6.11/2.31 YES 6.11/2.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 6.11/2.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.11/2.31 6.11/2.31 6.11/2.31 Termination of the given C Problem could be proven: 6.11/2.31 6.11/2.31 (0) C Problem 6.11/2.31 (1) CToIRSProof [EQUIVALENT, 0 ms] 6.11/2.31 (2) IntTRS 6.11/2.31 (3) TerminationGraphProcessor [SOUND, 52 ms] 6.11/2.31 (4) IntTRS 6.11/2.31 (5) IntTRSCompressionProof [EQUIVALENT, 22 ms] 6.11/2.31 (6) IntTRS 6.11/2.31 (7) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 6.11/2.31 (8) IntTRS 6.11/2.31 (9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 6.11/2.31 (10) IntTRS 6.11/2.31 (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 6.11/2.31 (12) YES 6.11/2.31 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (0) 6.11/2.31 Obligation: 6.11/2.31 c file /export/starexec/sandbox/benchmark/theBenchmark.c 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (1) CToIRSProof (EQUIVALENT) 6.11/2.31 Parsed C Integer Program as IRS. 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (2) 6.11/2.31 Obligation: 6.11/2.31 Rules: 6.11/2.31 f1(i, j, N) -> f2(i, j, x_1) :|: TRUE 6.11/2.31 f2(x, x1, x2) -> f3(x2, x1, x2) :|: TRUE 6.11/2.31 f4(x3, x4, x5) -> f5(x3, x5, x5) :|: TRUE 6.11/2.31 f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1 6.11/2.31 f5(x9, x10, x11) -> f6(x9, x10, x11) :|: x10 > 0 6.11/2.31 f7(x12, x13, x14) -> f5(x12, x13, x14) :|: TRUE 6.11/2.31 f5(x15, x16, x17) -> f8(x15, x16, x17) :|: x16 <= 0 6.11/2.31 f8(x30, x31, x32) -> f9(x33, x31, x32) :|: TRUE && x33 = x30 - 1 6.11/2.31 f3(x21, x22, x23) -> f4(x21, x22, x23) :|: x21 > 0 6.11/2.31 f9(x24, x25, x26) -> f3(x24, x25, x26) :|: TRUE 6.11/2.31 f3(x27, x28, x29) -> f10(x27, x28, x29) :|: x27 <= 0 6.11/2.31 Start term: f1(i, j, N) 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (3) TerminationGraphProcessor (SOUND) 6.11/2.31 Constructed the termination graph and obtained one non-trivial SCC. 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (4) 6.11/2.31 Obligation: 6.11/2.31 Rules: 6.11/2.31 f3(x21, x22, x23) -> f4(x21, x22, x23) :|: x21 > 0 6.11/2.31 f9(x24, x25, x26) -> f3(x24, x25, x26) :|: TRUE 6.11/2.31 f8(x30, x31, x32) -> f9(x33, x31, x32) :|: TRUE && x33 = x30 - 1 6.11/2.31 f5(x15, x16, x17) -> f8(x15, x16, x17) :|: x16 <= 0 6.11/2.31 f4(x3, x4, x5) -> f5(x3, x5, x5) :|: TRUE 6.11/2.31 f7(x12, x13, x14) -> f5(x12, x13, x14) :|: TRUE 6.11/2.31 f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1 6.11/2.31 f5(x9, x10, x11) -> f6(x9, x10, x11) :|: x10 > 0 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (5) IntTRSCompressionProof (EQUIVALENT) 6.11/2.31 Compressed rules. 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (6) 6.11/2.31 Obligation: 6.11/2.31 Rules: 6.11/2.31 f5(x15:0, x16:0, x17:0) -> f5(x15:0 - 1, x17:0, x17:0) :|: x16:0 < 1 && x15:0 > 1 6.11/2.31 f5(x9:0, x10:0, x11:0) -> f5(x9:0, x10:0 - 1, x11:0) :|: x10:0 > 0 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (7) PolynomialOrderProcessor (EQUIVALENT) 6.11/2.31 Found the following polynomial interpretation: 6.11/2.31 [f5(x, x1, x2)] = x^2 6.11/2.31 6.11/2.31 The following rules are decreasing: 6.11/2.31 f5(x15:0, x16:0, x17:0) -> f5(x15:0 - 1, x17:0, x17:0) :|: x16:0 < 1 && x15:0 > 1 6.11/2.31 The following rules are bounded: 6.11/2.31 f5(x15:0, x16:0, x17:0) -> f5(x15:0 - 1, x17:0, x17:0) :|: x16:0 < 1 && x15:0 > 1 6.11/2.31 f5(x9:0, x10:0, x11:0) -> f5(x9:0, x10:0 - 1, x11:0) :|: x10:0 > 0 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (8) 6.11/2.31 Obligation: 6.11/2.31 Rules: 6.11/2.31 f5(x9:0, x10:0, x11:0) -> f5(x9:0, x10:0 - 1, x11:0) :|: x10:0 > 0 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (9) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 6.11/2.31 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 6.11/2.31 6.11/2.31 f5(x1, x2, x3) -> f5(x2) 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (10) 6.11/2.31 Obligation: 6.11/2.31 Rules: 6.11/2.31 f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 0 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (11) PolynomialOrderProcessor (EQUIVALENT) 6.11/2.31 Found the following polynomial interpretation: 6.11/2.31 [f5(x)] = x 6.11/2.31 6.11/2.31 The following rules are decreasing: 6.11/2.31 f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 0 6.11/2.31 The following rules are bounded: 6.11/2.31 f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 0 6.11/2.31 6.11/2.31 ---------------------------------------- 6.11/2.31 6.11/2.31 (12) 6.11/2.31 YES 6.16/2.34 EOF