4.19/1.97 YES 4.19/1.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 4.19/1.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.19/1.98 4.19/1.98 4.19/1.98 Termination of the given C Problem could be proven: 4.19/1.98 4.19/1.98 (0) C Problem 4.19/1.98 (1) CToIRSProof [EQUIVALENT, 0 ms] 4.19/1.98 (2) IntTRS 4.19/1.98 (3) TerminationGraphProcessor [SOUND, 43 ms] 4.19/1.98 (4) IntTRS 4.19/1.98 (5) IntTRSCompressionProof [EQUIVALENT, 5 ms] 4.19/1.98 (6) IntTRS 4.19/1.98 (7) PolynomialOrderProcessor [EQUIVALENT, 9 ms] 4.19/1.98 (8) YES 4.19/1.98 4.19/1.98 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (0) 4.19/1.98 Obligation: 4.19/1.98 c file /export/starexec/sandbox/benchmark/theBenchmark.c 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (1) CToIRSProof (EQUIVALENT) 4.19/1.98 Parsed C Integer Program as IRS. 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (2) 4.19/1.98 Obligation: 4.19/1.98 Rules: 4.19/1.98 f1(i, j) -> f2(i, 1) :|: TRUE 4.19/1.98 f2(x, x1) -> f3(10000, x1) :|: TRUE 4.19/1.98 f4(x2, x3) -> f5(x2, arith) :|: TRUE && arith = x3 + 1 4.19/1.98 f5(x12, x13) -> f6(x14, x13) :|: TRUE && x14 = x12 - 1 4.19/1.98 f3(x6, x7) -> f4(x6, x7) :|: x6 - x7 >= 1 4.19/1.98 f6(x8, x9) -> f3(x8, x9) :|: TRUE 4.19/1.98 f3(x10, x11) -> f7(x10, x11) :|: x10 - x11 < 1 4.19/1.98 Start term: f1(i, j) 4.19/1.98 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (3) TerminationGraphProcessor (SOUND) 4.19/1.98 Constructed the termination graph and obtained one non-trivial SCC. 4.19/1.98 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (4) 4.19/1.98 Obligation: 4.19/1.98 Rules: 4.19/1.98 f3(x6, x7) -> f4(x6, x7) :|: x6 - x7 >= 1 4.19/1.98 f6(x8, x9) -> f3(x8, x9) :|: TRUE 4.19/1.98 f5(x12, x13) -> f6(x14, x13) :|: TRUE && x14 = x12 - 1 4.19/1.98 f4(x2, x3) -> f5(x2, arith) :|: TRUE && arith = x3 + 1 4.19/1.98 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (5) IntTRSCompressionProof (EQUIVALENT) 4.19/1.98 Compressed rules. 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (6) 4.19/1.98 Obligation: 4.19/1.98 Rules: 4.19/1.98 f5(x12:0, x13:0) -> f5(x12:0 - 1, x13:0 + 1) :|: x12:0 - 1 - x13:0 >= 1 4.19/1.98 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (7) PolynomialOrderProcessor (EQUIVALENT) 4.19/1.98 Found the following polynomial interpretation: 4.19/1.98 [f5(x, x1)] = -1 + x - x1 4.19/1.98 4.19/1.98 The following rules are decreasing: 4.19/1.98 f5(x12:0, x13:0) -> f5(x12:0 - 1, x13:0 + 1) :|: x12:0 - 1 - x13:0 >= 1 4.19/1.98 The following rules are bounded: 4.19/1.98 f5(x12:0, x13:0) -> f5(x12:0 - 1, x13:0 + 1) :|: x12:0 - 1 - x13:0 >= 1 4.19/1.98 4.19/1.98 ---------------------------------------- 4.19/1.98 4.19/1.98 (8) 4.19/1.98 YES 4.19/2.00 EOF