/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 10 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(c, x, y, z) -> f2(c, x_1, y, z) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x2, x5, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x8, x10) :|: TRUE
f4(x11, x12, x13, x14) -> f5(0, x12, x13, x14) :|: TRUE
f7(x15, x16, x17, x18) -> f8(x15, x16, arith, x18) :|: TRUE && arith = x17 - 1
f8(x55, x56, x57, x58) -> f9(x59, x56, x57, x58) :|: TRUE && x59 = x55 + 1
f6(x23, x24, x25, x26) -> f7(x23, x24, x25, x26) :|: x25 > x26
f9(x27, x28, x29, x30) -> f6(x27, x28, x29, x30) :|: TRUE
f6(x31, x32, x33, x34) -> f10(x31, x32, x33, x34) :|: x33 <= x34
f10(x60, x61, x62, x63) -> f11(x64, x61, x62, x63) :|: TRUE && x64 = x60 + 1
f11(x65, x66, x67, x68) -> f12(x65, x69, x67, x68) :|: TRUE && x69 = x66 - 1
f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x44 > x46
f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE
f5(x51, x52, x53, x54) -> f13(x51, x52, x53, x54) :|: x52 <= x54
Start term: f1(c, x, y, z)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained one non-trivial SCC.

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(4)
Obligation:
Rules:
f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x44 > x46
f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE
f11(x65, x66, x67, x68) -> f12(x65, x69, x67, x68) :|: TRUE && x69 = x66 - 1
f10(x60, x61, x62, x63) -> f11(x64, x61, x62, x63) :|: TRUE && x64 = x60 + 1
f6(x31, x32, x33, x34) -> f10(x31, x32, x33, x34) :|: x33 <= x34
f9(x27, x28, x29, x30) -> f6(x27, x28, x29, x30) :|: TRUE
f8(x55, x56, x57, x58) -> f9(x59, x56, x57, x58) :|: TRUE && x59 = x55 + 1
f7(x15, x16, x17, x18) -> f8(x15, x16, arith, x18) :|: TRUE && arith = x17 - 1
f6(x23, x24, x25, x26) -> f7(x23, x24, x25, x26) :|: x25 > x26

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x31:0, x32:0, x33:0, x34:0) -> f6(x31:0 + 1, x32:0 - 1, x33:0, x34:0) :|: x34:0 >= x33:0 && x34:0 < x32:0 - 1
f6(x23:0, x24:0, x25:0, x26:0) -> f6(x23:0 + 1, x24:0, x25:0 - 1, x26:0) :|: x26:0 < x25:0

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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, x4) -> f6(x2, x3, x4)

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(8)
Obligation:
Rules:
f6(x32:0, x33:0, x34:0) -> f6(x32:0 - 1, x33:0, x34:0) :|: x34:0 >= x33:0 && x34:0 < x32:0 - 1
f6(x24:0, x25:0, x26:0) -> f6(x24:0, x25:0 - 1, x26:0) :|: x26:0 < x25:0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1, x2)] = x1 - x2

The following rules are decreasing:
f6(x24:0, x25:0, x26:0) -> f6(x24:0, x25:0 - 1, x26:0) :|: x26:0 < x25:0
The following rules are bounded:
f6(x24:0, x25:0, x26:0) -> f6(x24:0, x25:0 - 1, x26:0) :|: x26:0 < x25:0

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(10)
Obligation:
Rules:
f6(x32:0, x33:0, x34:0) -> f6(x32:0 - 1, x33:0, x34:0) :|: x34:0 >= x33:0 && x34:0 < x32:0 - 1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f6 ] = -1*f6_3 + f6_1

The following rules are decreasing:
f6(x32:0, x33:0, x34:0) -> f6(x32:0 - 1, x33:0, x34:0) :|: x34:0 >= x33:0 && x34:0 < x32:0 - 1

The following rules are bounded:
f6(x32:0, x33:0, x34:0) -> f6(x32:0 - 1, x33:0, x34:0) :|: x34:0 >= x33:0 && x34:0 < x32:0 - 1


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(12)
YES