/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 56 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 12 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 9 ms]
(8) IntTRS
(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 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(i, j, n) -> f2(x_1, j, n) :|: TRUE
f2(x, x1, x2) -> f3(x, x3, x2) :|: TRUE
f3(x4, x5, x6) -> f4(x4, x5, x7) :|: TRUE
f5(x8, x9, x10) -> f6(x8, 0, x10) :|: TRUE
f7(x11, x12, x13) -> f8(x11, arith, x13) :|: TRUE && arith = x12 + 1
f6(x14, x15, x16) -> f7(x14, x15, x16) :|: x15 <= x14
f8(x17, x18, x19) -> f6(x17, x18, x19) :|: TRUE
f6(x20, x21, x22) -> f9(x20, x21, x22) :|: x21 > x20
f9(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 1
f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < x28
f10(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
f4(x32, x33, x34) -> f11(x32, x33, x34) :|: x32 >= x34
Start term: f1(i, j, 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:
f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < x28
f10(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
f9(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 1
f6(x20, x21, x22) -> f9(x20, x21, x22) :|: x21 > x20
f5(x8, x9, x10) -> f6(x8, 0, x10) :|: TRUE
f8(x17, x18, x19) -> f6(x17, x18, x19) :|: TRUE
f7(x11, x12, x13) -> f8(x11, arith, x13) :|: TRUE && arith = x12 + 1
f6(x14, x15, x16) -> f7(x14, x15, x16) :|: x15 <= x14

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x20:0, x21:0, x22:0) -> f6(x20:0 + 1, 0, x22:0) :|: x21:0 > x20:0 && x22:0 > x20:0 + 1
f6(x14:0, x15:0, x16:0) -> f6(x14:0, x15:0 + 1, x16:0) :|: x15:0 <= x14:0

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1, x2)] = -1 - x + x2

The following rules are decreasing:
f6(x20:0, x21:0, x22:0) -> f6(x20:0 + 1, 0, x22:0) :|: x21:0 > x20:0 && x22:0 > x20:0 + 1
The following rules are bounded:
f6(x20:0, x21:0, x22:0) -> f6(x20:0 + 1, 0, x22:0) :|: x21:0 > x20:0 && x22:0 > x20:0 + 1

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(8)
Obligation:
Rules:
f6(x14:0, x15:0, x16:0) -> f6(x14:0, x15:0 + 1, x16:0) :|: x15:0 <= x14:0

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

   f6(x1, x2, x3) -> f6(x1, x2)

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(10)
Obligation:
Rules:
f6(x14:0, x15:0) -> f6(x14:0, x15:0 + 1) :|: x15:0 <= x14:0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = x - x1

The following rules are decreasing:
f6(x14:0, x15:0) -> f6(x14:0, x15:0 + 1) :|: x15:0 <= x14:0
The following rules are bounded:
f6(x14:0, x15:0) -> f6(x14:0, x15:0 + 1) :|: x15:0 <= x14:0

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(12)
YES