/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 46 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 4 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
(8) AND
    (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
        (11) YES
    (12) IntTRS
        (13) RankingReductionPairProof [EQUIVALENT, 5 ms]
        (14) 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(x, y) -> f2(0, y) :|: TRUE
f2(x1, x2) -> f3(x1, 0) :|: TRUE
f5(x3, x4) -> f8(x3, arith) :|: TRUE && arith = x4 + 1
f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = x24 - 1
f4(x7, x8) -> f5(x7, x8) :|: x7 <= 50
f4(x9, x10) -> f6(x9, x10) :|: x9 > 50
f8(x11, x12) -> f7(x11, x12) :|: TRUE
f9(x13, x14) -> f7(x13, x14) :|: TRUE
f7(x26, x27) -> f10(x28, x27) :|: TRUE && x28 = x26 + 1
f3(x17, x18) -> f4(x17, x18) :|: x18 >= 0
f10(x19, x20) -> f3(x19, x20) :|: TRUE
f3(x21, x22) -> f11(x21, x22) :|: x22 < 0
Start term: f1(x, y)

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

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(4)
Obligation:
Rules:
f3(x17, x18) -> f4(x17, x18) :|: x18 >= 0
f10(x19, x20) -> f3(x19, x20) :|: TRUE
f7(x26, x27) -> f10(x28, x27) :|: TRUE && x28 = x26 + 1
f8(x11, x12) -> f7(x11, x12) :|: TRUE
f5(x3, x4) -> f8(x3, arith) :|: TRUE && arith = x4 + 1
f4(x7, x8) -> f5(x7, x8) :|: x7 <= 50
f9(x13, x14) -> f7(x13, x14) :|: TRUE
f6(x23, x24) -> f9(x23, x25) :|: TRUE && x25 = x24 - 1
f4(x9, x10) -> f6(x9, x10) :|: x9 > 50

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = 49 - x + x1

The following rules are decreasing:
f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49
The following rules are bounded:
f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = 49 - x

The following rules are decreasing:
f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50
The following rules are bounded:
f7(x, x1) -> f7(x + 1, x1 + 1) :|: x1 > -1 && x < 50

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(11)
YES

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(12)
Obligation:
Rules:
f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49

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(13) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f7 ] = f7_2

The following rules are decreasing:
f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49

The following rules are bounded:
f7(x26:0, x27:0) -> f7(x26:0 + 1, x27:0 - 1) :|: x27:0 > -1 && x26:0 > 49


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(14)
YES