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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 64 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) IntTRS
(11) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(12) IntTRS
(13) RankingReductionPairProof [EQUIVALENT, 3 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(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) -> f7(x8, x9, arith) :|: TRUE && arith = x10 - 1
f7(x38, x39, x40) -> f8(x41, x39, x40) :|: TRUE && x41 = x38 + 1
f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 > 0
f8(x17, x18, x19) -> f5(x17, x18, x19) :|: TRUE
f5(x20, x21, x22) -> f9(x20, x21, x22) :|: x22 <= 0
f9(x42, x43, x44) -> f10(x42, x45, x44) :|: TRUE && x45 = x43 - 1
f10(x46, x47, x48) -> f11(x49, x47, x48) :|: TRUE && x49 = x46 + 1
f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x30 > 0
f11(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE
f4(x35, x36, x37) -> f12(x35, x36, x37) :|: x36 <= 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(x29, x30, x31) -> f5(x29, x30, x31) :|: x30 > 0
f11(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE
f10(x46, x47, x48) -> f11(x49, x47, x48) :|: TRUE && x49 = x46 + 1
f9(x42, x43, x44) -> f10(x42, x45, x44) :|: TRUE && x45 = x43 - 1
f5(x20, x21, x22) -> f9(x20, x21, x22) :|: x22 <= 0
f8(x17, x18, x19) -> f5(x17, x18, x19) :|: TRUE
f7(x38, x39, x40) -> f8(x41, x39, x40) :|: TRUE && x41 = x38 + 1
f6(x8, x9, x10) -> f7(x8, x9, arith) :|: TRUE && arith = x10 - 1
f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 > 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x14:0, x15:0, x16:0) -> f5(x14:0 + 1, x15:0, x16:0 - 1) :|: x16:0 > 0
f5(x20:0, x21:0, x22:0) -> f5(x20:0 + 1, x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1

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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(x2, x3)

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(8)
Obligation:
Rules:
f5(x15:0, x16:0) -> f5(x15:0, x16:0 - 1) :|: x16:0 > 0
f5(x21:0, x22:0) -> f5(x21:0 - 1, x22:0) :|: x22:0 < 1 && x21:0 > 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f5(x, x1)] = -1 + x

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

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

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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 > 0

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(13) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = f5_1

The following rules are decreasing:
f5(x16:0) -> f5(x16:0 - 1) :|: x16:0 > 0

The following rules are bounded:
f5(x16:0) -> f5(x16:0 - 1) :|: x16:0 > 0


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(14)
YES