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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 16 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 5 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/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(x, y, r) -> f2(x_1, y, r) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, 1) :|: TRUE
f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 * x8
f6(x23, x24, x25) -> f7(x23, x26, x25) :|: TRUE && x26 = x24 - 1
f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > 0
f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x21 <= 0
Start term: f1(x, y, r)

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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(x14, x15, x16) -> f5(x14, x15, x16) :|: x15 > 0
f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
f6(x23, x24, x25) -> f7(x23, x26, x25) :|: TRUE && x26 = x24 - 1
f5(x8, x9, x10) -> f6(x8, x9, arith) :|: TRUE && arith = x10 * x8

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x23:0, x24:0, x25:0) -> f6(x23:0, x24:0 - 1, x25:0 * x23:0) :|: x24:0 > 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) -> f6(x2)

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(8)
Obligation:
Rules:
f6(x24:0) -> f6(x24:0 - 1) :|: x24:0 > 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x)] = x

The following rules are decreasing:
f6(x24:0) -> f6(x24:0 - 1) :|: x24:0 > 1
The following rules are bounded:
f6(x24:0) -> f6(x24:0 - 1) :|: x24:0 > 1

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(10)
YES