/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 49 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) RankingReductionPairProof [EQUIVALENT, 23 ms]
(8) 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
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
f3(x8, x9) -> f4(x8, x9) :|: x8 > x9
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f3(x12, x13) -> f7(x12, x13) :|: x12 <= x13
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(x8, x9) -> f4(x8, x9) :|: x8 > x9
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x14:0, x15:0) -> f5(x14:0 - 1, x15:0 + 1) :|: x15:0 + 1 < x14:0

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(7) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = -1/2*f5_2 + 1/2*f5_1

The following rules are decreasing:
f5(x14:0, x15:0) -> f5(x14:0 - 1, x15:0 + 1) :|: x15:0 + 1 < x14:0

The following rules are bounded:
f5(x14:0, x15:0) -> f5(x14:0 - 1, x15:0 + 1) :|: x15:0 + 1 < x14:0


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(8)
YES