/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.c
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 110 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 37 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 22 ms]
(8) YES


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(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
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(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
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(2)
Obligation:
Rules:
f1(x, tx, y, ty, n) -> f2(x_1, tx, y, ty, n) :|: TRUE
f2(x1, x2, x3, x4, x5) -> f3(x1, x6, x3, x4, x5) :|: TRUE
f3(x7, x8, x9, x10, x11) -> f4(x7, x8, x12, x10, x11) :|: TRUE
f4(x13, x14, x15, x16, x17) -> f5(x13, x14, x15, x18, x17) :|: TRUE
f5(x19, x20, x21, x22, x23) -> f6(x19, x20, x21, x22, x24) :|: TRUE
f11(x25, x26, x27, x28, x29) -> f14(x25, x25, x27, x28, x29) :|: TRUE
f14(x30, x31, x32, x33, x34) -> f15(x30, x31, x32, x32, x34) :|: TRUE
f15(x35, x36, x37, x38, x39) -> f16(x40, x36, x37, x38, x39) :|: TRUE
f16(x41, x42, x43, x44, x45) -> f17(x41, x42, x46, x44, x45) :|: TRUE
f12(x47, x48, x49, x50, x51) -> f18(x47, x47, x49, x50, x51) :|: TRUE
f18(x52, x53, x54, x55, x56) -> f19(x57, x53, x54, x55, x56) :|: TRUE
f10(x58, x59, x60, x61, x62) -> f11(x58, x59, x60, x61, x62) :|: x63 < 0
f10(x115, x116, x117, x118, x119) -> f11(x115, x116, x117, x118, x119) :|: x120 > 0
f10(x64, x65, x66, x67, x68) -> f12(x64, x65, x66, x67, x68) :|: x69 = 0
f17(x70, x71, x72, x73, x74) -> f13(x70, x71, x72, x73, x74) :|: TRUE
f19(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: TRUE
f7(x80, x81, x82, x83, x84) -> f10(x80, x81, x82, x83, x84) :|: x80 <= x84 && x80 >= 2 * x81 + x82 && x82 >= x83 + 1 && x80 >= x81 + 1
f13(x85, x86, x87, x88, x89) -> f7(x85, x86, x87, x88, x89) :|: TRUE
f7(x90, x91, x92, x93, x94) -> f20(x90, x91, x92, x93, x94) :|: x90 < x91 + 1
f7(x121, x122, x123, x124, x125) -> f20(x121, x122, x123, x124, x125) :|: x123 < x124 + 1
f7(x126, x127, x128, x129, x130) -> f20(x126, x127, x128, x129, x130) :|: x126 > x130
f7(x131, x132, x133, x134, x135) -> f20(x131, x132, x133, x134, x135) :|: x131 < 2 * x132 + x133
f6(x95, x96, x97, x98, x99) -> f7(x95, x96, x97, x98, x99) :|: x95 + x97 >= 0
f6(x100, x101, x102, x103, x104) -> f8(x100, x101, x102, x103, x104) :|: x100 + x102 < 0
f20(x105, x106, x107, x108, x109) -> f9(x105, x106, x107, x108, x109) :|: TRUE
f8(x110, x111, x112, x113, x114) -> f9(x110, x111, x112, x113, x114) :|: TRUE
Start term: f1(x, tx, y, ty, n)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained one non-trivial SCC.

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(4)
Obligation:
Rules:
f7(x80, x81, x82, x83, x84) -> f10(x80, x81, x82, x83, x84) :|: x80 <= x84 && x80 >= 2 * x81 + x82 && x82 >= x83 + 1 && x80 >= x81 + 1
f13(x85, x86, x87, x88, x89) -> f7(x85, x86, x87, x88, x89) :|: TRUE
f17(x70, x71, x72, x73, x74) -> f13(x70, x71, x72, x73, x74) :|: TRUE
f16(x41, x42, x43, x44, x45) -> f17(x41, x42, x46, x44, x45) :|: TRUE
f15(x35, x36, x37, x38, x39) -> f16(x40, x36, x37, x38, x39) :|: TRUE
f14(x30, x31, x32, x33, x34) -> f15(x30, x31, x32, x32, x34) :|: TRUE
f11(x25, x26, x27, x28, x29) -> f14(x25, x25, x27, x28, x29) :|: TRUE
f10(x58, x59, x60, x61, x62) -> f11(x58, x59, x60, x61, x62) :|: x63 < 0
f10(x115, x116, x117, x118, x119) -> f11(x115, x116, x117, x118, x119) :|: x120 > 0
f19(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: TRUE
f18(x52, x53, x54, x55, x56) -> f19(x57, x53, x54, x55, x56) :|: TRUE
f12(x47, x48, x49, x50, x51) -> f18(x47, x47, x49, x50, x51) :|: TRUE
f10(x64, x65, x66, x67, x68) -> f12(x64, x65, x66, x67, x68) :|: x69 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
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
f13(x, x1, x2, x3, x4) -> f13(x5, x, x2, x3, x4) :|: x3 + 1 <= x2 && x1 + 1 <= x && x >= 2 * x1 + x2 && x4 >= x
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

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f13(x, x1, x2, x3, x4)] = -1 - x1 + x4

The following rules are decreasing:
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
f13(x, x1, x2, x3, x4) -> f13(x5, x, x2, x3, x4) :|: x3 + 1 <= x2 && x1 + 1 <= x && x >= 2 * x1 + x2 && x4 >= x
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
The following rules are bounded:
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
f13(x, x1, x2, x3, x4) -> f13(x5, x, x2, x3, x4) :|: x3 + 1 <= x2 && x1 + 1 <= x && x >= 2 * x1 + x2 && x4 >= x
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

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(8)
YES