6.98/2.66 YES 6.98/2.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 6.98/2.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.98/2.67 6.98/2.67 6.98/2.67 Termination of the given C Problem could be proven: 6.98/2.67 6.98/2.67 (0) C Problem 6.98/2.67 (1) CToIRSProof [EQUIVALENT, 0 ms] 6.98/2.67 (2) IntTRS 6.98/2.67 (3) TerminationGraphProcessor [SOUND, 71 ms] 6.98/2.67 (4) IntTRS 6.98/2.67 (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] 6.98/2.67 (6) IntTRS 6.98/2.67 (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 6.98/2.67 (8) IntTRS 6.98/2.67 (9) PolynomialOrderProcessor [EQUIVALENT, 5 ms] 6.98/2.67 (10) IntTRS 6.98/2.67 (11) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 6.98/2.67 (12) IntTRS 6.98/2.67 (13) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 6.98/2.67 (14) YES 6.98/2.67 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (0) 6.98/2.67 Obligation: 6.98/2.67 c file /export/starexec/sandbox/benchmark/theBenchmark.c 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (1) CToIRSProof (EQUIVALENT) 6.98/2.67 Parsed C Integer Program as IRS. 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (2) 6.98/2.67 Obligation: 6.98/2.67 Rules: 6.98/2.67 f1(a, b, c, i, j, M, N) -> f2(a, b, c, x_1, j, M, N) :|: TRUE 6.98/2.67 f2(x, x1, x2, x3, x4, x5, x6) -> f3(x, x1, x2, x3, x7, x5, x6) :|: TRUE 6.98/2.67 f3(x8, x9, x10, x11, x12, x13, x14) -> f4(x8, x9, x10, x11, x12, x15, x14) :|: TRUE 6.98/2.67 f4(x16, x17, x18, x19, x20, x21, x22) -> f5(x16, x17, x18, x19, x20, x21, x23) :|: TRUE 6.98/2.67 f5(x24, x25, x26, x27, x28, x29, x30) -> f6(x27, x25, x26, x27, x28, x29, x30) :|: TRUE 6.98/2.67 f6(x31, x32, x33, x34, x35, x36, x37) -> f7(x31, x35, x33, x34, x35, x36, x37) :|: TRUE 6.98/2.67 f7(x38, x39, x40, x41, x42, x43, x44) -> f8(x38, x39, 0, x41, x42, x43, x44) :|: TRUE 6.98/2.67 f9(x45, x46, x47, x48, x49, x50, x51) -> f10(x45, x46, x47, arith, x49, x50, x51) :|: TRUE && arith = x48 + 1 6.98/2.67 f10(x87, x88, x89, x90, x91, x92, x93) -> f11(x87, x88, x89, x90, x94, x92, x93) :|: TRUE && x94 = x91 + 1 6.98/2.67 f11(x95, x96, x97, x98, x99, x100, x101) -> f12(x95, x96, x102, x98, x99, x100, x101) :|: TRUE && x102 = x97 + 1 6.98/2.67 f8(x66, x67, x68, x69, x70, x71, x72) -> f9(x66, x67, x68, x69, x70, x71, x72) :|: x69 < x71 6.98/2.67 f8(x103, x104, x105, x106, x107, x108, x109) -> f9(x103, x104, x105, x106, x107, x108, x109) :|: x107 < x109 6.98/2.67 f12(x73, x74, x75, x76, x77, x78, x79) -> f8(x73, x74, x75, x76, x77, x78, x79) :|: TRUE 6.98/2.67 f8(x80, x81, x82, x83, x84, x85, x86) -> f13(x80, x81, x82, x83, x84, x85, x86) :|: x83 >= x85 && x84 >= x86 6.98/2.67 Start term: f1(a, b, c, i, j, M, N) 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (3) TerminationGraphProcessor (SOUND) 6.98/2.67 Constructed the termination graph and obtained one non-trivial SCC. 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (4) 6.98/2.67 Obligation: 6.98/2.67 Rules: 6.98/2.67 f8(x66, x67, x68, x69, x70, x71, x72) -> f9(x66, x67, x68, x69, x70, x71, x72) :|: x69 < x71 6.98/2.67 f12(x73, x74, x75, x76, x77, x78, x79) -> f8(x73, x74, x75, x76, x77, x78, x79) :|: TRUE 6.98/2.67 f11(x95, x96, x97, x98, x99, x100, x101) -> f12(x95, x96, x102, x98, x99, x100, x101) :|: TRUE && x102 = x97 + 1 6.98/2.67 f10(x87, x88, x89, x90, x91, x92, x93) -> f11(x87, x88, x89, x90, x94, x92, x93) :|: TRUE && x94 = x91 + 1 6.98/2.67 f9(x45, x46, x47, x48, x49, x50, x51) -> f10(x45, x46, x47, arith, x49, x50, x51) :|: TRUE && arith = x48 + 1 6.98/2.67 f8(x103, x104, x105, x106, x107, x108, x109) -> f9(x103, x104, x105, x106, x107, x108, x109) :|: x107 < x109 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (5) IntTRSCompressionProof (EQUIVALENT) 6.98/2.67 Compressed rules. 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (6) 6.98/2.67 Obligation: 6.98/2.67 Rules: 6.98/2.67 f10(x87:0, x88:0, x89:0, x90:0, x91:0, x92:0, x93:0) -> f10(x87:0, x88:0, x89:0 + 1, x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0 6.98/2.67 f10(x, x1, x2, x3, x4, x5, x6) -> f10(x, x1, x2 + 1, x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 6.98/2.67 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 6.98/2.67 6.98/2.67 f10(x1, x2, x3, x4, x5, x6, x7) -> f10(x4, x5, x6, x7) 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (8) 6.98/2.67 Obligation: 6.98/2.67 Rules: 6.98/2.67 f10(x90:0, x91:0, x92:0, x93:0) -> f10(x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0 6.98/2.67 f10(x3, x4, x5, x6) -> f10(x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (9) PolynomialOrderProcessor (EQUIVALENT) 6.98/2.67 Found the following polynomial interpretation: 6.98/2.67 [f10(x, x1, x2, x3)] = -2 - 3*x1 - x3 + x3^2 6.98/2.67 6.98/2.67 The following rules are decreasing: 6.98/2.67 f10(x90:0, x91:0, x92:0, x93:0) -> f10(x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0 6.98/2.67 f10(x3, x4, x5, x6) -> f10(x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1 6.98/2.67 The following rules are bounded: 6.98/2.67 f10(x3, x4, x5, x6) -> f10(x3 + 1, x4 + 1, x5, x6) :|: x6 > x4 + 1 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (10) 6.98/2.67 Obligation: 6.98/2.67 Rules: 6.98/2.67 f10(x90:0, x91:0, x92:0, x93:0) -> f10(x90:0 + 1, x91:0 + 1, x92:0, x93:0) :|: x92:0 > x90:0 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (11) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 6.98/2.67 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 6.98/2.67 6.98/2.67 f10(x1, x2, x3, x4) -> f10(x1, x3) 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (12) 6.98/2.67 Obligation: 6.98/2.67 Rules: 6.98/2.67 f10(x90:0, x92:0) -> f10(x90:0 + 1, x92:0) :|: x92:0 > x90:0 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (13) PolynomialOrderProcessor (EQUIVALENT) 6.98/2.67 Found the following polynomial interpretation: 6.98/2.67 [f10(x, x1)] = -x + x1 6.98/2.67 6.98/2.67 The following rules are decreasing: 6.98/2.67 f10(x90:0, x92:0) -> f10(x90:0 + 1, x92:0) :|: x92:0 > x90:0 6.98/2.67 The following rules are bounded: 6.98/2.67 f10(x90:0, x92:0) -> f10(x90:0 + 1, x92:0) :|: x92:0 > x90:0 6.98/2.67 6.98/2.67 ---------------------------------------- 6.98/2.67 6.98/2.67 (14) 6.98/2.67 YES 7.21/2.71 EOF