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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 66 ms]
(4) AND
    (5) IntTRS
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IntTRS
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IntTRS
        (10) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
        (11) YES
    (12) IntTRS
        (13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (14) IntTRS
        (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) RankingReductionPairProof [EQUIVALENT, 21 ms]
        (18) 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, c) -> f2(i, j, 0) :|: TRUE
f2(x, x1, x2) -> f3(0, x1, x2) :|: TRUE
f4(x3, x4, x5) -> f5(x3, x4, arith) :|: TRUE && arith = x5 + 1
f5(x36, x37, x38) -> f6(x39, x37, x38) :|: TRUE && x39 = x36 + 1
f3(x9, x10, x11) -> f4(x9, x10, x11) :|: x9 < 100
f6(x12, x13, x14) -> f3(x12, x13, x14) :|: TRUE
f3(x15, x16, x17) -> f7(x15, x16, x17) :|: x15 >= 100
f7(x18, x19, x20) -> f8(x18, 5, x20) :|: TRUE
f9(x40, x41, x42) -> f10(x40, x41, x43) :|: TRUE && x43 = x42 + 1
f10(x44, x45, x46) -> f11(x44, x47, x46) :|: TRUE && x47 = x45 + 3
f8(x27, x28, x29) -> f9(x27, x28, x29) :|: x28 < 21
f11(x30, x31, x32) -> f8(x30, x31, x32) :|: TRUE
f8(x33, x34, x35) -> f12(x33, x34, x35) :|: x34 >= 21
Start term: f1(i, j, c)

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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(x9, x10, x11) -> f4(x9, x10, x11) :|: x9 < 100
f6(x12, x13, x14) -> f3(x12, x13, x14) :|: TRUE
f5(x36, x37, x38) -> f6(x39, x37, x38) :|: TRUE && x39 = x36 + 1
f4(x3, x4, x5) -> f5(x3, x4, arith) :|: TRUE && arith = x5 + 1

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
f5(x36:0, x37:0, x38:0) -> f5(x36:0 + 1, x37:0, x38:0 + 1) :|: x36:0 < 99

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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, x3) -> f5(x1)

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(9)
Obligation:
Rules:
f5(x36:0) -> f5(x36:0 + 1) :|: x36:0 < 99

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(10) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x)] = 98 - x

The following rules are decreasing:
f5(x36:0) -> f5(x36:0 + 1) :|: x36:0 < 99
The following rules are bounded:
f5(x36:0) -> f5(x36:0 + 1) :|: x36:0 < 99

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(11)
YES

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(12)
Obligation:
Rules:
f8(x27, x28, x29) -> f9(x27, x28, x29) :|: x28 < 21
f11(x30, x31, x32) -> f8(x30, x31, x32) :|: TRUE
f10(x44, x45, x46) -> f11(x44, x47, x46) :|: TRUE && x47 = x45 + 3
f9(x40, x41, x42) -> f10(x40, x41, x43) :|: TRUE && x43 = x42 + 1

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f10(x44:0, x45:0, x46:0) -> f10(x44:0, x45:0 + 3, x46:0 + 1) :|: x45:0 < 18

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

   f10(x1, x2, x3) -> f10(x2)

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(16)
Obligation:
Rules:
f10(x45:0) -> f10(x45:0 + 3) :|: x45:0 < 18

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f10 ] = -1/3*f10_1

The following rules are decreasing:
f10(x45:0) -> f10(x45:0 + 3) :|: x45:0 < 18

The following rules are bounded:
f10(x45:0) -> f10(x45:0 + 3) :|: x45:0 < 18


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(18)
YES