YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 24 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 28 ms]
(6) IntTRS
(7) CaseAnalysis [EQUIVALENT, 5 ms]
(8) AND
    (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IntTRS
        (15) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (16) 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(q, y) -> f2(x_1, y) :|: TRUE
f2(x, x1) -> f3(x, x2) :|: TRUE
f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
f3(x7, x8) -> f4(x7, x8) :|: x7 > 0
f6(x9, x10) -> f3(x9, x10) :|: TRUE
f3(x11, x12) -> f7(x11, x12) :|: x11 <= 0
Start term: f1(q, 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(x7, x8) -> f4(x7, x8) :|: x7 > 0
f6(x9, x10) -> f3(x9, x10) :|: TRUE
f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0

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(7) CaseAnalysis (EQUIVALENT)
Found the following inductive condition: 
f5(x0, x1): x1>=0

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 >= 0

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(10) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(11)
Obligation:
Rules:
f5(x13:0:0, x14:0:0) -> f5(x13:0:0 - (x14:0:0 + 1), x14:0:0 + 1) :|: x13:0:0 > 0 && x14:0:0 > -1

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = f5_1

The following rules are decreasing:
f5(x13:0:0, x14:0:0) -> f5(x13:0:0 - (x14:0:0 + 1), x14:0:0 + 1) :|: x13:0:0 > 0 && x14:0:0 > -1

The following rules are bounded:
f5(x13:0:0, x14:0:0) -> f5(x13:0:0 - (x14:0:0 + 1), x14:0:0 + 1) :|: x13:0:0 > 0 && x14:0:0 > -1


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(13)
YES

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(14)
Obligation:
Rules:
f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0

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(15) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = -x1

The following rules are decreasing:
f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0
The following rules are bounded:
f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > 0 && x14:0 < 0

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(16)
YES