/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 81 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 15 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 2 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) -> f2(c, x_1, y) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
f10(x53, x54, x55) -> f13(x53, x56, x55) :|: TRUE && x56 = x54 - 1
f11(x57, x58, x59) -> f14(x57, x58, x60) :|: TRUE && x60 = x59 - 1
f7(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 = x19
f7(x20, x21, x22) -> f11(x20, x21, x22) :|: x21 < x22
f7(x61, x62, x63) -> f11(x61, x62, x63) :|: x62 > x63
f13(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
f14(x26, x27, x28) -> f12(x26, x27, x28) :|: TRUE
f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x31
f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x34
f9(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
f12(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE
f8(x64, x65, x66) -> f15(x67, x65, x66) :|: TRUE && x67 = x64 + 1
f4(x44, x45, x46) -> f5(x44, x45, x46) :|: x45 + x46 > 0
f15(x47, x48, x49) -> f4(x47, x48, x49) :|: TRUE
f4(x50, x51, x52) -> f16(x50, x51, x52) :|: x51 + x52 <= 0
Start term: f1(c, x, y)

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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(x44, x45, x46) -> f5(x44, x45, x46) :|: x45 + x46 > 0
f15(x47, x48, x49) -> f4(x47, x48, x49) :|: TRUE
f8(x64, x65, x66) -> f15(x67, x65, x66) :|: TRUE && x67 = x64 + 1
f9(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x31
f12(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE
f13(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
f10(x53, x54, x55) -> f13(x53, x56, x55) :|: TRUE && x56 = x54 - 1
f7(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 = x19
f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x34
f14(x26, x27, x28) -> f12(x26, x27, x28) :|: TRUE
f11(x57, x58, x59) -> f14(x57, x58, x60) :|: TRUE && x60 = x59 - 1
f7(x20, x21, x22) -> f11(x20, x21, x22) :|: x21 < x22
f7(x61, x62, x63) -> f11(x61, x62, x63) :|: x62 > x63

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x64:0, x65:0, x66:0) -> f8(x64:0 + 1, x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0
f8(x, x1, x2) -> f8(x + 1, x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1
f8(x3, x4, x5) -> f8(x3 + 1, x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5

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

   f8(x1, x2, x3) -> f8(x2, x3)

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(8)
Obligation:
Rules:
f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0
f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1
f8(x4, x5) -> f8(x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1)] = x

The following rules are decreasing:
f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1
f8(x4, x5) -> f8(x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5
The following rules are bounded:
f8(x4, x5) -> f8(x4 - 1, x4) :|: x4 + x4 > 0 && x4 = x5

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(10)
Obligation:
Rules:
f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0
f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = f8_1 + f8_2

The following rules are decreasing:
f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0
f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1

The following rules are bounded:
f8(x65:0, x66:0) -> f8(x65:0, x66:0 - 1) :|: x65:0 + x66:0 > 0 && x66:0 > x65:0
f8(x1, x2) -> f8(x1 - 1, x2) :|: x1 + x2 > 0 && x2 < x1


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(12)
YES