3.93/1.93 YES 3.93/1.94 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 3.93/1.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.93/1.94 3.93/1.94 3.93/1.94 Termination of the given C Problem could be proven: 3.93/1.94 3.93/1.94 (0) C Problem 3.93/1.94 (1) CToIRSProof [EQUIVALENT, 0 ms] 3.93/1.94 (2) IntTRS 3.93/1.94 (3) TerminationGraphProcessor [SOUND, 42 ms] 3.93/1.94 (4) IntTRS 3.93/1.94 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 3.93/1.94 (6) IntTRS 3.93/1.94 (7) PolynomialOrderProcessor [EQUIVALENT, 1 ms] 3.93/1.94 (8) YES 3.93/1.94 3.93/1.94 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (0) 3.93/1.94 Obligation: 3.93/1.94 c file /export/starexec/sandbox/benchmark/theBenchmark.c 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (1) CToIRSProof (EQUIVALENT) 3.93/1.94 Parsed C Integer Program as IRS. 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (2) 3.93/1.94 Obligation: 3.93/1.94 Rules: 3.93/1.94 f1(x, y) -> f2(x_1, y) :|: TRUE 3.93/1.94 f2(x1, x2) -> f3(x1, x3) :|: TRUE 3.93/1.94 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1 3.93/1.94 f3(x6, x7) -> f4(x6, x7) :|: x6 > x7 3.93/1.94 f5(x8, x9) -> f3(x8, x9) :|: TRUE 3.93/1.94 f3(x10, x11) -> f6(x10, x11) :|: x10 <= x11 3.93/1.94 Start term: f1(x, y) 3.93/1.94 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (3) TerminationGraphProcessor (SOUND) 3.93/1.94 Constructed the termination graph and obtained one non-trivial SCC. 3.93/1.94 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (4) 3.93/1.94 Obligation: 3.93/1.94 Rules: 3.93/1.94 f3(x6, x7) -> f4(x6, x7) :|: x6 > x7 3.93/1.94 f5(x8, x9) -> f3(x8, x9) :|: TRUE 3.93/1.94 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1 3.93/1.94 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (5) IntTRSCompressionProof (EQUIVALENT) 3.93/1.94 Compressed rules. 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (6) 3.93/1.94 Obligation: 3.93/1.94 Rules: 3.93/1.94 f5(x8:0, x9:0) -> f5(x8:0 - 1, x9:0) :|: x9:0 < x8:0 3.93/1.94 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (7) PolynomialOrderProcessor (EQUIVALENT) 3.93/1.94 Found the following polynomial interpretation: 3.93/1.94 [f5(x, x1)] = x - x1 3.93/1.94 3.93/1.94 The following rules are decreasing: 3.93/1.94 f5(x8:0, x9:0) -> f5(x8:0 - 1, x9:0) :|: x9:0 < x8:0 3.93/1.94 The following rules are bounded: 3.93/1.94 f5(x8:0, x9:0) -> f5(x8:0 - 1, x9:0) :|: x9:0 < x8:0 3.93/1.94 3.93/1.94 ---------------------------------------- 3.93/1.94 3.93/1.94 (8) 3.93/1.94 YES 3.93/1.99 EOF