8.52/2.92 YES 8.52/2.92 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.52/2.92 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.52/2.92 8.52/2.92 8.52/2.92 Termination of the given C Problem could be proven: 8.52/2.92 8.52/2.92 (0) C Problem 8.52/2.92 (1) CToIRSProof [EQUIVALENT, 0 ms] 8.52/2.92 (2) IntTRS 8.52/2.92 (3) TerminationGraphProcessor [SOUND, 72 ms] 8.52/2.92 (4) IntTRS 8.52/2.92 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 8.52/2.92 (6) IntTRS 8.52/2.92 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 8.52/2.92 (8) IntTRS 8.52/2.92 (9) RankingReductionPairProof [EQUIVALENT, 32 ms] 8.52/2.92 (10) IntTRS 8.52/2.92 (11) TerminationGraphProcessor [EQUIVALENT, 9 ms] 8.52/2.92 (12) YES 8.52/2.92 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (0) 8.52/2.92 Obligation: 8.52/2.92 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (1) CToIRSProof (EQUIVALENT) 8.52/2.92 Parsed C Integer Program as IRS. 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (2) 8.52/2.92 Obligation: 8.52/2.92 Rules: 8.52/2.92 f1(x, b) -> f2(x_1, b) :|: TRUE 8.52/2.92 f2(x1, x2) -> f3(x1, x3) :|: TRUE 8.52/2.92 f4(x4, x5) -> f5(x4, x6) :|: TRUE 8.52/2.92 f5(x7, x8) -> f6(arith, x8) :|: TRUE && arith = x7 - 1 8.52/2.92 f7(x9, x10) -> f10(x9, 1) :|: TRUE 8.52/2.92 f8(x11, x12) -> f11(x11, 0) :|: TRUE 8.52/2.92 f6(x13, x14) -> f7(x13, x14) :|: x13 >= 0 8.52/2.92 f6(x15, x16) -> f8(x15, x16) :|: x15 < 0 8.52/2.92 f10(x17, x18) -> f9(x17, x18) :|: TRUE 8.52/2.92 f11(x19, x20) -> f9(x19, x20) :|: TRUE 8.52/2.92 f3(x21, x22) -> f4(x21, x22) :|: x22 < 0 8.52/2.92 f3(x27, x28) -> f4(x27, x28) :|: x28 > 0 8.52/2.92 f9(x23, x24) -> f3(x23, x24) :|: TRUE 8.52/2.92 f3(x25, x26) -> f12(x25, x26) :|: x26 = 0 8.52/2.92 Start term: f1(x, b) 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (3) TerminationGraphProcessor (SOUND) 8.52/2.92 Constructed the termination graph and obtained one non-trivial SCC. 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (4) 8.52/2.92 Obligation: 8.52/2.92 Rules: 8.52/2.92 f3(x21, x22) -> f4(x21, x22) :|: x22 < 0 8.52/2.92 f9(x23, x24) -> f3(x23, x24) :|: TRUE 8.52/2.92 f10(x17, x18) -> f9(x17, x18) :|: TRUE 8.52/2.92 f7(x9, x10) -> f10(x9, 1) :|: TRUE 8.52/2.92 f6(x13, x14) -> f7(x13, x14) :|: x13 >= 0 8.52/2.92 f5(x7, x8) -> f6(arith, x8) :|: TRUE && arith = x7 - 1 8.52/2.92 f4(x4, x5) -> f5(x4, x6) :|: TRUE 8.52/2.92 f3(x27, x28) -> f4(x27, x28) :|: x28 > 0 8.52/2.92 f11(x19, x20) -> f9(x19, x20) :|: TRUE 8.52/2.92 f8(x11, x12) -> f11(x11, 0) :|: TRUE 8.52/2.92 f6(x15, x16) -> f8(x15, x16) :|: x15 < 0 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (5) IntTRSCompressionProof (EQUIVALENT) 8.52/2.92 Compressed rules. 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (6) 8.52/2.92 Obligation: 8.52/2.92 Rules: 8.52/2.92 f9(x23:0, x24:0) -> f5(x23:0, x6:0) :|: x24:0 < 0 8.52/2.92 f5(x7:0, x8:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0 8.52/2.92 f5(x, x1) -> f9(x - 1, 0) :|: x < 1 8.52/2.92 f9(x2, x3) -> f5(x2, x4) :|: x3 > 0 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 8.52/2.92 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 8.52/2.92 8.52/2.92 f5(x1, x2) -> f5(x1) 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (8) 8.52/2.92 Obligation: 8.52/2.92 Rules: 8.52/2.92 f9(x23:0, x24:0) -> f5(x23:0) :|: x24:0 < 0 8.52/2.92 f5(x7:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0 8.52/2.92 f5(x) -> f9(x - 1, 0) :|: x < 1 8.52/2.92 f9(x2, x3) -> f5(x2) :|: x3 > 0 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (9) RankingReductionPairProof (EQUIVALENT) 8.52/2.92 Interpretation: 8.52/2.92 [ f9 ] = 3*f9_1 + 2 8.52/2.92 [ f5 ] = 3*f5_1 + 1 8.52/2.92 8.52/2.92 The following rules are decreasing: 8.52/2.92 f9(x23:0, x24:0) -> f5(x23:0) :|: x24:0 < 0 8.52/2.92 f5(x7:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0 8.52/2.92 f5(x) -> f9(x - 1, 0) :|: x < 1 8.52/2.92 f9(x2, x3) -> f5(x2) :|: x3 > 0 8.52/2.92 8.52/2.92 The following rules are bounded: 8.52/2.92 f5(x7:0) -> f9(x7:0 - 1, 1) :|: x7:0 > 0 8.52/2.92 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (10) 8.52/2.92 Obligation: 8.52/2.92 Rules: 8.52/2.92 f9(x23:0, x24:0) -> f5(x23:0) :|: x24:0 < 0 8.52/2.92 f5(x) -> f9(x - 1, 0) :|: x < 1 8.52/2.92 f9(x2, x3) -> f5(x2) :|: x3 > 0 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (11) TerminationGraphProcessor (EQUIVALENT) 8.52/2.92 Constructed the termination graph and obtained no non-trivial SCC(s). 8.52/2.92 8.52/2.92 ---------------------------------------- 8.52/2.92 8.52/2.92 (12) 8.52/2.92 YES 8.52/2.98 EOF