/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 51 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 13 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) IntTRS
(13) RankingReductionPairProof [EQUIVALENT, 6 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(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 - 1
f4(x8, x9) -> f5(x8, x9) :|: x8 >= 0
f4(x10, x11) -> f6(x10, x11) :|: x10 < 0
f8(x12, x13) -> f7(x12, x13) :|: TRUE
f9(x14, x15) -> f7(x14, x15) :|: TRUE
f3(x16, x17) -> f4(x16, x17) :|: x16 >= 0
f3(x25, x26) -> f4(x25, x26) :|: x26 >= 0
f7(x18, x19) -> f3(x18, x19) :|: TRUE
f3(x20, x21) -> f10(x20, x21) :|: x20 < 0 && x21 < 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(x16, x17) -> f4(x16, x17) :|: x16 >= 0
f7(x18, x19) -> f3(x18, x19) :|: TRUE
f8(x12, x13) -> f7(x12, x13) :|: TRUE
f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
f4(x8, x9) -> f5(x8, x9) :|: x8 >= 0
f3(x25, x26) -> f4(x25, x26) :|: x26 >= 0
f9(x14, x15) -> f7(x14, x15) :|: TRUE
f6(x22, x23) -> f9(x22, x24) :|: TRUE && x24 = x23 - 1
f4(x10, x11) -> f6(x10, x11) :|: x10 < 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > -1
f4(x10:0, x11:0) -> f7(x10:0, x11:0 - 1) :|: x10:0 < 0
f7(x, x1) -> f4(x, x1) :|: x > -1
f4(x8:0, x9:0) -> f7(x8:0 - 1, x9:0) :|: x8:0 > -1

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = x
[f4(x2, x3)] = x2

The following rules are decreasing:
f4(x8:0, x9:0) -> f7(x8:0 - 1, x9:0) :|: x8:0 > -1
The following rules are bounded:
f7(x, x1) -> f4(x, x1) :|: x > -1
f4(x8:0, x9:0) -> f7(x8:0 - 1, x9:0) :|: x8:0 > -1

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(8)
Obligation:
Rules:
f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 > -1
f4(x10:0, x11:0) -> f7(x10:0, x11:0 - 1) :|: x10:0 < 0
f7(x, x1) -> f4(x, x1) :|: x > -1

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0
f7(x:0, x1:0) -> f7(x:0, x1:0 - 1) :|: x:0 > -1 && x:0 < 0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = d + c*x + x1

The following rules are decreasing:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0
f7(x:0, x1:0) -> f7(x:0, x1:0 - 1) :|: x:0 > -1 && x:0 < 0
The following rules are bounded:
f7(x:0, x1:0) -> f7(x:0, x1:0 - 1) :|: x:0 > -1 && x:0 < 0

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(12)
Obligation:
Rules:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0

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

The following rules are decreasing:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0

The following rules are bounded:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 - 1) :|: x19:0:0 > -1 && x18:0:0 < 0


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(14)
YES