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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 45 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 25 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 6 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(x, y, random) -> f2(x_1, y, random) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f4(x5, x6, x7) -> f5(x5, x6, x8) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1
f9(x12, x13, x14) -> f10(x12, x13, x15) :|: TRUE
f10(x16, x17, x18) -> f11(x16, x18, x18) :|: TRUE
f7(x43, x44, x45) -> f12(x43, x46, x45) :|: TRUE && x46 = x44 - 1
f5(x22, x23, x24) -> f6(x22, x23, x24) :|: x24 < 42
f5(x25, x26, x27) -> f7(x25, x26, x27) :|: x27 >= 42
f11(x28, x29, x30) -> f8(x28, x29, x30) :|: TRUE
f12(x31, x32, x33) -> f8(x31, x32, x33) :|: TRUE
f3(x34, x35, x36) -> f4(x34, x35, x36) :|: x34 > 0 && x35 > 0
f8(x37, x38, x39) -> f3(x37, x38, x39) :|: TRUE
f3(x40, x41, x42) -> f13(x40, x41, x42) :|: x40 <= 0
f3(x47, x48, x49) -> f13(x47, x48, x49) :|: x48 <= 0
Start term: f1(x, y, random)

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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(x34, x35, x36) -> f4(x34, x35, x36) :|: x34 > 0 && x35 > 0
f8(x37, x38, x39) -> f3(x37, x38, x39) :|: TRUE
f11(x28, x29, x30) -> f8(x28, x29, x30) :|: TRUE
f10(x16, x17, x18) -> f11(x16, x18, x18) :|: TRUE
f9(x12, x13, x14) -> f10(x12, x13, x15) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1
f5(x22, x23, x24) -> f6(x22, x23, x24) :|: x24 < 42
f4(x5, x6, x7) -> f5(x5, x6, x8) :|: TRUE
f12(x31, x32, x33) -> f8(x31, x32, x33) :|: TRUE
f7(x43, x44, x45) -> f12(x43, x46, x45) :|: TRUE && x46 = x44 - 1
f5(x25, x26, x27) -> f7(x25, x26, x27) :|: x27 >= 42

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x25:0, x26:0, x27:0) -> f5(x25:0, x26:0 - 1, x8:0) :|: x25:0 > 0 && x26:0 > 1 && x27:0 > 41
f5(x, x1, x2) -> f5(x - 1, x3, x4) :|: x > 1 && x3 > 0 && x2 < 42

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1, x2)] = x

The following rules are decreasing:
f5(x, x1, x2) -> f5(x - 1, x3, x4) :|: x > 1 && x3 > 0 && x2 < 42
The following rules are bounded:
f5(x25:0, x26:0, x27:0) -> f5(x25:0, x26:0 - 1, x8:0) :|: x25:0 > 0 && x26:0 > 1 && x27:0 > 41
f5(x, x1, x2) -> f5(x - 1, x3, x4) :|: x > 1 && x3 > 0 && x2 < 42

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(8)
Obligation:
Rules:
f5(x25:0, x26:0, x27:0) -> f5(x25:0, x26:0 - 1, x8:0) :|: x25:0 > 0 && x26:0 > 1 && x27:0 > 41

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f5(x25:0:0, x26:0:0, x27:0:0) -> f5(x25:0:0, x26:0:0 - 1, x8:0:0) :|: x25:0:0 > 0 && x26:0:0 > 1 && x27:0:0 > 41

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = f5_2

The following rules are decreasing:
f5(x25:0:0, x26:0:0, x27:0:0) -> f5(x25:0:0, x26:0:0 - 1, x8:0:0) :|: x25:0:0 > 0 && x26:0:0 > 1 && x27:0:0 > 41

The following rules are bounded:
f5(x25:0:0, x26:0:0, x27:0:0) -> f5(x25:0:0, x26:0:0 - 1, x8:0:0) :|: x25:0:0 > 0 && x26:0:0 > 1 && x27:0:0 > 41


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(12)
YES