/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 44 ms]
(4) AND
    (5) IntTRS
        (6) IntTRSCompressionProof [EQUIVALENT, 6 ms]
        (7) IntTRS
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) IntTRS
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IntTRS
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (18) 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(i, j) -> f2(0, j) :|: TRUE
f2(x, x1) -> f3(x, 5) :|: TRUE
f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
f3(x4, x5) -> f4(x4, x5) :|: x4 < 100
f5(x6, x7) -> f3(x6, x7) :|: TRUE
f3(x8, x9) -> f6(x8, x9) :|: x8 >= 100
f7(x18, x19) -> f8(x18, x20) :|: TRUE && x20 = x19 + 3
f6(x12, x13) -> f7(x12, x13) :|: x13 < 21
f8(x14, x15) -> f6(x14, x15) :|: TRUE
f6(x16, x17) -> f9(x16, x17) :|: x17 >= 21
Start term: f1(i, j)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained 2 non-trivial SCCs.

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(4)
Complex Obligation (AND)

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(5)
Obligation:
Rules:
f3(x4, x5) -> f4(x4, x5) :|: x4 < 100
f5(x6, x7) -> f3(x6, x7) :|: TRUE
f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f5(x6:0, x7:0) -> f5(x6:0 + 1, x7:0) :|: x6:0 < 100

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

   f5(x1, x2) -> f5(x1)

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(9)
Obligation:
Rules:
f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 100

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(10) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = -1*f5_1

The following rules are decreasing:
f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 100

The following rules are bounded:
f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 100


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(11)
YES

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(12)
Obligation:
Rules:
f6(x12, x13) -> f7(x12, x13) :|: x13 < 21
f8(x14, x15) -> f6(x14, x15) :|: TRUE
f7(x18, x19) -> f8(x18, x20) :|: TRUE && x20 = x19 + 3

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f8(x14:0, x15:0) -> f8(x14:0, x15:0 + 3) :|: x15:0 < 21

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

   f8(x1, x2) -> f8(x2)

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(16)
Obligation:
Rules:
f8(x15:0) -> f8(x15:0 + 3) :|: x15:0 < 21

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x)] = 20 - x

The following rules are decreasing:
f8(x15:0) -> f8(x15:0 + 3) :|: x15:0 < 21
The following rules are bounded:
f8(x15:0) -> f8(x15:0 + 3) :|: x15:0 < 21

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(18)
YES