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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 60 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 10 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 4 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(c, i, j) -> f2(c, x_1, j) :|: TRUE
f2(x, x1, x2) -> f3(x, x1, x3) :|: TRUE
f3(x4, x5, x6) -> f4(0, x5, x6) :|: TRUE
f5(x7, x8, x9) -> f6(x7, x8, 0) :|: TRUE
f7(x10, x11, x12) -> f8(x10, x11, arith) :|: TRUE && arith = x12 + 1
f8(x37, x38, x39) -> f9(x40, x38, x39) :|: TRUE && x40 = x37 + 1
f6(x16, x17, x18) -> f7(x16, x17, x18) :|: x18 <= x17 - 1
f9(x19, x20, x21) -> f6(x19, x20, x21) :|: TRUE
f6(x22, x23, x24) -> f10(x22, x23, x24) :|: x24 > x23 - 1
f10(x41, x42, x43) -> f11(x41, x44, x43) :|: TRUE && x44 = x42 - 1
f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x29 >= 0
f11(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
f4(x34, x35, x36) -> f12(x34, x35, x36) :|: x35 < 0
Start term: f1(c, 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:
f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x29 >= 0
f11(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
f10(x41, x42, x43) -> f11(x41, x44, x43) :|: TRUE && x44 = x42 - 1
f6(x22, x23, x24) -> f10(x22, x23, x24) :|: x24 > x23 - 1
f5(x7, x8, x9) -> f6(x7, x8, 0) :|: TRUE
f9(x19, x20, x21) -> f6(x19, x20, x21) :|: TRUE
f8(x37, x38, x39) -> f9(x40, x38, x39) :|: TRUE && x40 = x37 + 1
f7(x10, x11, x12) -> f8(x10, x11, arith) :|: TRUE && arith = x12 + 1
f6(x16, x17, x18) -> f7(x16, x17, x18) :|: x18 <= x17 - 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x16:0, x17:0, x18:0) -> f6(x16:0 + 1, x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1
f6(x22:0, x23:0, x24:0) -> f6(x22:0, x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0

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

   f6(x1, x2, x3) -> f6(x2, x3)

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(8)
Obligation:
Rules:
f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1
f6(x23:0, x24:0) -> f6(x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = -1 + x

The following rules are decreasing:
f6(x23:0, x24:0) -> f6(x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0
The following rules are bounded:
f6(x23:0, x24:0) -> f6(x23:0 - 1, 0) :|: x24:0 > x23:0 - 1 && x23:0 > 0

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(10)
Obligation:
Rules:
f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f6 ] = -1*f6_2 + f6_1

The following rules are decreasing:
f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1

The following rules are bounded:
f6(x17:0, x18:0) -> f6(x17:0, x18:0 + 1) :|: x18:0 <= x17:0 - 1


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(12)
YES