5.23/2.09 YES 5.23/2.11 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.23/2.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.23/2.11 5.23/2.11 5.23/2.11 Termination of the given C Problem could be proven: 5.23/2.11 5.23/2.11 (0) C Problem 5.23/2.11 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.23/2.11 (2) IntTRS 5.23/2.11 (3) TerminationGraphProcessor [SOUND, 65 ms] 5.23/2.11 (4) IntTRS 5.23/2.11 (5) IntTRSCompressionProof [EQUIVALENT, 18 ms] 5.23/2.11 (6) IntTRS 5.23/2.11 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.23/2.11 (8) IntTRS 5.23/2.11 (9) PolynomialOrderProcessor [EQUIVALENT, 2 ms] 5.23/2.11 (10) YES 5.23/2.11 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (0) 5.23/2.11 Obligation: 5.23/2.11 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (1) CToIRSProof (EQUIVALENT) 5.23/2.11 Parsed C Integer Program as IRS. 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (2) 5.23/2.11 Obligation: 5.23/2.11 Rules: 5.23/2.11 f1(i, j, k, tmp) -> f2(x_1, j, k, tmp) :|: TRUE 5.23/2.11 f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE 5.23/2.11 f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE 5.23/2.11 f4(x10, x11, x12, x13) -> f5(x10, x11, x12, x14) :|: TRUE 5.23/2.11 f6(x15, x16, x17, x18) -> f7(x15, x16, x17, x15) :|: TRUE 5.23/2.11 f7(x19, x20, x21, x22) -> f8(x20, x20, x21, x22) :|: TRUE 5.23/2.11 f8(x23, x24, x25, x26) -> f9(x23, arith, x25, x26) :|: TRUE && arith = x26 + 1 5.23/2.11 f9(x43, x44, x45, x46) -> f10(x43, x44, x47, x46) :|: TRUE && x47 = x45 - 1 5.23/2.11 f5(x31, x32, x33, x34) -> f6(x31, x32, x33, x34) :|: x31 <= 100 && x32 <= x33 5.23/2.11 f10(x35, x36, x37, x38) -> f5(x35, x36, x37, x38) :|: TRUE 5.23/2.11 f5(x39, x40, x41, x42) -> f11(x39, x40, x41, x42) :|: x39 > 100 5.23/2.11 f5(x48, x49, x50, x51) -> f11(x48, x49, x50, x51) :|: x49 > x50 5.23/2.11 Start term: f1(i, j, k, tmp) 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (3) TerminationGraphProcessor (SOUND) 5.23/2.11 Constructed the termination graph and obtained one non-trivial SCC. 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (4) 5.23/2.11 Obligation: 5.23/2.11 Rules: 5.23/2.11 f5(x31, x32, x33, x34) -> f6(x31, x32, x33, x34) :|: x31 <= 100 && x32 <= x33 5.23/2.11 f10(x35, x36, x37, x38) -> f5(x35, x36, x37, x38) :|: TRUE 5.23/2.11 f9(x43, x44, x45, x46) -> f10(x43, x44, x47, x46) :|: TRUE && x47 = x45 - 1 5.23/2.11 f8(x23, x24, x25, x26) -> f9(x23, arith, x25, x26) :|: TRUE && arith = x26 + 1 5.23/2.11 f7(x19, x20, x21, x22) -> f8(x20, x20, x21, x22) :|: TRUE 5.23/2.11 f6(x15, x16, x17, x18) -> f7(x15, x16, x17, x15) :|: TRUE 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (5) IntTRSCompressionProof (EQUIVALENT) 5.23/2.11 Compressed rules. 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (6) 5.23/2.11 Obligation: 5.23/2.11 Rules: 5.23/2.11 f7(x19:0, x20:0, x21:0, x22:0) -> f7(x20:0, x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.23/2.11 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.23/2.11 5.23/2.11 f7(x1, x2, x3, x4) -> f7(x2, x3, x4) 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (8) 5.23/2.11 Obligation: 5.23/2.11 Rules: 5.23/2.11 f7(x20:0, x21:0, x22:0) -> f7(x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (9) PolynomialOrderProcessor (EQUIVALENT) 5.23/2.11 Found the following polynomial interpretation: 5.23/2.11 [f7(x, x1, x2)] = 98 - x + x1 - x2 5.23/2.11 5.23/2.11 The following rules are decreasing: 5.23/2.11 f7(x20:0, x21:0, x22:0) -> f7(x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1 5.23/2.11 The following rules are bounded: 5.23/2.11 f7(x20:0, x21:0, x22:0) -> f7(x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1 5.23/2.11 5.23/2.11 ---------------------------------------- 5.23/2.11 5.23/2.11 (10) 5.23/2.11 YES 5.50/2.14 EOF