9.11/3.20 YES 9.37/3.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 9.37/3.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.37/3.21 9.37/3.21 9.37/3.21 Termination of the given C Problem could be proven: 9.37/3.21 9.37/3.21 (0) C Problem 9.37/3.21 (1) CToIRSProof [EQUIVALENT, 0 ms] 9.37/3.21 (2) IntTRS 9.37/3.21 (3) TerminationGraphProcessor [SOUND, 115 ms] 9.37/3.21 (4) IntTRS 9.37/3.21 (5) IntTRSCompressionProof [EQUIVALENT, 6 ms] 9.37/3.21 (6) IntTRS 9.37/3.21 (7) PolynomialOrderProcessor [EQUIVALENT, 19 ms] 9.37/3.21 (8) YES 9.37/3.21 9.37/3.21 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (0) 9.37/3.21 Obligation: 9.37/3.21 c file /export/starexec/sandbox/benchmark/theBenchmark.c 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (1) CToIRSProof (EQUIVALENT) 9.37/3.21 Parsed C Integer Program as IRS. 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (2) 9.37/3.21 Obligation: 9.37/3.21 Rules: 9.37/3.21 f1(x, tx, y, ty, n) -> f2(x_1, tx, y, ty, n) :|: TRUE 9.37/3.21 f2(x1, x2, x3, x4, x5) -> f3(x1, x6, x3, x4, x5) :|: TRUE 9.37/3.21 f3(x7, x8, x9, x10, x11) -> f4(x7, x8, x12, x10, x11) :|: TRUE 9.37/3.21 f4(x13, x14, x15, x16, x17) -> f5(x13, x14, x15, x18, x17) :|: TRUE 9.37/3.21 f5(x19, x20, x21, x22, x23) -> f6(x19, x20, x21, x22, x24) :|: TRUE 9.37/3.21 f11(x25, x26, x27, x28, x29) -> f14(x25, x25, x27, x28, x29) :|: TRUE 9.37/3.21 f14(x30, x31, x32, x33, x34) -> f15(x30, x31, x32, x32, x34) :|: TRUE 9.37/3.21 f15(x35, x36, x37, x38, x39) -> f16(x40, x36, x37, x38, x39) :|: TRUE 9.37/3.21 f16(x41, x42, x43, x44, x45) -> f17(x41, x42, x46, x44, x45) :|: TRUE 9.37/3.21 f12(x47, x48, x49, x50, x51) -> f18(x47, x47, x49, x50, x51) :|: TRUE 9.37/3.21 f18(x52, x53, x54, x55, x56) -> f19(x57, x53, x54, x55, x56) :|: TRUE 9.37/3.21 f10(x58, x59, x60, x61, x62) -> f11(x58, x59, x60, x61, x62) :|: x63 < 0 9.37/3.21 f10(x115, x116, x117, x118, x119) -> f11(x115, x116, x117, x118, x119) :|: x120 > 0 9.37/3.21 f10(x64, x65, x66, x67, x68) -> f12(x64, x65, x66, x67, x68) :|: x69 = 0 9.37/3.21 f17(x70, x71, x72, x73, x74) -> f13(x70, x71, x72, x73, x74) :|: TRUE 9.37/3.21 f19(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: TRUE 9.37/3.21 f7(x80, x81, x82, x83, x84) -> f10(x80, x81, x82, x83, x84) :|: x80 <= x84 && x80 >= 2 * x81 + x82 && x82 >= x83 + 1 && x80 >= x81 + 1 9.37/3.21 f13(x85, x86, x87, x88, x89) -> f7(x85, x86, x87, x88, x89) :|: TRUE 9.37/3.21 f7(x90, x91, x92, x93, x94) -> f20(x90, x91, x92, x93, x94) :|: x90 < x91 + 1 9.37/3.21 f7(x121, x122, x123, x124, x125) -> f20(x121, x122, x123, x124, x125) :|: x123 < x124 + 1 9.37/3.21 f7(x126, x127, x128, x129, x130) -> f20(x126, x127, x128, x129, x130) :|: x126 > x130 9.37/3.21 f7(x131, x132, x133, x134, x135) -> f20(x131, x132, x133, x134, x135) :|: x131 < 2 * x132 + x133 9.37/3.21 f6(x95, x96, x97, x98, x99) -> f7(x95, x96, x97, x98, x99) :|: x95 + x97 >= 0 9.37/3.21 f6(x100, x101, x102, x103, x104) -> f8(x100, x101, x102, x103, x104) :|: x100 + x102 < 0 9.37/3.21 f20(x105, x106, x107, x108, x109) -> f9(x105, x106, x107, x108, x109) :|: TRUE 9.37/3.21 f8(x110, x111, x112, x113, x114) -> f9(x110, x111, x112, x113, x114) :|: TRUE 9.37/3.21 Start term: f1(x, tx, y, ty, n) 9.37/3.21 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (3) TerminationGraphProcessor (SOUND) 9.37/3.21 Constructed the termination graph and obtained one non-trivial SCC. 9.37/3.21 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (4) 9.37/3.21 Obligation: 9.37/3.21 Rules: 9.37/3.21 f7(x80, x81, x82, x83, x84) -> f10(x80, x81, x82, x83, x84) :|: x80 <= x84 && x80 >= 2 * x81 + x82 && x82 >= x83 + 1 && x80 >= x81 + 1 9.37/3.21 f13(x85, x86, x87, x88, x89) -> f7(x85, x86, x87, x88, x89) :|: TRUE 9.37/3.21 f17(x70, x71, x72, x73, x74) -> f13(x70, x71, x72, x73, x74) :|: TRUE 9.37/3.21 f16(x41, x42, x43, x44, x45) -> f17(x41, x42, x46, x44, x45) :|: TRUE 9.37/3.21 f15(x35, x36, x37, x38, x39) -> f16(x40, x36, x37, x38, x39) :|: TRUE 9.37/3.21 f14(x30, x31, x32, x33, x34) -> f15(x30, x31, x32, x32, x34) :|: TRUE 9.37/3.21 f11(x25, x26, x27, x28, x29) -> f14(x25, x25, x27, x28, x29) :|: TRUE 9.37/3.21 f10(x58, x59, x60, x61, x62) -> f11(x58, x59, x60, x61, x62) :|: x63 < 0 9.37/3.21 f10(x115, x116, x117, x118, x119) -> f11(x115, x116, x117, x118, x119) :|: x120 > 0 9.37/3.21 f19(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: TRUE 9.37/3.21 f18(x52, x53, x54, x55, x56) -> f19(x57, x53, x54, x55, x56) :|: TRUE 9.37/3.21 f12(x47, x48, x49, x50, x51) -> f18(x47, x47, x49, x50, x51) :|: TRUE 9.37/3.21 f10(x64, x65, x66, x67, x68) -> f12(x64, x65, x66, x67, x68) :|: x69 = 0 9.37/3.21 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (5) IntTRSCompressionProof (EQUIVALENT) 9.37/3.21 Compressed rules. 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (6) 9.37/3.21 Obligation: 9.37/3.21 Rules: 9.37/3.21 f13(x85:0, x86:0, x87:0, x88:0, x89:0) -> f13(x40:0, x85:0, x46:0, x87:0, x89:0) :|: x86:0 + 1 <= x85:0 && x63:0 < 0 && x88:0 + 1 <= x87:0 && x85:0 >= 2 * x86:0 + x87:0 && x89:0 >= x85:0 9.37/3.21 f13(x, x1, x2, x3, x4) -> f13(x5, x, x2, x3, x4) :|: x3 + 1 <= x2 && x1 + 1 <= x && x >= 2 * x1 + x2 && x4 >= x 9.37/3.21 f13(x6, x7, x8, x9, x10) -> f13(x11, x6, x12, x8, x10) :|: x7 + 1 <= x6 && x13 > 0 && x9 + 1 <= x8 && x6 >= 2 * x7 + x8 && x10 >= x6 9.37/3.21 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (7) PolynomialOrderProcessor (EQUIVALENT) 9.37/3.21 Found the following polynomial interpretation: 9.37/3.21 [f13(x, x1, x2, x3, x4)] = -1 - x1 + x4 9.37/3.21 9.37/3.21 The following rules are decreasing: 9.37/3.21 f13(x85:0, x86:0, x87:0, x88:0, x89:0) -> f13(x40:0, x85:0, x46:0, x87:0, x89:0) :|: x86:0 + 1 <= x85:0 && x63:0 < 0 && x88:0 + 1 <= x87:0 && x85:0 >= 2 * x86:0 + x87:0 && x89:0 >= x85:0 9.37/3.21 f13(x, x1, x2, x3, x4) -> f13(x5, x, x2, x3, x4) :|: x3 + 1 <= x2 && x1 + 1 <= x && x >= 2 * x1 + x2 && x4 >= x 9.37/3.21 f13(x6, x7, x8, x9, x10) -> f13(x11, x6, x12, x8, x10) :|: x7 + 1 <= x6 && x13 > 0 && x9 + 1 <= x8 && x6 >= 2 * x7 + x8 && x10 >= x6 9.37/3.21 The following rules are bounded: 9.37/3.21 f13(x85:0, x86:0, x87:0, x88:0, x89:0) -> f13(x40:0, x85:0, x46:0, x87:0, x89:0) :|: x86:0 + 1 <= x85:0 && x63:0 < 0 && x88:0 + 1 <= x87:0 && x85:0 >= 2 * x86:0 + x87:0 && x89:0 >= x85:0 9.37/3.21 f13(x, x1, x2, x3, x4) -> f13(x5, x, x2, x3, x4) :|: x3 + 1 <= x2 && x1 + 1 <= x && x >= 2 * x1 + x2 && x4 >= x 9.37/3.21 f13(x6, x7, x8, x9, x10) -> f13(x11, x6, x12, x8, x10) :|: x7 + 1 <= x6 && x13 > 0 && x9 + 1 <= x8 && x6 >= 2 * x7 + x8 && x10 >= x6 9.37/3.21 9.37/3.21 ---------------------------------------- 9.37/3.21 9.37/3.21 (8) 9.37/3.21 YES 9.45/3.34 EOF