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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 59 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 4 ms]
(12) 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(x1, x2) -> f2(x_1, x2) :|: TRUE
f2(x, x3) -> f3(x, x4) :|: TRUE
f4(x5, x6) -> f5(x5, 10) :|: TRUE
f6(x7, x8) -> f7(x7, arith) :|: TRUE && arith = x8 - 1
f5(x9, x10) -> f6(x9, x10) :|: x10 > 1
f7(x11, x12) -> f5(x11, x12) :|: TRUE
f5(x13, x14) -> f8(x13, x14) :|: x14 <= 1
f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
f3(x17, x18) -> f4(x17, x18) :|: x17 <= 10
f9(x19, x20) -> f3(x19, x20) :|: TRUE
f3(x21, x22) -> f10(x21, x22) :|: x21 > 10
Start term: f1(x1, x2)

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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(x17, x18) -> f4(x17, x18) :|: x17 <= 10
f9(x19, x20) -> f3(x19, x20) :|: TRUE
f8(x23, x24) -> f9(x25, x24) :|: TRUE && x25 = x23 + 1
f5(x13, x14) -> f8(x13, x14) :|: x14 <= 1
f7(x11, x12) -> f5(x11, x12) :|: TRUE
f6(x7, x8) -> f7(x7, arith) :|: TRUE && arith = x8 - 1
f5(x9, x10) -> f6(x9, x10) :|: x10 > 1
f4(x5, x6) -> f5(x5, 10) :|: TRUE

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x13:0, x14:0) -> f5(x13:0 + 1, 10) :|: x14:0 < 2 && x13:0 < 10
f5(x9:0, x10:0) -> f5(x9:0, x10:0 - 1) :|: x10:0 > 1

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = 9 - x

The following rules are decreasing:
f5(x13:0, x14:0) -> f5(x13:0 + 1, 10) :|: x14:0 < 2 && x13:0 < 10
The following rules are bounded:
f5(x13:0, x14:0) -> f5(x13:0 + 1, 10) :|: x14:0 < 2 && x13:0 < 10

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(8)
Obligation:
Rules:
f5(x9:0, x10:0) -> f5(x9:0, x10:0 - 1) :|: x10:0 > 1

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

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

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(10)
Obligation:
Rules:
f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = f5_1

The following rules are decreasing:
f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 1

The following rules are bounded:
f5(x10:0) -> f5(x10:0 - 1) :|: x10:0 > 1


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(12)
YES