/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 56 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 4 ms]
(10) YES


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(0)
Obligation:
c file /export/starexec/sandbox/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
f3(x1, x2) -> f4(x1, 0) :|: TRUE
f5(x3, x4) -> f6(x3, arith) :|: TRUE && arith = x4 + 1
f4(x5, x6) -> f5(x5, x6) :|: x6 < x5
f6(x7, x8) -> f4(x7, x8) :|: TRUE
f4(x9, x10) -> f7(x9, x10) :|: x10 >= x9
f7(x19, x20) -> f8(x21, x20) :|: TRUE && x21 = x19 - 1
f2(x13, x14) -> f3(x13, x14) :|: x13 > 0
f8(x15, x16) -> f2(x15, x16) :|: TRUE
f2(x17, x18) -> f9(x17, x18) :|: x17 <= 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:
f2(x13, x14) -> f3(x13, x14) :|: x13 > 0
f8(x15, x16) -> f2(x15, x16) :|: TRUE
f7(x19, x20) -> f8(x21, x20) :|: TRUE && x21 = x19 - 1
f4(x9, x10) -> f7(x9, x10) :|: x10 >= x9
f3(x1, x2) -> f4(x1, 0) :|: TRUE
f6(x7, x8) -> f4(x7, x8) :|: TRUE
f5(x3, x4) -> f6(x3, arith) :|: TRUE && arith = x4 + 1
f4(x5, x6) -> f5(x5, x6) :|: x6 < x5

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f4(x9:0, x10:0) -> f4(x9:0 - 1, 0) :|: x9:0 <= x10:0 && x9:0 > 1
f4(x5:0, x6:0) -> f4(x5:0, x6:0 + 1) :|: x6:0 < x5:0

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4(x, x1)] = -1 + x

The following rules are decreasing:
f4(x9:0, x10:0) -> f4(x9:0 - 1, 0) :|: x9:0 <= x10:0 && x9:0 > 1
The following rules are bounded:
f4(x9:0, x10:0) -> f4(x9:0 - 1, 0) :|: x9:0 <= x10:0 && x9:0 > 1

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(8)
Obligation:
Rules:
f4(x5:0, x6:0) -> f4(x5:0, x6:0 + 1) :|: x6:0 < x5:0

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(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4 ] = -1*f4_2 + f4_1

The following rules are decreasing:
f4(x5:0, x6:0) -> f4(x5:0, x6:0 + 1) :|: x6:0 < x5:0

The following rules are bounded:
f4(x5:0, x6:0) -> f4(x5:0, x6:0 + 1) :|: x6:0 < x5:0


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(10)
YES