/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 51 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 3 ms]
(10) 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(i, j) -> f2(0, j) :|: TRUE
f2(x, x1) -> f3(x, 3) :|: TRUE
f5(x2, x3) -> f6(x2, arith) :|: TRUE && arith = x3 - 1
f6(x20, x21) -> f7(x20, x22) :|: TRUE && x22 = x21 + 2
f4(x6, x7) -> f5(x6, x7) :|: x7 < 12
f7(x8, x9) -> f4(x8, x9) :|: TRUE
f4(x10, x11) -> f8(x10, x11) :|: x11 >= 12
f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
f3(x14, x15) -> f4(x14, x15) :|: x14 < 10
f9(x16, x17) -> f3(x16, x17) :|: TRUE
f3(x18, x19) -> f10(x18, x19) :|: x18 >= 10
Start term: f1(i, j)

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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(x14, x15) -> f4(x14, x15) :|: x14 < 10
f9(x16, x17) -> f3(x16, x17) :|: TRUE
f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
f4(x10, x11) -> f8(x10, x11) :|: x11 >= 12
f7(x8, x9) -> f4(x8, x9) :|: TRUE
f6(x20, x21) -> f7(x20, x22) :|: TRUE && x22 = x21 + 2
f5(x2, x3) -> f6(x2, arith) :|: TRUE && arith = x3 - 1
f4(x6, x7) -> f5(x6, x7) :|: x7 < 12

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f4(x10:0, x11:0) -> f4(x10:0 + 1, x11:0) :|: x11:0 > 11 && x10:0 < 9
f4(x6:0, x7:0) -> f4(x6:0, x7:0 + 1) :|: x7:0 < 12

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4(x, x1)] = 11 - x1

The following rules are decreasing:
f4(x6:0, x7:0) -> f4(x6:0, x7:0 + 1) :|: x7:0 < 12
The following rules are bounded:
f4(x6:0, x7:0) -> f4(x6:0, x7:0 + 1) :|: x7:0 < 12

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(8)
Obligation:
Rules:
f4(x10:0, x11:0) -> f4(x10:0 + 1, x11:0) :|: x11:0 > 11 && x10:0 < 9

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4(x, x1)] = 8 - x

The following rules are decreasing:
f4(x10:0, x11:0) -> f4(x10:0 + 1, x11:0) :|: x11:0 > 11 && x10:0 < 9
The following rules are bounded:
f4(x10:0, x11:0) -> f4(x10:0 + 1, x11:0) :|: x11:0 > 11 && x10:0 < 9

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(10)
YES