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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 51 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 2 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 8 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) 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, c) -> f2(0, c) :|: TRUE
f2(x, x1) -> f3(x, 0) :|: TRUE
f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
f7(x20, x21) -> f9(x20, x22) :|: TRUE && x22 = x21 + 1
f5(x6, x7) -> f6(x6, x7) :|: x6 <= 10
f5(x8, x9) -> f7(x8, x9) :|: x8 > 10
f6(x10, x11) -> f8(x10, x11) :|: TRUE
f9(x12, x13) -> f8(x12, x13) :|: TRUE
f3(x14, x15) -> f4(x14, x15) :|: x14 < 20
f8(x16, x17) -> f3(x16, x17) :|: TRUE
f3(x18, x19) -> f10(x18, x19) :|: x18 >= 20
Start term: f1(i, c)

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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 < 20
f8(x16, x17) -> f3(x16, x17) :|: TRUE
f6(x10, x11) -> f8(x10, x11) :|: TRUE
f5(x6, x7) -> f6(x6, x7) :|: x6 <= 10
f4(x2, x3) -> f5(arith, x3) :|: TRUE && arith = x2 + 1
f9(x12, x13) -> f8(x12, x13) :|: TRUE
f7(x20, x21) -> f9(x20, x22) :|: TRUE && x22 = x21 + 1
f5(x8, x9) -> f7(x8, x9) :|: x8 > 10

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x8:0, x9:0) -> f5(x8:0 + 1, x9:0 + 1) :|: x8:0 > 10 && x8:0 < 20
f5(x6:0, x7:0) -> f5(x6:0 + 1, x7:0) :|: x6:0 < 11 && x6:0 < 20

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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(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20
f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 11 && x6:0 < 20

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x)] = 297 - 39*x + x^2

The following rules are decreasing:
f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 11 && x6:0 < 20
The following rules are bounded:
f5(x6:0) -> f5(x6:0 + 1) :|: x6:0 < 11 && x6:0 < 20

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(10)
Obligation:
Rules:
f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x)] = 19 - x

The following rules are decreasing:
f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20
The following rules are bounded:
f5(x8:0) -> f5(x8:0 + 1) :|: x8:0 > 10 && x8:0 < 20

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(12)
YES