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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 35 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 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(x4, arith) :|: TRUE && arith = x5 + 1
f3(x6, x7) -> f4(x6, x7) :|: x6 > x7
f5(x8, x9) -> f3(x8, x9) :|: TRUE
f3(x10, x11) -> f6(x10, x11) :|: x10 <= x11
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(x6, x7) -> f4(x6, x7) :|: x6 > x7
f5(x8, x9) -> f3(x8, x9) :|: TRUE
f4(x4, x5) -> f5(x4, arith) :|: TRUE && arith = x5 + 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0

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

The following rules are decreasing:
f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0
The following rules are bounded:
f5(x8:0, x9:0) -> f5(x8:0, x9:0 + 1) :|: x9:0 < x8:0

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(8)
YES