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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 57 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 40 ms]
(6) IntTRS
(7) RankingReductionPairProof [EQUIVALENT, 28 ms]
(8) IntTRS
(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [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, j, N) -> f2(i, j, x_1) :|: TRUE
f2(x, x1, x2) -> f3(x2, x1, x2) :|: TRUE
f4(x3, x4, x5) -> f5(x3, x5, x5) :|: TRUE
f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1
f5(x9, x10, x11) -> f6(x9, x10, x11) :|: x10 > 0
f7(x12, x13, x14) -> f5(x12, x13, x14) :|: TRUE
f5(x15, x16, x17) -> f8(x15, x16, x17) :|: x16 <= 0
f8(x30, x31, x32) -> f9(x33, x31, x32) :|: TRUE && x33 = x30 - 1
f3(x21, x22, x23) -> f4(x21, x22, x23) :|: x21 > 0
f9(x24, x25, x26) -> f3(x24, x25, x26) :|: TRUE
f3(x27, x28, x29) -> f10(x27, x28, x29) :|: x27 <= 0
Start term: f1(i, j, 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(x21, x22, x23) -> f4(x21, x22, x23) :|: x21 > 0
f9(x24, x25, x26) -> f3(x24, x25, x26) :|: TRUE
f8(x30, x31, x32) -> f9(x33, x31, x32) :|: TRUE && x33 = x30 - 1
f5(x15, x16, x17) -> f8(x15, x16, x17) :|: x16 <= 0
f4(x3, x4, x5) -> f5(x3, x5, x5) :|: TRUE
f7(x12, x13, x14) -> f5(x12, x13, x14) :|: TRUE
f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1
f5(x9, x10, x11) -> f6(x9, x10, x11) :|: x10 > 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x15:0, x16:0, x17:0) -> f5(x15:0 - 1, x17:0, x17:0) :|: x16:0 < 1 && x15:0 > 1
f5(x9:0, x10:0, x11:0) -> f5(x9:0, x10:0 - 1, x11:0) :|: x10:0 > 0

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(7) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = 2*f5_1

The following rules are decreasing:
f5(x15:0, x16:0, x17:0) -> f5(x15:0 - 1, x17:0, x17:0) :|: x16:0 < 1 && x15:0 > 1

The following rules are bounded:
f5(x15:0, x16:0, x17:0) -> f5(x15:0 - 1, x17:0, x17:0) :|: x16:0 < 1 && x15:0 > 1


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(8)
Obligation:
Rules:
f5(x9:0, x10:0, x11:0) -> f5(x9:0, x10:0 - 1, x11:0) :|: x10:0 > 0

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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, x3) -> f5(x2)

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

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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 > 0

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


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(12)
YES