/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 28 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 33 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 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(i, n) -> f2(i, x_1) :|: TRUE
f2(x, x1) -> f3(arith, x1) :|: TRUE && arith = x1 - 1
f4(x10, x11) -> f5(x12, x11) :|: TRUE && x12 = x10 - 1
f3(x4, x5) -> f4(x4, x5) :|: x4 > 1
f5(x6, x7) -> f3(x6, x7) :|: TRUE
f3(x8, x9) -> f6(x8, x9) :|: x8 <= 1
Start term: f1(i, n)

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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(x4, x5) -> f4(x4, x5) :|: x4 > 1
f5(x6, x7) -> f3(x6, x7) :|: TRUE
f4(x10, x11) -> f5(x12, x11) :|: TRUE && x12 = x10 - 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x6:0, x7:0) -> f5(x6:0 - 1, x7:0) :|: x6:0 > 1

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(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f5(x1, x2) -> f5(x1)

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(8)
Obligation:
Rules:
f5(x6:0) -> f5(x6:0 - 1) :|: x6:0 > 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x)] = x

The following rules are decreasing:
f5(x6:0) -> f5(x6:0 - 1) :|: x6:0 > 1
The following rules are bounded:
f5(x6:0) -> f5(x6:0 - 1) :|: x6:0 > 1

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(10)
YES