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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 39 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 25 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 11 ms]
(10) 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(k, i, j, tmp) -> f2(x_1, i, j, tmp) :|: TRUE
f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x11) :|: TRUE
f6(x14, x15, x16, x17) -> f7(x14, x16, x16, x17) :|: TRUE
f7(x18, x19, x20, x21) -> f8(x18, x19, arith, x21) :|: TRUE && arith = x21 + 1
f8(x38, x39, x40, x41) -> f9(x42, x39, x40, x41) :|: TRUE && x42 = x38 - 1
f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 <= 100 && x28 <= x26
f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
f4(x34, x35, x36, x37) -> f10(x34, x35, x36, x37) :|: x35 > 100
f4(x43, x44, x45, x46) -> f10(x43, x44, x45, x46) :|: x45 > x43
Start term: f1(k, i, j, tmp)

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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(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 <= 100 && x28 <= x26
f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
f8(x38, x39, x40, x41) -> f9(x42, x39, x40, x41) :|: TRUE && x42 = x38 - 1
f7(x18, x19, x20, x21) -> f8(x18, x19, arith, x21) :|: TRUE && arith = x21 + 1
f6(x14, x15, x16, x17) -> f7(x14, x16, x16, x17) :|: TRUE
f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x11) :|: TRUE

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x14:0, x15:0, x16:0, x17:0) -> f6(x14:0 - 1, x16:0, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 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:

   f6(x1, x2, x3, x4) -> f6(x1, x3, x4)

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(8)
Obligation:
Rules:
f6(x14:0, x16:0, x17:0) -> f6(x14:0 - 1, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1, x2)] = 98 + x - x1 - x2

The following rules are decreasing:
f6(x14:0, x16:0, x17:0) -> f6(x14:0 - 1, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1
The following rules are bounded:
f6(x14:0, x16:0, x17:0) -> f6(x14:0 - 1, x17:0 + 1, x16:0) :|: x16:0 < 101 && x17:0 + 1 <= x14:0 - 1

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(10)
YES