5.94/2.67 YES 5.94/2.69 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.94/2.69 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.94/2.69 5.94/2.69 5.94/2.69 Termination of the given C Problem could be proven: 5.94/2.69 5.94/2.69 (0) C Problem 5.94/2.69 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.94/2.69 (2) IntTRS 5.94/2.69 (3) TerminationGraphProcessor [SOUND, 60 ms] 5.94/2.69 (4) IntTRS 5.94/2.69 (5) IntTRSCompressionProof [EQUIVALENT, 27 ms] 5.94/2.69 (6) IntTRS 5.94/2.69 (7) PolynomialOrderProcessor [EQUIVALENT, 14 ms] 5.94/2.69 (8) IntTRS 5.94/2.69 (9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.94/2.69 (10) IntTRS 5.94/2.69 (11) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 5.94/2.69 (12) YES 5.94/2.69 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (0) 5.94/2.69 Obligation: 5.94/2.69 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (1) CToIRSProof (EQUIVALENT) 5.94/2.69 Parsed C Integer Program as IRS. 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (2) 5.94/2.69 Obligation: 5.94/2.69 Rules: 5.94/2.69 f1(x, y, z) -> f2(x_1, y, z) :|: TRUE 5.94/2.69 f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE 5.94/2.69 f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE 5.94/2.69 f6(x9, x10, x11) -> f7(x9, arith, x11) :|: TRUE && arith = x10 - 1 5.94/2.69 f5(x12, x13, x14) -> f6(x12, x13, x14) :|: x13 > x14 5.94/2.69 f7(x15, x16, x17) -> f5(x15, x16, x17) :|: TRUE 5.94/2.69 f5(x18, x19, x20) -> f8(x18, x19, x20) :|: x19 <= x20 5.94/2.69 f8(x33, x34, x35) -> f9(x36, x34, x35) :|: TRUE && x36 = x33 - 1 5.94/2.69 f4(x24, x25, x26) -> f5(x24, x25, x26) :|: x24 > x26 5.94/2.69 f9(x27, x28, x29) -> f4(x27, x28, x29) :|: TRUE 5.94/2.69 f4(x30, x31, x32) -> f10(x30, x31, x32) :|: x30 <= x32 5.94/2.69 Start term: f1(x, y, z) 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (3) TerminationGraphProcessor (SOUND) 5.94/2.69 Constructed the termination graph and obtained one non-trivial SCC. 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (4) 5.94/2.69 Obligation: 5.94/2.69 Rules: 5.94/2.69 f4(x24, x25, x26) -> f5(x24, x25, x26) :|: x24 > x26 5.94/2.69 f9(x27, x28, x29) -> f4(x27, x28, x29) :|: TRUE 5.94/2.69 f8(x33, x34, x35) -> f9(x36, x34, x35) :|: TRUE && x36 = x33 - 1 5.94/2.69 f5(x18, x19, x20) -> f8(x18, x19, x20) :|: x19 <= x20 5.94/2.69 f7(x15, x16, x17) -> f5(x15, x16, x17) :|: TRUE 5.94/2.69 f6(x9, x10, x11) -> f7(x9, arith, x11) :|: TRUE && arith = x10 - 1 5.94/2.69 f5(x12, x13, x14) -> f6(x12, x13, x14) :|: x13 > x14 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (5) IntTRSCompressionProof (EQUIVALENT) 5.94/2.69 Compressed rules. 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (6) 5.94/2.69 Obligation: 5.94/2.69 Rules: 5.94/2.69 f5(x12:0, x13:0, x14:0) -> f5(x12:0, x13:0 - 1, x14:0) :|: x14:0 < x13:0 5.94/2.69 f5(x18:0, x19:0, x20:0) -> f5(x18:0 - 1, x19:0, x20:0) :|: x20:0 >= x19:0 && x20:0 < x18:0 - 1 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (7) PolynomialOrderProcessor (EQUIVALENT) 5.94/2.69 Found the following polynomial interpretation: 5.94/2.69 [f5(x, x1, x2)] = -2 + x - x2 5.94/2.69 5.94/2.69 The following rules are decreasing: 5.94/2.69 f5(x18:0, x19:0, x20:0) -> f5(x18:0 - 1, x19:0, x20:0) :|: x20:0 >= x19:0 && x20:0 < x18:0 - 1 5.94/2.69 The following rules are bounded: 5.94/2.69 f5(x18:0, x19:0, x20:0) -> f5(x18:0 - 1, x19:0, x20:0) :|: x20:0 >= x19:0 && x20:0 < x18:0 - 1 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (8) 5.94/2.69 Obligation: 5.94/2.69 Rules: 5.94/2.69 f5(x12:0, x13:0, x14:0) -> f5(x12:0, x13:0 - 1, x14:0) :|: x14:0 < x13:0 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (9) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.94/2.69 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.94/2.69 5.94/2.69 f5(x1, x2, x3) -> f5(x2, x3) 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (10) 5.94/2.69 Obligation: 5.94/2.69 Rules: 5.94/2.69 f5(x13:0, x14:0) -> f5(x13:0 - 1, x14:0) :|: x14:0 < x13:0 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (11) PolynomialOrderProcessor (EQUIVALENT) 5.94/2.69 Found the following polynomial interpretation: 5.94/2.69 [f5(x, x1)] = x - x1 5.94/2.69 5.94/2.69 The following rules are decreasing: 5.94/2.69 f5(x13:0, x14:0) -> f5(x13:0 - 1, x14:0) :|: x14:0 < x13:0 5.94/2.69 The following rules are bounded: 5.94/2.69 f5(x13:0, x14:0) -> f5(x13:0 - 1, x14:0) :|: x14:0 < x13:0 5.94/2.69 5.94/2.69 ---------------------------------------- 5.94/2.69 5.94/2.69 (12) 5.94/2.69 YES 5.94/2.73 EOF