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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 87 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 14 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 9 ms]
(12) IntTRS
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IntTRS
(15) RankingReductionPairProof [EQUIVALENT, 6 ms]
(16) 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(x50, x51, x52) -> f13(x50, x51, x53) :|: TRUE && x53 = x52 - 1
f7(x14, x15, x16) -> f10(x14, x15, x16) :|: x16 > 0
f7(x17, x18, x19) -> f11(x17, x18, x19) :|: x19 <= 0
f13(x20, x21, x22) -> f12(x20, x21, x22) :|: TRUE
f11(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x27 > 0
f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x30 <= 0
f9(x32, x33, x34) -> f8(x32, x33, x34) :|: TRUE
f12(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
f8(x54, x55, x56) -> f14(x57, x55, x56) :|: TRUE && x57 = x54 + 1
f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x42 > 0
f4(x58, x59, x60) -> f5(x58, x59, x60) :|: x60 > 0
f14(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE
f4(x47, x48, x49) -> f15(x47, x48, x49) :|: x48 <= 0 && x49 <= 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(x41, x42, x43) -> f5(x41, x42, x43) :|: x42 > 0
f14(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE
f8(x54, x55, x56) -> f14(x57, x55, x56) :|: TRUE && x57 = x54 + 1
f9(x32, x33, x34) -> f8(x32, x33, x34) :|: TRUE
f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x27 > 0
f4(x58, x59, x60) -> f5(x58, x59, x60) :|: x60 > 0
f12(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
f13(x20, x21, x22) -> f12(x20, x21, x22) :|: TRUE
f10(x50, x51, x52) -> f13(x50, x51, x53) :|: TRUE && x53 = x52 - 1
f7(x14, x15, x16) -> f10(x14, x15, x16) :|: x16 > 0
f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x30 <= 0
f11(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
f7(x17, x18, x19) -> f11(x17, x18, x19) :|: x19 <= 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x54:0, x55:0, x56:0) -> f5(x54:0 + 1, x55:0, x56:0) :|: x56:0 > 0
f5(x29:0, x30:0, x31:0) -> f8(x29:0, x30:0, x31:0 - 1) :|: x30:0 < 1 && x31:0 > 0
f5(x, x1, x2) -> f8(x, x1, x2) :|: x1 < 1 && x2 < 1
f8(x3, x4, x5) -> f5(x3 + 1, x4, x5) :|: x4 > 0
f5(x26:0, x27:0, x28:0) -> f8(x26:0, x27:0 - 1, x28:0) :|: x27:0 > 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:

   f8(x1, x2, x3) -> f8(x2, x3)
   f5(x1, x2, x3) -> f5(x2, x3)

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(8)
Obligation:
Rules:
f8(x55:0, x56:0) -> f5(x55:0, x56:0) :|: x56:0 > 0
f5(x30:0, x31:0) -> f8(x30:0, x31:0 - 1) :|: x30:0 < 1 && x31:0 > 0
f5(x1, x2) -> f8(x1, x2) :|: x1 < 1 && x2 < 1
f8(x4, x5) -> f5(x4, x5) :|: x4 > 0
f5(x27:0, x28:0) -> f8(x27:0 - 1, x28:0) :|: x27:0 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1)] = -1 + x
[f5(x2, x3)] = -1 + x2

The following rules are decreasing:
f5(x27:0, x28:0) -> f8(x27:0 - 1, x28:0) :|: x27:0 > 0
The following rules are bounded:
f8(x4, x5) -> f5(x4, x5) :|: x4 > 0
f5(x27:0, x28:0) -> f8(x27:0 - 1, x28:0) :|: x27:0 > 0

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(10)
Obligation:
Rules:
f8(x55:0, x56:0) -> f5(x55:0, x56:0) :|: x56:0 > 0
f5(x30:0, x31:0) -> f8(x30:0, x31:0 - 1) :|: x30:0 < 1 && x31:0 > 0
f5(x1, x2) -> f8(x1, x2) :|: x1 < 1 && x2 < 1
f8(x4, x5) -> f5(x4, x5) :|: x4 > 0

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = 3*f8_2
[ f5 ] = 3*f5_2

The following rules are decreasing:
f5(x30:0, x31:0) -> f8(x30:0, x31:0 - 1) :|: x30:0 < 1 && x31:0 > 0

The following rules are bounded:
f5(x30:0, x31:0) -> f8(x30:0, x31:0 - 1) :|: x30:0 < 1 && x31:0 > 0


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(12)
Obligation:
Rules:
f8(x55:0, x56:0) -> f5(x55:0, x56:0) :|: x56:0 > 0
f5(x1, x2) -> f8(x1, x2) :|: x1 < 1 && x2 < 1
f8(x4, x5) -> f5(x4, x5) :|: x4 > 0

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f8(x4:0, x5:0) -> f8(x4:0, x5:0) :|: x4:0 < 1 && x5:0 < 1 && x4:0 > 0
f8(x55:0:0, x56:0:0) -> f8(x55:0:0, x56:0:0) :|: x55:0:0 < 1 && x56:0:0 < 1 && x56:0:0 > 0

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(15) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = 0

The following rules are decreasing:
f8(x4:0, x5:0) -> f8(x4:0, x5:0) :|: x4:0 < 1 && x5:0 < 1 && x4:0 > 0
f8(x55:0:0, x56:0:0) -> f8(x55:0:0, x56:0:0) :|: x55:0:0 < 1 && x56:0:0 < 1 && x56:0:0 > 0

The following rules are bounded:
f8(x4:0, x5:0) -> f8(x4:0, x5:0) :|: x4:0 < 1 && x5:0 < 1 && x4:0 > 0
f8(x55:0:0, x56:0:0) -> f8(x55:0:0, x56:0:0) :|: x55:0:0 < 1 && x56:0:0 < 1 && x56:0:0 > 0


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(16)
YES