/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 69 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) YES


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(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
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(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
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(2)
Obligation:
Rules:
f1(c, u, v, w, x, y, z) -> f2(c, u, v, w, x_1, y, z) :|: TRUE
f2(x1, x2, x3, x4, x5, x6, x7) -> f3(x1, x2, x3, x4, x5, x8, x7) :|: TRUE
f3(x9, x10, x11, x12, x13, x14, x15) -> f4(x9, x10, x11, x12, x13, x14, x16) :|: TRUE
f4(x17, x18, x19, x20, x21, x22, x23) -> f5(x17, x21, x19, x20, x21, x22, x23) :|: TRUE
f5(x24, x25, x26, x27, x28, x29, x30) -> f6(x24, x25, x29, x27, x28, x29, x30) :|: TRUE
f6(x31, x32, x33, x34, x35, x36, x37) -> f7(x31, x32, x33, x37, x35, x36, x37) :|: TRUE
f7(x38, x39, x40, x41, x42, x43, x44) -> f8(0, x39, x40, x41, x42, x43, x44) :|: TRUE
f9(x45, x46, x47, x48, x49, x50, x51) -> f10(arith, x46, x47, x48, x49, x50, x51) :|: TRUE && arith = x45 + 1
f11(x122, x123, x124, x125, x126, x127, x128) -> f14(x122, x123, x124, x125, x126, x127, x129) :|: TRUE && x129 = x128 - 1
f14(x130, x131, x132, x133, x134, x135, x136) -> f15(x130, x131, x132, x133, x137, x135, x136) :|: TRUE && x137 = x134 + x136
f12(x138, x139, x140, x141, x142, x143, x144) -> f16(x138, x139, x140, x141, x142, x145, x144) :|: TRUE && x145 = x143 + 1
f10(x73, x74, x75, x76, x77, x78, x79) -> f11(x73, x74, x75, x76, x77, x78, x79) :|: x79 > 1
f10(x80, x81, x82, x83, x84, x85, x86) -> f12(x80, x81, x82, x83, x84, x85, x86) :|: x86 <= 1
f15(x87, x88, x89, x90, x91, x92, x93) -> f13(x87, x88, x89, x90, x91, x92, x93) :|: TRUE
f16(x94, x95, x96, x97, x98, x99, x100) -> f13(x94, x95, x96, x97, x98, x99, x100) :|: TRUE
f8(x101, x102, x103, x104, x105, x106, x107) -> f9(x101, x102, x103, x104, x105, x106, x107) :|: x105 >= x106
f13(x108, x109, x110, x111, x112, x113, x114) -> f8(x108, x109, x110, x111, x112, x113, x114) :|: TRUE
f8(x115, x116, x117, x118, x119, x120, x121) -> f17(x115, x116, x117, x118, x119, x120, x121) :|: x119 < x120
Start term: f1(c, u, v, w, x, y, z)

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

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(4)
Obligation:
Rules:
f8(x101, x102, x103, x104, x105, x106, x107) -> f9(x101, x102, x103, x104, x105, x106, x107) :|: x105 >= x106
f13(x108, x109, x110, x111, x112, x113, x114) -> f8(x108, x109, x110, x111, x112, x113, x114) :|: TRUE
f15(x87, x88, x89, x90, x91, x92, x93) -> f13(x87, x88, x89, x90, x91, x92, x93) :|: TRUE
f14(x130, x131, x132, x133, x134, x135, x136) -> f15(x130, x131, x132, x133, x137, x135, x136) :|: TRUE && x137 = x134 + x136
f11(x122, x123, x124, x125, x126, x127, x128) -> f14(x122, x123, x124, x125, x126, x127, x129) :|: TRUE && x129 = x128 - 1
f10(x73, x74, x75, x76, x77, x78, x79) -> f11(x73, x74, x75, x76, x77, x78, x79) :|: x79 > 1
f9(x45, x46, x47, x48, x49, x50, x51) -> f10(arith, x46, x47, x48, x49, x50, x51) :|: TRUE && arith = x45 + 1
f16(x94, x95, x96, x97, x98, x99, x100) -> f13(x94, x95, x96, x97, x98, x99, x100) :|: TRUE
f12(x138, x139, x140, x141, x142, x143, x144) -> f16(x138, x139, x140, x141, x142, x145, x144) :|: TRUE && x145 = x143 + 1
f10(x80, x81, x82, x83, x84, x85, x86) -> f12(x80, x81, x82, x83, x84, x85, x86) :|: x86 <= 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f10(x80:0, x81:0, x82:0, x83:0, x84:0, x85:0, x86:0) -> f10(x80:0 + 1, x81:0, x82:0, x83:0, x84:0, x85:0 + 1, x86:0) :|: x86:0 < 2 && x85:0 + 1 <= x84:0
f10(x73:0, x74:0, x75:0, x76:0, x77:0, x78:0, x79:0) -> f10(x73:0 + 1, x74:0, x75:0, x76:0, x77:0 + (x79:0 - 1), x78:0, x79:0 - 1) :|: x79:0 > 1 && x78:0 <= x77:0 + (x79:0 - 1)

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(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f10(x1, x2, x3, x4, x5, x6, x7) -> f10(x5, x6, x7)

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(8)
Obligation:
Rules:
f10(x84:0, x85:0, x86:0) -> f10(x84:0, x85:0 + 1, x86:0) :|: x86:0 < 2 && x85:0 + 1 <= x84:0
f10(x77:0, x78:0, x79:0) -> f10(x77:0 + (x79:0 - 1), x78:0, x79:0 - 1) :|: x79:0 > 1 && x78:0 <= x77:0 + (x79:0 - 1)

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f10(x, x1, x2)] = -2 + x2

The following rules are decreasing:
f10(x77:0, x78:0, x79:0) -> f10(x77:0 + (x79:0 - 1), x78:0, x79:0 - 1) :|: x79:0 > 1 && x78:0 <= x77:0 + (x79:0 - 1)
The following rules are bounded:
f10(x77:0, x78:0, x79:0) -> f10(x77:0 + (x79:0 - 1), x78:0, x79:0 - 1) :|: x79:0 > 1 && x78:0 <= x77:0 + (x79:0 - 1)

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(10)
Obligation:
Rules:
f10(x84:0, x85:0, x86:0) -> f10(x84:0, x85:0 + 1, x86:0) :|: x86:0 < 2 && x85:0 + 1 <= x84:0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f10(x, x1, x2)] = x - x1

The following rules are decreasing:
f10(x84:0, x85:0, x86:0) -> f10(x84:0, x85:0 + 1, x86:0) :|: x86:0 < 2 && x85:0 + 1 <= x84:0
The following rules are bounded:
f10(x84:0, x85:0, x86:0) -> f10(x84:0, x85:0 + 1, x86:0) :|: x86:0 < 2 && x85:0 + 1 <= x84:0

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(12)
YES