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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 51 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 8 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(x, y, z, res) -> f2(x_1, y, z, res) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x8, 0) :|: TRUE
f5(x10, x11, x12, x13) -> f6(x10, x11, x10, x13) :|: TRUE
f6(x14, x15, x16, x17) -> f7(arith, x15, x16, x17) :|: TRUE && arith = x15 - 1
f7(x18, x19, x20, x21) -> f8(x18, x20, x20, x21) :|: TRUE
f8(x42, x43, x44, x45) -> f9(x42, x43, x44, x46) :|: TRUE && x46 = x45 + 1
f4(x26, x27, x28, x29) -> f5(x26, x27, x28, x29) :|: x27 > 0
f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
f4(x34, x35, x36, x37) -> f10(x34, x35, x36, x37) :|: x35 <= 0
f10(x47, x48, x49, x50) -> f11(x47, x48, x49, x51) :|: TRUE && x51 = x50 + x47
Start term: f1(x, y, z, res)

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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 > 0
f9(x30, x31, x32, x33) -> f4(x30, x31, x32, x33) :|: TRUE
f8(x42, x43, x44, x45) -> f9(x42, x43, x44, x46) :|: TRUE && x46 = x45 + 1
f7(x18, x19, x20, x21) -> f8(x18, x20, x20, x21) :|: TRUE
f6(x14, x15, x16, x17) -> f7(arith, x15, x16, x17) :|: TRUE && arith = x15 - 1
f5(x10, x11, x12, x13) -> f6(x10, x11, x10, x13) :|: 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(x15:0 - 1, x16:0, x15:0 - 1, x17:0 + 1) :|: x16:0 > 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:

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

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(8)
Obligation:
Rules:
f6(x15:0, x16:0) -> f6(x16:0, x15:0 - 1) :|: x16:0 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = -2 + x^2 + 2*x1 + x1^2

The following rules are decreasing:
f6(x15:0, x16:0) -> f6(x16:0, x15:0 - 1) :|: x16:0 > 0
The following rules are bounded:
f6(x15:0, x16:0) -> f6(x16:0, x15:0 - 1) :|: x16:0 > 0

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(10)
YES