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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 61 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) 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) -> f2(x_1, j) :|: TRUE
f2(x, x1) -> f3(x, x2) :|: TRUE
f4(x3, x4) -> f5(x3, 0) :|: TRUE
f6(x5, x6) -> f7(x5, arith) :|: TRUE && arith = x6 + 1
f5(x7, x8) -> f6(x7, x8) :|: x7 > 2 && x8 <= 9
f7(x9, x10) -> f5(x9, x10) :|: TRUE
f5(x11, x12) -> f8(x11, x12) :|: x11 <= 2
f5(x21, x22) -> f8(x21, x22) :|: x22 > 9
f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
f3(x15, x16) -> f4(x15, x16) :|: x15 < 5
f9(x17, x18) -> f3(x17, x18) :|: TRUE
f3(x19, x20) -> f10(x19, x20) :|: x19 >= 5
Start term: f1(i, j)

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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(x15, x16) -> f4(x15, x16) :|: x15 < 5
f9(x17, x18) -> f3(x17, x18) :|: TRUE
f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
f5(x11, x12) -> f8(x11, x12) :|: x11 <= 2
f4(x3, x4) -> f5(x3, 0) :|: TRUE
f7(x9, x10) -> f5(x9, x10) :|: TRUE
f6(x5, x6) -> f7(x5, arith) :|: TRUE && arith = x6 + 1
f5(x7, x8) -> f6(x7, x8) :|: x7 > 2 && x8 <= 9
f5(x21, x22) -> f8(x21, x22) :|: x22 > 9

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
f5(x11:0, x12:0) -> f5(x11:0 + 1, 0) :|: x11:0 < 3 && x11:0 < 4
f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = 2 - x

The following rules are decreasing:
f5(x11:0, x12:0) -> f5(x11:0 + 1, 0) :|: x11:0 < 3 && x11:0 < 4
f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4
The following rules are bounded:
f5(x11:0, x12:0) -> f5(x11:0 + 1, 0) :|: x11:0 < 3 && x11:0 < 4

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(8)
Obligation:
Rules:
f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10
f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = 3 - x

The following rules are decreasing:
f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4
The following rules are bounded:
f5(x21:0, x22:0) -> f5(x21:0 + 1, 0) :|: x22:0 > 9 && x21:0 < 4

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(10)
Obligation:
Rules:
f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = -1*f5_2

The following rules are decreasing:
f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10

The following rules are bounded:
f5(x7:0, x8:0) -> f5(x7:0, x8:0 + 1) :|: x7:0 > 2 && x8:0 < 10


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(12)
YES