcessor [SOUND, 53 ms] 5.40/2.25 (4) IntTRS 5.40/2.25 (5) IntTRSCompressionProof [EQUIVALENT, 4 ms] 5.40/2.25 (6) IntTRS 5.40/2.25 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.40/2.25 (8) IntTRS 5.40/2.25 (9) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 5.40/2.25 (10) IntTRS 5.40/2.25 (11) RankingReductionPairProof [EQUIVALENT, 0 ms] 5.40/2.25 (12) YES 5.40/2.25 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (0) 5.40/2.25 Obligation: 5.40/2.25 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (1) CToIRSProof (EQUIVALENT) 5.40/2.25 Parsed C Integer Program as IRS. 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (2) 5.40/2.25 Obligation: 5.40/2.25 Rules: 5.40/2.25 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 5.40/2.25 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 5.40/2.25 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 5.40/2.25 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 + 1 5.40/2.25 f6(x11, x12, x13) -> f7(x11, x12, 1) :|: TRUE 5.40/2.25 f8(x41, x42, x43) -> f9(x41, x42, x44) :|: TRUE && x44 = x43 + 1 5.40/2.25 f9(x45, x46, x47) -> f10(x48, x46, x47) :|: TRUE && x48 = x45 + 1 5.40/2.25 f7(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 > x22 5.40/2.25 f10(x23, x24, x25) -> f7(x23, x24, x25) :|: TRUE 5.40/2.25 f7(x26, x27, x28) -> f11(x26, x27, x28) :|: x27 <= x28 5.40/2.25 f11(x49, x50, x51) -> f12(x49, x52, x51) :|: TRUE && x52 = x50 - 2 5.40/2.25 f4(x32, x33, x34) -> f5(x32, x33, x34) :|: x33 >= 0 5.40/2.25 f12(x35, x36, x37) -> f4(x35, x36, x37) :|: TRUE 5.40/2.25 f4(x38, x39, x40) -> f13(x38, x39, x40) :|: x39 < 0 5.40/2.25 Start term: f1(c, x, y) 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (3) TerminationGraphProcessor (SOUND) 5.40/2.25 Constructed the termination graph and obtained one non-trivial SCC. 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (4) 5.40/2.25 Obligation: 5.40/2.25 Rules: 5.40/2.25 f4(x32, x33, x34) -> f5(x32, x33, x34) :|: x33 >= 0 5.40/2.25 f12(x35, x36, x37) -> f4(x35, x36, x37) :|: TRUE 5.40/2.25 f11(x49, x50, x51) -> f12(x49, x52, x51) :|: TRUE && x52 = x50 - 2 5.40/2.25 f7(x26, x27, x28) -> f11(x26, x27, x28) :|: x27 <= x28 5.40/2.25 f6(x11, x12, x13) -> f7(x11, x12, 1) :|: TRUE 5.40/2.25 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 + 1 5.40/2.25 f10(x23, x24, x25) -> f7(x23, x24, x25) :|: TRUE 5.40/2.25 f9(x45, x46, x47) -> f10(x48, x46, x47) :|: TRUE && x48 = x45 + 1 5.40/2.25 f8(x41, x42, x43) -> f9(x41, x42, x44) :|: TRUE && x44 = x43 + 1 5.40/2.25 f7(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 > x22 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (5) IntTRSCompressionProof (EQUIVALENT) 5.40/2.25 Compressed rules. 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (6) 5.40/2.25 Obligation: 5.40/2.25 Rules: 5.40/2.25 f7(x20:0, x21:0, x22:0) -> f7(x20:0 + 1, x21:0, x22:0 + 1) :|: x22:0 < x21:0 5.40/2.25 f7(x26:0, x27:0, x28:0) -> f7(x26:0, x27:0 - 1, 1) :|: x28:0 >= x27:0 && x27:0 > 1 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.40/2.25 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.40/2.25 5.40/2.25 f7(x1, x2, x3) -> f7(x2, x3) 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (8) 5.40/2.25 Obligation: 5.40/2.25 Rules: 5.40/2.25 f7(x21:0, x22:0) -> f7(x21:0, x22:0 + 1) :|: x22:0 < x21:0 5.40/2.25 f7(x27:0, x28:0) -> f7(x27:0 - 1, 1) :|: x28:0 >= x27:0 && x27:0 > 1 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (9) PolynomialOrderProcessor (EQUIVALENT) 5.40/2.25 Found the following polynomial interpretation: 5.40/2.25 [f7(x, x1)] = -1 + x 5.40/2.25 5.40/2.25 The following rules are decreasing: 5.40/2.25 f7(x27:0, x28:0) -> f7(x27:0 - 1, 1) :|: x28:0 >= x27:0 && x27:0 > 1 5.40/2.25 The following rules are bounded: 5.40/2.25 f7(x27:0, x28:0) -> f7(x27:0 - 1, 1) :|: x28:0 >= x27:0 && x27:0 > 1 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (10) 5.40/2.25 Obligation: 5.40/2.25 Rules: 5.40/2.25 f7(x21:0, x22:0) -> f7(x21:0, x22:0 + 1) :|: x22:0 < x21:0 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (11) RankingReductionPairProof (EQUIVALENT) 5.40/2.25 Interpretation: 5.40/2.25 [ f7 ] = -1*f7_2 + f7_1 5.40/2.25 5.40/2.25 The following rules are decreasing: 5.40/2.25 f7(x21:0, x22:0) -> f7(x21:0, x22:0 + 1) :|: x22:0 < x21:0 5.40/2.25 5.40/2.25 The following rules are bounded: 5.40/2.25 f7(x21:0, x22:0) -> f7(x21:0, x22:0 + 1) :|: x22:0 < x21:0 5.40/2.25 5.40/2.25 5.40/2.25 ---------------------------------------- 5.40/2.25 5.40/2.25 (12) 5.40/2.25 YES 5.90/2.28 EOF