4.68/2.06 YES 4.68/2.07 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 4.68/2.07 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.68/2.07 4.68/2.07 4.68/2.07 Termination of the given C Problem could be proven: 4.68/2.07 4.68/2.07 (0) C Problem 4.68/2.07 (1) CToIRSProof [EQUIVALENT, 0 ms] 4.68/2.07 (2) IntTRS 4.68/2.07 (3) TerminationGraphProcessor [SOUND, 49 ms] 4.68/2.07 (4) IntTRS 4.68/2.07 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 4.68/2.07 (6) IntTRS 4.68/2.07 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 4.68/2.07 (8) IntTRS 4.68/2.07 (9) RankingReductionPairProof [EQUIVALENT, 5 ms] 4.68/2.07 (10) YES 4.68/2.07 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (0) 4.68/2.07 Obligation: 4.68/2.07 c file /export/starexec/sandbox/benchmark/theBenchmark.c 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (1) CToIRSProof (EQUIVALENT) 4.68/2.07 Parsed C Integer Program as IRS. 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (2) 4.68/2.07 Obligation: 4.68/2.07 Rules: 4.68/2.07 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 4.68/2.07 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 4.68/2.07 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 4.68/2.07 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 + 1 4.68/2.07 f6(x26, x27, x28) -> f7(x26, x27, x29) :|: TRUE && x29 = x28 + 2 4.68/2.07 f7(x30, x31, x32) -> f8(x33, x31, x32) :|: TRUE && x33 = x30 + 1 4.68/2.07 f4(x17, x18, x19) -> f5(x17, x18, x19) :|: x18 > x19 4.68/2.07 f8(x20, x21, x22) -> f4(x20, x21, x22) :|: TRUE 4.68/2.07 f4(x23, x24, x25) -> f9(x23, x24, x25) :|: x24 <= x25 4.68/2.07 Start term: f1(c, x, y) 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (3) TerminationGraphProcessor (SOUND) 4.68/2.07 Constructed the termination graph and obtained one non-trivial SCC. 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (4) 4.68/2.07 Obligation: 4.68/2.07 Rules: 4.68/2.07 f4(x17, x18, x19) -> f5(x17, x18, x19) :|: x18 > x19 4.68/2.07 f8(x20, x21, x22) -> f4(x20, x21, x22) :|: TRUE 4.68/2.07 f7(x30, x31, x32) -> f8(x33, x31, x32) :|: TRUE && x33 = x30 + 1 4.68/2.07 f6(x26, x27, x28) -> f7(x26, x27, x29) :|: TRUE && x29 = x28 + 2 4.68/2.07 f5(x8, x9, x10) -> f6(x8, arith, x10) :|: TRUE && arith = x9 + 1 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (5) IntTRSCompressionProof (EQUIVALENT) 4.68/2.07 Compressed rules. 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (6) 4.68/2.07 Obligation: 4.68/2.07 Rules: 4.68/2.07 f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 1, x27:0 + 1, x28:0 + 2) :|: x28:0 + 2 < x27:0 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 4.68/2.07 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 4.68/2.07 4.68/2.07 f6(x1, x2, x3) -> f6(x2, x3) 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (8) 4.68/2.07 Obligation: 4.68/2.07 Rules: 4.68/2.07 f6(x27:0, x28:0) -> f6(x27:0 + 1, x28:0 + 2) :|: x28:0 + 2 < x27:0 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (9) RankingReductionPairProof (EQUIVALENT) 4.68/2.07 Interpretation: 4.68/2.07 [ f6 ] = -1*f6_2 + f6_1 4.68/2.07 4.68/2.07 The following rules are decreasing: 4.68/2.07 f6(x27:0, x28:0) -> f6(x27:0 + 1, x28:0 + 2) :|: x28:0 + 2 < x27:0 4.68/2.07 4.68/2.07 The following rules are bounded: 4.68/2.07 f6(x27:0, x28:0) -> f6(x27:0 + 1, x28:0 + 2) :|: x28:0 + 2 < x27:0 4.68/2.07 4.68/2.07 4.68/2.07 ---------------------------------------- 4.68/2.07 4.68/2.07 (10) 4.68/2.07 YES 4.84/2.11 EOF