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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 52 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 12 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
(8) AND
    (9) IntTRS
        (10) TerminationGraphProcessor [EQUIVALENT, 0 ms]
        (11) YES
    (12) IntTRS
        (13) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (14) IntTRS
        (15) RankingReductionPairProof [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(x, y) -> f2(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f5(x4, x5) -> f6(arith, x5) :|: TRUE && arith = x4 - 1
f6(x20, x21) -> f7(x20, x22) :|: TRUE && x22 = x21 - 1
f4(x8, x9) -> f5(x8, x9) :|: x9 > 0
f7(x10, x11) -> f4(x10, x11) :|: TRUE
f4(x12, x13) -> f8(x12, x13) :|: x13 <= 0
f3(x14, x15) -> f4(x14, x15) :|: x14 = x15 && x14 > 0
f8(x16, x17) -> f3(x16, x17) :|: TRUE
f3(x18, x19) -> f9(x18, x19) :|: x18 <= 0
f3(x23, x24) -> f9(x23, x24) :|: x23 < x24
f3(x25, x26) -> f9(x25, x26) :|: x25 > x26
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(x14, x15) -> f4(x14, x15) :|: x14 = x15 && x14 > 0
f8(x16, x17) -> f3(x16, x17) :|: TRUE
f4(x12, x13) -> f8(x12, x13) :|: x13 <= 0
f7(x10, x11) -> f4(x10, x11) :|: TRUE
f6(x20, x21) -> f7(x20, x22) :|: TRUE && x22 = x21 - 1
f5(x4, x5) -> f6(arith, x5) :|: TRUE && arith = x4 - 1
f4(x8, x9) -> f5(x8, x9) :|: x9 > 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f4(x8:0, x9:0) -> f4(x8:0 - 1, x9:0 - 1) :|: x9:0 > 0
f4(x12:0, x12:01) -> f4(x12:0, x12:0) :|: x12:0 < 1 && x12:0 > 0 && x12:0 = x12:01

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4(x, x1)] = d + x1

The following rules are decreasing:
f4(x8:0, x9:0) -> f4(x8:0 - 1, x9:0 - 1) :|: x9:0 > 0
The following rules are bounded:
f4(x12:0, x12:01) -> f4(x12:0, x12:0) :|: x12:0 < 1 && x12:0 > 0 && x12:0 = x12:01

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f4(x12:0, x12:01) -> f4(x12:0, x12:0) :|: x12:0 < 1 && x12:0 > 0 && x12:0 = x12:01

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(10) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained no non-trivial SCC(s).

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(11)
YES

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(12)
Obligation:
Rules:
f4(x8:0, x9:0) -> f4(x8:0 - 1, x9:0 - 1) :|: x9:0 > 0

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

   f4(x1, x2) -> f4(x2)

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(14)
Obligation:
Rules:
f4(x9:0) -> f4(x9:0 - 1) :|: x9:0 > 0

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(15) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4 ] = f4_1

The following rules are decreasing:
f4(x9:0) -> f4(x9:0 - 1) :|: x9:0 > 0

The following rules are bounded:
f4(x9:0) -> f4(x9:0 - 1) :|: x9:0 > 0


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(16)
YES