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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 46 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 5 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
(10) IntTRS
(11) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
(14) 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(i, j, c) -> f2(i, j, 0) :|: TRUE
f2(x, x1, x2) -> f3(0, x1, x2) :|: TRUE
f4(x3, x4, x5) -> f5(x3, 3, x5) :|: TRUE
f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1
f7(x36, x37, x38) -> f8(x36, x37, x39) :|: TRUE && x39 = x38 + 1
f8(x40, x41, x42) -> f9(x40, x43, x42) :|: TRUE && x43 = x41 + 2
f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x16 < 12
f9(x18, x19, x20) -> f5(x18, x19, x20) :|: TRUE
f5(x21, x22, x23) -> f10(x21, x22, x23) :|: x22 >= 12
f10(x44, x45, x46) -> f11(x47, x45, x46) :|: TRUE && x47 = x44 + 1
f3(x27, x28, x29) -> f4(x27, x28, x29) :|: x27 < 10
f11(x30, x31, x32) -> f3(x30, x31, x32) :|: TRUE
f3(x33, x34, x35) -> f12(x33, x34, x35) :|: x33 >= 10
Start term: f1(i, j, 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(x27, x28, x29) -> f4(x27, x28, x29) :|: x27 < 10
f11(x30, x31, x32) -> f3(x30, x31, x32) :|: TRUE
f10(x44, x45, x46) -> f11(x47, x45, x46) :|: TRUE && x47 = x44 + 1
f5(x21, x22, x23) -> f10(x21, x22, x23) :|: x22 >= 12
f9(x18, x19, x20) -> f5(x18, x19, x20) :|: TRUE
f8(x40, x41, x42) -> f9(x40, x43, x42) :|: TRUE && x43 = x41 + 2
f7(x36, x37, x38) -> f8(x36, x37, x39) :|: TRUE && x39 = x38 + 1
f6(x6, x7, x8) -> f7(x6, arith, x8) :|: TRUE && arith = x7 - 1
f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x16 < 12
f4(x3, x4, x5) -> f5(x3, 3, x5) :|: TRUE

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x21:0, x22:0, x23:0) -> f5(x21:0 + 1, 3, x23:0) :|: x22:0 > 11 && x21:0 < 9
f5(x15:0, x16:0, x17:0) -> f5(x15:0, x16:0 + 1, x17:0 + 1) :|: x16:0 < 12

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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, x3) -> f5(x1, x2)

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(8)
Obligation:
Rules:
f5(x21:0, x22:0) -> f5(x21:0 + 1, 3) :|: x22:0 > 11 && x21:0 < 9
f5(x15:0, x16:0) -> f5(x15:0, x16:0 + 1) :|: x16:0 < 12

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = 8 - x

The following rules are decreasing:
f5(x21:0, x22:0) -> f5(x21:0 + 1, 3) :|: x22:0 > 11 && x21:0 < 9
The following rules are bounded:
f5(x21:0, x22:0) -> f5(x21:0 + 1, 3) :|: x22:0 > 11 && x21:0 < 9

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(10)
Obligation:
Rules:
f5(x15:0, x16:0) -> f5(x15:0, x16:0 + 1) :|: x16:0 < 12

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(11) 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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(12)
Obligation:
Rules:
f5(x16:0) -> f5(x16:0 + 1) :|: x16:0 < 12

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

The following rules are decreasing:
f5(x16:0) -> f5(x16:0 + 1) :|: x16:0 < 12
The following rules are bounded:
f5(x16:0) -> f5(x16:0 + 1) :|: x16:0 < 12

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(14)
YES