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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 68 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) RankingReductionPairProof [EQUIVALENT, 6 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) -> f10(x15, arith, x17, x18) :|: TRUE && arith = x16 + 1
f8(x55, x56, x57, x58) -> f11(x55, x56, x57, x59) :|: TRUE && x59 = x58 + 1
f6(x23, x24, x25, x26) -> f7(x23, x24, x25, x26) :|: x24 < x26
f6(x27, x28, x29, x30) -> f8(x27, x28, x29, x30) :|: x28 >= x30
f10(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE
f11(x35, x36, x37, x38) -> f9(x35, x36, x37, x38) :|: TRUE
f9(x60, x61, x62, x63) -> f12(x64, x61, x62, x63) :|: TRUE && x64 = x60 + 1
f5(x43, x44, x45, x46) -> f6(x43, x44, x45, x46) :|: x44 < x45
f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE
f5(x51, x52, x53, x54) -> f13(x51, x52, x53, x54) :|: x52 >= x53
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 < x45
f12(x47, x48, x49, x50) -> f5(x47, x48, x49, x50) :|: TRUE
f9(x60, x61, x62, x63) -> f12(x64, x61, x62, x63) :|: TRUE && x64 = x60 + 1
f10(x31, x32, x33, x34) -> f9(x31, x32, x33, x34) :|: TRUE
f7(x15, x16, x17, x18) -> f10(x15, arith, x17, x18) :|: TRUE && arith = x16 + 1
f6(x23, x24, x25, x26) -> f7(x23, x24, x25, x26) :|: x24 < x26
f11(x35, x36, x37, x38) -> f9(x35, x36, x37, x38) :|: TRUE
f8(x55, x56, x57, x58) -> f11(x55, x56, x57, x59) :|: TRUE && x59 = x58 + 1
f6(x27, x28, x29, x30) -> f8(x27, x28, x29, x30) :|: x28 >= x30

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f9(x60:0, x61:0, x62:0, x63:0) -> f9(x60:0 + 1, x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0
f9(x, x1, x2, x3) -> f9(x + 1, x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1

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

   f9(x1, x2, x3, x4) -> f9(x2, x3, x4)

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(8)
Obligation:
Rules:
f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0
f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f9(x, x1, x2)] = -x + x1

The following rules are decreasing:
f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1
The following rules are bounded:
f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0
f9(x1, x2, x3) -> f9(x1 + 1, x2, x3) :|: x2 > x1 && x3 > x1

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(10)
Obligation:
Rules:
f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f9 ] = f9_1 + -1*f9_3

The following rules are decreasing:
f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0

The following rules are bounded:
f9(x61:0, x62:0, x63:0) -> f9(x61:0, x62:0, x63:0 + 1) :|: x62:0 > x61:0 && x63:0 <= x61:0


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(12)
YES