YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 28 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 2 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) 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(y) -> f2(x_1) :|: TRUE
f3(x) -> f4(arith) :|: TRUE && arith = x - 1
f2(x1) -> f3(x1) :|: x1 >= 0
f4(x2) -> f2(x2) :|: TRUE
f2(x3) -> f5(x3) :|: x3 < 0
Start term: f1(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(x1) -> f3(x1) :|: x1 >= 0
f4(x2) -> f2(x2) :|: TRUE
f3(x) -> f4(arith) :|: TRUE && arith = x - 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f4(x2:0) -> f4(x2:0 - 1) :|: x2:0 > -1

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4(x)] = x

The following rules are decreasing:
f4(x2:0) -> f4(x2:0 - 1) :|: x2:0 > -1
The following rules are bounded:
f4(x2:0) -> f4(x2:0 - 1) :|: x2:0 > -1

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(8)
YES