YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 42 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) RankingReductionPairProof [EQUIVALENT, 21 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, 23) :|: TRUE
f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - 1
f3(x5, x6) -> f4(x5, x6) :|: x5 >= x6
f5(x7, x8) -> f3(x7, x8) :|: TRUE
f3(x9, x10) -> f6(x9, x10) :|: x9 < x10
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(x5, x6) -> f4(x5, x6) :|: x5 >= x6
f5(x7, x8) -> f3(x7, x8) :|: TRUE
f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x7:0, x8:0) -> f5(x7:0 - 1, x8:0) :|: x8:0 <= x7:0

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

The following rules are decreasing:
f5(x7:0, x8:0) -> f5(x7:0 - 1, x8:0) :|: x8:0 <= x7:0

The following rules are bounded:
f5(x7:0, x8:0) -> f5(x7:0 - 1, x8:0) :|: x8:0 <= x7:0


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(8)
YES