5.88/2.42 YES 5.88/2.43 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 5.88/2.43 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.88/2.43 5.88/2.43 5.88/2.43 Termination of the given C Problem could be proven: 5.88/2.43 5.88/2.43 (0) C Problem 5.88/2.43 (1) CToIRSProof [EQUIVALENT, 0 ms] 5.88/2.43 (2) IntTRS 5.88/2.43 (3) TerminationGraphProcessor [SOUND, 81 ms] 5.88/2.43 (4) IntTRS 5.88/2.43 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 5.88/2.43 (6) IntTRS 5.88/2.43 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 5.88/2.43 (8) IntTRS 5.88/2.43 (9) PolynomialOrderProcessor [EQUIVALENT, 24 ms] 5.88/2.43 (10) AND 5.88/2.43 (11) IntTRS 5.88/2.43 (12) TerminationGraphProcessor [EQUIVALENT, 0 ms] 5.88/2.43 (13) YES 5.88/2.43 (14) IntTRS 5.88/2.43 (15) TerminationGraphProcessor [EQUIVALENT, 0 ms] 5.88/2.43 (16) YES 5.88/2.43 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (0) 5.88/2.43 Obligation: 5.88/2.43 c file /export/starexec/sandbox/benchmark/theBenchmark.c 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (1) CToIRSProof (EQUIVALENT) 5.88/2.43 Parsed C Integer Program as IRS. 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (2) 5.88/2.43 Obligation: 5.88/2.43 Rules: 5.88/2.43 f1(i, j, nondetNat, nondetPos) -> f2(x_1, j, nondetNat, nondetPos) :|: TRUE 5.88/2.43 f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE 5.88/2.43 f4(x5, x6, x7, x8) -> f5(x5, x6, x9, x8) :|: TRUE 5.88/2.43 f6(x10, x11, x12, x13) -> f9(x10, x11, arith, x13) :|: TRUE && arith = 0 - x12 5.88/2.43 f5(x14, x15, x16, x17) -> f6(x14, x15, x16, x17) :|: x16 < 0 5.88/2.43 f5(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x20 >= 0 5.88/2.43 f9(x22, x23, x24, x25) -> f8(x22, x23, x24, x25) :|: TRUE 5.88/2.43 f7(x26, x27, x28, x29) -> f8(x26, x27, x28, x29) :|: TRUE 5.88/2.43 f8(x79, x80, x81, x82) -> f10(x83, x80, x81, x82) :|: TRUE && x83 = x79 - x81 5.88/2.43 f10(x34, x35, x36, x37) -> f11(x34, x35, x36, x38) :|: TRUE 5.88/2.43 f12(x84, x85, x86, x87) -> f15(x84, x85, x86, x88) :|: TRUE && x88 = 0 - x87 5.88/2.43 f11(x43, x44, x45, x46) -> f12(x43, x44, x45, x46) :|: x46 < 0 5.88/2.43 f11(x47, x48, x49, x50) -> f13(x47, x48, x49, x50) :|: x50 >= 0 5.88/2.43 f15(x51, x52, x53, x54) -> f14(x51, x52, x53, x54) :|: TRUE 5.88/2.43 f13(x55, x56, x57, x58) -> f14(x55, x56, x57, x58) :|: TRUE 5.88/2.43 f14(x89, x90, x91, x92) -> f16(x89, x90, x91, x93) :|: TRUE && x93 = x92 + 1 5.88/2.43 f16(x94, x95, x96, x97) -> f17(x94, x98, x96, x97) :|: TRUE && x98 = x95 + x97 5.88/2.43 f3(x67, x68, x69, x70) -> f4(x67, x68, x69, x70) :|: x67 - x68 >= 1 5.88/2.43 f17(x71, x72, x73, x74) -> f3(x71, x72, x73, x74) :|: TRUE 5.88/2.43 f3(x75, x76, x77, x78) -> f18(x75, x76, x77, x78) :|: x75 - x76 < 1 5.88/2.43 Start term: f1(i, j, nondetNat, nondetPos) 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (3) TerminationGraphProcessor (SOUND) 5.88/2.43 Constructed the termination graph and obtained one non-trivial SCC. 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (4) 5.88/2.43 Obligation: 5.88/2.43 Rules: 5.88/2.43 f3(x67, x68, x69, x70) -> f4(x67, x68, x69, x70) :|: x67 - x68 >= 1 5.88/2.43 f17(x71, x72, x73, x74) -> f3(x71, x72, x73, x74) :|: TRUE 5.88/2.43 f16(x94, x95, x96, x97) -> f17(x94, x98, x96, x97) :|: TRUE && x98 = x95 + x97 5.88/2.43 f14(x89, x90, x91, x92) -> f16(x89, x90, x91, x93) :|: TRUE && x93 = x92 + 1 5.88/2.43 f15(x51, x52, x53, x54) -> f14(x51, x52, x53, x54) :|: TRUE 5.88/2.43 f12(x84, x85, x86, x87) -> f15(x84, x85, x86, x88) :|: TRUE && x88 = 0 - x87 5.88/2.43 f11(x43, x44, x45, x46) -> f12(x43, x44, x45, x46) :|: x46 < 0 5.88/2.43 f10(x34, x35, x36, x37) -> f11(x34, x35, x36, x38) :|: TRUE 5.88/2.43 f8(x79, x80, x81, x82) -> f10(x83, x80, x81, x82) :|: TRUE && x83 = x79 - x81 5.88/2.43 f9(x22, x23, x24, x25) -> f8(x22, x23, x24, x25) :|: TRUE 5.88/2.43 f6(x10, x11, x12, x13) -> f9(x10, x11, arith, x13) :|: TRUE && arith = 0 - x12 5.88/2.43 f5(x14, x15, x16, x17) -> f6(x14, x15, x16, x17) :|: x16 < 0 5.88/2.43 f4(x5, x6, x7, x8) -> f5(x5, x6, x9, x8) :|: TRUE 5.88/2.43 f7(x26, x27, x28, x29) -> f8(x26, x27, x28, x29) :|: TRUE 5.88/2.43 f5(x18, x19, x20, x21) -> f7(x18, x19, x20, x21) :|: x20 >= 0 5.88/2.43 f13(x55, x56, x57, x58) -> f14(x55, x56, x57, x58) :|: TRUE 5.88/2.43 f11(x47, x48, x49, x50) -> f13(x47, x48, x49, x50) :|: x50 >= 0 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (5) IntTRSCompressionProof (EQUIVALENT) 5.88/2.43 Compressed rules. 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (6) 5.88/2.43 Obligation: 5.88/2.43 Rules: 5.88/2.43 f8(x79:0, x80:0, x81:0, x82:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0, 0 - x38:0 + 1) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1 5.88/2.43 f8(x, x1, x2, x3) -> f5(x - x2, x1 + (x4 + 1), x5, x4 + 1) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1 5.88/2.43 f5(x18:0, x19:0, x20:0, x21:0) -> f8(x18:0, x19:0, x20:0, x21:0) :|: x20:0 > -1 5.88/2.43 f5(x14:0, x15:0, x16:0, x17:0) -> f8(x14:0, x15:0, 0 - x16:0, x17:0) :|: x16:0 < 0 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 5.88/2.43 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 5.88/2.43 5.88/2.43 f8(x1, x2, x3, x4) -> f8(x1, x2, x3) 5.88/2.43 f5(x1, x2, x3, x4) -> f5(x1, x2, x3) 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (8) 5.88/2.43 Obligation: 5.88/2.43 Rules: 5.88/2.43 f8(x79:0, x80:0, x81:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1 5.88/2.43 f8(x, x1, x2) -> f5(x - x2, x1 + (x4 + 1), x5) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1 5.88/2.43 f5(x18:0, x19:0, x20:0) -> f8(x18:0, x19:0, x20:0) :|: x20:0 > -1 5.88/2.43 f5(x14:0, x15:0, x16:0) -> f8(x14:0, x15:0, 0 - x16:0) :|: x16:0 < 0 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (9) PolynomialOrderProcessor (EQUIVALENT) 5.88/2.43 Found the following polynomial interpretation: 5.88/2.43 [f8(x, x1, x2)] = -2 + x - x1 - x2 5.88/2.43 [f5(x3, x4, x5)] = -1 + x3 - x4 5.88/2.43 5.88/2.43 The following rules are decreasing: 5.88/2.43 f8(x79:0, x80:0, x81:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1 5.88/2.43 f5(x18:0, x19:0, x20:0) -> f8(x18:0, x19:0, x20:0) :|: x20:0 > -1 5.88/2.43 f5(x14:0, x15:0, x16:0) -> f8(x14:0, x15:0, 0 - x16:0) :|: x16:0 < 0 5.88/2.43 The following rules are bounded: 5.88/2.43 f8(x79:0, x80:0, x81:0) -> f5(x79:0 - x81:0, x80:0 + (0 - x38:0 + 1), x9:0) :|: x38:0 < 0 && x79:0 - x81:0 - (x80:0 + (0 - x38:0 + 1)) >= 1 5.88/2.43 f8(x, x1, x2) -> f5(x - x2, x1 + (x4 + 1), x5) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (10) 5.88/2.43 Complex Obligation (AND) 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (11) 5.88/2.43 Obligation: 5.88/2.43 Rules: 5.88/2.43 f8(x, x1, x2) -> f5(x - x2, x1 + (x4 + 1), x5) :|: x4 > -1 && x - x2 - (x1 + (x4 + 1)) >= 1 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (12) TerminationGraphProcessor (EQUIVALENT) 5.88/2.43 Constructed the termination graph and obtained no non-trivial SCC(s). 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (13) 5.88/2.43 YES 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (14) 5.88/2.43 Obligation: 5.88/2.43 Rules: 5.88/2.43 f5(x18:0, x19:0, x20:0) -> f8(x18:0, x19:0, x20:0) :|: x20:0 > -1 5.88/2.43 f5(x14:0, x15:0, x16:0) -> f8(x14:0, x15:0, 0 - x16:0) :|: x16:0 < 0 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (15) TerminationGraphProcessor (EQUIVALENT) 5.88/2.43 Constructed the termination graph and obtained no non-trivial SCC(s). 5.88/2.43 5.88/2.43 ---------------------------------------- 5.88/2.43 5.88/2.43 (16) 5.88/2.43 YES 6.33/2.46 EOF