5.63/2.27 YES 5.63/2.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.63/2.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.63/2.28 5.63/2.28 5.63/2.28 Termination of the given C Problem could be proven: 5.63/2.28 5.63/2.28 (0) C Problem 5.63/2.28 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.63/2.28 (2) IntTRS 5.63/2.28 (3) TerminationGraphProcessor [SOUND, 69 ms] 5.63/2.28 (4) IntTRS 5.63/2.28 (5) IntTRSCompressionProof [EQUIVALENT, 12 ms] 5.63/2.28 (6) IntTRS 5.63/2.28 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.63/2.28 (8) IntTRS 5.63/2.28 (9) RankingReductionPairProof [EQUIVALENT, 28 ms] 5.63/2.28 (10) YES 5.63/2.28 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (0) 5.63/2.28 Obligation: 5.63/2.28 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (1) CToIRSProof (EQUIVALENT) 5.63/2.28 Parsed C Integer Program as IRS. 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (2) 5.63/2.28 Obligation: 5.63/2.28 Rules: 5.63/2.28 f1(c, x, y) -> f2(c, x_1, y) :|: TRUE 5.63/2.28 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 5.63/2.28 f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE 5.63/2.28 f9(x8, x9, x10) -> f12(x8, x10, x10) :|: TRUE 5.63/2.28 f10(x11, x12, x13) -> f13(x11, arith, x13) :|: TRUE && arith = x12 - 1 5.63/2.28 f8(x14, x15, x16) -> f9(x14, x15, x16) :|: x15 > x16 5.63/2.28 f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 <= x19 5.63/2.28 f12(x20, x21, x22) -> f11(x20, x21, x22) :|: TRUE 5.63/2.28 f13(x23, x24, x25) -> f11(x23, x24, x25) :|: TRUE 5.63/2.28 f11(x50, x51, x52) -> f14(x53, x51, x52) :|: TRUE && x53 = x50 + 1 5.63/2.28 f5(x29, x30, x31) -> f8(x29, x30, x31) :|: x30 > 0 5.63/2.28 f14(x32, x33, x34) -> f5(x32, x33, x34) :|: TRUE 5.63/2.28 f5(x35, x36, x37) -> f15(x35, x36, x37) :|: x36 <= 0 5.63/2.28 f4(x38, x39, x40) -> f5(x38, x39, x40) :|: x40 > 0 5.63/2.28 f4(x41, x42, x43) -> f6(x41, x42, x43) :|: x43 <= 0 5.63/2.28 f15(x44, x45, x46) -> f7(x44, x45, x46) :|: TRUE 5.63/2.28 f6(x47, x48, x49) -> f7(x47, x48, x49) :|: TRUE 5.63/2.28 Start term: f1(c, x, y) 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (3) TerminationGraphProcessor (SOUND) 5.63/2.28 Constructed the termination graph and obtained one non-trivial SCC. 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (4) 5.63/2.28 Obligation: 5.63/2.28 Rules: 5.63/2.28 f5(x29, x30, x31) -> f8(x29, x30, x31) :|: x30 > 0 5.63/2.28 f14(x32, x33, x34) -> f5(x32, x33, x34) :|: TRUE 5.63/2.28 f11(x50, x51, x52) -> f14(x53, x51, x52) :|: TRUE && x53 = x50 + 1 5.63/2.28 f12(x20, x21, x22) -> f11(x20, x21, x22) :|: TRUE 5.63/2.28 f9(x8, x9, x10) -> f12(x8, x10, x10) :|: TRUE 5.63/2.28 f8(x14, x15, x16) -> f9(x14, x15, x16) :|: x15 > x16 5.63/2.28 f13(x23, x24, x25) -> f11(x23, x24, x25) :|: TRUE 5.63/2.28 f10(x11, x12, x13) -> f13(x11, arith, x13) :|: TRUE && arith = x12 - 1 5.63/2.28 f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 <= x19 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (5) IntTRSCompressionProof (EQUIVALENT) 5.63/2.28 Compressed rules. 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (6) 5.63/2.28 Obligation: 5.63/2.28 Rules: 5.63/2.28 f11(x50:0, x51:0, x52:0) -> f11(x50:0 + 1, x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0 5.63/2.28 f11(x, x1, x2) -> f11(x + 1, x1 - 1, x2) :|: x1 > 0 && x2 >= x1 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.63/2.28 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.63/2.28 5.63/2.28 f11(x1, x2, x3) -> f11(x2, x3) 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (8) 5.63/2.28 Obligation: 5.63/2.28 Rules: 5.63/2.28 f11(x51:0, x52:0) -> f11(x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0 5.63/2.28 f11(x1, x2) -> f11(x1 - 1, x2) :|: x1 > 0 && x2 >= x1 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (9) RankingReductionPairProof (EQUIVALENT) 5.63/2.28 Interpretation: 5.63/2.28 [ f11 ] = f11_1 5.63/2.28 5.63/2.28 The following rules are decreasing: 5.63/2.28 f11(x51:0, x52:0) -> f11(x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0 5.63/2.28 f11(x1, x2) -> f11(x1 - 1, x2) :|: x1 > 0 && x2 >= x1 5.63/2.28 5.63/2.28 The following rules are bounded: 5.63/2.28 f11(x51:0, x52:0) -> f11(x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0 5.63/2.28 f11(x1, x2) -> f11(x1 - 1, x2) :|: x1 > 0 && x2 >= x1 5.63/2.28 5.63/2.28 5.63/2.28 ---------------------------------------- 5.63/2.28 5.63/2.28 (10) 5.63/2.28 YES 5.98/2.31 EOF